+++ /dev/null
-<html>\r
-<head>\r
-<title>NBO 3.0 Program Manual</title>\r
-</head>\r
-<body bgcolor=#FFFFFF>\r
-<p>\r
-<center>\r
-<h2>NBO 3.0 Program Manual</h2>\r
-<p>\r
-(<i>Natural Bond Orbital / Natural Population Analysis /\r
-Natural Localized Molecular Orbital Programs</i>)\r
-<p>\r
-E. D. Glendening, A. E. Reed,* J. E. Carpenter,** and F. Weinhold\r
-<p>\r
-<i>Theoretical Chemistry Institute and Department of Chemistry,\r
-University of Wisconsin, Madison, Wisconsin 53706</i>\r
-<p>\r
-</center>\r
-* Present address: Bayer AG, Abteilung AV-IM-AM,\r
-5090 Leverkusen, Bayerwerk, Federal Republic of Germany.\r
-<p>\r
-** Present address: Department of Chemistry, University of\r
-California-Irvine, Irvine, California 92717.\r
-<p>\r
-<center>\r
-<h2>Table of Contents</h2>\r
-</center>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td align=left> </td><td align=left><b>Table of Contents</b></td><td align=right><i>i</i></td></tr>\r
-<tr><td align=left> </td><td align=left><b>Preface: HOW TO USE THIS MANUAL</b></td><td align=right><i>iii</i></td></tr>\r
-<tr><td align=left><h2>A.</td><td align=left>GENERAL INTRODUCTION AND INSTALLATION</td><td align=right> </td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left><b>A.1</b></td><td align=left>INTRODUCTION TO THE NBO PROGRAM</td><td align=right><i>A-1</i></td></tr>\r
-<tr><td align=left><i>A.1.1</i></td><td align=left>What does the NBO Program Do?</td><td align=right><i>A-1</i></td></tr>\r
-<tr><td align=left><i>A.1.2</i></td><td align=left>Structure of the NBO Program</td><td align=right><i>A-3</i></td></tr>\r
-<tr><td align=left><i>A.1.3</i></td><td align=left>Input and Output</td><td align=right><i>A-5</i></td></tr>\r
-<tr><td align=left><i>A.1.4</i></td><td align=left>General Capabilities and Restrictions</td><td align=right><i>A-6</i></td></tr>\r
-<tr><td align=left><i>A.1.5</i></td><td align=left>References and Relationship to Previous Versions</td><td align=right><i>A-7</i></td></tr>\r
-<tr><td align=left><b>A.2</b></td><td align=left>INSTALLING THE NBO PROGRAM</td><td align=right><i>A-10</i></td></tr>\r
-<tr><td align=left><b>A.3</b></td><td align=left>TUTORIAL EXAMPLE FOR METHYLAMINE</td><td align=right><i>A-12</i></td></tr>\r
-<tr><td align=left><i>A.3.1</i></td><td align=left>Running the Example</td><td align=right><i>A-12</i></td></tr>\r
-<tr><td align=left><i>A.3.2</i></td><td align=left>Natural Population Analysis</td><td align=right><i>A-13</i></td></tr>\r
-<tr><td align=left><i>A.3.3</i></td><td align=left>Natural Bond Orbital Analysis</td><td align=right><i>A-16</i></td></tr>\r
-<tr><td align=left><i>A.3.4</i></td><td align=left>NHO Directional Analysis</td><td align=right><i>A-20</i></td></tr>\r
-<tr><td align=left><i>A.3.5</i></td><td align=left>Perturbation Theory Energy Analysis</td><td align=right><i>A-21</i></td></tr>\r
-<tr><td align=left><i>A.3.6</i></td><td align=left>NBO Summary</td><td align=right><i>A-22</i></td></tr>\r
-<tr><td align=left><h2>B.</td><td align=left>NBO USER'S GUIDE</td><td align=right> </td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left><b>B.1</b></td><td align=left>INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS</td><td align=right><i>B-1</i></td></tr>\r
-<tr><td align=left><b>B.2</b></td><td align=left>THE $NBO KEYLIST</td><td align=right><i>B-2</i></td></tr>\r
-<tr><td align=left><i>B.2.1</i></td><td align=left>Overview of $NBO Keywords</td><td align=right><i>B-2</i></td></tr>\r
-<tr><td align=left><i>B.2.2</i></td><td align=left>Job Control Keywords</td><td align=right><i>B-3</i></td></tr>\r
-<tr><td align=left><i>B.2.3</i></td><td align=left>Job Threshold Keywords</td><td align=right><i>B-4</i></td></tr>\r
-<tr><td align=left><i>B.2.4</i></td><td align=left>Matrix Output Keywords</td><td align=right><i>B-6</i></td></tr>\r
-<tr><td align=left><i>B.2.5</i></td><td align=left>Other Output Control Keywords</td><td align=right><i>B-9</i></td></tr>\r
-<tr><td align=left><i>B.2.6</i></td><td align=left>Print Level Keywords</td><td align=right><i>B-10</i></td></tr>\r
-<tr><td align=left><i>B.2.7</i></td><td align=left>Semi-Documented Additional Keywords</td><td align=right><i>B-11</i></td></tr>\r
-<tr><td align=left><b>B.3</b></td><td align=left>THE $CORE LIST</td><td align=right><i>B-12</i></td></tr>\r
-<tr><td align=left><b>B.4</b></td><td align=left>THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)</td><td align=right><i>B-14</i></td></tr>\r
-<tr><td align=left><b>B.5</b></td><td align=left>THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)</td><td align=right><i>B-16</i></td></tr>\r
-<tr><td align=left><i>B.5.1</i></td><td align=left>Introduction to NBO Energetic Analysis</td><td align=right><i>B-16</i></td></tr>\r
-<tr><td align=left><i>B.5.2</i></td><td align=left>The Nine Deletion Types</td><td align=right><i>B-17</i></td></tr>\r
-<tr><td align=left><i>B.5.3</i></td><td align=left>Input for UHF Analysis</td><td align=right><i>B-20</i></td></tr>\r
-<tr><td align=left><b>B.6</b></td><td align=left>NBO KEYLIST ILLUSTRATIONS</td><td align=right><i>B-21</i></td></tr>\r
-<tr><td align=left><i>B.6.1</i></td><td align=left>Introduction</td><td align=right><i>B-21</i></td></tr>\r
-<tr><td align=left><i>B.6.2</i></td><td align=left>NLMO Keyword</td><td align=right><i>B-22</i></td></tr>\r
-<tr><td align=left><i>B.6.3</i></td><td align=left>DIPOLE Keyword</td><td align=right><i>B-24</i></td></tr>\r
-<tr><td align=left><i>B.6.4</i></td><td align=left>Matrix Output Keywords</td><td align=right><i>B-26</i></td></tr>\r
-<tr><td align=left><i>B.6.5</i></td><td align=left>BNDIDX Keyword</td><td align=right><i>B-29</i></td></tr>\r
-<tr><td align=left><i>B.6.6</i></td><td align=left>RESONANCE Keyword: Benzene</td><td align=right><i>B-32</i></td></tr>\r
-<tr><td align=left><i>B.6.7</i></td><td align=left>NOBOND Keyword: Hydrogen Fluoride</td><td align=right><i>B-37</i></td></tr>\r
-<tr><td align=left><i>B.6.8</i></td><td align=left>3CBOND Keyword: Diborane</td><td align=right><i>B-40</i></td></tr>\r
-<tr><td align=left><i>B.6.9</i></td><td align=left>NBO Directed Search ($CHOOSE Keylist)</td><td align=right><i>B-44</i></td></tr>\r
-<tr><td align=left><i>B.6.10</i></td><td align=left>NBO Energetic Analysis ($DEL Keylist)</td><td align=right><i>B-48</i></td></tr>\r
-<tr><td align=left><i>B.6.11</i></td><td align=left>Open-Shell UHF Output: Methyl Radical</td><td align=right><i>B-52</i></td></tr>\r
-<tr><td align=left><i>B.6.12</i></td><td align=left>Effective Core Potential: Cu<sub>2</sub> Dimer</td><td align=right><i>B-56</i></td></tr>\r
-<tr><td align=left><b>B.7</b></td><td align=left>FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM</td><td align=right><i>B-62</i></td></tr>\r
-<tr><td align=left><i>B.7.1</i></td><td align=left>Introduction</td><td align=right><i>B-62</i></td></tr>\r
-<tr><td align=left><i>B.7.2</i></td><td align=left>Format of the FILE47 Input File</td><td align=right><i>B-63</i></td></tr>\r
-<tr><td align=left><i>B.7.3</i></td><td align=left>$GENNBO Keylist</td><td align=right><i>B-65</i></td></tr>\r
-<tr><td align=left><i>B.7.4</i></td><td align=left>$COORD Keylist</td><td align=right><i>B-66</i></td></tr>\r
-<tr><td align=left><i>B.7.5</i></td><td align=left>$BASIS Datalist</td><td align=right><i>B-67</i></td></tr>\r
-<tr><td align=left><i>B.7.6</i></td><td align=left>$CONTRACT Datalist</td><td align=right><i>B-69</i></td></tr>\r
-<tr><td align=left><i>B.7.7</i></td><td align=left>Matrix Datalists</td><td align=right><i>B-71</i></td></tr>\r
-<tr><td align=left><h2>C.</td><td align=left>NBO PROGRAMMER'S GUIDE</td><td align=right> </td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left><b>C.1</b></td><td align=left>INTRODUCTION</td><td align=right><i>C-1</i></td></tr>\r
-<tr><td align=left><b>C.2</b></td><td align=left>OVERVIEW OF NBO.SRC SOURCE PROGRAM GROUPS</td><td align=right><i>C-2</i></td></tr>\r
-<tr><td align=left><b>C.3</b></td><td align=left>LABELLED COMMON BLOCKS</td><td align=right><i>C-4</i></td></tr>\r
-<tr><td align=left><b>C.4</b></td><td align=left>DIRECT ACCESS FILE AND OTHER I/O</td><td align=right><i>C-14</i></td></tr>\r
-<tr><td align=left><b>C.5</b></td><td align=left>NAO/NBO/NLMO ROUTINES (GROUP I)</td><td align=right><i>C-16</i></td></tr>\r
-<tr><td align=left><i>C.5.1</i></td><td align=left>SR NBO Master Routine</td><td align=right><i>C-16</i></td></tr>\r
-<tr><td align=left><i>C.5.2</i></td><td align=left>Job Initialization Routines</td><td align=right><i>C-18</i></td></tr>\r
-<tr><td align=left><i>C.5.3</i></td><td align=left>NAO Formation Routines</td><td align=right><i>C-19</i></td></tr>\r
-<tr><td align=left><i>C.5.4</i></td><td align=left>NBO/NLMO Formation Routines</td><td align=right><i>C-22</i></td></tr>\r
-<tr><td align=left><b>C.6</b></td><td align=left>ENERGY ANALYSIS ROUTINES (GROUP II)</td><td align=right><i>C-26</i></td></tr>\r
-<tr><td align=left><b>C.7</b></td><td align=left>DIRECT ACCESS FILE (DAF) ROUTINES (GROUP III)</td><td align=right><i>C-27</i></td></tr>\r
-<tr><td align=left><b>C.8</b></td><td align=left>FREE FORMAT INPUT ROUTINES (GROUP IV)</td><td align=right><i>C-29</i></td></tr>\r
-<tr><td align=left><b>C.9</b></td><td align=left>OTHER SYSTEM INDEPENDENT I/O ROUTINES (GROUP V)</td><td align=right><i>C-30</i></td></tr>\r
-<tr><td align=left><b>C.10</b></td><td align=left>GENERAL UTILITY ROUTINES (GROUP VI)</td><td align=right><i>C-33</i></td></tr>\r
-<tr><td align=left><b>C.11</b></td><td align=left>SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)</td><td align=right><i>C-36</i></td></tr>\r
-<tr><td align=left><b>C.12</b></td><td align=left>GENNBO AUXILLIARY ROUTINES</td><td align=right><i>C-37</i></td></tr>\r
-<tr><td align=left><b>C.13</b></td><td align=left>ATTACHING NBO TO A NEW ESS PROGRAM</td><td align=right><i>C-38</i></td></tr>\r
-<tr><td align=left> </td><td align=left><b>APPENDIX: Specific ESS Versions</b></td><td align=right> </td></tr>\r
-<tr><td align=left> </td><td align=left><b>INDEX</b></td><td align=right> </td></tr>\r
-</table>\r
-<p>\r
-<h2>PREFACE: HOW TO USE THIS MANUAL</h2>\r
-<p>\r
- The NBO manual is divided into three major sections:\r
-<p>\r
- Section A ("General Introduction and Installation")\r
-contains general introductory and 'one-time' information\r
-for the novice user: what the program does, program structure and\r
-relationship to driver electronic structure package, initial installation,\r
-'quick start' sample input data, and a brief tutorial on sample output.\r
-<p>\r
- Section B ("NBO User's Guide")\r
-is for the intermediate user who has an installed program\r
-and general familiarity with the standard (default) options of the NBO\r
-program. This section documents the list of <i>keywords</i> that can be used\r
-to alter the standard NBO job options, \r
-with examples of the resulting output. This \r
-section is mandatory for users who wish to use\r
-the program to its full potential, to 'turn off' or\r
-'turn on' various NBO options for their specialized applications.\r
-<p>\r
- Section C ("NBO Programmer's Guide")\r
-is for accomplished programmers who\r
-are interested in program logic and the detailed layout of\r
-the source code. This section describes the relationship of the\r
-source code subprograms\r
-to the published algorithms for NAO, NBO, and NLMO determination,\r
-providing documentation at the level of individual\r
-common blocks, functions, and subroutines. This in turn serves as a\r
-bridge to the 'micro-documentation' included\r
-as comment statements within the source code. Section C also\r
-provides guidelines for constructing 'driver' routines to attach\r
-the NBO programs to new electronic structure packages.\r
-<p>\r
-<center>\r
-<h2>Section A: GENERAL INTRODUCTION AND INSTALLATION</h2>\r
-</center>\r
-<p>\r
-<p>\r
-<b>A.1 INTRODUCTION TO THE NBO PROGRAM</b>\r
-<p>\r
-<i>A.1.1 What Does the NBO Program Do?</i>\r
-<p>\r
- The NBO program performs the analysis of a many-electron\r
-molecular wavefunction in terms of localized electron-pair\r
-'bonding' units. The program carries out the determination of\r
-natural atomic orbitals (NAOs), natural hybrid orbitals (NHOs),\r
-natural bond orbitals (NBOs), and natural localized molecular\r
-orbitals (NLMOs), and uses these to perform natural population\r
-analysis (NPA), NBO energetic analysis, and other tasks pertaining\r
-to localized analysis of wavefunction properties. The NBO \r
-method makes use of only the first-order\r
-reduced density matrix of the wavefunction, and hence is applicable\r
-to wavefunctions of general mathematical form; in the open-shell\r
-case, the analysis is performed in terms of "different NBOs for\r
-different spins," based on distinct density matrices for <img src=alpha.gif>\r
-and <img src=beta.gif> spin.* This\r
-section provides a brief introduction to NBO algorithms and\r
-nomenclature.\r
-<p>\r
- NBO analysis is based\r
-on a method for optimally transforming a given wavefunction into\r
-localized form, corresponding to the one-center ("lone pair")\r
-and two-center ("bond") elements of the chemist's Lewis structure \r
-picture. The NBOs are obtained as local block eigenfunctions \r
-of the one-electron density matrix, and are hence "natural" in the sense \r
-of Löwdin, having optimal convergence properties for describing the \r
-electron density. The set of high-occupancy NBOs, each taken doubly\r
-occupied, is said to represent the "natural Lewis structure" of\r
-the molecule. Delocalization effects appear as weak departures \r
-from this idealized localized picture. \r
-<p>\r
- The various natural localized sets \r
-can be considered to result\r
-from a sequence of transformations of the input atomic orbital basis set\r
-{<img src=chi.gif><sub>i</sub>},**\r
-<font size=-1>\r
-_______________\r
-<p>\r
-*Note, however,\r
-that some electronic structure packages do not make provision\r
-for calculating the spin density matrices for some types of\r
-open-shell wavefunctions (e.g., MCSCF wavefunctions calculated\r
-by the GUGA formalism in the GAMESS system), so that NBO analysis\r
-cannot be applied in these cases.\r
-<p>\r
-**If the wavefunction is not calculated in an atom-centered\r
-basis set, it would be necessary to first compute a wavefunction\r
-for each isolated atom of the molecule (in the actual basis set\r
-and geometry of the molecular calculation), then select the\r
-most highly occupied natural orbitals of each atomic wavefunction\r
-to compose a final set of linearly independent atom-centered basis\r
-functions of the required dimensionality. Since atom-centered\r
-basis functions are the nearly universal choice for molecular\r
-calculations, the current NBO program makes no provision for\r
-this step.\r
-<p>\r
-</font>\r
-<p>\r
-<center>\r
-input basis <img src=rarr.gif> NAOs <img src=rarr.gif> NHOs <img src=rarr.gif> NBOs <img src=rarr.gif> NLMOs\r
-</center>\r
-<p>\r
-Each natural localized set forms a complete orthonormal \r
-set of one-electron functions \r
-for expanding the delocalized molecular \r
-orbitals (MOs) or forming matrix representations of one-electron \r
-operators. The overlap of associated "pre-orthogonal" \r
-NAOs (PNAOs), lacking only the interatomic orthogonalization \r
-step of the NAO procedure, can be used to estimate the strength\r
-of orbital interactions in the usual way.\r
-<p>\r
- The optimal condensation of occupancy in the natural\r
-localized orbitals leads to partitioning into high- and\r
-low-occupancy orbital types (reduction in dimensionality\r
-of the orbitals having significant occupancy), as reflected \r
-in the orbital labelling. The small set of most\r
-highly-occupied NAOs, having a close\r
-correspondence with the effective minimal basis set of semi-empirical\r
-quantum chemistry, is referred to as the "natural minimal basis"\r
-(NMB) set. The NMB (core + valence) functions are \r
-distinguished from the weakly occupied "Rydberg" \r
-(extra-valence-shell) functions that complete the span of the NAO space,\r
-but typically make little contribution to molecular properties. Similarly\r
-in the NBO space,\r
-the highly occupied NBOs of the natural Lewis structure\r
-can be distinguished from the "non-Lewis" antibond and Rydberg\r
-orbitals that complete the span of the NBO space. Each pair of valence hybrids\r
-<i>h<sub>A</sub></i>, <i>h<sub>B</sub></i> in the NHO basis give rise to a bond (<img src=sigma.gif><sub>AB</sub>) and antibond (<img src=sigma.gif>*<sub>AB</sub>)\r
-in the NBO basis,\r
-<p>\r
-<center>\r
-<img src=sigma.gif><sub>AB</sub> = <i>c<sub>A</sub></i><i>h<sub>A</sub></i> + <i>c<sub>B</sub></i><i>h<sub>B</sub></i>\r
-<p>\r
-<img src=sigma.gif>*<sub>AB</sub> = <i>c<sub>B</sub></i><i>h<sub>A</sub></i> - <i>c<sub>A</sub></i><i>h<sub>B</sub></i>\r
-<p>\r
-</center>\r
-the former a Lewis (L) and the latter a non-Lewis (NL) orbital. The \r
-antibonds (valence shell non-Lewis orbitals) typically play the primary\r
-role in departures (delocalization) from the idealized Lewis structure.\r
-<p>\r
- The NBO program also makes extensive provision for energetic\r
-analysis of NBO interactions, based on the availability of a 1-electron\r
-effective energy operator (Fock matrix) for the system. Estimates\r
-of energy effects are\r
-based on second-order perturbation theory,\r
-or on the effect of deleting certain orbitals or matrix elements and\r
-recalculating the total energy. NBO energy analysis is dependent\r
-on the specific ESS to which the NBO program\r
-is attached, as described in the Appendix.\r
-<p>\r
- The program is provided in a core set of NBO routines that can be\r
-attached to an electronic structure system of the user's choice. In\r
-addition, specific 'driver' routines are provided that facilitate\r
-the attachment to popular <i>ab initio</i> and\r
-semi-empirical packages (GAUSSIAN-8X, GAMESS, HONDO, AMPAC,\r
-etc.). These versions are described in\r
-individual Appendices.\r
-<p>\r
-<p>\r
-<i>A.1.2 Structure of the NBO Program</i>\r
-<p>\r
- The overall logical structure of the NBO program and its attachment\r
-to an electronic structure system (ESS) are \r
-illustrated in the block diagram, Fig. 1. This figure illustrates how\r
-the ESS and its scratch\r
-files (in the upper part of the diagram) communicate through \r
-the interface routines RUNNBO, FEAOIN, and DELSCF \r
-with the main NBO modules and associated direct access file (in\r
-the lower part).\r
-<p>\r
- The main NBO program is represented by modules labelled "NBO"\r
-and "NBOEAN." These refer to the construction of NBOs (including\r
-natural population analysis, construction of NAOs, NLMOs, etc.) and to\r
-NBO energy analysis, respectively. Each module consists\r
-of subroutines and functions that perform the required \r
-operations. These two modules communicate with the\r
-direct-access disk file NBODAF (LFN 48, labelled "FILE48"\r
-elsewhere in this manual) that is created and\r
-maintained by the\r
-NBO routines. Details of the NBO and NBOEAN\r
-modules, common blocks, and direct-access file are described \r
-in the Programmer's Guide,\r
-Section C.\r
-<p>\r
- The NBO program blocks communicate with the attached\r
-ESS through three system-dependent 'driver' subroutines \r
-(RUNNBO, FEAOIN, DELSCF). The purpose of these drivers\r
-is to load needed information about the wavefunction and\r
-various matrices into the FILE48 direct access file\r
-and NBO common blocks. Although the ESS\r
-is usually thought of as 'driving' the NBO program, \r
-from the point of view of the NBO program the \r
-ESS is merely a 'device' that provides\r
-initial input (e.g., a density matrix and label information) or\r
-other feedback (a calculated energy value) upon\r
-request. Each such ESS device therefore requires special drivers\r
-to make this feedback possible. Versions of the driver subroutines are\r
-included for several popular packages. The driver routines are \r
-described in more detail in the Programmer's Guide, Section C.\r
-<p>\r
-<center>\r
-<img src="nbofig1.gif">\r
-</center>\r
-<p>\r
-<b>Figure 1:</b> Schematic diagram depicting flow of information\r
-between the electronic\r
-structure system (ESS) and the NBO program, \r
-and the communication lines connecting these programs to\r
-the ESS scratch file\r
-(called the "dictionary file," "read-write file,"\r
-etc., in various systems) and the NBO direct access file (NBODAF). Heavier \r
-box borders mark the ESS-specific driver \r
-routines (RUNNBO, FEAOIN,\r
-DELSCF) that directly interface the ESS program. The heavy dashed\r
-lines denote calls from the NBO program 'backward' to the ESS program\r
-for information needed to carry out its tasks. Otherwise, the sequential\r
-flow of program control is generally from top to bottom\r
-and from left to right in the diagram.\r
-<p>\r
-<p>\r
-<i>A.1.3 Input and Output</i>\r
-<p>\r
- From the user's point of view, the <u>input</u> to the NBO program\r
-attached to an ESS program consists simply of one or\r
-more keywords (an NBO <i>keylist</i>) included in the ESS input\r
-file. In effect, the NBO program reads these keywords to set\r
-various job options, then interrogates the ESS program through\r
-the DELSCF and FEAOIN drivers for additional information\r
-concerning the wavefunction. The general form of NBO keylists and\r
-the specific functions associated with each keyword are detailed\r
-in the User's Guide, Section B. The method of \r
-including NBO keylists in the input file for each\r
-ESS is detailed in the specific Appendix for the ESS.\r
-<p>\r
- The following information is passed from\r
-the ESS to the NBO program (transparent to the user):\r
-<p>\r
-1. The one-electron density matrix <b>D</b> (or density matrices in the\r
-open-shell case) in the chosen atomic orbital (AO) basis set;\r
-<p>\r
-2. The AO overlap matrix <b>S</b>, and label information identifying the\r
-symmetry (angular momentum type) and location (number of the atom\r
-to which affixed) for each AO;\r
-<p>\r
-3. Atomic number (nuclear charge) of each atom.\r
-<p>\r
-Certain additional information is written on the FILE48 direct\r
-access file and may be used\r
-in response to specific job\r
-options,\r
-such as the AO Fock matrix <b>F</b>, if energy analysis is requested; the\r
-AO dipole matrix <b>M</b>, if dipole moment analysis is requested; or\r
-information concerning the mathematical form of the AOs (orbital\r
-exponents, contraction coefficients, etc.), if orbital plotting\r
-information is requested\r
-to be saved as input for a contour plotting program.\r
-<p>\r
- The principal <u>output</u> from the NBO program \r
-consists of the tables and summaries describing\r
-the results of NBO analysis, included in the ESS output\r
-file. Sample NBO output is described in Section A.2.4 \r
-below. If requested, the NBO program may also write out transformation\r
-matrices or other data to disk files. The NBO program also\r
-creates or updates two files, the direct-access \r
-file (FILE48) and the 'archive' file (FILE47) that\r
-can be used to repeat NBO analysis with different options,\r
-without running the ESS program to recalculate the \r
-wavefunction. Necessary details of these files are given\r
-in Section B.7 and the Programmer's Guide,\r
-Section C.\r
-<p>\r
-<p>\r
-<i>A.1.4 General Capabilities and Restrictions</i>\r
-<p>\r
- Principal capabilities of the NBO program are:\r
-<p>\r
-1. Natural population, natural bond orbital, and natural localized\r
-molecular orbital analysis of SCF, MCSCF, CI, and Møller-Plesset\r
-wavefunctions (main subroutine: NBO);\r
-<p>\r
-2. For RHF closed-shell and UHF wavefunctions only,\r
-energetic analysis of the wavefunction in terms of the interactions\r
-(Fock matrix elements) between NBOs (main subroutine: NBOEAN);\r
-<p>\r
-3. Localized analysis of molecular dipole moment in terms of NLMO\r
-and NBO bond moments and their interactions (main subroutine: DIPANL).\r
-<p>\r
- A highly transportable subset of standard FORTRAN 77 is employed,\r
-with no special compiler extensions of any vendor,\r
-and all variable names of six characters or less. Common\r
-abbreviations used in naming subprograms, variables, and keywords are:\r
-<p>\r
-S = overlap matrix\r
-<br>DM = density matrix (or D)\r
-<br>F = Fock matrix\r
-<br>DI = dipole matrix (or DXYZ, or DX, DY, DZ)\r
-<br>NPA = Natural Population Analysis\r
-<br>NAO = Natural Atomic Orbital\r
-<br>NBO = Natural Bond Orbital\r
-<br>NLMO = Natural Localized Molecular Orbital\r
-<br>PNAO = pre-orthogonal NAO (i.e., omit interatomic orthogonalization)\r
-<br>PNHO, PNBO, PNLMO = pre-orthogonal NHO, etc. (formed from PNAOs)  \r
-<p>\r
- Most of the NBO storage is allocated dynamically, to conform to\r
-the minimum required for the molecular system under study. However,\r
-certain NBO common blocks of fixed dimensionality are used for\r
-integer storage. These are currently dimensioned to accomodate\r
-up to 99 atoms and 500 basis functions. Section C.3 describes how\r
-these restrictions can be altered. The program is not set up to\r
-handle complex wavefunctions, but can treat any real RHF, ROHF, UHF, MCSCF\r
-(including GVB), CI, or Møller-Plesset-type wavefunction\r
-(i.e., any form of wavefunction for which the requisite density\r
-matrices are available) for ground or excited states of general\r
-open- or closed-shell molecules. Effective core potentials\r
-("pseudopotentials") can be handled, including complete neglect\r
-of core electrons as assumed in semi-empirical treatments. The\r
-atomic orbital basis functions (up to <i>f</i> orbitals in angular\r
-symmetry) may be of general Slater-type, contracted Gaussian-type,\r
-or other general composition,\r
-including the "effective" orthonormal valence-shell AOs of\r
-semi-empirical treatments. AO basis functions are\r
-assumed to be normalized, but in general non-orthogonal.\r
-<p>\r
-<p>\r
-<i>A.1.5 References and Relationship to Previous Versions</i>\r
-<p>\r
- This program ("version 3.0") is an extension of previous versions of the\r
-NBO method incorporated in the semi-empirical program <i>BONDO</i>\r
-[F. Weinhold, <i>Quantum Chemistry Program Exchange No. 408</i>\r
-(1980); "version 1.0"]\r
-and in a GAUSSIAN-82 implementation [A. E. Reed and F. Weinhold, <i>QCPE \r
-Bull. <b>5</b></i>, 141 (1985); "version 2.0"], and should be considered to supplant\r
-those versions. Version 3.0 also supplants the various specific versions \r
-("the GAMESS version," "the AMPAC version," etc.) \r
-that have been informally created and distributed to individual users outside\r
-the QCPE framework.\r
-<p>\r
-Principal contributors to the development of\r
-the NBO methods and programs (1975-1990) are\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td>T. K. Brunck</td><td align=left>A. E. Reed</td></tr>\r
-<tr><td>J. P. Foster</td><td align=left>J. E. Carpenter</td></tr>\r
-<tr><td>A. B. Rives</td><td align=left>E. D. Glendening</td></tr>\r
-<tr><td>R. B. Weinstock</td><td align=left>F. Weinhold</td></tr>\r
-</table>\r
-Principal references to the development and applications of NAO/NBO/NLMO\r
-methods are:\r
-<p>\r
-<u>Natural Bond Orbitals:</u> <p>\r
-J. P. Foster and F. Weinhold, <i>J. Am. Chem. Soc. <b>102</b></i>, 7211-7218\r
-(1980). \r
-<p>\r
-<u>Natural Atomic Orbitals and Natural Population Analysis:</u> <p>\r
-A. E. Reed and F. Weinhold, <i>J. Chem. Phys. <b>78</b></i>, 4066-4073 (1983);\r
-A. E. Reed, R. B. Weinstock, and F. Weinhold, <i>J. Chem. Phys. <b>83</b></i>,\r
-735-746 (1985). \r
-<p>\r
-<u>Natural Localized Molecular Orbitals:</u> <p>\r
- A. E. Reed and F. Weinhold, <i>J. Chem. Phys. <b>83</b></i>, 1736-1740 (1985).\r
-<p>\r
-<u>Open-Shell NBO:</u> <p>\r
-J. E. Carpenter and F. Weinhold, <i>J. Molec. Struct. (Theochem) <b>169</b></i>,\r
-41-62 (1988); J. E. Carpenter, <i>Ph. D. Thesis</i>, University of Wisconsin,\r
-Madison, 1987.\r
-<p>\r
-<u>Review Articles:</u> <p>\r
-A. E. Reed, L. A. Curtiss, and F. Weinhold, <i>Chem. Rev. <b>88</b></i>, \r
-899-926 (1988); F. Weinhold and J. E. Carpenter, in, R. Naaman\r
-and Z. Vager (eds.), "The Structure of Small Molecules and\r
-Ions," (Plenum, New York, 1988), pp. 227-236.\r
-<p>\r
- The principal enhancements of version 3.0 include:\r
-<p>\r
-1. <i>Generalized Program Interface.</i>\r
-Overall program organization (Fig. 1) has been modified to\r
-standardize communication with the main ESS program. This\r
-insures that all special ESS "versions" of the NBO program \r
-now have consistent options and capabilities\r
-(as long as the option is meaningful in the context of the ESS), and enables\r
-the program to be offered in a greater number of specialized ESS versions\r
-than were previously available.\r
-<p>\r
-2. <i>NAO/NPA Summary Table.</i>\r
-New tables give improved display of NAOs and \r
-natural populations, including\r
-the "natural electron configuration" of\r
-each atom (i.e., the occupancy and type of NAOs describing\r
-the atomic electron configuration of each atom). The new NAO\r
-summary tables (Section A.3.2)\r
-include an SCF atomic orbital energy (if available),\r
-a conventional atomic orbital label (1<i>s</i>,\r
-2<i>s</i>, 2<i>p</i>, etc., in accordance with the labelling\r
-in isolated atoms), and a shell designation (Cor = core, Val = valence, \r
-or Ryd = Rydberg) to aid characterization of the NAO.\r
-<p>\r
-3. <i>NBO Summary Table.</i>\r
-A new NBO summary table (Section A.3.6) has been \r
-provided to summarize the energetics\r
-and delocalization patterns of the principal NBOs. This succinctly\r
-combines the most important information from the full NBO table, diagonal\r
-NBO Fock matrix elements, and\r
-2nd-order energy analysis.\r
-<p>\r
-4. <i>Bond Bending Analysis.</i>\r
-The program includes a new analysis of hydrid directionality\r
-and bond "bending" (keyword BEND, Section A.3.4).\r
-<p>\r
-5. <i>Dipole Moment Analysis.</i>\r
-The program includes new optional provision (keyword DIPOLE, Section\r
-B.6.3) for\r
-analysis of the molecular dipole moment in terms of localized\r
-NLMOs and NBOs.\r
-<p>\r
-6. <i>Print options.</i>\r
-The program offers new structured printing options (Section B.2.4) that give\r
-greater convenience and flexibility in controlling printed output,\r
-with improved provision for printing matrices or\r
-basis transformations involving general NAO, NHO, NBO, NLMO or\r
-pre-orthogonal (PNAO, PNHO, PNBO, PNLMO) basis sets.\r
-<p>\r
-7. <i>Orbital Contour Info.</i>\r
-The program makes optional provision (keyword PLOT, Section B.2.5) for\r
-writing out files that can be used by an orbital plotting\r
-program (available separately through QCPE) to \r
-draw contour diagrams of the NBOs or\r
-other natural localized orbitals.\r
-<p>\r
-8. <i>Effective Core Potentials.</i>\r
-The program now handles effective core potentials (pseudopotentials),\r
-or the complete neglect of core levels characteristic of semi-empirical\r
-wavefunctions (Section B.6.12).\r
-<p>\r
-The program also includes three changes to \r
-correct problems of the previous version (which may have\r
-affected a small number of users):\r
-<p>\r
-9. <i>Unpolarized Cores.</i>\r
-NAOs identified as "core" orbitals are now automatically carried over\r
-as unhybridized 1-center core NBOs \r
-(Section B.3). This has virtually no effect on\r
-the form or occupancy of a core NBO, but averts the (rare) problem of \r
-unphysical mixing between core and\r
-valence lone pairs when the occupancies are 'accidentally'\r
-degenerate (usually, both very close to 2.000...)\r
-within the numerical machine precision. A warning message\r
-is printed when the core occupancy is less than 1.9990, indicating\r
-a possible "core polarization" effect of physical significance.\r
-<p>\r
-10. <i>Excited State Antibond Labels.</i>\r
-The program now directly investigates the nodal structure of an NBO (by\r
-examining the overlap matrix in the PNHO basis) before assigning it a\r
-label as a "bond" (unstarred) or "antibond" (starred) NBO. In previous\r
-versions, these labels were assigned on the basis of the presumed higher\r
-occupancy of the in-phase bond combination, which \r
-was generally true for ground\r
-states, but not for excited states. The program now\r
-prints a warning message whenever it encounters the "anomalous"\r
-situation of an out-of-phase antibond NBO having higher occupancy than\r
-the corresponding in-phase bond NBO, indicative of an excited-state\r
-configuration. [WARNING: the overlap test cannot be applied to\r
-semi-empirical methods with orthogonal AOs (e.g., AMPAC), \r
-so antibond labels for these methods are assigned, as in previous\r
-versions, on the basis of occupancy.]\r
-<p>\r
-11. <i>Alternative Resonance Structures.</i> The program now institutes a\r
-search for alternative Lewis ('resonance') structures when two or\r
-more structures may be competitive, and returns the\r
-structure of lowest non-Lewis occupancy. This corrects a possible\r
-dependence on atomic numbering in cases of strong delocalization.\r
-<p>\r
-Despite these changes and extensions, version 3.0 has been\r
-designed to be upward compatible with v. 2.0, as nearly as \r
-possible. Previous users of NBO 2.0 should find that their jobs\r
-run similarly (i.e., most keywords \r
-continue to function\r
-as in previous versions). Thus, experienced \r
-NBO users should find little difficulty\r
-in adapting to, and experimenting with, \r
-the new capabilities of the program.\r
-<p>\r
-<p>\r
-<b>A.2 INSTALLING THE NBO PROGRAM</b>\r
-<p>\r
- The NBO programs and manual are provided on a distribution tape. The \r
-tape contains three files: the TechSet code of this\r
-manual (file NBO.MAN), a file containing the core NBO source routines\r
-and supporting driver routines (file NBO.SRC), and the Fortran\r
-"enabler" program (file ENABLE.FOR). \r
-<p>\r
- In overview, the installation procedure involves the following steps\r
-(the details of each step being dependent on your operating system):\r
-<p>\r
-1. <i>Enabling the NBO routines.</i> Copy the contents of the distribution\r
-tape onto your system. Using your system Fortran 77 compiler, compile\r
-and link the enabler program to create the ENABLE.EXE executable;\r
-for example, the VMS commands to create ENABLE.EXE are\r
- <pre>\r
- FOR ENABLE\r
- LINK ENABLE\r
-\r
-</pre>Now, run the ENABLE program (e.g., type "RUN ENABLE" in\r
-a VMS system), and \r
-answer the prompt\r
- <pre>\r
- NBO program version to enable?\r
-\r
-</pre>by selecting from the available offerings. Each ESS package is\r
-associated with a 3-letter identifier\r
-("G88" for GAUSSIAN-88, "GMS" for GAMESS,\r
-"AMP" for AMPAC, etc.). The ENABLE program will create\r
-a file <i>XXX</i>NBO.FOR (where '<i>XXX</i>' is the identifier)\r
-that incorporates the appropriate drivers for\r
-your ESS. \r
-<p>\r
-2. <i>Compiling the NBO routines.</i> Using your system Fortran 77 compiler,\r
-compile the <i>XXX</i>NBO.FOR file to an object code file (say, \r
-<i>XXX</i>NBO.OBJ). [Compiler\r
-errors (if any) should be fixed before proceeding. Please notify the\r
-authors if you encounter undue difficulties in this step.]\r
-<p>\r
-3. <i>Modifying the ESS routines.</i> In general, the ESS source Fortran code\r
-must be modified to call the NBO routines near the\r
-point where the ESS performs Mulliken Population Analysis or evaluates\r
-properties of the final wavefunction. The modification generally\r
-consists of inserting a single statement (viz., "CALL RUNNBO") in\r
-one subroutine of your ESS system. See the appropriate Appendix\r
-of this Manual for detailed information on exactly how to modify\r
-the ESS code for your chosen system.\r
-<p>\r
-4. <i>Rebuilding the integrated ESS/NBO program.</i> Re-compile your modified\r
-ESS programs and link the resulting object file (say, ESS.OBJ) with\r
-the <i>XXX</i>NBO.OBJ file to form the \r
-final ESS.EXE executable. In general, this\r
-step will closely follow the initial installation procedure for\r
-your ESS, with the exception that the <i>XXX</i>NBO.OBJ file must be included\r
-in the link statement (or deposited in one of the libraries accessed\r
-by the linker, etc.).\r
-<p>\r
-Note that installation of the NBO programs into your ESS system in no way\r
-affects the way your system processes standard input files. The only\r
-change involves enabling the reading of NBO keylists \r
-(if detected in your input\r
-file), performance of the tasks requested in the keylist, and return \r
-of control to the parent ESS program in the state in which the\r
-NBO call was encountered.\r
-<p>\r
- If you are interfacing the NBO programs to a new ESS package (not\r
-represented in the driver routines provided with this distribution),\r
-see Section C for guidance on how to create drivers for your ESS\r
-to provide the necessary information. Alternatively, see\r
-Section B.7 for a description of the input file to GENNBO,\r
-the stand-alone version of the NBO program.\r
-<p>\r
- The TechSet-coded version of this manual, NBO.MAN, can be\r
-printed on an HP LaserJet printer \r
-('F' cartridge) with the TECHSET \r
-technical typesetting program [ACS Software, American Chemical Society, \r
-Marketing Communications\r
-Dept., 1155 Sixteenth Street, N.W., Washington, D.C. 20036].\r
-<p>\r
-<p>\r
-<b>A.3 TUTORIAL EXAMPLE FOR METHYLAMINE</b>\r
-<p>\r
-<i>A.3.1 Running the Example</i>\r
-<p>\r
- This section provides an introductory 'quick start' tutorial \r
-on running a simple NBO job and interpreting the output. The example\r
-chosen is that of methylamine (CH<sub>3</sub>NH<sub>2</sub>) in\r
-Pople-Gordon idealized geometry, treated at the <i>ab initio</i>\r
-RHF/3-21G level. This simple split-valence\r
-basis set consists of 28 AOs (nine each\r
-on C and N, two on each H), extended by 13 AOs beyond\r
-the minimal basis level.\r
-<p>\r
- Input files to run this job (or its nearest equivalent) with\r
-each ESS are given in the Appendix. (The output shown below was\r
-created with the GAMESS system.) In most cases, you can modify\r
-the standard ESS input file to produce NBO output by\r
-simply including the line\r
- <pre>\r
- $NBO $END\r
-\r
-</pre>at the end of the file. This is an 'empty' NBO keylist, specifying\r
-that NBO analysis should be carried out at the <i>default</i> level.\r
-<p>\r
- The default NBO output produced by this example is shown below,\r
-just as it appears in your output file. The \r
-start of the NBO section is marked\r
-by a standard header and storage info:\r
-<p>\r
- <pre>\r
-*******************************************************************************\r
- N A T U R A L A T O M I C O R B I T A L A N D\r
- N A T U R A L B O N D O R B I T A L A N A L Y S I S\r
-*******************************************************************************\r
-\r
-Job title: Methylamine...RHF/3-21G//Pople-Gordon standard geometry \r
-\r
-Storage needed: 2505 in NPA, 2569 in NBO ( 750000 available)\r
-\r
-</pre>Note that all NBO output is formatted to a maximum 80-character\r
-width for convenient display on a computer terminal. The NBO heading\r
-echoes any requested keywords (none for the present default case)\r
-and shows an estimate of the memory requirements \r
-(in double precision words) for the separate \r
-steps of the NBO process, compared\r
-to the total allocated memory available through your ESS\r
-process. Increase the memory allocated to your\r
-ESS process if the estimated NBO requests exceed the available storage.\r
-<p>\r
-<i>A.3.2 Natural Population Analysis</i>\r
-<p>\r
- The next four NBO output segments \r
-summarize the results of natural population\r
-analysis (NPA). The first segment is the main NAO table, as shown\r
-below: \r
-<p>\r
- <pre>\r
-NATURAL POPULATIONS: Natural atomic orbital occupancies \r
- \r
- NAO Atom # lang Type(AO) Occupancy Energy \r
----------------------------------------------------------\r
- 1 C 1 s Cor( 1s) 1.99900 -11.04184\r
- 2 C 1 s Val( 2s) 1.09038 -0.28186\r
- 3 C 1 s Ryd( 3s) 0.00068 1.95506\r
- 4 C 1 px Val( 2p) 0.89085 -0.01645\r
- 5 C 1 px Ryd( 3p) 0.00137 0.93125\r
- 6 C 1 py Val( 2p) 1.21211 -0.07191\r
- 7 C 1 py Ryd( 3p) 0.00068 1.03027\r
- 8 C 1 pz Val( 2p) 1.24514 -0.08862\r
- 9 C 1 pz Ryd( 3p) 0.00057 1.01801\r
-\r
- 10 N 2 s Cor( 1s) 1.99953 -15.25950\r
- 11 N 2 s Val( 2s) 1.42608 -0.71700\r
- 12 N 2 s Ryd( 3s) 0.00016 2.75771\r
- 13 N 2 px Val( 2p) 1.28262 -0.18042\r
- 14 N 2 px Ryd( 3p) 0.00109 1.57018\r
- 15 N 2 py Val( 2p) 1.83295 -0.33858\r
- 16 N 2 py Ryd( 3p) 0.00190 1.48447\r
- 17 N 2 pz Val( 2p) 1.35214 -0.19175\r
- 18 N 2 pz Ryd( 3p) 0.00069 1.59492\r
-\r
- 19 H 3 s Val( 1s) 0.81453 0.13283\r
- 20 H 3 s Ryd( 2s) 0.00177 0.95067\r
-\r
- 21 H 4 s Val( 1s) 0.78192 0.15354\r
- 22 H 4 s Ryd( 2s) 0.00096 0.94521\r
-\r
- 23 H 5 s Val( 1s) 0.78192 0.15354\r
- 24 H 5 s Ryd( 2s) 0.00096 0.94521\r
-\r
- 25 H 6 s Val( 1s) 0.63879 0.20572\r
- 26 H 6 s Ryd( 2s) 0.00122 0.99883\r
-\r
- 27 H 7 s Val( 1s) 0.63879 0.20572\r
- 28 H 7 s Ryd( 2s) 0.00122 0.99883\r
-\r
-</pre>For each \r
-of the 28 NAO functions, this table lists the atom\r
-to which NAO is attached (in the numbering scheme of the ESS program),\r
-the angular momentum type 'lang' (<i>s</i>, <i>p<sub>x</sub></i>, etc., in the coordinate\r
-system of the ESS program), the orbital type (whether core, valence, or\r
-Rydberg, and a conventional\r
-hydrogenic-type label), the orbital occupancy (number of\r
-electrons, or 'natural \r
-population' of the orbital), and the orbital energy (in the favored units\r
-of the ESS program, in this case atomic units: 1 a.u. = 627.5 \r
-kcal/mol). [For example, NAO 4 (the highest energy C orbital of the\r
-NMB set) is the valence shell 2<i>p</i><sub>x</sub> orbital on carbon, occupied\r
-by 0.8909 electrons, whereas NAO 5 is a Rydberg \r
-3<i>p</i><sub>x</sub> orbital with only 0.0014 electrons.] Note that the \r
-occupancies of the Rydberg (Ryd) NAOs are\r
-typically much lower than those of the core (Cor) plus\r
-valence (Val)\r
-NAOs of the natural minimum basis set, reflecting \r
-the dominant role of the NMB orbitals \r
-in describing molecular properties. \r
-<p>\r
- The principal quantum numbers for the\r
-NAO labels (1<i>s</i>, 2<i>s</i>, 3<i>s</i>, etc.) are assigned on the\r
-basis of the energy order if a Fock matrix is available, or on the\r
-basis of occupancy otherwise. A message is printed warning of\r
-a 'population inversion' if the occupancy and energy\r
-ordering do not coincide.\r
-<p>\r
-<p>\r
-The next segment is an atomic summary showing the \r
-natural atomic charges (nuclear\r
-charge minus summed\r
-natural populations of NAOs on the atom) and total\r
-core, valence, and Rydberg populations on each atom:\r
-<p>\r
- <pre>\r
-Summary of Natural Population Analysis: \r
- \r
- Natural Population \r
- Natural -----------------------------------------------\r
- Atom # Charge Core Valence Rydberg Total\r
------------------------------------------------------------------------\r
- C 1 -0.44079 1.99900 4.43848 0.00331 6.44079\r
- N 2 -0.89715 1.99953 5.89378 0.00384 7.89715\r
- H 3 0.18370 0.00000 0.81453 0.00177 0.81630\r
- H 4 0.21713 0.00000 0.78192 0.00096 0.78287\r
- H 5 0.21713 0.00000 0.78192 0.00096 0.78287\r
- H 6 0.35999 0.00000 0.63879 0.00122 0.64001\r
- H 7 0.35999 0.00000 0.63879 0.00122 0.64001\r
-=======================================================================\r
- * Total * 0.00000 3.99853 13.98820 0.01328 18.00000\r
-\r
-</pre>This table succinctly describes the molecular\r
-charge distribution in terms of NPA charges. [For example,\r
-the carbon atom of methylamine is assigned a net NPA \r
-charge of -0.441\r
-at this level; note also the slightly less positive charge\r
-on H(3) than on the other two methyl hydrogens: +0.184 vs. +0.217.]\r
-<p>\r
-<p>\r
-Next follows a summary of the NMB and NRB populations\r
-for the composite\r
-system, summed over atoms:\r
-<p>\r
- <pre>\r
- Natural Population \r
---------------------------------------------------------\r
- Core 3.99853 ( 99.9632% of 4)\r
- Valence 13.98820 ( 99.9157% of 14)\r
- Natural Minimal Basis 17.98672 ( 99.9262% of 18)\r
- Natural Rydberg Basis 0.01328 ( 0.0738% of 18)\r
---------------------------------------------------------\r
-\r
-</pre>This exhibits the high percentage contribution (typically, > 99%) \r
-of the NMB set to the molecular charge distribution. [In the present\r
-case, for example, the 13 Rydberg orbitals of the \r
-NRB set contribute only 0.07%\r
-of the electron density, whereas the 15 NMB functions account\r
-for 99.93% of the total.]\r
-<p>\r
-<p>\r
-Finally, the natural populations are summarized as an effective\r
-valence electron configuration ("natural electron configuration")\r
-for each atom:\r
-<p>\r
- <pre>\r
- Atom # Natural Electron Configuration\r
-----------------------------------------------------------------------------\r
- C 1 [core]2s( 1.09)2p( 3.35)\r
- N 2 [core]2s( 1.43)2p( 4.47)\r
- H 3 1s( 0.81)\r
- H 4 1s( 0.78)\r
- H 5 1s( 0.78)\r
- H 6 1s( 0.64)\r
- H 7 1s( 0.64)\r
-\r
-</pre>Although the occupancies of the atomic orbitals are non-integer\r
-in the molecular environment, the effective atomic configurations\r
-can be related to idealized atomic states in\r
-'promoted' configurations. [For example, the carbon atom in\r
-the above table is most nearly described by an idealized\r
-1s<sup>2</sup>2s<sup>1</sup>2p<sup>3</sup> electron configuration.]\r
-<p>\r
-<p>\r
-<i>A.3.3 Natural Bond Orbital Analysis</i>\r
-<p>\r
- The next segments of the output summarize the results \r
-of NBO analysis. The first segment reports on details of the search for\r
-an NBO natural Lewis structure: \r
-<p>\r
- <pre>\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 17.95048 0.04952 2 6 0 1 0 0 0.02\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
-</pre>Normally, there is but one cycle of the NBO search (cf. the\r
-"RESONANCE" keyword, Section B.6.6). The table summarizes\r
-a variety of information for each cycle:\r
-the occupancy threshold for a 'good' pair in the NBO search; \r
-the total populations of Lewis and non-Lewis\r
-NBOs; the number of core (CR), 2-center bond (BD), \r
-3-center bond (3C), and lone pair (LP) NBOs in\r
-the natural Lewis structure; the number of low-occupancy Lewis (L)\r
-and 'high-occupancy' (> 0.1e) non-Lewis (NL) orbitals; and the\r
-maximum deviation ('Dev') of any formal bond order from a \r
-nominal estimate (NAO Wiberg bond index) for the structure. [If\r
-the latter exceeds 0.1, additional NBO searches are initiated\r
-(indicated by the parenthesized number under 'Cycle') for alternative\r
-Lewis structures.] The Lewis \r
-structure is accepted if all orbitals of the formal Lewis structure\r
-exceed the occupancy threshold (default, 1.90 electrons).\r
-<p>\r
-<p>\r
- Next follows a more detailed breakdown of the Lewis and non-Lewis\r
-occupancies into core, valence, and Rydberg shell contributions:\r
-<p>\r
- <pre>\r
-WARNING: 1 low occupancy (<1.9990e) core orbital found on C 1\r
-\r
---------------------------------------------------------\r
- Core 3.99853 ( 99.963% of 4)\r
- Valence Lewis 13.95195 ( 99.657% of 14)\r
- ================== ============================\r
- Total Lewis 17.95048 ( 99.725% of 18)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.03977 ( 0.221% of 18)\r
- Rydberg non-Lewis 0.00975 ( 0.054% of 18)\r
- ================== ============================\r
- Total non-Lewis 0.04952 ( 0.275% of 18)\r
---------------------------------------------------------\r
-\r
-</pre>This shows the general quality of the natural Lewis structure\r
-description in terms of the percentage of the total electron\r
-density (e.g., in the above case, about 99.7%). The table also\r
-exhibits the relatively important role of the valence non-Lewis\r
-orbitals (i.e., the six valence antibonds, NBOs 23-28) relative to\r
-the extra-valence orbitals (the 13 Rydberg NBOs 10-22) in the\r
-slight departures from a localized Lewis structure model. (In\r
-this case, the table also includes a warning about a carbon core\r
-orbital with slightly less than double occupancy.)\r
-<p>\r
-<p>\r
-Next follows the main listing of NBOs, displaying the form and occupancy\r
-of the complete set of NBOs that span the input AO space: \r
- <pre>\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (1.99858) BD ( 1) C 1- N 2 \r
- ( 40.07%) 0.6330* C 1 s( 21.71%)p 3.61( 78.29%)\r
- -0.0003 -0.4653 -0.0238 -0.8808 -0.0291\r
- -0.0786 -0.0110 0.0000 0.0000\r
- ( 59.93%) 0.7742* N 2 s( 30.88%)p 2.24( 69.12%)\r
- -0.0001 -0.5557 0.0011 0.8302 0.0004\r
- 0.0443 -0.0098 0.0000 0.0000\r
- 2. (1.99860) BD ( 1) C 1- H 3 \r
- ( 59.71%) 0.7727* C 1 s( 25.78%)p 2.88( 74.22%)\r
- -0.0002 -0.5077 0.0069 0.1928 0.0098\r
- 0.8396 -0.0046 0.0000 0.0000\r
- ( 40.29%) 0.6347* H 3 s(100.00%)\r
- -1.0000 -0.0030\r
- 3. (1.99399) BD ( 1) C 1- H 4 \r
- ( 61.02%) 0.7812* C 1 s( 26.28%)p 2.80( 73.72%)\r
- 0.0001 0.5127 -0.0038 -0.3046 -0.0015\r
- 0.3800 -0.0017 0.7070 -0.0103\r
- ( 38.98%) 0.6243* H 4 s(100.00%)\r
- 1.0000 0.0008\r
- 4. (1.99399) BD ( 1) C 1- H 5 \r
- ( 61.02%) 0.7812* C 1 s( 26.28%)p 2.80( 73.72%)\r
- 0.0001 0.5127 -0.0038 -0.3046 -0.0015\r
- 0.3800 -0.0017 -0.7070 0.0103\r
- ( 38.98%) 0.6243* H 5 s(100.00%)\r
- 1.0000 0.0008\r
- 5. (1.99442) BD ( 1) N 2- H 6 \r
- ( 68.12%) 0.8253* N 2 s( 25.62%)p 2.90( 74.38%)\r
- 0.0000 0.5062 0.0005 0.3571 0.0171\r
- -0.3405 0.0069 -0.7070 -0.0093\r
- ( 31.88%) 0.5646* H 6 s(100.00%)\r
- 1.0000 0.0020\r
- 6. (1.99442) BD ( 1) N 2- H 7 \r
- ( 68.12%) 0.8253* N 2 s( 25.62%)p 2.90( 74.38%)\r
- 0.0000 0.5062 0.0005 0.3571 0.0171\r
- -0.3405 0.0069 0.7070 0.0093\r
- ( 31.88%) 0.5646* H 7 s(100.00%)\r
- 1.0000 0.0020\r
- 7. (1.99900) CR ( 1) C 1 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0003 0.0000 -0.0002 0.0000\r
- 0.0001 0.0000 0.0000 0.0000\r
- 8. (1.99953) CR ( 1) N 2 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0001 0.0000 0.0001 0.0000\r
- 0.0000 0.0000 0.0000 0.0000\r
- 9. (1.97795) LP ( 1) N 2 s( 17.85%)p 4.60( 82.15%)\r
- 0.0000 0.4225 0.0002 0.2360 -0.0027\r
- 0.8749 -0.0162 0.0000 0.0000\r
- 10. (0.00105) RY*( 1) C 1 s( 1.57%)p62.84( 98.43%)\r
- 0.0000 -0.0095 0.1248 -0.0305 0.7302\r
- -0.0046 0.6710 0.0000 0.0000\r
- 11. (0.00034) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0146 0.9999\r
- 12. (0.00022) RY*( 3) C 1 s( 56.51%)p 0.77( 43.49%)\r
- 0.0000 -0.0023 0.7517 -0.0237 0.3710\r
- -0.0094 -0.5447 0.0000 0.0000\r
- 13. (0.00002) RY*( 4) C 1 s( 41.87%)p 1.39( 58.13%)\r
- 14. (0.00116) RY*( 1) N 2 s( 1.50%)p65.53( 98.50%)\r
- 0.0000 -0.0062 0.1224 0.0063 0.0371\r
- 0.0197 0.9915 0.0000 0.0000\r
- 15. (0.00044) RY*( 2) N 2 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 -0.0132 0.9999\r
- 16. (0.00038) RY*( 3) N 2 s( 33.38%)p 2.00( 66.62%)\r
- 0.0000 0.0133 0.5776 0.0087 -0.8150\r
- -0.0121 -0.0405 0.0000 0.0000\r
- 17. (0.00002) RY*( 4) N 2 s( 65.14%)p 0.54( 34.86%)\r
- 18. (0.00178) RY*( 1) H 3 s(100.00%)\r
- -0.0030 1.0000\r
- 19. (0.00096) RY*( 1) H 4 s(100.00%)\r
- -0.0008 1.0000\r
- 20. (0.00096) RY*( 1) H 5 s(100.00%)\r
- -0.0008 1.0000\r
- 21. (0.00122) RY*( 1) H 6 s(100.00%)\r
- -0.0020 1.0000\r
- 22. (0.00122) RY*( 1) H 7 s(100.00%)\r
- -0.0020 1.0000\r
- 23. (0.00016) BD*( 1) C 1- N 2 \r
- ( 59.93%) 0.7742* C 1 s( 21.71%)p 3.61( 78.29%)\r
- -0.0003 -0.4653 -0.0238 -0.8808 -0.0291\r
- -0.0786 -0.0110 0.0000 0.0000\r
- ( 40.07%) -0.6330* N 2 s( 30.88%)p 2.24( 69.12%)\r
- -0.0001 -0.5557 0.0011 0.8302 0.0004\r
- 0.0443 -0.0098 0.0000 0.0000\r
- 24. (0.01569) BD*( 1) C 1- H 3 \r
- ( 40.29%) 0.6347* C 1 s( 25.78%)p 2.88( 74.22%)\r
- 0.0002 0.5077 -0.0069 -0.1928 -0.0098\r
- -0.8396 0.0046 0.0000 0.0000\r
- ( 59.71%) -0.7727* H 3 s(100.00%)\r
- 1.0000 0.0030\r
- 25. (0.00769) BD*( 1) C 1- H 4 \r
- ( 38.98%) 0.6243* C 1 s( 26.28%)p 2.80( 73.72%)\r
- -0.0001 -0.5127 0.0038 0.3046 0.0015\r
- -0.3800 0.0017 -0.7070 0.0103\r
- ( 61.02%) -0.7812* H 4 s(100.00%)\r
- -1.0000 -0.0008\r
- 26. (0.00769) BD*( 1) C 1- H 5 \r
- ( 38.98%) 0.6243* C 1 s( 26.28%)p 2.80( 73.72%)\r
- -0.0001 -0.5127 0.0038 0.3046 0.0015\r
- -0.3800 0.0017 0.7070 -0.0103\r
- ( 61.02%) -0.7812* H 5 s(100.00%)\r
- -1.0000 -0.0008\r
- 27. (0.00426) BD*( 1) N 2- H 6 \r
- ( 31.88%) 0.5646* N 2 s( 25.62%)p 2.90( 74.38%)\r
- 0.0000 -0.5062 -0.0005 -0.3571 -0.0171\r
- 0.3405 -0.0069 0.7070 0.0093\r
- ( 68.12%) -0.8253* H 6 s(100.00%)\r
- -1.0000 -0.0020\r
- 28. (0.00426) BD*( 1) N 2- H 7 \r
- ( 31.88%) 0.5646* N 2 s( 25.62%)p 2.90( 74.38%)\r
- 0.0000 -0.5062 -0.0005 -0.3571 -0.0171\r
- 0.3405 -0.0069 -0.7070 -0.0093\r
- ( 68.12%) -0.8253* H 7 s(100.00%)\r
- -1.0000 -0.0020\r
-\r
-</pre>For each NBO (1-28), the\r
-first line of printout\r
-shows the occupancy (between 0 and 2.0000 electrons) and unique label\r
-of the NBO. This \r
-label gives the type\r
-("BD" for 2-center bond, "CR" for 1-center core pair, "LP" for 1-center\r
-valence lone pair, "RY*" for 1-center Rydberg, and "BD*" for 2-center\r
-antibond, the unstarred and starred labels corresponding to Lewis\r
-and non-Lewis NBOs, respectively), a serial number (1, 2,... if there is a\r
-single, double,... bond between the pair of atoms), and the atom(s) to\r
-which the NBO is affixed. [For example, the first NBO in the sample\r
-output is the 2-center bond (with 1.99858 electrons)\r
-between carbon (atom 1) and nitrogen (atom 2), the <img src=sigma.gif><sub>CN</sub> \r
-bond.] The next lines summarize\r
-the natural atomic hybrids <i>h</i><sub>A</sub>\r
-of which the NBO is composed, giving the\r
-percentage (100|<i>c</i><sub>A</sub>|<sup>2</sup>) of the NBO on each hybrid (in parentheses),\r
-the polarization coefficient <i>c</i><sub>A</sub>, the atom label, and a hybrid\r
-label showing the <i>sp</i><sup><img src=lambda.gif></sup> composition \r
-(percentage <i>s</i>-character, <i>p</i>-character, etc.) of\r
-each <i>h</i><sub>A</sub>. [For example, the <img src=sigma.gif><sub>CN</sub> NBO \r
-is formed from an <i>sp</i><sup>3.61</sup> hybrid (78.3%\r
-<i>p</i>-character) on carbon interacting with an <i>sp</i><sup>2.24</sup> hybrid\r
-(69.1% <i>p</i>-character) on nitrogen,\r
-<p>\r
-<center>\r
-<img src=sigma.gif><sub>CN</sub> = 0.633(<i>sp</i><sup>3.61</sup>)<sub>C</sub> + 0.774(<i>sp</i><sup>2.24</sup>)<sub>N</sub> \r
-</center>\r
-<p>\r
-corresponding roughly to the qualitative concept \r
-of interacting <i>sp</i><sup>3</sup> hybrids (75% <i>p</i>-character) and the higher\r
-electronegativity (larger polarization coefficient) of N.] Below \r
-each NHO label is the set of\r
-coefficients that specify how the NHO is written explicitly as a linear\r
-combination of NAOs on the atom. The order of NAO coefficients follows\r
-the numbering of the NAO tables. [For example, in the first NBO entry,\r
-the carbon hybrid <i>h</i><sub>C</sub> \r
-of the <img src=sigma.gif><sub>CN</sub> bond has largest coefficients for the 2<sup>nd</sup>\r
-and 4<sup>th</sup> NAOs, corresponding to the approximate description\r
-<p>\r
-<center>\r
-<i>h</i><sub>C</sub> <img src=ca.gif> -0.4653(2<i>s</i>)<sub>C</sub> - 0.8808(2<i>p</i><sub>x</sub>)<sub>C</sub>\r
-</center>\r
-<p>\r
-in terms of the valence NAOs of the carbon atom.] In \r
-the CH<sub>3</sub>NH<sub>2</sub> example, the NBO search\r
-finds the C-N bond (NBO 1), three C-H bonds (NBOs 2, 3, 4), two N-H\r
-bonds (NBOs 5, 6), N lone pair (NBO 9), and C and N\r
-core pairs (NBOs 7, 8) of the expected Lewis structure. NBOs 10-28\r
-represent the residual non-Lewis NBOs of low occupancy. In this\r
-example, it is also interesting to note the slight asymmetry of the three\r
-<img src=sigma.gif><sub>CH</sub> NBOs, and the slightly higher occupancy \r
-(0.01569 <i>vs.</i> 0.0077\r
-electrons) in the <img src=sigma.gif>*<sub>C<sub>1</sub>H<sub>3</sub></sub> antibond \r
-(NBO 24) lying <i>trans</i> to the\r
-nitrogen lone pair.\r
-<p>\r
-<i>A.3.4 NHO Directional Analysis</i>\r
-<p>\r
- The next segment of output\r
-summarizes the angular properties of\r
-the natural hybrid orbitals: \r
-<p>\r
- <pre>\r
-NHO Directionality and "Bond Bending" (deviations from line of nuclear centers)\r
-\r
- [Thresholds for printing: angular deviation > 1.0 degree]\r
- hybrid p-character > 25.0%\r
- orbital occupancy > 0.10e\r
-\r
- Line of Centers Hybrid 1 Hybrid 2\r
- --------------- ------------------- ------------------\r
- NBO Theta Phi Theta Phi Dev Theta Phi Dev\r
-===============================================================================\r
- 1. BD ( 1) C 1- N 2 90.0 5.4 -- -- -- 90.0 182.4 3.0\r
- 3. BD ( 1) C 1- H 4 35.3 130.7 34.9 129.0 1.0 -- -- --\r
- 4. BD ( 1) C 1- H 5 144.7 130.7 145.1 129.0 1.0 -- -- --\r
- 5. BD ( 1) N 2- H 6 144.7 310.7 145.0 318.3 4.4 -- -- --\r
- 6. BD ( 1) N 2- H 7 35.3 310.7 35.0 318.3 4.4 -- -- --\r
- 9. LP ( 1) N 2 -- -- 90.0 74.8 -- -- -- --\r
-\r
-</pre>The 'direction' of a hybrid is specified \r
-in terms of the polar (<img src=theta.gif>) and \r
-azimuthal (<img src=phi.gif>) angles (in the ESS coordinate system) of the vector\r
-describing its <i>p</i>-component. The hybrid direction is\r
-compared with the direction of the line of centers between the two\r
-nuclei to determine the 'bending' of the bond, expressed as\r
-the deviation angle ("Dev," in degrees) between these two directions. For\r
-example, in the CH<sub>3</sub>NH<sub>2</sub> case shown above, the nitrogen NHO\r
-of the <img src=sigma.gif><sub>CN</sub> bond (NBO 1) is bent away \r
-from the line of C-N\r
-centers by 3.0°, whereas the carbon NHO is approximately \r
-aligned with the C-N axis (within the 1.0° threshold for \r
-printing). The N-H bonds (NBOs 5, 6) are \r
-bent even further (4.4°). The information in this table\r
-is often useful in anticipating the direction of geometry changes\r
-resulting from geometry optimization (viz., likely reduced pyramidalization\r
-of the -NH<sub>2</sub> group to relieve the nitrogen bond 'kinks' found\r
-in the tetrahedral Pople-Gordon geometry).\r
-<p>\r
-<p>\r
-<i>A.3.5 Perturbation Theory Energy Analysis</i>\r
-<p>\r
- The next segment summarizes the second-order perturbative estimates\r
-of 'donor-acceptor' (bond-antibond) interactions in the NBO basis:\r
-<p>\r
- <pre>\r
-Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis\r
-\r
- Threshold for printing: 0.50 kcal/mol\r
- E(2) E(j)-E(i) F(i,j)\r
- Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u. \r
-===============================================================================\r
-\r
-within unit 1\r
- 2. BD ( 1) C 1- H 3 / 14. RY*( 1) N 2 0.84 2.18 0.038\r
- 3. BD ( 1) C 1- H 4 / 26. BD*( 1) C 1- H 5 0.52 1.39 0.024\r
- 3. BD ( 1) C 1- H 4 / 27. BD*( 1) N 2- H 6 3.03 1.37 0.057\r
- 4. BD ( 1) C 1- H 5 / 25. BD*( 1) C 1- H 4 0.52 1.39 0.024\r
- 4. BD ( 1) C 1- H 5 / 28. BD*( 1) N 2- H 7 3.03 1.37 0.057\r
- 5. BD ( 1) N 2- H 6 / 10. RY*( 1) C 1 0.56 1.78 0.028\r
- 5. BD ( 1) N 2- H 6 / 25. BD*( 1) C 1- H 4 2.85 1.51 0.059\r
- 6. BD ( 1) N 2- H 7 / 10. RY*( 1) C 1 0.56 1.78 0.028\r
- 6. BD ( 1) N 2- H 7 / 26. BD*( 1) C 1- H 5 2.85 1.51 0.059\r
- 7. CR ( 1) C 1 / 16. RY*( 3) N 2 0.61 13.11 0.080\r
- 7. CR ( 1) C 1 / 18. RY*( 1) H 3 1.40 11.99 0.116\r
- 7. CR ( 1) C 1 / 19. RY*( 1) H 4 1.55 11.99 0.122\r
- 7. CR ( 1) C 1 / 20. RY*( 1) H 5 1.55 11.99 0.122\r
- 8. CR ( 1) N 2 / 10. RY*( 1) C 1 1.51 16.23 0.140\r
- 8. CR ( 1) N 2 / 12. RY*( 3) C 1 0.84 16.77 0.106\r
- 8. CR ( 1) N 2 / 21. RY*( 1) H 6 0.61 16.26 0.089\r
- 8. CR ( 1) N 2 / 22. RY*( 1) H 7 0.61 16.26 0.089\r
- 9. LP ( 1) N 2 / 24. BD*( 1) C 1- H 3 8.13 1.13 0.086\r
- 9. LP ( 1) N 2 / 25. BD*( 1) C 1- H 4 1.46 1.14 0.037\r
- 9. LP ( 1) N 2 / 26. BD*( 1) C 1- H 5 1.46 1.14 0.037\r
-\r
-</pre>This is carried out by examining all possible\r
-interactions between\r
-'filled' (donor) Lewis-type NBOs and 'empty' (acceptor) non-Lewis\r
-NBOs, and estimating their energetic importance by 2nd-order perturbation\r
-theory. Since these interactions lead to loss of occupancy from the\r
-localized NBOs of the idealized Lewis structure into \r
-the empty non-Lewis orbitals (and thus, to departures from the\r
-idealized Lewis structure description), they are referred to\r
-as 'delocalization' corrections to the zeroth-order natural Lewis\r
-structure. For each donor NBO (<i>i</i>) and acceptor NBO (<i>j</i>), \r
-the stabilization energy E(2) associated with delocalization\r
-("2e-stabilization") <i>i <img src=rarr.gif> j</i> is estimated as\r
-<p>\r
-<center>\r
-E(2) = <img src=delta.gif>E<sub>ij</sub> = q<sub>i</sub> (F(i,j)<sup>2</sup>)/(<img src=epsilon.gif><sub>j</sub> - <img src=epsilon.gif><sub>i</sub>)\r
-</center>\r
-<p>\r
-where <i>q</i><sub>i</sub> is the donor orbital occupancy,\r
-<img src=epsilon.gif><sub>i</sub>, <img src=epsilon.gif><sub>j</sub> are diagonal elements (orbital energies)\r
-and F(i,j) is the off-diagonal NBO Fock matrix element. [In the example\r
-above, the <i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>CH</sub> interaction between the\r
-nitrogen lone pair (NBO 8) and the antiperiplanar C<sub>1</sub>-H<sub>3</sub> antibond\r
-(NBO 24) is seen to give the strongest\r
-stabilization, 8.13 kcal/mol.] As the heading\r
-indicates, entries are included in this table only when the interaction\r
-energy exceeds a default threshold of 0.5 kcal/mol.\r
-<p>\r
-<i>A.3.6 NBO Summary</i>\r
-<p>\r
- Next appears a condensed summary of the principal NBOs, showing the\r
-occupancy, orbital energy, and the qualitative pattern of delocalization\r
-interactions associated with each:\r
-<p>\r
- <pre>\r
-Natural Bond Orbitals (Summary):\r
-\r
- Principal Delocalizations\r
- NBO Occupancy Energy (geminal,vicinal,remote)\r
-===============================================================================\r
-Molecular unit 1 (CH5N)\r
- 1. BD ( 1) C 1- N 2 1.99858 -0.89908\r
- 2. BD ( 1) C 1- H 3 1.99860 -0.69181 14(v)\r
- 3. BD ( 1) C 1- H 4 1.99399 -0.68892 27(v),26(g)\r
- 4. BD ( 1) C 1- H 5 1.99399 -0.68892 28(v),25(g)\r
- 5. BD ( 1) N 2- H 6 1.99442 -0.80951 25(v),10(v)\r
- 6. BD ( 1) N 2- H 7 1.99442 -0.80951 26(v),10(v)\r
- 7. CR ( 1) C 1 1.99900 -11.04131 19(v),20(v),18(v),16(v)\r
- 8. CR ( 1) N 2 1.99953 -15.25927 10(v),12(v),21(v),22(v)\r
- 9. LP ( 1) N 2 1.97795 -0.44592 24(v),25(v),26(v)\r
- 10. RY*( 1) C 1 0.00105 0.97105\r
- 11. RY*( 2) C 1 0.00034 1.02120\r
- 12. RY*( 3) C 1 0.00022 1.51414\r
- 13. RY*( 4) C 1 0.00002 1.42223\r
- 14. RY*( 1) N 2 0.00116 1.48790\r
- 15. RY*( 2) N 2 0.00044 1.59323\r
- 16. RY*( 3) N 2 0.00038 2.06475\r
- 17. RY*( 4) N 2 0.00002 2.25932\r
- 18. RY*( 1) H 3 0.00178 0.94860\r
- 19. RY*( 1) H 4 0.00096 0.94464\r
- 20. RY*( 1) H 5 0.00096 0.94464\r
- 21. RY*( 1) H 6 0.00122 0.99735\r
- 22. RY*( 1) H 7 0.00122 0.99735\r
- 23. BD*( 1) C 1- N 2 0.00016 0.57000\r
- 24. BD*( 1) C 1- H 3 0.01569 0.68735\r
- 25. BD*( 1) C 1- H 4 0.00769 0.69640\r
- 26. BD*( 1) C 1- H 5 0.00769 0.69640\r
- 27. BD*( 1) N 2- H 6 0.00426 0.68086\r
- 28. BD*( 1) N 2- H 7 0.00426 0.68086\r
- -------------------------------\r
- Total Lewis 17.95048 ( 99.7249%)\r
- Valence non-Lewis 0.03977 ( 0.2209%)\r
- Rydberg non-Lewis 0.00975 ( 0.0542%)\r
- -------------------------------\r
- Total unit 1 18.00000 (100.0000%)\r
- Charge unit 1 0.00000\r
-\r
-</pre>This table allows one to quickly identify the principal delocalizing\r
-acceptor orbitals associated with each donor NBO, and their\r
-topological relationship to this NBO, i.e., whether attached to the same\r
-atom (geminal, "g"), to an adjacent bonded atom (vicinal, "v"), or\r
-to a more remote ("r") site. These acceptor NBOs will generally \r
-correspond to the principal 'delocalization tails' of the NLMO\r
-associated with the parent donor NBO. [For example, in the table above,\r
-the nitrogen lone pair (NBO 9) is seen to be the lowest-occupancy\r
-(1.97795 electrons) and highest-energy \r
-(-0.44592 a.u.) Lewis NBO, and to\r
-be primarily\r
-delocalized into antibonds 24, 25, 26 (the vicinal <img src=sigma.gif>*<sub>CH</sub>\r
-NBOs). The summary at the bottom of the table shows that the\r
-Lewis NBOs 1-9 describe about 99.7% of the total electron density,\r
-with the remaining non-Lewis density found primarily in the\r
-valence-shell antibonds (particularly, NBO 24).]\r
-<p>\r
-<center>\r
-<h2>Section B: NBO USER'S GUIDE</h2>\r
-</center>\r
-<p>\r
-<b>B.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS</b>\r
-<p>\r
- Section B constitutes the general \r
-user's guide to the NBO program. It\r
-assumes that the user has an installed \r
-electronic structure system (ESS) with attached NBO program,\r
-a general idea of what the \r
-NBO method is about, and some\r
-acquaintance with standard NBO terminology and output data. If you are\r
-completely inexperienced in these areas, read Section A\r
-(General Introduction and Installation) for the necessary background\r
-to this Section.\r
-<p>\r
- The User's Guide describes how to use the NBO program\r
-by modifying your input file to the ESS program\r
-to get some NBO output. The modification consists of adding a list\r
-of <i>keywords</i> in a prescribed <i>keylist</i> format. Four distinct\r
-keylist ($KEY) types are recognized ($NBO, $CORE, $CHOOSE, and $DEL), and\r
-these will be described in turn in Sections B.2-B.5. Some of the details\r
-of inserting NBO keylists into the input file depend on the details\r
-of your ESS method, and are described in the appropriate Appendix for\r
-the ESS. However, the general form of NBO keylists and the meaning and\r
-function of each keyword are identical for all versions (insofar as the\r
-option is meaningful for the ESS), and are described herein. \r
-<p>\r
- The four keylist types have common rules of syntax: Keylist\r
-delimiters are identified by a "$" prefix. Each keylist\r
-begins with the parent keylist name (e.g., "$NBO"), followed\r
-by any number of keywords, and ended\r
-with the word "$END"; for example,\r
- <pre>\r
- $NBO keyword1 keyword2 . . . $END !comment\r
-\r
-</pre>(The allowed keyword entries for each type of keylist are described\r
-in Sections B.2-B.5.) The keylist is "free format," with keywords\r
-separated by commas or any number of spaces. An NBO option is\r
-activated by simply including its keyword in the appropriate keylist. The\r
-order of keywords in the principal $NBO keylist\r
-does not matter, but multiple keylists must be given\r
-in the order (1) $NBO, (2) $CORE, (3) $CHOOSE, (4) $DEL of presentation\r
-in Sections B.2-B.5. Keywords may be typed in upper or lower case,\r
-and will be echoed near the top of the NBO output. A $KEY list can\r
-be continued to any number of lines, but all the entries of a $KEY list must\r
-appear in a distinct set of lines, starting with the $KEY name on the\r
-first line and ending with the closing $END on the last line (i.e.,\r
-no two $KEY lists should share parts of the same line). As the\r
-above example\r
-indicates, any line in the keylist input may terminate with an exclamation\r
-point (!) followed by 'comment' of your choice; the "!" is \r
-considered to terminate\r
-the line, and the trailing 'comment' is ignored by the program.\r
-<p>\r
-<p>\r
-<b>B.2 THE $NBO KEYLIST</b>\r
-<p>\r
-<i>B.2.1 Overview of $NBO keywords</i>\r
-<p>\r
- The $NBO keylist is the principal means of specifying NBO\r
-job options and controlling output, and must precede \r
-any other keylist ($CORE, $CHOOSE,\r
-or $DEL) in your input file. The allowed keywords that can\r
-appear in a $NBO keylist are grouped as follows:\r
-<p>\r
-<p>\r
-<i>Job Control Keywords:</i>\r
-<table border=0 width=100%>\r
-<tr><td align=left>NPA</td><td align=left>NBOSUM</td><td align=left>NOBOND</td><td align=left>SKIPBO</td></tr>\r
-<tr><td align=left>NBO</td><td align=left>RESONANCE</td><td align=left>3CBOND</td><td align=left>NLMO</td></tr>\r
-</table>\r
-<i>Job Threshold Keywords:</i>\r
-<table border=0 width=100%>\r
-<tr><td align=left>BEND(=ang,pct,occ)</td></tr>\r
-<tr><td align=left>E2PERT(=val)</td></tr>\r
-<tr><td align=left>DIPOLE(=val)</td></tr>\r
-</table>\r
-<p>\r
-<i>Matrix Output Keywords:</i>\r
-<table border=0 width=100%>\r
-<tr><td align=left>AONAO</td><td align=left>NAONHO</td><td align=left>NHONBO</td><td align=left>NBONLMO</td><td align=left>NLMOMO</td></tr>\r
-<tr><td align=left>AONHO</td><td align=left>NAONBO</td><td align=left>NHONLMO</td><td align=left>NBOMO</td><td align=left> </td></tr>\r
-<tr><td align=left>AONBO</td><td align=left>NAONLMO</td><td align=left>NHOMO</td><td align=left> </td><td align=left> </td></tr>\r
-<tr><td align=left>AONLMO</td><td align=left>NAOMO</td><td align=left> </td><td align=left> </td><td align=left> </td></tr>\r
-<tr><td align=left>AOMO</td><td align=left> </td><td align=left> </td><td align=left> </td><td align=left> </td></tr>\r
-<tr><td align=left>AOPNAO</td><td align=left>AOPNHO</td><td align=left>AOPNBO</td><td align=left>AOPNLMO</td><td align=left> </td></tr>\r
-<tr><td align=left colspan=1>DMAO</td><td align=left colspan=1>FAO</td><td align=left colspan=1>DIAO</td><td align=left colspan=1>SAO</td></tr>\r
-<tr><td align=left colspan=1>DMNAO</td><td align=left colspan=1>FNAO</td><td align=left colspan=1>DINAO</td><td align=left colspan=1>SPNAO</td></tr>\r
-<tr><td align=left colspan=1>DMNHO</td><td align=left colspan=1>FNHO</td><td align=left colspan=1>DINHO</td><td align=left colspan=1>SPNHO</td></tr>\r
-<tr><td align=left colspan=1>DMNBO</td><td align=left colspan=1>FNBO</td><td align=left colspan=1>DINBO</td><td align=left colspan=1>SPNBO</td></tr>\r
-<tr><td align=left colspan=1>DMNLMO</td><td align=left colspan=1>FNLMO</td><td align=left colspan=1>DINLMO</td><td align=left colspan=1>SPNLMO</td></tr>\r
-</table>\r
-<p>\r
-<i>Other Output Control Keywords:</i>\r
-<table border=0 width=100%>\r
-<tr><td align=left>LFNPR</td><td align=left>DETAIL</td><td align=left>BNDIDX</td><td align=left>AOINFO</td></tr>\r
-<tr><td align=left>PLOT</td><td align=left>ARCHIVE</td><td align=left>NBODAF</td><td align=left> </td></tr>\r
-</table>\r
-<p>\r
-<i>Print Level Control:</i>\r
-PRINT=n\r
-<p>\r
-Keywords are first listed and described according to these formal\r
-groupings in Sections B.2.2-B.2.6. Section B.6 illustrates \r
-the effect of commonly used $NBO \r
-keywords (as well as other $KEY lists) on the\r
-successive stages of NAO/NBO/NLMO transformation and subsequent\r
-energy or dipole analysis, with sample output for these keyword\r
-options.\r
-<p>\r
- Some keywords of the $NBO keylist\r
-require (or allow) numerical values or other parameters\r
-to specify their exact function. In this\r
-case, the numerical value or parameter must immediately follow the keyword\r
-after an equal sign (=) or any number of blank spaces. Examples:\r
- <pre>\r
- E2PERT=2.5 LFNPR 16 NBOMO=W25\r
-\r
-</pre>(The equal sign is recommended, and will be used in the remaining\r
-examples.)\r
-<p>\r
-[ Although the general user's interaction with the NBO programs is usually\r
-through the documented keywords of Sections B.2.2-B.2.6, some additional\r
-'semi-documented' keywords are listed in Section B.2.7 which may be of\r
-interest to the specialist.]\r
-<p>\r
-<i>B.2.2 Job Control Keywords</i>\r
-<p>\r
- The keywords in this group activate or deactivate \r
-basic tasks to be performed by\r
-the NBO programs, or change the way the NBO search is conducted. Each\r
-keyword is described in terms of the option it activates (together with an \r
-indication of where the option is useful):\r
-<p>\r
-<i>KEYWORD</i> <i>OPTION DESCRIPTION</i>\r
-<p>\r
-NPA Request Natural Population Analysis and printing of NPA summary\r
-tables (Section A.3.2). This keyword also activates calculation\r
-of NAOs, except for semi-empirical ESS methods.\r
-<p>\r
-NBO Request calculation of NBOs and printing of the main NBO table\r
-(Section A.3.3).\r
-<p>\r
-NBOSUM Request printing of the NBO summary table (Section A.3.6). This\r
-combines elements of the NBO table and 2nd-order perturbation\r
-theory analysis table (see below) in a convenient form for recognizing\r
-the principal delocalization patterns.\r
-<p>\r
-RESONANCE Request search for highly delocalized structures \r
-(Section B.6.6). The NBO search\r
-normally aborts when one or more Lewis NBOs has less\r
-than the default occupancy threshold of\r
-1.90 electrons for a 'good' electron\r
-pair. When the RESONANCE keyword is activated, this threshold\r
-is successively lowered in 0.10 decrements to 1.50,\r
-and the NBO search repeated to find the best Lewis structure\r
-within each occupancy threshold. The program returns with the best\r
-overall Lewis structure (lowest total non-Lewis occupancy) found\r
-in these searches. (Useful for benzene and other highly\r
-delocalized molecules.)\r
-<p>\r
-NOBOND Request that no bonds (2-center NBOs) are to be formed in the\r
-NBO procedure (Section B.6.7). The \r
-resulting NBOs will then simply be 1-center\r
-atomic hybrids. (Useful for highly ionic species.)\r
-<p>\r
-3CBOND Request search for 3-center bonds (Section B.6.8). The normal \r
-default is to search\r
-for only 1- and 2-center NBOs. (Useful for diborane and other\r
-electron-deficient 'bridged' species.)\r
-<p>\r
-SKIPBO Skip the computation of NBOs, i.e., only determine NAOs and\r
-perform natural population analysis. (Useful when only NPA is\r
-desired.)\r
-<p>\r
-NLMO Compute and print out the summary table of Natural Localized\r
-Molecular Orbitals (Section B.6.2). NLMOs are similar to Boys or \r
-Edmiston-Ruedenberg LMOs, but more efficiently calculated. (Useful\r
-for 'semi-localized' description of an SCF or correlated \r
-wavefunction.) Activated automatically by all keywords that pertain\r
-to NLMOs (e.g., AONLMO, SPNLMO, DIPOLE).\r
-<p>\r
-Note that the SKIPBO keyword has higher precedence than other\r
-keywords in this list, so that keywords with which it is\r
-implicitly in conflict (e.g., NBO, 3CBOND, NLMO) will be ignored\r
-if SKIPBO is included in the $NBO keylist.\r
-<p>\r
-<i>B.2.3 Job Threshold Keywords</i>\r
-<p>\r
- The keywords in this group also activate new tasks to be\r
-performed by the NBO program, but these keywords may be modified\r
-by one or more parameters (thresholds) that control the precise\r
-action to be taken. (In each case the keywords may also be used\r
-without parameters, accepting the default values [in brackets].)\r
-<p>\r
-<i>KEYWORD parameter(s)</i> <i>OPTION DESCRIPTION</i>\r
-<p>\r
-BEND ang, pct, occ Request the NHO Directional Analysis table (Section A.3.4). The\r
-three parameters [and default values] have the following\r
-significance:\r
-<p>\r
-= threshold angular deviation for printing\r
-<br>pct [25] = threshold percentage <i>p</i>-character for printing\r
-<br>occ [0.1] = threshold NBO occupancy for printing\r
-<p>\r
-Parameter values may be separated by a space or a comma.\r
-<p>\r
- Example:<pre> BEND=2,10,1.9\r
-\r
-</pre>This example specifies that the bond-bending table should\r
-only include entries for angular deviations of at least 2° (ang),\r
-hybrids of at least 10% <i>p</i>-character (pct), and NBOs of occupancy\r
-at least 1.9 electrons (occ).\r
-<p>\r
-<p>\r
-E2PERT eval Request the Perturbation Theory Energy Analysis \r
-table (Section A.3.5), where\r
-<p>\r
-eval [0.5] = threshold energy (in kcal/mol) for printing\r
-<p>\r
-Entries will be printed for NBO donor-acceptor interaction energies\r
-that exceed the 'eval' threshold.\r
-<p>\r
- Example:<pre> E2PERT=5.0\r
-\r
-</pre>This example would print only interactions of at least 5 kcal/mol\r
-(i.e., only the single entry for the 8.13 kcal/mol\r
-<i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>CH</sub> interaction in the output\r
-of Section A.3.5).\r
-<p>\r
-<p>\r
-DIPOLE dval Request the Molecular Dipole Moment Analysis table (Section B.6.3), where\r
-<p>\r
-dval [0.02] = threshold dipole moment (Debye) for printing\r
-<p>\r
-The program will carry out a decomposition of the total molecular\r
-dipole moment in terms of localized NLMO and NBO\r
-contributions, including all terms whose contribution (in vector norm)\r
-exceeds the 'dval' threshold.\r
-<p>\r
- Example:<pre> DIPOLE=0.1\r
-\r
-</pre>This example would print out dipole contributions of all NBOs (and\r
-their delocalization interactions) of magnitude <img src=ge.gif> 0.1 D.\r
-<p>\r
-Both the BEND and E2PERT keywords are activated by default\r
-at the standard PRINT level option (see Section B.2.6); to get an\r
-example of dipole moment analysis, include the keylist\r
- <pre>\r
- $NBO DIPOLE $END\r
-\r
-</pre>in your input file. Note that the DIPOLE keyword leads to an\r
-analysis in terms of both NBOs and NLMOs, so that the NLMO keyword\r
-(Section B.2.2) is automatically activated in this case.\r
-<p>\r
-<i>B.2.4 Matrix Output Keywords</i>\r
-<p>\r
- The keywords in this group activate the printing of various\r
-matrices to the output file, or their writing\r
-to (or reading from) external disk files. The large number\r
-of keywords in this group provide great flexibility in printing\r
-out the details of the successive transformations,\r
-<p>\r
-<center>\r
-input AOs <img src=rarr.gif> (PNAOs) <img src=rarr.gif> NAOs <img src=rarr.gif> NHOs <img src=rarr.gif> NBOs <img src=rarr.gif> NLMOs <img src=rarr.gif> canonical MOs\r
-</center>\r
-<p>\r
-or the matrices of various operators in the natural\r
-localized basis sets. This ordered sequence of transformations\r
-forms the basis for naming the keywords.\r
-<p>\r
-<u>Keyword Names</u>\r
-<p>\r
- The keyword for printing the matrix for a particular basis\r
-transformation, IN <img src=rarr.gif> OUT, is constructed from the \r
-corresponding acronymns\r
-for the two sets in the generic form "INOUT". For example,\r
-the transformation AO <img src=rarr.gif> NBO is keyed as "AONBO", \r
-while that from NBOs to\r
-NLMOs is correspondingly "NBONLMO". The transformations are\r
-always specified in the ordered sequence shown above (i.e., "AONBO"\r
-is allowed, but "NBOAO" is an unrecognized 'backward' \r
-keyword). Keywords are recognized for <i>all possible</i> transformations\r
-from the input AOs to other sets \r
-(NAO, NHO, NBO, NLMO, MO, or the pre-orthogonal PNAO, PNHO, PNBO,\r
-PNLMO sets) in the\r
-overall sequence leading to canonical MOs, i.e.,\r
-<p>\r
-<i>AO basis:</i> AONAO AONHO AONBO AONLMO AOMO \r
-AOPNAO AOPNHO AOPNBO AOPNLMO\r
-<p>\r
-and from each of the orthonormal natural localized sets to sets\r
-lying to the right in the sequence, i.e.,\r
-<p>\r
-<p>\r
-NAONHO NAONBO NAONLMO NAOMO\r
-<p>\r
-NHONBO NHONLMO NHOMO\r
-<p>\r
-NBONLMO NBOMO\r
-<p>\r
-NLMOMO\r
-<p>\r
-The matrix T<sub>IN,OUT</sub> for a specified IN <img src=rarr.gif> OUT transform has\r
-rows labelled by the IN set and columns labelled by the OUT set.\r
-<p>\r
- One can also print out the matrix representations of the Fock\r
-matrix (F), density matrix (DM), or dipole moment matrix (DI)\r
-in the input AO set or any of the natural localized sets (NAO,\r
-NHO, NBO, or NLMO). The corresponding keyword is constructed by\r
-combining the abbreviation (M) for the operator with that\r
-for the set (SET) in the generic form "MSET". For example,\r
-to print the Fock matrix (F) in the NBO set, use the\r
-keyword "FNBO", or to print the dipole matrix in the NLMO\r
-basis, use "DINLMO". (For the dipole matrix keywords, all\r
-three vector components will be printed.) One can also print \r
-out elements of the overlap matrix (S) in the input AO basis \r
-or any of the 'pre-orthogonal' sets\r
-(PNAO, PNHO, PNBO, or PNLMO), using, e.g., "SPNAO" for the\r
-overlap matrix in the PNAO basis. The complete set of allowed\r
-keywords for operator matrices is:\r
-<p>\r
-<p>\r
-FAO FNAO FNHO FNBO FNLMO\r
-<p>\r
-DMAO DMNAO DMNHO DMNBO DMNLMO\r
-<p>\r
-DIAO DINAO DINHO DINBO DINLMO\r
-<p>\r
-SAO SPNAO SPNHO SPNBO SPNLMO\r
-<p>\r
-Other desired transformations\r
-can be readily obtained from the keyword transformations\r
-by matrix multiplication.\r
-<p>\r
-<p>\r
-<u>Keyword Parameters</u>\r
-<p>\r
- Each generic matrix keyword ("MATKEY") can include\r
-a parameter that specifies the output operation to\r
-be performed on the matrix. The allowed MATKEY parameters\r
-are of two types (three for AONAO, NAONBO; see below):\r
- \r
-<br>MATKEY=P[c] (print out the matrix in the standard output file, 'c' columns)\r
-<p>\r
-MATKEY=W[n] (write out the matrix to disk file <i>n</i>)\r
-<p>\r
-The first (P[c]) parameter is used to control output to the standard\r
-output file. When the MATKEY keyword is inserted in the $NBO keylist with\r
-no parameters, the matrix is by default printed (in its\r
-entirety) in the standard output file. Thus, "MATKEY=P"\r
-would be equivalent to "MATKEY", with no parameters. The complete\r
-'P[c]' form of the print parameter serves to truncate the \r
-printed matrix output\r
-to a specified number of columns [c]. For example, to print out\r
-only the first 16 columns of a matrix, use the form\r
- <pre>\r
- MATKEY=P16 (print 16 columns)\r
-\r
-</pre>For certain matrices, one can also restrict \r
-printing to only the valence (VAL) or\r
-Lewis (LEW) columns with modified '[c]' \r
-specifiers. For the transformations\r
-to MOs, use the form\r
- <pre>\r
- MATKEY=PVAL (print core + valence MO columns only)\r
-\r
-</pre>where "MATKEY" is AOMO, NAOMO, NHOMO, NBOMO, or NLMOMO (only). This\r
-will print out only the occupied MOs \r
-and the lowest few unoccupied MOs, e.g., the six lowest virtual MOs of\r
-the methylamine example (Section A.3), though\r
-not necessarily those with predominant valence character. Similarly,\r
-for the transformations to NBOs or NLMOs, use the form\r
- <pre>\r
- MATKEY=PLEW (print Lewis orbital columns only)\r
-\r
-</pre>where "MATKEY" is AONBO, NHONBO, NAONBO, AONLMO, NAONLMO, \r
-NHONLMO, NBONLMO (or AOMO, NAOMO, NHOMO, NBOMO, NLMOMO). This\r
-prints out the Lewis NBOs or occupied MOs only, e.g., only the nine\r
-occupied NBOs or MOs of the methylamine example. Judicious use of\r
-these print parameters keeps printed\r
-output within reasonable bounds\r
-in calculations with large basis sets.\r
-<p>\r
-The second type of MATKEY parameter (W[n]) is used to\r
-write the matrix (in its entirety) to a specified disk\r
-file [n]. By default, each keyword transformation matrix is associated with\r
-a particular logical file number (LFN) in the range 31-49, as shown in\r
-the table below:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td align=center><i> </i></td><td align=center>default</td><td align=center> </td><td align=center>default</td><td align=center> </td><td align=center>default</td></tr>\r
-<tr><td align=center>matrix</td><td align=center>LFN</td><td align=center>matrix</td><td align=center>LFN</td><td align=center>matrix</td><td align=center>LFN</td></tr>\r
-<tr><td align=left colspan=2>_</td><td align=left colspan=2>_</td><td align=left colspan=2>_</td></tr>\r
-<tr><td align=left>AONAO</td><td align=center>33</td><td align=left>NHONBO</td><td align=center>49</td><td align=left>DMNHO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AONHO</td><td align=center>35</td><td align=left>NHONLMO</td><td align=center>49</td><td align=left>DMNBO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AONBO</td><td align=center>37</td><td align=left>NHOMO</td><td align=center>49</td><td align=left>DMNLMO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AONLMO</td><td align=center>39</td><td align=left>NBONLMO</td><td align=center>49</td><td align=left>DIAO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AOMO</td><td align=center>40</td><td align=left>NBOMO</td><td align=center>49</td><td align=left>DINAO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AOPNAO</td><td align=center>32</td><td align=left>NLMOMO</td><td align=center>49</td><td align=left>DINHO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AOPNHO</td><td align=center>34</td><td align=left>FAO</td><td align=center>49</td><td align=left>DINBO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AOPNBO</td><td align=center>36</td><td align=left>FNAO</td><td align=center>49</td><td align=left>DINLMO</td><td align=center>49</td></tr>\r
-<tr><td align=left>AOPNLMO</td><td align=center>38</td><td align=left>FNHO</td><td align=center>49</td><td align=left>SAO</td><td align=center>49</td></tr>\r
-<tr><td align=left>NAONHO</td><td align=center>49</td><td align=left>FNBO</td><td align=center>49</td><td align=left>SPNAO</td><td align=center>49</td></tr>\r
-<tr><td align=left>NAONBO</td><td align=center>42</td><td align=left>FNLMO</td><td align=center>49</td><td align=left>SPNHO</td><td align=center>49</td></tr>\r
-<tr><td align=left>NAONLMO</td><td align=center>49</td><td align=left>DMAO</td><td align=center>41</td><td align=left>SPNBO</td><td align=center>49</td></tr>\r
-<tr><td align=left>NAOMO</td><td align=center>49</td><td align=left>DMNAO</td><td align=center>49</td><td align=left>SPNLMO</td><td align=center>49</td></tr>\r
-</table>\r
-When the "MATKEY=Wn" keyword is inserted in the $NBO keylist with\r
-no 'n' specifier, the matrix is by default written out (in its\r
-entirety) to this LFN. Thus, "MATKEY=W" \r
-is equivalent to "MATKEY=Wn" if "n" is the default LFN for\r
-that keyword. Use the "Wn" parameter to direct output to\r
-any non-default LFN disk file. For example, the keyword\r
- <pre>\r
- AONBO=W22\r
-\r
-</pre>would write out the AO <img src=rarr.gif> NBO transformation to LFN = 22 (rather\r
-than the default LFN = 37). \r
-<p>\r
- The format of the printed output under the print 'P' parameter\r
-differs from that written to an external file under\r
-the 'W' parameter. The 'P' output (intended for a human reader)\r
-includes an identifying label for each row, and gives the \r
-numerical entries to somewhat lesser precision (F8.4 format) than\r
-the corresponding 'W' output (F15.9 format), which is usually\r
-intended as input to another program. Use the "MATKEY=W6"\r
-keyword to route the more precise 'W' form of the matrix to\r
-the standard output file, LFN 6.\r
-<p>\r
- For the AONAO, NAONBO matrices (only), one can also include a \r
-read parameter (R),\r
- <pre>\r
- AONAO=Rn\r
- NAONBO=Rn\r
-\r
-</pre>which causes the matrix to be input to the\r
-program from LFN <i>n</i>. This \r
-parameter has the\r
-effect of 'freezing' orbitals to a\r
-set prescribed in the input file (thus \r
-bypassing the NBO optimization of these orbitals for the molecular\r
-system). For example, the keyword "NAONBO=R44" would have the\r
-effect of freezing the NAO <img src=rarr.gif> NBO \r
-transformation coefficients to the form specified in LFN 44 (perhaps\r
-written with the "NAONBO=W44" keyword in a previous calculation\r
-on isolated molecules, and now to be used in a calculation on a\r
-molecular complex). Similarly, the keyword "AONAO=R45" could\r
-be used to force the analysis of an excited state to be\r
-carried out in terms of the NAOs of the ground state (previously \r
-written out with the "AONAO=W45"\r
-keyword).\r
-<p>\r
-<i>B.2.5 Other Output Control Keywords</i>\r
-<p>\r
- The keywords in this group also help to control\r
-the I/O produced \r
-by a specified set of job options, and thus supplement the\r
-keywords of the previous section. However, the keywords\r
-of this section 'steer' the flow of information that is\r
-routinely produced by the NBO program (or can be passed through\r
-from the ESS program) without materially affecting the actual\r
-jobs performed by the NBO program. The options associated with\r
-each keyword are tabulated below:\r
-<p>\r
-<i>KEYWORD</i> <i>OPTION DESCRIPTION</i>\r
-<p>\r
-LFNPR=n Set the logical file number (LFN) for NBO program output. The default\r
-LFN is <i>n</i> = 6, the usual LFN for output from the ESS program. This\r
-option can be used to steer the NBO section of the job output to a\r
-desired file.\r
- \r
- Example:<pre> LFNPR=25 (re-direct NBO output to LFN 25)\r
- </pre>\r
-<br>DETAIL Request additional details of the NBO search. This option (primarily\r
-for programming and debugging purposes) records details of the \r
-NBO loops over atoms\r
-and atom pairs, enroute to the final NBOs.\r
-<p>\r
-BNDIDX Request print-out of the NAO-Wiberg Bond Index \r
-array and related valency indices (Section B.6.5). The elements of\r
-this array are the sums of squares of off-diagonal density matrix\r
-elements between pairs of atoms in the NAO basis, and are the NAO\r
-counterpart of the Wiberg bond index [K. Wiberg, Tetrahedron <b>24</b>,\r
-1083-1096 (1968)]. (This bond index is routinely used\r
-to 'screen' atom pairs for possible bonding in the NBO\r
-search, but the values\r
-are not printed unless the BNDIDX keyword is activated.)\r
-<p>\r
-AOINFO Request writing of information concerning the AO basis set (geometrical\r
-positions, orbital exponents, contraction coefficients, etc.) to an\r
-external file, LFN 31. This is a portion of the information needed\r
-by the ORBPLOT orbital contour plotting programs (cf. "PLOT"\r
-keyword below.)\r
-<p>\r
-<p>\r
-PLOT Request writing of <i>all</i> files required by orbital contour plotting\r
-programs ORBPLOT. This activates the AOINFO keyword, as well\r
-as all the necessary matrix output keywords (AONBO=W37, etc.) \r
-that could be required for ORBPLOT.\r
-<p>\r
-ARCHIVE=n Request writing the FILE47 'archive' file to external disk\r
-file LFN = <i>n</i> (or, if "=n" is not present, to the default\r
-LFN = 47). This file can serve as the input file to run the\r
-GENNBO program in stand-alone mode, to repeat the NBO analysis\r
-(possibly with new job options) without repeating the calculation\r
-of the wavefunction (Section B.7).\r
-<p>\r
-NBODAF=n Request writing the NBO direct access file (DAF) to external\r
-disk file LFN = <i>n</i> (or, if "=n" is not present, to the\r
-default LFN =48).\r
-<p>\r
-<i>B.2.6 Print Level Keywords</i>\r
-<p>\r
- The keyword "PRINT=n" (<i>n</i> = 0-4) can be used to give\r
-convenient, flexible control of all NBO output in terms of\r
-a specified print level <i>n</i>. This keyword\r
-activates groups of keywords in a heirarchical manner, and\r
-thus incrementally increases the volume of output, ranging\r
-from <i>no</i> NBO output (PRINT=0) to a considerable volume of\r
-detail (PRINT=4). The keywords associated with each\r
-print level are tabulated below [default value, PRINT=2]:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td align=center><i>print level</i></td><td align=left><i>additional output or activated keywords</i></td></tr>\r
-<tr><td align=center>_</td><td align=left>_</td></tr>\r
-<tr><td align=center>0</td><td align=left>suppress <i>all</i> output from the NBO program</td></tr>\r
-<tr><td align=center>1</td><td align=left>activate NPA and NBO keywords</td></tr>\r
-<tr><td align=center>[2]</td><td align=left>activate BEND, NBOSUM, and E2PERT keywords</td></tr>\r
-<tr><td align=center>3</td><td align=left>activate NLMO, DIPOLE, and BNDIDX keywords</td></tr>\r
-<tr><td align=center>4</td><td align=left>activate all(!) keywords</td></tr>\r
-</table>\r
-For each print level <i>n</i>, the NBO output will include items activated\r
-by the listed keywords, as well as all items from lower\r
-print levels.\r
-<p>\r
- When additional keywords \r
-are included with a "PRINT=n" keyword\r
-in the $NBO keylist, the NBO output includes the additional keyword\r
-items as well as those implied by the print level. This can be used\r
-to tailor the NBO output to virtually any selection of output\r
-items. For example, the keylist\r
- <pre>\r
- $NBO PRINT=2 NLMO FNBO=P NAOMO=P11 $END\r
-\r
-</pre>would add to the standard methylamine output file of Section A.3\r
-an NLMO summary table, the Fock matrix in\r
-the NBO basis, and the transformation coefficients\r
-for the first 11 molecular orbitals in terms of NAOs. Similarly,\r
-to produce the NPA listing only, one could use\r
- <pre>\r
- $NBO PRINT=1 SKIPBO $END\r
-\r
-</pre>or\r
- <pre>\r
- $NBO PRINT=0 NPA $END\r
-\r
-</pre>[There is actually a slight difference between \r
-the two examples: The\r
-NBOs are determined by default (once the $NBO keylist is encountered),\r
-even if all output is suppressed with PRINT=0; in the first example,\r
-the keyword SKIPBO bypasses NBO determination, whereas in\r
-the second example the NBOs are still determined 'in background.']\r
-<p>\r
-<i>B.2.7 Semi-Documented Additional Keywords</i>\r
-<p>\r
- Some additional keywords are listed below that may of use\r
-to specialists or program developers:\r
-<p>\r
-<i>KEYWORD</i> <i>OPTION DESCRIPTION</i>\r
-<p>\r
-THRESH=val Set the threshold of orbital occupancy desired for bond\r
-orbital selection. If this is not included, the default\r
-occupancy [1.90] will be used (or values decreasing from 1.90\r
-to 1.50 by 0.10 steps,\r
-if the RESONANCE keyword is included).\r
-<p>\r
-PRJTHR=val Set the projection threshold [default 0.20] to determine if\r
-a 'new' hybrid orbital has too high overlap with hybrids\r
-previously found.\r
-<p>\r
-MULAT Print total gross Mulliken populations by atom.\r
-<p>\r
-MULORB Print gross Mulliken populations, by orbital and atom.\r
-<p>\r
-RPNAO Revises PAO to PNAO transformation matrix by post-multiplying\r
-by <b>T</b><sub>Ryd</sub> and <b>T</b><sub>red</sub> [see the NPA paper:\r
-A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. <b>83</b>,\r
-735-746 (1985)].\r
-<p>\r
-PAOPNAO Input or output of pure AO (PAO) to pre-NAO (PNAO) transformation. The\r
-PAOs are AOs of pure angular momentum symmetry (rather than\r
-cartesian gaussians). This keyword can be used with read ('R'),\r
-write ('W', default LFN 43) or print ('P') parameters.\r
-<p>\r
-BOAO Print out the bond-order matrix (Fock-Dirac density matrix) in the\r
-basis set of input AOs. This keyword can be used with write\r
-('W', default LFN 49) or print ('P') parameters.\r
-<p>\r
-<p>\r
-<b>B.3 THE $CORE LIST</b>\r
-<p>\r
- In the Lewis structure picture, the inner 'core' electron pairs\r
-are pictured as occupying orbitals having essentially \r
-isolated atomic orbital character. In NBO parlance, these core orbitals\r
-correspond to 1-center unhybridized NAOs of near-maximum occupancy,\r
-which are isolated on each center before the main NBO search\r
-begins for localized valence electron pairs. A warning message\r
-is printed if the occupancy of a presumed closed-shell\r
-core NBO falls below 1.9990 electrons (or 0.9990 in the open-shell \r
-case), indicative of a possible core-valence mixing effect of\r
-physical significance.\r
-<p>\r
- [In previous versions\r
-of the NBO program, core orbitals having the expected pure atomic\r
-character are found in essentially all\r
-cases, except where an 'accidental' degeneracy in occupancy of\r
-core and valence lone pairs leads to undesirable core-valence\r
-mixing; the present version explicitly isolates core pairs \r
-as unhybridized NAOs prior\r
-to the main NBO search to prevent this unphysical effect.]\r
-<p>\r
- The NBO program contains a table giving the nominal number of\r
-core orbitals to be isolated on each type of atom (e.g., 1<i>s</i> for\r
-first-row atoms Li-Ne, 1<i>s</i>, 2<i>s</i>, 2<i>p</i> for second-row atoms\r
-Na-Ar, etc.). At times, however, it is interesting to examine the\r
-effect of allowing core orbitals to mix into the bonding hybrids, or\r
-to hybridize (polarize) among themselves. This can be accomplished\r
-by including a $CORE keylist to specify the number of core\r
-orbitals to be isolated on each atomic center, thus modifying\r
-the nominal core table. Unlike other NBO keylists, the $CORE list\r
-includes only integers (rather than keywords) to specify the\r
-core modifications, but the rules \r
-are otherwise similar to those for\r
-other keylists. The $CORE list (if included) must follow the $NBO\r
-keylist and precede the $CHOOSE or $DEL keylists.\r
-<p>\r
-<p>\r
- The format of the $CORE modification list is:\r
-<p>\r
-first line: The keyword "$CORE"\r
-<p>\r
-next lines: Pairs of integers, one pair for each center. The first integer\r
-indicates the atomic center (in the numbering of the main ESS)\r
-and the second is the number of core orbitals to be isolated on\r
-that atom. Note that atomic centers not included in the CORE list\r
-are assigned default cores.\r
-<p>\r
-last line: The keyword "$END", to indicate the end of core input.\r
-<p>\r
-The entire list may also be condensed to a single line, \r
-but the word "$CORE" must occur as the first word of the line\r
-and "$END" as\r
-the last word; that is, the core\r
-modification keylist cannot continue on a line that contains other\r
-keylist information.\r
-<p>\r
- The core orbitals are isolated by occupancy, the most occupied NAOs\r
-being first selected, and full subshells are isolated at a time. Thus,\r
-for example, to select the five orbitals of the\r
-<i>n</i> = 1 and <i>n</i> = 2 shells\r
-as core orbitals, it would make no difference \r
-to select "3" or "4" (instead\r
-of "5"), since all three of these\r
-choices would specify a core containing a 1<i>s</i>, 2<i>s</i>, and \r
-all three 2<i>p</i> orbitals. The $CORE modification list \r
-is read only once, and applies to both\r
-<img src=alpha.gif> and <img src=beta.gif> spin manifolds in an open-shell calculation.\r
-<p>\r
-<p>\r
-An example, appropriate for Ni(1)-C(2)-O(3) with the indicated numbering\r
-of atoms, is shown below:\r
- <pre>\r
- $CORE\r
- 1 5\r
- $END\r
-\r
-</pre>This would direct the NBO program to isolate only 5 core orbitals\r
-on Nickel (atom 1), rather than the nominal 9 core orbitals. In\r
-other words, only 1<i>s</i>, 2<i>s</i>, and 2<i>p</i> orbitals will be considered\r
-as core orbitals in the search for NBOs of NiCO, allowing the 3<i>s</i>\r
-and 3<i>p</i> orbitals to mix with valence NAOs in bond formation. Since\r
-the carbon and oxygen atoms were not included in the modification list,\r
-the nominal set of core orbitals (1<i>s</i> only) is isolated on each\r
-of these atoms. \r
-<p>\r
-<p>\r
-[The alternative example\r
- <pre>\r
- $CORE 1 0 2 0 3 0 $END\r
-\r
-</pre>(no cores) would allow all NAOs to be included in the NBO search;\r
-this would be equivalent to the default treatment in \r
-the earlier version of the program (see Section A.1.5).]\r
-<p>\r
-<b>B.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)</b>\r
-<p>\r
- A $CHOOSE keylist requests that the NBO search be directed\r
-to find a particular Lewis structure ('resonance structure') \r
-chosen by the user. (This\r
-is useful for testing the accuracy of alternative resonance structure\r
-representations of the wavefunction, relative to the optimal\r
-Lewis structure returned in a free NBO search.) In the\r
-$CHOOSE list, a resonance structure is specified by indicating\r
-where lone pairs and bonds (including multiple bonds) are to\r
-be found in the molecule. In some cases, the user may wish to\r
-specify only the location of bonds, letting the NBO algorithm\r
-seek the best location for lone pairs, but it is usually safest to\r
-completely specify the resonance structure, both lone \r
-pairs and bonds. \r
-<p>\r
- The format of the $CHOOSE list is:\r
-<p>\r
-first line: The keyword "$CHOOSE"\r
-<p>\r
-next line: The keyword "ALPHA" (only for open-shell wavefunction)\r
-<p>\r
-next lines: If one-center ('lone') NBOs are to be searched for, type the\r
-keyword "LONE" followed by a list of pairs of numbers, the\r
-first number of each pair being the atomic center and the \r
-second the number of valence lone pairs on that atom. Terminate the \r
-list with "END". (Note that only the occupied <i>valence</i> lone pairs\r
-should be entered, since the number of core orbitals on each\r
-center is presumed known.)\r
-<p>\r
-If two-center ('bond') NBOs are to be searched for, type\r
-the keyword "BOND", followed by the list of bond specifiers,\r
-and terminated by "END". Each bond specifier is one of the\r
-letters\r
-<p>\r
-"S" single bond\r
-<br>"D" double bond\r
-<br>"T" triple bond\r
-<br>"Q" quadruple bond\r
-<p>\r
-followed by the two atomic centers of the bond (e.g., "D 9 16" for\r
-a double bond between atoms 9 and 16).\r
-<p>\r
-If three-center NBOs are to be searched for, type\r
-the keyword "3CBOND", followed by the list of 3-c bond\r
-specifiers, and terminated by "END". Each 3-c bond specifier\r
-is again one of the letters "S" (single), "D" (double), "T"\r
-(triple), or "Q" (quadruple), followed by three integers for\r
-the three atomic centers (e.g., "S 4 8 10" for a single\r
-three-center bond 4-8-10). (Note that the 3CBOND keyword \r
-of the $NBO keylist is implicitly activated\r
-if 3-c bonds are included in a $CHOOSE list.)\r
-<p>\r
-next line: The word "END" to signal the end of the <img src=alpha.gif> spin list.\r
-<p>\r
-next line: The keyword "BETA" (for open-shell wavefunctions)\r
-<p>\r
-next lines: The input for <img src=beta.gif> spin, same format as above. The overall $CHOOSE\r
-list should always end with the "$END" keyword.\r
-<p>\r
-<p>\r
-Two examples will serve to illustrate the $CHOOSE format (each is\r
-rather artificial, inasmuch as the specified $CHOOSE structure\r
-corresponds to the 'normal' structure that would be found by\r
-the NBO program):\r
-<p>\r
-The closed-shell H-bonded complex FH...CO,\r
-with atom numbering F(1)-H(2)...C(3)-O(4), might be specified as\r
- <pre>\r
- $CHOOSE\r
- LONE 1 3\r
- 3 1\r
- 4 1 END\r
- BOND S 1 2\r
- T 3 4 END\r
- $END\r
-\r
-</pre>This would direct the NBO program to search for three lone pairs\r
-on atom F(1), one lone pair on atom C(3), one lone pair on atom \r
-O(4), one bond between F(1)-H(2), and three bonds between C(3)-O(4).\r
-<p>\r
-<p>\r
-(2) The open-shell FH...O<sub>2</sub> complex, with\r
-atom numbering F(1)-H(2)...O(3)-O(4), \r
-and with the unpaired electrons on O<sub>2</sub> being of \r
-<img src=alpha.gif> spin, might be specified as\r
- <pre>\r
- $CHOOSE\r
- ALPHA\r
- LONE 1 3\r
- 3 3\r
- 4 3 END\r
- BOND S 1 2\r
- S 3 4 END\r
- END\r
- BETA\r
- LONE 1 3\r
- 3 1\r
- 4 1 END\r
- BOND S 1 2\r
- T 3 4 END\r
- END\r
- $END\r
-\r
-</pre>Note that this example incorporates the idea of "different Lewis\r
-structures for different spins," with a distinct pattern of localized\r
-1-c ('lone') and 2-c ('bond') functions for <img src=alpha.gif> and <img src=beta.gif> spin.\r
-<p>\r
- As with other keylists, the $CHOOSE keylist can be condensed to\r
-a smaller number of lines, as long as no line is shared with another\r
-keylist. The order of keywords within the $CHOOSE keylist should\r
-be as shown above (i.e., ALPHA before BETA, LONE before BOND, etc.),\r
-but the order of entries within a LONE or BOND list is\r
-immaterial. A $CORE keylist (if present) must precede the $CHOOSE list.\r
-<p>\r
-<b>B.5 THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)</b>\r
-<p>\r
-<i>B.5.1 Introduction to NBO Energetic Analysis</i>\r
-<p>\r
- The fourth and final type of keylist is a 'deletions' ($DEL)\r
-keylist, to activate NBO energetic analysis. This analysis is\r
-performed by (1) deleting specified elements (or blocks of elements)\r
-from the NBO Fock matrix, (2) diagonalizing this new Fock matrix\r
-to obtain a new density matrix, and (3) passing this density matrix\r
-to the SCF routines for a single pass through the SCF energy\r
-evaluator. The difference between this 'deletion' energy and\r
-the original SCF energy provides a useful measure of the\r
-energy contribution of the deleted terms. Since a Fock matrix\r
-is required, the energetic analysis is performed for RHF and\r
-UHF wavefunctions only.\r
-<p>\r
- Input for the NBO energetic analysis is through the $DEL keylist,\r
-which specifies the deletions to be performed. Multiple analyses\r
-(deletions) can be performed during a single job, with each deletion\r
-included in the overall $DEL keylist. The nine distinct\r
-types of deletions input are described in Section B.5.2 below.\r
-<p>\r
- The deletions keylist begins with the "$DEL" keyword. For \r
-the analysis of UHF wavefunctions, the deletions for\r
-the <img src=alpha.gif> and <img src=beta.gif> spin manifolds must be separately \r
-specified (see Section B.5.3). Otherwise, the input for closed\r
-shells RHF and UHF is identical. The input is free format and\r
-the input for a single deletion can be spread over as many lines\r
-as desired. The desired deletions should be listed one after the\r
-other. After the last deletion, the word "$END" signals the\r
-end of the keylist.\r
-<p>\r
-<p>\r
-<center>\r
-<b>WARNING</b>\r
-</center>\r
-<p>\r
-If symmetry is used, one must be careful to only do deletions\r
-that will preserve the symmetry of the electronic \r
-wavefunction!! If this is not done, the energy of the\r
-deletion will be incorrect because the assumption is made in\r
-evaluating the energy that the original symmetry still exists,\r
-and the variational principle may be violated. (For example,\r
-if symmetry is used for ethane, is is permissible to do\r
-a "NOSTAR" deletion, but not the deletion of a single C-H\r
-antibond.) The remedy is not to use symmetry in the SCF\r
-calculation.\r
-<p>\r
- In describing the deletion types, use is made of the terms\r
-"molecular unit" and "chemical fragment." The NBO program\r
-looks at the chemical bonding pattern produced by the bonding NBOs\r
-and identifies the groups of atoms that are linked together\r
-in distinct "molecular units" (usually synonymous with "molecules"\r
-in the chemical sense). The first atom that is not in molecular\r
-unit 1 will be in molecular unit 2, and so forth. For example, if\r
-the list of atoms is C(1), H(2), F(3), O(4), and bonding NBOs are\r
-found between C(1)-O(4) and H(2)-F(3), then molecular unit 1\r
-will be CO and molecular unit 2 will be HF. A "chemical fragment"\r
-is taken to be any subset of the atoms, usually (but not\r
-necessarily) in the same molecular unit, and usually (but not\r
-necessarily) connected\r
-by bond NBOs. Typically, a chemical fragment might be \r
-specified to be a single atom, the four atoms of a\r
-methyl group, or any other 'radical' of a molecular unit, identified\r
-by giving the atom numbers of which the fragment consists.\r
-<p>\r
-<i>B.5.2 The Nine Deletion Types</i>\r
-<p>\r
- The keywords and format to specify each of the nine allowed\r
-deletion types are described below:\r
-<p>\r
-<u>(1) Deletion of entire orbitals.</u>\r
-<p>\r
-This is called for by typing "DELETE", then the number of orbitals\r
-to be deleted, then the keyword "ORBITAL" (or "ORBITALS"), then\r
-the list of the orbitals to be deleted.\r
-<p>\r
- Example: <pre>DELETE 3 ORBITALS 15 18 29\r
-\r
-</pre>[See also deletion types (4) and (7) for deleting sets of orbitals.]\r
-<p>\r
-<p>\r
-<center>\r
-<b>WARNING</b>\r
-</center>\r
-<p>\r
-The "single-pass" method of evaluating deletion energies is\r
-appropriate only for deletions of <i>low</i>-occupancy (non-Lewis)\r
-orbitals, for which the loss of self-consistency in the Coulomb\r
-and exchange potentials (due to redistribution of the electron\r
-density of deleted orbitals) is small compared to the net\r
-energy change of deletion. It is fundamentally erroneous\r
-to delete <i>high</i>-occupancy (Lewis) orbitals by this\r
-procedure.\r
-<p>\r
-<u>(2) Deletion of specific Fock matrix elements.</u>\r
-<p>\r
-This is called for by typing "DELETE", then the number of elements\r
-to be deleted, then the keyword "ELEMENT" (or "ELEMENTS"), then\r
-the list of the elements to be deleted (each as a pair of integers).\r
-<p>\r
- Example: <pre>DELETE 3 ELEMENTS 1 15 3 19 23 2\r
-\r
-</pre>This example would result in the zeroing of the following Fock\r
-matrix elements: (1,15), (15,1), (3,19), (19,3), (23,2), (2,23). [See\r
-also deletion types (3), (5), (6), (8), (9) for deleting sets of elements.]\r
-<p>\r
-<u>(3) Deletion of off-diagonal blocks of the Fock matrix.</u>\r
-<p>\r
-Each block is specified by two sets of orbitals, and all Fock\r
-matrix elements in common between these two sets are set to\r
-zero. This is called for by typing "ZERO", then the number\r
-of off-diagonal blocks to be zeroed, and then, for each block,\r
-the following:\r
-<p>\r
-<p>\r
-(1) the dimensions of the block, separated by the word "BY" (e.g.,\r
-"6 BY 3" if the first set has 6 orbitals and the second set\r
-has 3 orbitals);\r
-<p>\r
-(2) the list of orbitals in the first set;\r
-<p>\r
-(3) the list of orbitals in the second set.\r
-<p>\r
-<p>\r
-An example is shown below:\r
- <pre>\r
- ZERO 2 BLOCKS 2 BY 5\r
- 3 4\r
- 9 10 11 14 19\r
- 3 BY 2\r
- 1 2 7\r
- 20 24\r
-\r
-</pre>This will set the following Fock matrix elements to zero:\r
-<p>\r
-(3,9), (3,10), (3,11), (3,14), (3,19),\r
-(9,3), (10,3), (11,3), (14,3), (19,3),\r
-(4,9), (4,10), (4,11), (4,14), (4,19),\r
-(9,4), (10,4), (11,4), (14,4), (19,4),\r
-(1,20), (1,24), (2,20), (2,24), (7,20), (7,24)\r
-(20,1), (24,1), (20,2), (24,2), (20,7), (24,7)\r
-<p>\r
-[Usually, in studying the total delocalization from one\r
-molecular unit to another, it is much easier to use deletion\r
-type (8) below. Similarly, in studying the total delocalization\r
-from one chemical fragment to another, it is easier to use\r
-deletion type (9).]\r
-<p>\r
-<u>(4) Deletion of all Rydberg and antibond orbitals.</u>\r
-<p>\r
-The Rydberg and antibond orbitals are the non-Lewis NBO orbitals\r
-that have stars in their labels (RY*, BD*) in the NBO analysis\r
-output. To delete all these orbitals, simply enter "NOSTAR". The\r
-result of this deletion is the energy of the idealized NBO natural\r
-Lewis structure, with all Lewis NBOs doubly occupied. (Unlike other\r
-deletions, in which there is a slight loss of variational\r
-self-consistency due to the redistributed occupancy of the deleted\r
-orbitals, the result of a "NOSTAR" deletion corresponds rigorously\r
-to the variational expectation value of the determinant of doubly\r
-occupied Lewis NBOs).\r
-<p>\r
-<p>\r
-<u>(5) Deletion of all vicinal delocalizations.</u>\r
-<p>\r
-To delete all Fock matrix elements between Lewis NBOs and the\r
-vicinal non-Lewis NBOs, simply enter "NOVIC".\r
-<p>\r
-<p>\r
-<u>(6) Deletion of all geminal delocalizations.</u>\r
-<p>\r
-To delete all Fock matrix elements between Lewis NBOs and the\r
-geminal non-Lewis NBOs, simply enter "NOGEM".\r
-<p>\r
-<p>\r
-<u>(7) Deletion of all starred (antibond/Rydberg) orbitals on a\r
-particular molecular unit.</u>\r
-<p>\r
-This is called for by typing "DESTAR", then the number of \r
-molecular units to be destarred, then the keyword "UNIT" \r
-(or "UNITS"), then the list of units.\r
-<p>\r
- Example: <pre>DESTAR 2 UNITS 3 4\r
- </pre>\r
-<p>\r
-<p>\r
-<u>(8) Zeroing all delocalization from one molecular unit to another.</u>\r
-<p>\r
-This is called for by typing "ZERO", then the number of delocalizations\r
-to zero, then the keyword "DELOCALIZATION" (can be abbreviated\r
-to "DELOC"), and then, for each delocalization, the word "FROM",\r
-the number of the donor unit, the word "TO", and\r
-the number of the acceptor unit.\r
-<p>\r
- Example: <pre>ZERO 2 DELOC FROM 1 TO 2 FROM 2 TO 1\r
-\r
-</pre>The above example would zero <i>all</i> intermolecular\r
-delocalizations between units 1 and 2 (i.e., both 1 <img src=rarr.gif> 2 and\r
-2 <img src=rarr.gif> 1). The\r
-effect is to remove all Fock matrix elements between high-occupancy\r
-(core/lone pair/bond) NBOs of the donor unit to the low-occupancy\r
-(antibond/Rydberg) NBOs of the acceptor unit. The donor and acceptor\r
-units may be the same.\r
-<p>\r
-<p>\r
-<u>(9) Zeroing all delocalization from one chemical fragment to another.</u>\r
-<p>\r
-This is called for by typing "ZERO", then the number of inter-fragment\r
-delocalizations to be zeroed, then the words "ATOM BLOCKS",\r
-and then, for each delocalization,\r
-the following:\r
-<p>\r
-(1) the number of atoms in the two fragments, separated by the word "BY"\r
-(e.g., "6 BY 3" if the first fragment has 6 atoms and the second\r
-has 3 atoms);\r
-<p>\r
-(2) the list of atoms in the first fragment;\r
-<p>\r
-(3) the list of atoms in the second fragment.\r
-<p>\r
-For example, to zero all delocalizations between the fragments\r
-defined by atoms (1,2) and by atoms (3,4,5), the $DEL entries would be\r
- <pre>\r
- ZERO 2 ATOM BLOCKS\r
- 2 BY 3\r
- 1 2\r
- 3 4 5\r
- 3 BY 2\r
- 3 4 5\r
- 1 2\r
-\r
-</pre>In this example, the first block removes the (1,2) <img src=rarr.gif> (3,4,5)\r
-delocalizations, while the second removes the (3,4,5) <img src=rarr.gif> (1,2)\r
-delocalizations.\r
-<p>\r
- For additional examples of $DEL input, see Section B.6.10.\r
-<p>\r
-<i>B.5.3 Input for UHF Analysis</i>\r
-<p>\r
- Deletions of the alpha and beta Fock matrices can be done\r
-independently. The deletions are input as above (Section B.5.2) for\r
-RHF closed shell, but they must be specified separately for alpha\r
-and beta in the UHF case.\r
-<p>\r
- The deletion to be done on the alpha Fock matrix must be preceded\r
-by the keyword "ALPHA", and the deletion of the beta Fock matrix\r
-must be preceded by the keyword "BETA". (Actually, only the first\r
-letter "A" or "B" is searched for by the program.) The ALPHA\r
-deletion must precede the BETA deletion. The BETA deletion\r
-may be the same as the ALPHA deletion, or different.\r
-<p>\r
- NOTE: The types of the <img src=alpha.gif> NBOs often differ from those of\r
-the <img src=beta.gif> NBOs, so that distinct <img src=alpha.gif>, <img src=beta.gif> deletions\r
-lists are generally required. For example, O<sub>2</sub> (triplet) has one bond in\r
-the <img src=alpha.gif> system and three in the <img src=beta.gif> system, if the unpaired\r
-electrons are in the <img src=alpha.gif> system.\r
-<p>\r
- Here are three examples to illustrate UHF open-shell deletions:\r
-<p>\r
-<p>\r
-Example 1:\r
- <pre>\r
- ALPHA ZERO 1 DELOC FROM 1 TO 2\r
- BETA NOSTAR\r
-\r
-<p>\r
-</pre>Example 2:\r
- <pre>\r
- ALPHA ZERO 1 DELOC FROM 1 TO 2\r
- BETA ZERO 0 DELOC\r
-\r
-<p>\r
-</pre>Example 3:\r
- <pre>\r
- ALPHA DELETE 0 ORBITALS\r
- BETA DELETE 1 ORBITAL 8\r
-\r
-</pre>If no deletion is done, this must be specified using zero (0) with\r
-one of the deletion input formats, as shown in Examples 2,3 above.\r
-<p>\r
-<b>B.6 NBO KEYLIST ILLUSTRATIONS</b>\r
-<p>\r
-<i>B.6.1 Introduction</i>\r
-<p>\r
- This section illustrates the output produced by several\r
-important keyword options of the NBO \r
-keylists ($NBO, $CHOOSE, $DEL, $CORE lists), \r
-supplementing the illustrations \r
-of Section A.3. Excerpts are provided\r
-rather than full output, since, e.g., NPA analysis is\r
-unaffected by keywords that modify the NBO search. Keywords\r
-of general applicability are illustrated with the\r
-methylamine example (RHF/3-21G, Pople-Gordon geometry) of\r
-Section A.3, which should be consulted for further \r
-information. More specialized keywords (RESONANCE, 3CBOND, etc.)\r
-are illustrated with prototype molecules (benzene, diborane, etc.) \r
-chosen for the keyword.\r
-<p>\r
- Sections B.6.2-B.6.8 illustrate representative examples\r
-from the $NBO keyword groups, including NLMO, DIPOLE, BNDIDX,\r
-RESONANCE, NOBOND, 3CBOND, and matrix output \r
-keywords. Section B.6.9 and B.6.10 similarly illustrate\r
-the use of the $CHOOSE and $DEL keylists. Section B.6.11\r
-illustrates the output for open-shell UHF cases, emphasizing\r
-features associated with the "different Lewis \r
-structures for different spins" representation of <img src=alpha.gif> and\r
-<img src=beta.gif> spin manifolds. Section B.6.12 shows the effect of using\r
-effective core potentials for Cu<sub>2</sub>, also illustrating\r
-aspects of the inclusion of <i>d</i> functions.\r
-<p>\r
-<i>B.6.2 NLMO Keyword</i>\r
-<p>\r
- When the NLMO keyword is activated, the program computes the\r
-NLMOs and prints out three tables summarizing their form. For\r
-the RHF/3-21G methylamine example (cf. Section A.3), the principal\r
-NLMO table is shown below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL LOCALIZED MOLECULAR ORBITAL (NLMO) ANALYSIS:\r
-\r
-Maximum off-diagonal element of DM in NLMO basis: 0.00000\r
-\r
-Hybridization/Polarization Analysis of NLMOs in NAO Basis:\r
-NLMO/Occupancy/Percent from Parent NBO/ Atomic Hybrid Contributions\r
--------------------------------------------------------------------------------\r
- 1. (2.00000) 99.9290% BD ( 1) C 1- N 2 \r
- 40.039% C 1 s( 21.54%)p 3.64( 78.46%)\r
- 59.891% N 2 s( 30.98%)p 2.23( 69.02%)\r
- 0.015% H 3 s(100.00%)\r
- 0.021% H 6 s(100.00%)\r
- 0.021% H 7 s(100.00%)\r
- 2. (2.00000) 99.9301% BD ( 1) C 1- H 3 \r
- 59.675% C 1 s( 25.44%)p 2.93( 74.56%)\r
- 0.040% N 2 s( 1.99%)p49.22( 98.01%)\r
- 40.258% H 3 s(100.00%)\r
- 3. (2.00000) 99.6996% BD ( 1) C 1- H 4 \r
- 60.848% C 1 s( 25.25%)p 2.96( 74.75%)\r
- 0.093% N 2 s( 13.08%)p 6.65( 86.92%)\r
- 0.014% H 3 s(100.00%)\r
- 38.861% H 4 s(100.00%)\r
- 0.017% H 5 s(100.00%)\r
- 0.158% H 6 s(100.00%)\r
- 4. (2.00000) 99.6996% BD ( 1) C 1- H 5 \r
- 60.848% C 1 s( 25.25%)p 2.96( 74.75%)\r
- 0.093% N 2 s( 13.08%)p 6.65( 86.92%)\r
- 0.014% H 3 s(100.00%)\r
- 0.017% H 4 s(100.00%)\r
- 38.861% H 5 s(100.00%)\r
- 0.158% H 7 s(100.00%)\r
- 5. (2.00000) 99.7206% BD ( 1) N 2- H 6 \r
- 0.113% C 1 s( 5.15%)p18.41( 94.85%)\r
- 67.929% N 2 s( 25.82%)p 2.87( 74.18%)\r
- 0.137% H 4 s(100.00%)\r
- 0.014% H 5 s(100.00%)\r
- 31.793% H 6 s(100.00%)\r
- 6. (2.00000) 99.7206% BD ( 1) N 2- H 7 \r
- 0.113% C 1 s( 5.15%)p18.41( 94.85%)\r
- 67.929% N 2 s( 25.82%)p 2.87( 74.18%)\r
- 0.014% H 4 s(100.00%)\r
- 0.137% H 5 s(100.00%)\r
- 31.793% H 7 s(100.00%)\r
- 7. (2.00000) 99.9499% CR ( 1) C 1 \r
- 99.951% C 1 s(100.00%)p 0.00( 0.00%)\r
- 0.013% H 3 s(100.00%)\r
- 0.013% H 4 s(100.00%)\r
- 0.013% H 5 s(100.00%)\r
- 8. (2.00000) 99.9763% CR ( 1) N 2 \r
- 0.010% C 1 s( 22.30%)p 3.48( 77.70%)\r
- 99.980% N 2 s(100.00%)p 0.00( 0.00%)\r
- 9. (2.00000) 98.8972% LP ( 1) N 2 \r
- 0.440% C 1 s( 1.05%)p94.15( 98.95%)\r
- 98.897% N 2 s( 17.85%)p 4.60( 82.15%)\r
- 0.489% H 3 s(100.00%)\r
- 0.085% H 4 s(100.00%)\r
- 0.085% H 5 s(100.00%)\r
-\r
-</pre>For each of the nine occuplied NLMOs, the table shows first the\r
-NLMO occupancy (necessarily 2.0000 at SCF level, as in the\r
-present example), the percentage\r
-of the total NLMO composition represented by this parent NBO\r
-(usually > 99%), and the label of the 'parent' \r
-NBO. Below this, there follows an NAO decomposition\r
-of the NLMO, showing the percentage of the NLMO on each atom\r
-and the hybrid composition ratios (effective\r
-<i>sp</i><sup><img src=lambda.gif></sup> character and percentage <i>s-</i> and \r
-<i>p</i>-character) of the NAOs. For \r
-example, NLMO 9 is the most delocalized NLMO\r
-of the table, having only about a 98.9% contribution from\r
-the localized N(2) parent lone pair NBO,\r
-with 'delocalization tails' composed\r
-primarily of contributions (~0.4% each) from C(1) and H(3), and \r
-smaller contributions (~0.09%) from H(4) and H(5). This \r
-corresponds to what might have been anticipated from the\r
-NBO summary table (Section A.3.6) or perturbation theory\r
-energy analysis table (Section A.3.5), which showed that\r
-the N(2) lone pair, NBO 9, is principally delocalized\r
-onto NBO 24, the vicinal C(1)-H(3) antibond [with lesser\r
-delocalizations onto NBOs 25, 26, the C(1)-H(4) and C(1)-H(5)\r
-antibonds].\r
-<p>\r
-<i>B.6.3 DIPOLE Keyword</i>\r
-<p>\r
- The DIPOLE keyword activates the NBO/NLMO analysis of the\r
-molecular dipole moment, as shown below for the example\r
-of RHF/3-21G methylamine (cf. Section A.3):\r
-<p>\r
- <pre>\r
-\r
-Dipole moment analysis:\r
-\r
-[Print threshold: Net dipole > 0.02 Debye]\r
-\r
- NLMO bond dipole NBO bond dipole\r
- ------------------------- ------------------------\r
- Orbital x y z Total x y z Total\r
-===============================================================================\r
- 1. BD ( 1) C 1- N 2 -0.76 -0.08 0.00 0.76 -0.76 -0.09 0.00 0.77\r
-\r
- 2. BD ( 1) C 1- H 3 0.49 1.90 0.00 1.96 0.50 1.90 0.00 1.97\r
- deloc 14: 0.03 -0.01 0.00 0.03\r
- deloc 25: -0.01 0.00 0.02 0.02\r
- deloc 26: -0.01 0.00 -0.02 0.02\r
-\r
- 3. BD ( 1) C 1- H 4 0.67 -0.77 -1.50 1.81 0.71 -0.79 -1.50 1.84\r
- deloc 27: -0.05 0.00 0.00 0.05\r
- deloc 26: -0.02 0.03 -0.03 0.04\r
- deloc 24: -0.01 -0.02 0.00 0.02\r
-\r
- 4. BD ( 1) C 1- H 5 0.67 -0.77 1.50 1.81 0.71 -0.79 1.50 1.84\r
- deloc 28: -0.05 0.00 0.00 0.05\r
- deloc 25: -0.02 0.03 0.03 0.04\r
- deloc 24: -0.01 -0.02 0.00 0.02\r
-\r
- 5. BD ( 1) N 2- H 6 -0.45 0.44 0.86 1.06 -0.50 0.44 0.89 1.11\r
- deloc 25: 0.06 -0.01 -0.02 0.06\r
-\r
- 6. BD ( 1) N 2- H 7 -0.45 0.44 -0.86 1.06 -0.50 0.44 -0.89 1.11\r
- deloc 26: 0.06 -0.01 0.02 0.06\r
-\r
- 7. CR ( 1) C 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00\r
-\r
- 8. CR ( 1) N 2 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00\r
-\r
- 9. LP ( 1) N 2 -0.63 -2.85 0.00 2.91 -0.88 -2.93 0.00 3.06\r
- deloc 24: 0.16 0.09 0.00 0.18\r
- deloc 25: 0.03 0.01 0.01 0.03\r
- deloc 26: 0.03 0.01 -0.01 0.03\r
- deloc 10: 0.02 -0.02 0.00 0.03\r
- ----------------------------------------------------\r
- Net dipole moment -0.45 -1.67 0.00 1.73 -0.71 -1.82 0.00 1.95\r
-Delocalization correction 0.27 0.14 0.00 0.30\r
- ----------------------------------------------------\r
- Total dipole moment -0.45 -1.67 0.00 1.73 -0.45 -1.67 0.00 1.73\r
- \r
-\r
-<p>\r
-</pre>The bottom line of the table shows the individual (x,y,z) vector components \r
-(-0.45,-1.67,0.00)\r
-and length (1.73 D) of the total molecular dipole moment, in the coordinate\r
-system of the ESS program. This is decomposed in the main body of\r
-the table into the individual contributions of "NLMO bond dipoles"\r
-(which strictly add to give the net molecule dipole at the SCF level)\r
-and "NBO bond dipoles" (which must be added with their\r
-off-diagonal 'deloc' contributions to give the net molecular \r
-moment). Each NLMO or NBO bond dipole \r
-vector <b><img src=mu.gif></b><sub>AB </sub> is evaluated as\r
-<center>\r
-<p>\r
-<b><img src=mu.gif></b><sub>AB</sub> = <b><img src=mu.gif></b><sub>AB</sub><sup><sup>(elec)</sup></sup> + <b><img src=mu.gif></b><sub>AB</sub><sup><sup>(nuc)</sup></sup>\r
-<p>\r
-</center>\r
-where\r
-<b><img src=mu.gif></b><sub>AB</sub><sup><sup>(elec)</sup></sup> = 2<i>e</i><<img src=sigma.gif><sub>AB</sub> | <b>r</b> | <img src=sigma.gif><sub>AB</sub>>\r
-is the electronic dipole expectation value for an electron\r
-pair in the <img src=sigma.gif><sub>AB</sub> NLMO\r
-or NBO, and <b><img src=mu.gif></b><sub>AB</sub><sup><sup>(nuc)</sup></sup> is the nuclear contribution of compensating\r
-unit positive charges at the positions of nuclei A and B (or both\r
-on A for a 1-center NBO). The 'deloc' contributions \r
-below each NBO bond dipole \r
-show the off-diagonal corrections\r
-to an additive bond dipole approximation (i.e.,\r
-the corrections to localized NBO bond dipoles to get the NLMO bond dipoles)\r
-to account for the delocalization from parent NBO <i>i</i> onto\r
-other (primarily, non-Lewis) NBOs <i>j</i>; in terms of the expansion\r
-of an NLMO in the set {<img src=sigma.gif><sub>j</sub>} of NBOs,\r
-<p>\r
-<center>\r
-<img src=sigma.gif><sub>i</sub><sup><sup>(NLMO)</sup></sup> = <i>c</i><sub>ii</sub><img src=sigma.gif><sub>i</sub> + <img src=sum.gif><sub>(j)</sub><i>c</i><sub>ji</sub><img src=sigma.gif><sub>j</sub>\r
-</center>\r
-<p>\r
-this correction is (for each electron, <img src=alpha.gif> or <img src=beta.gif> spin)\r
-<p>\r
-<i>c</i><sub>ji</sub><sup>2</sup>[<<img src=sigma.gif><sub>j</sub> | <b><img src=mu.gif></b> | <img src=sigma.gif><sub>j</sub>>-<<img src=sigma.gif><sub>i</sub> | <b><img src=mu.gif></b> | <img src=sigma.gif><sub>i</sub>>] + 2<i>c</i><sub>ii</sub><i>c</i><sub>ji</sub><<img src=sigma.gif><sub>i</sub> | <b><img src=mu.gif></b> | <img src=sigma.gif><sub>j</sub>> \r
-+ <img src=sum.gif><sub>(k)</sub>"<i>c</i><sub>ji</sub><i>c</i><sub>ki</sub><<img src=sigma.gif><sub>j</sub> | <b><img src=mu.gif></b> | <img src=sigma.gif><sub>k</sub>>\r
-<p>\r
-where the primes on the summation denote omission of\r
-terms <i>k</i> equal to <i>i</i> or <i>j</i>. For example, in the above table the\r
-largest individual contribution to <b><img src=mu.gif></b> is from the\r
-nitrogen lone pair, table entry 9, which has an NLMO dipole\r
-of 2.91 Debye or NBO dipole of 3.06. The latter has also the\r
-largest off-diagonal delocalization correction in the table,\r
-a 0.18 D correction due to the \r
-<i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>CH</sub> delocalization into the\r
-vicinal C(1)-H(3) antibond, NBO 24. \r
-<p>\r
- For a post-SCF (correlated) calculation, the dipole table would also\r
-include an additional line for the correction due to non-additivity\r
-of the NLMO bond dipoles. For an ionic species, there \r
-would also be an additional\r
-line for the "residual nuclear charge" contribution; here, one must\r
-be aware that the dipole moment is calculated with respect\r
-to the origin of the cartesian coordinate system chosen by the ESS\r
-program (since the dipole moment is origin-dependent in\r
-this case).\r
-<p>\r
- Note that the amount of detail in the\r
-dipole table can be altered by using the "DIPOLE=thr" form\r
-of the keyword to alter the threshold dipole ('thr') for printing\r
-[default: 0.02 D].\r
-<p>\r
-<i>B.6.4 Matrix Output Keywords</i>\r
-<p>\r
- Two simple examples will be given to illustrate the \r
-formatting of output for\r
-operators or basis set transformation matrices using the matrix\r
-output keywords of Section B.2.4. For the RHF/3-21G methylamine\r
-example of Section A.3, the keyword "FNHO" would cause the\r
-Fock matrix in the NHO basis to be printed out. Shown below is\r
-a reproduction of the first eight columns (out of 28) of this output:\r
-<p>\r
- <pre>\r
-\r
-NHO Fock matrix: \r
-\r
- NHO 1 2 3 4 5 6 7 8\r
- ---------- ------- ------- ------- ------- ------- ------- ------- -------\r
- 1. C1 ( N2 ) -0.0208 -0.7203 -0.0571 -0.0665 0.0438 0.0672 0.0438 0.0672\r
- 2. N2 ( C1 ) -0.7203 -0.3083 -0.0773 -0.0627 0.0835 0.0646 0.0835 0.0646\r
- 3. C1 ( H3 ) -0.0571 -0.0773 -0.1394 -0.6758 0.0638 0.0746 0.0638 0.0746\r
- 4. H3 ( C1 ) -0.0665 -0.0627 -0.6758 0.1349 0.0740 0.0672 0.0740 0.0672\r
- 5. C1 ( H4 ) 0.0438 0.0835 0.0638 0.0740 -0.1466 -0.6761 -0.0548 -0.0759\r
- 6. H4 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.6761 0.1541 -0.0759 -0.0697\r
- 7. C1 ( H5 ) 0.0438 0.0835 0.0638 0.0740 -0.0548 -0.0759 -0.1466 -0.6761\r
- 8. H5 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.0759 -0.0697 -0.6761 0.1541\r
- 9. N2 ( H6 ) 0.0926 0.1499 0.0240 -0.0113 0.0912 -0.0078 -0.0349 0.0134\r
- 10. H6 ( N2 ) 0.1083 0.0826 -0.0010 0.0232 -0.0118 -0.0242 0.0017 -0.0224\r
- 11. N2 ( H7 ) 0.0926 0.1499 0.0240 -0.0113 -0.0349 0.0134 0.0912 -0.0078\r
- 12. H7 ( N2 ) 0.1083 0.0826 -0.0010 0.0232 0.0017 -0.0224 -0.0118 -0.0242\r
- 13. C1 (cr) 0.3962 0.4168 0.4400 0.3893 -0.4447 -0.3869 -0.4447 -0.3869\r
- 14. N2 (cr) 0.6147 0.7083 0.0039 0.0249 -0.0130 -0.0251 -0.0130 -0.0251\r
- 15. N2 (lp) 0.0762 0.0955 -0.1043 0.0254 -0.0386 0.0160 -0.0386 0.0160\r
- 16. C1 (ry*) -0.1320 0.0924 0.0705 -0.0815 0.0022 -0.0037 0.0022 -0.0037\r
- 17. C1 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0719 -0.0910 -0.0719 0.0910\r
- 18. C1 (ry*) -0.1023 0.0764 -0.0643 0.0795 -0.0074 0.0105 -0.0074 0.0105\r
- 19. C1 (ry*) 0.0266 -0.0213 0.0019 -0.0057 0.0667 -0.0788 0.0667 -0.0788\r
- 20. N2 (ry*) 0.0151 -0.0177 -0.0351 -0.0172 -0.0179 -0.0146 -0.0179 -0.0146\r
- 21. N2 (ry*) 0.0000 0.0000 0.0000 0.0000 -0.0158 -0.0249 0.0158 0.0249\r
- 22. N2 (ry*) 0.1799 -0.1440 -0.0064 0.0295 0.0038 -0.0289 0.0038 -0.0289\r
- 23. N2 (ry*) 0.0183 -0.0136 -0.0051 0.0213 0.0032 -0.0095 0.0032 -0.0095\r
- 24. H3 (ry*) 0.0253 -0.0038 0.2834 -0.3497 -0.0248 0.0047 -0.0248 0.0047\r
- 25. H4 (ry*) 0.0223 -0.0071 0.0211 -0.0068 -0.2789 0.3553 -0.0227 0.0069\r
- 26. H5 (ry*) 0.0223 -0.0071 0.0211 -0.0068 -0.0227 0.0069 -0.2789 0.3553\r
- 27. H6 (ry*) 0.0124 0.0172 -0.0067 0.0219 -0.0080 0.0097 0.0057 -0.0222\r
- 28. H7 (ry*) 0.0124 0.0172 -0.0067 0.0219 0.0057 -0.0222 -0.0080 0.0097\r
- \r
- </pre>\r
-<p>\r
- The NHO labels on each row identify the atom to which the NHO\r
-belongs, and (in parentheses) the atom toward which the hybrid is\r
-pointed, if a bond hybrid, or a 1-center label (cr, lp, lp*, or ry*), if\r
-a non-bonded hybrid. Thus, "C 1 (N 2)" (NHO 1) \r
-is the bonding hybrid on C(1) directed\r
-toward N(2), "N 2(lp)" (NBO 15) is a non-bonded (lone pair) hybrid\r
-on N(2), etc. This label allows one to find the precise form of \r
-the NHO in the main listing of NBOs. The FNHO matrix shows, for\r
-example, that \r
-the (1,2) Fock matrix element between the directly\r
-interacting NHOs forming the C-N bond NBO is -0.7203 a.u.,\r
-whereas the (1,9) matrix element,\r
-between the C(1) hybrid pointing toward N(2)\r
-and the N(2) hybrid pointing toward H(6), is 0.0926 a.u.\r
-<p>\r
- As a second example, the keyword "NBOMO=PVAL" would print out\r
-the core + valence columns of the NBO <img src=rarr.gif> MO transformation, \r
-as reproduced below:\r
-<p>\r
- <pre>\r
-\r
-MOs in the NBO basis: \r
-\r
- NBO 1 2 3 4 5 6 7 8\r
- ---------- ------- ------- ------- ------- ------- ------- ------- -------\r
- 1. C1 - N2 -0.0661 -0.0574 0.6288 -0.1243 0.0000 -0.3239 0.6816 0.0000\r
- 2. C1 - H3 -0.0018 -0.0578 0.2061 -0.4716 0.0000 0.7747 0.1386 0.0000\r
- 3. C1 - H4 0.0023 0.0579 -0.1836 0.4908 0.3813 0.2304 0.3921 0.5940\r
- 4. C1 - H5 0.0023 0.0579 -0.1836 0.4908 -0.3813 0.2304 0.3921 -0.5940\r
- 5. N2 - H6 0.0570 0.0000 -0.4742 -0.3567 -0.5937 -0.1954 0.3035 0.3814\r
- 6. N2 - H7 0.0570 0.0000 -0.4742 -0.3567 0.5937 -0.1954 0.3035 -0.3814\r
- 7. C1 (cr) -0.0021 0.9931 0.0692 -0.0920 0.0000 0.0006 0.0019 0.0000\r
- 8. N2 (cr) 0.9935 -0.0019 0.1048 0.0348 0.0000 -0.0131 0.0022 0.0000\r
- 9. N2 (lp) 0.0432 -0.0037 -0.1676 -0.1219 0.0000 0.3312 0.1525 0.0000\r
- 10. C1 (ry*) -0.0088 -0.0005 0.0114 0.0089 0.0000 -0.0016 -0.0086 0.0000\r
- 11. C1 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0109 0.0000 0.0000 -0.0070\r
- 12. C1 (ry*) -0.0063 0.0001 -0.0050 -0.0035 0.0000 -0.0030 0.0026 0.0000\r
- 13. C1 (ry*) 0.0020 -0.0002 -0.0003 -0.0003 0.0000 -0.0009 0.0002 0.0000\r
- 14. N2 (ry*) -0.0041 -0.0003 -0.0006 0.0016 0.0000 0.0192 0.0107 0.0000\r
- 15. N2 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0080 0.0000 0.0000 0.0124\r
- 16. N2 (ry*) 0.0035 -0.0060 -0.0039 0.0102 0.0000 -0.0023 0.0040 0.0000\r
- 17. N2 (ry*) -0.0018 0.0023 -0.0007 0.0013 0.0000 -0.0007 0.0005 0.0000\r
- 18. H3 (ry*) -0.0008 -0.0094 -0.0103 0.0146 0.0000 0.0017 -0.0021 0.0000\r
- 19. H4 (ry*) -0.0008 -0.0100 -0.0061 0.0119 0.0062 0.0004 -0.0054 -0.0098\r
- 20. H5 (ry*) -0.0008 -0.0100 -0.0061 0.0119 -0.0062 0.0004 -0.0054 0.0098\r
- 21. H6 (ry*) -0.0052 -0.0013 -0.0147 -0.0018 -0.0027 -0.0016 -0.0097 -0.0159\r
- 22. H7 (ry*) -0.0052 -0.0013 -0.0147 -0.0018 0.0027 -0.0016 -0.0097 0.0159\r
- 23. C1 - N2 * -0.0019 -0.0035 -0.0026 0.0025 0.0000 0.0043 0.0049 0.0000\r
- 24. C1 - H3 * -0.0013 -0.0024 0.0059 -0.0018 0.0000 -0.0349 -0.0139 0.0000\r
- 25. C1 - H4 * 0.0009 0.0028 -0.0138 0.0033 -0.0408 -0.0188 0.0061 0.0148\r
- 26. C1 - H5 * 0.0009 0.0028 -0.0138 0.0033 0.0408 -0.0188 0.0061 -0.0148\r
- 27. N2 - H6 * -0.0010 0.0051 -0.0047 0.0182 0.0179 0.0122 0.0154 0.0322\r
- 28. N2 - H7 * -0.0010 0.0051 -0.0047 0.0182 -0.0179 0.0122 0.0154 -0.0322\r
-\r
- NBO 9 10 11 12 13 14 15\r
- ---------- ------- ------- ------- ------- ------- ------- -------\r
- 1. C1 - N2 0.1062 -0.0143 0.0006 0.0000 0.0049 0.0000 -0.0061\r
- 2. C1 - H3 -0.3343 -0.0044 0.0015 0.0000 0.0007 0.0000 -0.0080\r
- 3. C1 - H4 -0.1186 -0.0186 0.0103 0.0258 -0.0048 -0.0272 -0.0104\r
- 4. C1 - H5 -0.1186 -0.0186 0.0103 -0.0258 -0.0048 0.0272 -0.0104\r
- 5. N2 - H6 -0.1167 -0.0024 -0.0145 -0.0293 -0.0162 -0.0253 0.0040\r
- 6. N2 - H7 -0.1167 -0.0024 -0.0145 0.0293 -0.0162 0.0253 0.0040\r
- 7. C1 (cr) 0.0037 -0.0134 -0.0082 0.0000 0.0008 0.0000 -0.0008\r
- 8. N2 (cr) -0.0189 -0.0055 0.0030 0.0000 -0.0026 0.0000 0.0035\r
- 9. N2 (lp) 0.9007 -0.0144 0.0055 0.0000 0.0925 0.0000 0.0130\r
- 10. C1 (ry*) -0.0128 -0.0993 0.0553 0.0000 0.0536 0.0000 0.3301\r
- 11. C1 (ry*) 0.0000 0.0000 0.0000 0.0836 0.0000 0.1845 0.0000\r
- 12. C1 (ry*) -0.0039 -0.0612 0.0748 0.0000 -0.1160 0.0000 0.1213\r
- 13. C1 (ry*) -0.0018 0.0936 0.0192 0.0000 0.1022 0.0000 -0.1516\r
- 14. N2 (ry*) -0.0086 -0.0232 0.0071 0.0000 -0.0461 0.0000 -0.0178\r
- 15. N2 (ry*) 0.0000 0.0000 0.0000 0.0176 0.0000 -0.0856 0.0000\r
- 16. N2 (ry*) 0.0006 0.0395 -0.0836 0.0000 0.0221 0.0000 -0.1565\r
- 17. N2 (ry*) 0.0003 0.0614 -0.0222 0.0000 0.0114 0.0000 0.0584\r
- 18. H3 (ry*) -0.0218 -0.2483 -0.2232 0.0000 0.4827 0.0000 0.0001\r
- 19. H4 (ry*) 0.0060 -0.1973 -0.3224 -0.3372 -0.2069 -0.2151 -0.0483\r
- 20. H5 (ry*) 0.0060 -0.1973 -0.3224 0.3372 -0.2069 0.2151 -0.0483\r
- 21. H6 (ry*) 0.0027 -0.2869 0.2132 0.2297 -0.0372 -0.3543 -0.1737\r
- 22. H7 (ry*) 0.0027 -0.2869 0.2132 -0.2297 -0.0372 0.3543 -0.1737\r
- 23. C1 - N2 * -0.0031 -0.2357 0.2598 0.0000 -0.1096 0.0000 0.8051\r
- 24. C1 - H3 * -0.0799 -0.3214 -0.2654 0.0000 0.6687 0.0000 0.1133\r
- 25. C1 - H4 * -0.0369 0.2559 0.3890 0.4699 0.2968 0.3193 -0.0477\r
- 26. C1 - H5 * -0.0369 0.2559 0.3890 -0.4699 0.2968 -0.3193 -0.0477\r
- 27. N2 - H6 * -0.0031 0.4339 -0.3112 -0.3280 0.0474 0.4519 0.2168\r
- 28. N2 - H7 * -0.0031 0.4339 -0.3112 0.3280 0.0474 -0.4519 0.2168\r
- \r
- </pre>\r
-<p>\r
- In this transformation matrix, rows correspond to NBOs and\r
-columns to MOs (in the ordering used elesewhere in the program),\r
-and each basis NBO is further identified with \r
-a row label. The print parameter\r
-"PVAL" specified that only 15 MOs (the\r
-number of core + valence orbitals) \r
-should be printed, corresponding to the nine\r
-occupied MOs 1-9 and the lowest six virtual MOs 10-15. The matrix\r
-allows one to see the composition of each canonical MO in terms of\r
-localized bond NBOs. For example, MOs 5 and 8 \r
-can be approximately described as\r
-<center>\r
-<p>\r
-<img src=phi.gif><sub>5</sub> <img src=ca.gif> -0.594(<img src=sigma.gif><sub>N<sub>2</sub>H<sub>6</sub></sub> - <img src=sigma.gif><sub>N<sub>2</sub>H<sub>7</sub></sub>) + 0.381(<img src=sigma.gif><sub>C<sub>1</sub>H<sub>4</sub></sub> - <img src=sigma.gif><sub>C<sub>1</sub>H<sub>5</sub></sub>)\r
-<p>\r
-<img src=phi.gif><sub>8</sub> <img src=ca.gif> 0.381(<img src=sigma.gif><sub>N<sub>2</sub>H<sub>6</sub></sub> - <img src=sigma.gif><sub>N<sub>2</sub>H<sub>7</sub></sub>) + 0.594(<img src=sigma.gif><sub>C<sub>1</sub>H<sub>4</sub></sub> - <img src=sigma.gif><sub>C<sub>1</sub>H<sub>5</sub></sub>)\r
-<p>\r
-</center>\r
-whereas <img src=phi.gif><sub>6</sub> is primarily the C-H(3) NBO and <img src=phi.gif><sub>9</sub> \r
-the N lone pair NBO.\r
-<p>\r
-<i>B.6.5 BNDIDX Keyword</i>\r
-<p>\r
- The BNDIDX keyword activates the printing of several types\r
-of 'bond order' and valency indices, based on different assumptions\r
-and formulas, but all having some connection to the NAO/NBO/NLMO\r
-formalism. We illustrate these bond\r
-order tables for the example of RHF/3-21G methylamine (Section A.3).\r
-<p>\r
- The first segment of BNDIDX output shows the Wiberg bond index (the sum of\r
-squares of off-diagonal density matrix elements between\r
-atoms), as formulated\r
-in terms of the NAO basis set:\r
-<p>\r
- <pre>\r
-\r
-Wiberg bond index matrix in the NAO basis: \r
-\r
- Atom 1 2 3 4 5 6 7\r
- ---- ------ ------ ------ ------ ------ ------ ------\r
- 1. C 0.0000 0.9964 0.9472 0.9394 0.9394 0.0020 0.0020\r
- 2. N 0.9964 0.0000 0.0208 0.0052 0.0052 0.8611 0.8611\r
- 3. H 0.9472 0.0208 0.0000 0.0004 0.0004 0.0002 0.0002\r
- 4. H 0.9394 0.0052 0.0004 0.0000 0.0009 0.0079 0.0005\r
- 5. H 0.9394 0.0052 0.0004 0.0009 0.0000 0.0005 0.0079\r
- 6. H 0.0020 0.8611 0.0002 0.0079 0.0005 0.0000 0.0003\r
- 7. H 0.0020 0.8611 0.0002 0.0005 0.0079 0.0003 0.0000\r
-\r
-\r
-Wiberg bond index, Totals by atom: \r
-\r
- Atom 1\r
- ---- ------\r
- 1. C 3.8265\r
- 2. N 2.7499\r
- 3. H 0.9691\r
- 4. H 0.9544\r
- 5. H 0.9544\r
- 6. H 0.8720\r
- 7. H 0.8720\r
- \r
- </pre>\r
-<p>\r
- This index is intrinsically a positive quantity, making no\r
-distinction between net bonding\r
-or antibonding character of the density matrix elements.\r
-<p>\r
-<p>\r
- The next segment tabulates the "overlap-weighted\r
-NAO bond order," as shown below:\r
-<p>\r
- <pre>\r
-\r
-Atom-atom overlap-weighted NAO bond order: \r
-\r
- Atom 1 2 3 4 5 6 7\r
- ---- ------ ------ ------ ------ ------ ------ ------\r
- 1. C 0.0000 0.7815 0.7614 0.7633 0.7633 -0.0103 -0.0103\r
- 2. N 0.7815 0.0000 -0.0225 -0.0097 -0.0097 0.6688 0.6688\r
- 3. H 0.7614 -0.0225 0.0000 -0.0039 -0.0039 -0.0019 -0.0019\r
- 4. H 0.7633 -0.0097 -0.0039 0.0000 0.0024 0.0038 -0.0032\r
- 5. H 0.7633 -0.0097 -0.0039 0.0024 0.0000 -0.0032 0.0038\r
- 6. H -0.0103 0.6688 -0.0019 0.0038 -0.0032 0.0000 -0.0069\r
- 7. H -0.0103 0.6688 -0.0019 -0.0032 0.0038 -0.0069 0.0000\r
-\r
-\r
-Atom-atom overlap-weighted NAO bond order, Totals by atom: \r
-\r
- Atom 1\r
- ---- ------\r
- 1. C 3.0488\r
- 2. N 2.0772\r
- 3. H 0.7273\r
- 4. H 0.7527\r
- 5. H 0.7527\r
- 6. H 0.6503\r
- 7. H 0.6503\r
- \r
- </pre>\r
-<p>\r
- This index corresponds to a sum of off-diagonal\r
-NAO density matrix elements between atoms,\r
-each multiplied by the corresponding PNAO overlap integral.\r
-<p>\r
- Another type of BNDIDX output appears if the NLMO\r
-keyword is included, summarizing a formal\r
-"NLMO/NPA bond order" that can be associated with each NLMO:\r
-<p>\r
- <pre>\r
-\r
-Individual LMO bond orders greater than 0.002 in magnitude,\r
- with the overlap between the hybrids in the NLMO given:\r
-\r
-Atom I / Atom J / NLMO / Bond Order / Hybrid Overlap /\r
- 1 2 1 0.8007741 0.7314361\r
- 1 2 5 0.0022694 0.1796696\r
- 1 2 6 0.0022694 0.1796696\r
- 1 2 9 0.0088061 0.3053730\r
- 1 3 2 0.8051647 0.7862263\r
- 1 3 9 -0.0088061 -0.5762575\r
- 1 4 3 0.7772179 0.7874312\r
- 1 4 5 -0.0022694 -0.5396947\r
- 1 5 4 0.7772179 0.7874312\r
- 1 5 6 -0.0022694 -0.5396947\r
- 1 6 3 -0.0031652 -0.0920524\r
- 1 6 5 0.0022694 0.0852070\r
- 1 7 4 -0.0031652 -0.0920524\r
- 1 7 6 0.0022694 0.0852070\r
- 2 3 9 -0.0097841 -0.0930204\r
- 2 4 5 -0.0027437 -0.0701717\r
- 2 5 6 -0.0027437 -0.0701717\r
- 2 6 5 0.6358512 0.7286061\r
- 2 7 6 0.6358512 0.7286061\r
- 4 6 3 0.0031652 0.0429202\r
- 4 6 5 0.0027437 0.0399352\r
- 5 7 4 0.0031652 0.0429202\r
- 5 7 6 0.0027437 0.0399352\r
- \r
-\r
-</pre>This NLMO bond order is calculated by the method described by\r
-A. E. Reed and P. v.R. Schleyer [<i>Inorg. Chem. <b>27</b></i>, 3969-3987 (1988);\r
-<i>J. Am. Chem. Soc.</i> (to be published)],\r
-based on the shared occupancies and hybrid overlaps (last column)\r
-of NAOs composing the NLMO. In the above table, for example, NLMO 1\r
-occurs only in the first line,\r
-contributing a bond of formal order 0.801 between C(1) and N(2), whereas\r
-NLMO 9 (the nitrogen lone pair) contributes a slight strengthening\r
-(+0.0088) of the C(1)-N(2) bond, a weakening (-0.0088) of the\r
-vicinal C(1)-H(3) bond, and a slight negative bond order (-0.0098)\r
-between atoms N(2), H(3).\r
-<p>\r
- The NLMO bond order contributions are then summed for each\r
-atom pair to give the net NLMO/NPA bond orders shown below:\r
-<p>\r
- <pre>\r
-\r
-Atom-Atom Net Linear NLMO/NPA Bond Orders: \r
-\r
- Atom 1 2 3 4 5 6 7\r
- ---- ------ ------ ------ ------ ------ ------ ------\r
- 1. C 0.0000 0.8174 0.7960 0.7732 0.7732 -0.0013 -0.0013\r
- 2. N 0.8174 0.0000 -0.0104 -0.0030 -0.0030 0.6337 0.6337\r
- 3. H 0.7960 -0.0104 0.0000 -0.0020 -0.0020 0.0001 0.0001\r
- 4. H 0.7732 -0.0030 -0.0020 0.0000 0.0020 0.0062 0.0000\r
- 5. H 0.7732 -0.0030 -0.0020 0.0020 0.0000 0.0000 0.0062\r
- 6. H -0.0013 0.6337 0.0001 0.0062 0.0000 0.0000 -0.0001\r
- 7. H -0.0013 0.6337 0.0001 0.0000 0.0062 -0.0001 0.0000\r
- \r
-\r
-</pre>For example, the table attributes a formal bond order of 0.8174 to the\r
-C(1)-N(2) bond of methylamine, the highest bond order in this \r
-molecule. (The higher value for C(1)-H(3) than for the other\r
-two CH bonds reflects an unsatisfactory aspect of this\r
-method of assessing bond order.)\r
-<p>\r
- These bond indices are based on different\r
-assumptions, and each has certain advantages and\r
-disadvantages. <i>Caveat emptor!</i>\r
-<p>\r
-<i>B.6.6 RESONANCE Keyword: Benzene</i>\r
-<p>\r
- When NBO analysis is performed on a wavefunction that cannot\r
-be satisfactorily localized [i.e., in which one or more NBOs of\r
-the natural Lewis structure fail to achieve\r
-the threshold occupancy (1.90) for a satisfactory\r
-'pair'], the NBO program aborts with a message indicating that\r
-the wavefunction is unsuitable for localized analysis. For example,\r
-when benzene (RHF/STO-3G level, idealized Pople-Gordon geometry)\r
-is treated by the NBO program in default mode, one obtains the output:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 2(2) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44\r
------------------------------------------------------------------------------\r
-\r
-Only strongly delocalized resonance structures can be found.\r
-The default procedure is to abort the NBO search.\r
- \r
-\r
- </pre>When the RESONANCE keyword is activated for this same example,\r
-one obtains a summary of NBO search cycles as shown below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 2(2) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 3(1) 1.80 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 4(2) 1.80 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 5(1) 1.70 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 6(2) 1.70 38.87476 3.12524 6 12 0 3 3 3 0.44\r
- 7(1) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44\r
- 8(2) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44\r
- 9(1) 1.50 40.87476 1.12524 6 15 0 0 0 3 0.44\r
- 10(2) 1.50 40.87476 1.12524 6 15 0 0 0 3 0.44\r
- 11(1) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: RESONANCE keyword permits strongly delocalized structure\r
-\r
- </pre>\r
-<p>\r
- As this table shows, the occupancy threshold was successively\r
-lowered from 1.90 to 1.50 by 0.1e for each cycle, \r
-and the NBO search repeated. In\r
-this case, the 'best' Lewis structure (lowest overall non-Lewis\r
-occupancy, 1.12524e) was found in cycle 7, with occupancy\r
-threshold 1.60e. The NBO program therefore reset the \r
-threshold to this value and calculated\r
-the set of NBOs corresponding to this\r
-'best' Lewis structure, as shown below:\r
-<p>\r
- <pre>\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (1.98940) BD ( 1) C 1- C 2 \r
- ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.8109 0.0097 0.0000\r
- ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.8109 0.0097 0.0000\r
- 2. (1.98940) BD ( 1) C 1- C 6 \r
- ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.4138 -0.6974 0.0000\r
- ( 50.00%) 0.7071* C 6 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.3971 0.7071 0.0000\r
- 3. (1.66667) BD ( 2) C 1- C 6 \r
- ( 50.00%) 0.7071* C 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) 0.7071* C 6 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 4. (1.98977) BD ( 1) C 1- H 7 \r
- ( 51.73%) 0.7193* C 1 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 0.4137 0.7166 0.0000\r
- ( 48.27%) 0.6947* H 7 s(100.00%)\r
- 1.0000\r
- 5. (1.98940) BD ( 1) C 2- C 3 \r
- ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.4138 -0.6974 0.0000\r
- ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.3971 0.7071 0.0000\r
- 6. (1.66667) BD ( 2) C 2- C 3 \r
- ( 50.00%) 0.7071* C 2 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) 0.7071* C 3 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 7. (1.98977) BD ( 1) C 2- H 8 \r
- ( 51.73%) 0.7193* C 2 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 -0.4137 0.7166 0.0000\r
- ( 48.27%) 0.6947* H 8 s(100.00%)\r
- 1.0000\r
- 8. (1.98940) BD ( 1) C 3- C 4 \r
- ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.3971 -0.7071 0.0000\r
- ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.4138 0.6974 0.0000\r
- 9. (1.98977) BD ( 1) C 3- H 9 \r
- ( 51.73%) 0.7193* C 3 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 -0.8275 0.0000 0.0000\r
- ( 48.27%) 0.6947* H 9 s(100.00%)\r
- 1.0000\r
- 10. (1.66667) BD ( 2) C 4- C 5 \r
- ( 50.00%) 0.7071* C 4 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) 0.7071* C 5 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 11. (1.98940) BD ( 1) C 4- C 5 \r
- ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.8109 -0.0097 0.0000\r
- ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.8109 -0.0097 0.0000\r
- 12. (1.98977) BD ( 1) C 4- H10 \r
- ( 51.73%) 0.7193* C 4 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 -0.4137 -0.7166 0.0000\r
- ( 48.27%) 0.6947* H10 s(100.00%)\r
- 1.0000\r
- 13. (1.98940) BD ( 1) C 5- C 6 \r
- ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.4138 0.6974 0.0000\r
- ( 50.00%) 0.7071* C 6 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.3971 -0.7071 0.0000\r
- 14. (1.98977) BD ( 1) C 5- H11 \r
- ( 51.73%) 0.7193* C 5 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 0.4137 -0.7166 0.0000\r
- ( 48.27%) 0.6947* H11 s(100.00%)\r
- 1.0000\r
- 15. (1.98977) BD ( 1) C 6- H12 \r
- ( 51.73%) 0.7193* C 6 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 0.5615 0.8275 0.0000 0.0000\r
- ( 48.27%) 0.6947* H12 s(100.00%)\r
- 1.0000\r
- 16. (1.99995) CR ( 1) C 1 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 17. (1.99995) CR ( 1) C 2 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 18. (1.99995) CR ( 1) C 3 s(100.00%)\r
- 1.0000 0.0000 -0.0001 0.0000 0.0000\r
- 19. (1.99995) CR ( 1) C 4 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 20. (1.99995) CR ( 1) C 5 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 21. (1.99995) CR ( 1) C 6 s(100.00%)\r
- 1.0000 0.0000 0.0001 0.0000 0.0000\r
- 22. (0.01077) BD*( 1) C 1- C 2 \r
- ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.8109 0.0097 0.0000\r
- ( 50.00%) -0.7071* C 2 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.8109 0.0097 0.0000\r
- 23. (0.01077) BD*( 1) C 1- C 6 \r
- ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.4138 -0.6974 0.0000\r
- ( 50.00%) -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.3971 0.7071 0.0000\r
- 24. (0.33333) BD*( 2) C 1- C 6 \r
- ( 50.00%) 0.7071* C 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) -0.7071* C 6 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 25. (0.01011) BD*( 1) C 1- H 7 \r
- ( 48.27%) 0.6947* C 1 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 -0.4137 -0.7166 0.0000\r
- ( 51.73%) -0.7193* H 7 s(100.00%)\r
- -1.0000\r
- 26. (0.01077) BD*( 1) C 2- C 3 \r
- ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.4138 -0.6974 0.0000\r
- ( 50.00%) -0.7071* C 3 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.3971 0.7071 0.0000\r
- 27. (0.33333) BD*( 2) C 2- C 3 \r
- ( 50.00%) 0.7071* C 2 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) -0.7071* C 3 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 28. (0.01011) BD*( 1) C 2- H 8 \r
- ( 48.27%) 0.6947* C 2 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 0.4137 -0.7166 0.0000\r
- ( 51.73%) -0.7193* H 8 s(100.00%)\r
- -1.0000\r
- 29. (0.01077) BD*( 1) C 3- C 4 \r
- ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.3971 -0.7071 0.0000\r
- ( 50.00%) -0.7071* C 4 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.4138 0.6974 0.0000\r
- 30. (0.01011) BD*( 1) C 3- H 9 \r
- ( 48.27%) 0.6947* C 3 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 0.8275 0.0000 0.0000\r
- ( 51.73%) -0.7193* H 9 s(100.00%)\r
- -1.0000\r
- 31. (0.33333) BD*( 2) C 4- C 5 \r
- ( 50.00%) 0.7071* C 4 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- ( 50.00%) -0.7071* C 5 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 1.0000\r
- 32. (0.01077) BD*( 1) C 4- C 5 \r
- ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.8109 -0.0097 0.0000\r
- ( 50.00%) -0.7071* C 5 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.8109 -0.0097 0.0000\r
- 33. (0.01011) BD*( 1) C 4- H10 \r
- ( 48.27%) 0.6947* C 4 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 0.4137 0.7166 0.0000\r
- ( 51.73%) -0.7193* H10 s(100.00%)\r
- -1.0000\r
- 34. (0.01077) BD*( 1) C 5- C 6 \r
- ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 0.4138 0.6974 0.0000\r
- ( 50.00%) -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)\r
- 0.0000 0.5851 -0.3971 -0.7071 0.0000\r
- 35. (0.01011) BD*( 1) C 5- H11 \r
- ( 48.27%) 0.6947* C 5 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 -0.4137 0.7166 0.0000\r
- ( 51.73%) -0.7193* H11 s(100.00%)\r
- -1.0000\r
- 36. (0.01011) BD*( 1) C 6- H12 \r
- ( 48.27%) 0.6947* C 6 s( 31.53%)p 2.17( 68.47%)\r
- 0.0000 -0.5615 -0.8275 0.0000 0.0000\r
- ( 51.73%) -0.7193* H12 s(100.00%)\r
- -1.0000\r
-\r
- </pre>\r
-<p>\r
- As one can see from this table, the set of NBOs \r
-obtained by the program corresponds\r
-to one of the two equivalent Kekulée structures, with \r
-reasonably well\r
-localized <img src=sigma.gif><sub>CC</sub> and <img src=sigma.gif><sub>CH</sub> NBOs (1.98940 and 1.98977\r
-electrons, respectively), but three severely depleted <img src=pi.gif><sub>CC</sub>\r
-bonds (1.66667e) and corresponding high occupancy \r
-<img src=pi.gif>*<sub>CC</sub> antibonds (0.33333e). Other sections of the NBO\r
-output (not shown) will similarly exhibit the sharp distinctions \r
-between benzene and more 'typical' non-aromatic compounds.\r
-<p>\r
-<center>\r
-<b>WARNING</b>\r
-</center>\r
-<p>\r
-If you attempt to analyze an open-shell wavefunction with an\r
-ESS method that produces only the "spinless" (spin-averaged) density\r
-matrix, rather than the separate density matrices for <img src=alpha.gif> \r
-and <img src=beta.gif> spin, the job will likely abort, as in the default\r
-benzene example. However, you should <i>not</i> use the RESONANCE\r
-keyword to bypass this abort! NBO analysis of an open-shell \r
-spinless density matrix is a fundamental misuse\r
-of the program.\r
-<p>\r
-<p>\r
-<i>B.6.7 NOBOND Keyword</i>\r
-<p>\r
- The NOBOND keyword forces the NBO program to analyze the\r
-wavefunction in terms of 1-center functions only, thus forcing\r
-a description of the bonding in terms of atomic or \r
-ionic hybrids. The modifications of NBO output that result\r
-from activating this keyword can be illustrated for the \r
-HF molecule (RHF/3-21G//RHF/3-21G level). This molecule\r
-might be described in terms of a polar covalent H-F\r
-bond or in terms of ionic H<sup>+</sup> F<sup>-</sup> interactions.\r
-<p>\r
- The default NBO analysis of this example is shown below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 9.99942 0.00058 1 1 0 3 0 0 0.00\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
---------------------------------------------------------\r
- Core 1.99994 ( 99.997% of 2)\r
- Valence Lewis 7.99948 ( 99.994% of 8)\r
- ================== ============================\r
- Total Lewis 9.99942 ( 99.994% of 10)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.00000 ( 0.000% of 10)\r
- Rydberg non-Lewis 0.00058 ( 0.006% of 10)\r
- ================== ============================\r
- Total non-Lewis 0.00058 ( 0.006% of 10)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (2.00000) BD ( 1) F 1- H 2 \r
- ( 75.22%) 0.8673* F 1 s( 16.31%)p 5.13( 83.69%)\r
- 0.0000 0.4036 0.0158 0.0000 0.0000\r
- 0.0000 0.0000 0.9148 0.0001\r
- ( 24.78%) 0.4978* H 2 s(100.00%)\r
- 1.0000 0.0000\r
- 2. (1.99994) CR ( 1) F 1 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000\r
- 3. (2.00000) LP ( 1) F 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 1.0000 -0.0013\r
- 0.0000 0.0000 0.0000 0.0000\r
- 4. (2.00000) LP ( 2) F 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 1.0000 -0.0013 0.0000 0.0000\r
- 5. (1.99948) LP ( 3) F 1 s( 83.71%)p 0.19( 16.29%)\r
- 0.0000 0.9149 -0.0052 0.0000 0.0000\r
- 0.0000 0.0000 -0.4036 -0.0062\r
- 6. (0.00002) RY*( 1) F 1 s( 0.00%)p 1.00(100.00%)\r
- 7. (0.00000) RY*( 2) F 1 s( 0.00%)p 1.00(100.00%)\r
- 8. (0.00000) RY*( 3) F 1 s( 0.00%)p 1.00(100.00%)\r
- 9. (0.00000) RY*( 4) F 1 s( 99.97%)p 0.00( 0.03%)\r
- 10. (0.00056) RY*( 1) H 2 s(100.00%)\r
- 0.0000 1.0000\r
- 11. (0.00000) BD*( 1) F 1- H 2 \r
- ( 24.78%) 0.4978* F 1 s( 16.31%)p 5.13( 83.69%)\r
- ( 75.22%) -0.8673* H 2 s(100.00%)\r
- \r
- </pre>\r
-<p>\r
-As the output shows, default NBO analysis\r
-leads to a polar covalent description of HF. The\r
-<img src=sigma.gif><sub>HF</sub> bond, NBO 1, is formed from a <i>p</i>-rich \r
-(<i>sp</i><sup>5.13</sup>) hybrid on F and the 1<i>s</i> AO on H,\r
-strongly polarized (about 75.22%) toward F. This provides a\r
-satisfactory Lewis structure, describing 99.994% of\r
-the total electron density.\r
-<p>\r
- When the NOBOND keyword is activated to bypass\r
-the search for 2-center bonds, the NBO output is\r
-modified as shown below:\r
-<p>\r
- <pre>\r
-\r
-\r
- /NOBOND / : No two-center NBO search\r
-\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.00 9.50378 0.49622 1 0 0 4 0 1 0.75\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: Search for bonds prevented by NOBOND keyword\r
-\r
---------------------------------------------------------\r
- Core 1.99993 ( 99.997% of 2)\r
- Valence Lewis 7.50385 ( 93.798% of 8)\r
- ================== ============================\r
- Total Lewis 9.50378 ( 95.038% of 10)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.49564 ( 4.956% of 10)\r
- Rydberg non-Lewis 0.00058 ( 0.006% of 10)\r
- ================== ============================\r
- Total non-Lewis 0.49622 ( 4.962% of 10)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (1.99993) CR ( 1) F 1 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0001 0.0000\r
- 2. (2.00000) LP ( 1) F 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 1.0000 -0.0013\r
- 0.0000 0.0000 0.0000 0.0000\r
- 3. (2.00000) LP ( 2) F 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 1.0000 -0.0013 0.0000 0.0000\r
- 4. (1.99948) LP ( 3) F 1 s( 83.71%)p 0.19( 16.29%)\r
- 0.0000 0.9149 -0.0052 0.0000 0.0000\r
- 0.0000 0.0000 -0.4036 -0.0062\r
- 5. (1.50436) LP ( 4) F 1 s( 16.31%)p 5.13( 83.69%)\r
- -0.0001 0.4036 0.0158 0.0000 0.0000\r
- 0.0000 0.0000 0.9148 0.0001\r
- 6. (0.49564) LP*( 1) H 2 s(100.00%)\r
- 1.0000 0.0000\r
- 7. (0.00002) RY*( 1) F 1 s( 0.00%)p 1.00(100.00%)\r
- 8. (0.00000) RY*( 2) F 1 s( 0.00%)p 1.00(100.00%)\r
- 9. (0.00000) RY*( 3) F 1 s( 0.00%)p 1.00(100.00%)\r
- 10. (0.00000) RY*( 4) F 1 s( 99.97%)p 0.00( 0.03%)\r
- 11. (0.00056) RY*( 1) H 2 s(100.00%)\r
- 0.0000 1.0000\r
- \r
- </pre>\r
-<p>\r
- In this case, the NBO output indicates a rather poor Lewis\r
-structure (4.962% non-Lewis density), with a severely\r
-depleted F<sup>-</sup> lone pair (NBO 5, the <i>sp</i><sup>5.13</sup> hybrid)\r
-and significant occupancy (about 0.496e) in the 'empty' H<sup>+</sup>\r
-1<i>s</i> orbital (NBO 6) of the cation. The NOBOND comparison\r
-would therefore indicate the superiority of a polar\r
-covalent description in this case.\r
-<p>\r
-<i>B.6.8 3CBOND Keyword: Diborane</i>\r
-<p>\r
- When the default NBO analysis is applied to diborane or\r
-related electron-deficient compounds, there is a dramatic\r
-failure to represent the electronic distribution in terms of\r
-1- and 2-center functions only. For example, for\r
-B<sub>2</sub>H<sub>6</sub> at the RHF/3-21G//RHF/3-21G level,\r
-the default NBO search (if the RESONANCE keyword is activated\r
-to allow NBO printout) returns\r
-a fractured set of 4 units (two BH<sub>2</sub><sup>+</sup> and two H<sup>-</sup>\r
-fragments), with about 2.13 electrons unaccounted for (~15%\r
-non-Lewis occupancy), symptomatic of general breakdown of the\r
-conventional Lewis structure representation.\r
-<p>\r
- However, when the NBO search is extended to 3-center bonds\r
-by activating the 3CBOND keyword, one obtains\r
-the NBO output shown below:\r
-<p>\r
- <pre>\r
-\r
-\r
- /3CBOND / : Search for 3-center bonds\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 15.94335 0.05665 2 4 2 0 0 0 0.15\r
- 2(2) 1.90 15.94335 0.05665 2 4 2 0 0 0 0.15\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
-WARNING: 1 low occupancy (<1.9990e) core orbital found on B 1\r
- 1 low occupancy (<1.9990e) core orbital found on B 2\r
-\r
---------------------------------------------------------\r
- Core 3.99702 ( 99.925% of 4)\r
- Valence Lewis 11.94633 ( 99.553% of 12)\r
- ================== ============================\r
- Total Lewis 15.94335 ( 99.646% of 16)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.04565 ( 0.285% of 16)\r
- Rydberg non-Lewis 0.01100 ( 0.069% of 16)\r
- ================== ============================\r
- Total non-Lewis 0.05665 ( 0.354% of 16)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (1.98467) 3C ( 1) B 1- B 2- H 3 \r
- ( 26.43%) 0.5141* B 1 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 26.43%) 0.5141* B 2 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 -0.5657 0.0007\r
- ( 47.14%) 0.6866* H 3 s(100.00%)\r
- 1.0000 0.0066\r
- 2. (1.98467) 3C ( 1) B 1- B 2- H 4 \r
- ( 26.43%) 0.5141* B 1 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 0.7067 0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 26.43%) 0.5141* B 2 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 0.7067 0.0245\r
- 0.0000 0.0000 -0.5657 0.0007\r
- ( 47.14%) 0.6866* H 4 s(100.00%)\r
- 1.0000 0.0066\r
- 3. (1.99425) BD ( 1) B 1- H 6 \r
- ( 48.80%) 0.6985* B 1 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- 0.7067 -0.0243 -0.4239 -0.0222\r
- ( 51.20%) 0.7156* H 6 s(100.00%)\r
- 1.0000 0.0004\r
- 4. (1.99425) BD ( 1) B 1- H 7 \r
- ( 48.80%) 0.6985* B 1 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- -0.7067 0.0243 -0.4239 -0.0222\r
- ( 51.20%) 0.7156* H 7 s(100.00%)\r
- 1.0000 0.0004\r
- 5. (1.99425) BD ( 1) B 2- H 5 \r
- ( 48.80%) 0.6985* B 2 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- -0.7067 0.0243 0.4239 0.0222\r
- ( 51.20%) 0.7156* H 5 s(100.00%)\r
- 1.0000 0.0004\r
- 6. (1.99425) BD ( 1) B 2- H 8 \r
- ( 48.80%) 0.6985* B 2 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- 0.7067 -0.0243 0.4239 0.0222\r
- ( 51.20%) 0.7156* H 8 s(100.00%)\r
- 1.0000 0.0004\r
- 7. (1.99851) CR ( 1) B 1 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0002 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 -0.0007 0.0000\r
- 8. (1.99851) CR ( 1) B 2 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0002 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0007 0.0000\r
- 9. (0.00147) RY*( 1) B 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0344 0.9994 0.0000 0.0000\r
- 10. (0.00080) RY*( 2) B 1 s( 4.02%)p23.87( 95.98%)\r
- 0.0000 0.0245 0.1990 0.0000 0.0000\r
- 0.0000 0.0000 -0.0214 0.9795\r
- 11. (0.00002) RY*( 3) B 1 s( 96.01%)p 0.04( 3.99%)\r
- 12. (0.00000) RY*( 4) B 1 s( 0.00%)p 1.00(100.00%)\r
- 13. (0.00147) RY*( 1) B 2 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0344 0.9994 0.0000 0.0000\r
- 14. (0.00080) RY*( 2) B 2 s( 4.02%)p23.87( 95.98%)\r
- 0.0000 0.0245 0.1990 0.0000 0.0000\r
- 0.0000 0.0000 0.0214 -0.9795\r
- 15. (0.00002) RY*( 3) B 2 s( 96.01%)p 0.04( 3.99%)\r
- 16. (0.00000) RY*( 4) B 2 s( 0.00%)p 1.00(100.00%)\r
- 17. (0.00181) RY*( 1) H 3 s(100.00%)\r
- -0.0066 1.0000\r
- 18. (0.00181) RY*( 1) H 4 s(100.00%)\r
- -0.0066 1.0000\r
- 19. (0.00070) RY*( 1) H 5 s(100.00%)\r
- -0.0004 1.0000\r
- 20. (0.00070) RY*( 1) H 6 s(100.00%)\r
- -0.0004 1.0000\r
- 21. (0.00070) RY*( 1) H 7 s(100.00%)\r
- -0.0004 1.0000\r
- 22. (0.00070) RY*( 1) H 8 s(100.00%)\r
- -0.0004 1.0000\r
- 23. (0.01464) 3C*( 1) B 1- B 2- H 3 \r
- ( 23.57%) 0.4855* B 1 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 23.57%) -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 0.7067 0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 52.86%) -0.7271* H 3 s(100.00%)\r
- 1.0000 0.0066\r
- 24. (0.00026) 3C*( 1) B 1- B 2- H 3 \r
- ( 50.00%) 0.7071* B 1 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 0.7067 0.0245\r
- 0.0000 0.0000 -0.5657 0.0007\r
- ( 50.00%) -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 0.7067 0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 0.00%) 0.0000* H 3 s( 0.00%)\r
- 0.0000 0.0000\r
- 25. (0.01464) 3C*( 1) B 1- B 2- H 4 \r
- ( 23.57%) 0.4855* B 1 s( 18.00%)p 4.55( 82.00%)\r
- 0.0005 0.4241 0.0124 0.7067 0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 23.57%) -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 52.86%) -0.7271* H 4 s(100.00%)\r
- 1.0000 0.0066\r
- 26. (0.00026) 3C*( 1) B 1- B 2- H 4 \r
- ( 50.00%) 0.7071* B 1 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 -0.5657 0.0007\r
- ( 50.00%) -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)\r
- -0.0005 -0.4241 -0.0124 -0.7067 -0.0245\r
- 0.0000 0.0000 0.5657 -0.0007\r
- ( 0.00%) 0.0000* H 4 s( 0.00%)\r
- 0.0000 0.0000\r
- 27. (0.00396) BD*( 1) B 2- H 5 \r
- ( 51.20%) 0.7156* B 2 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- -0.7067 0.0243 0.4239 0.0222\r
- ( 48.80%) -0.6985* H 5 s(100.00%)\r
- 1.0000 0.0004\r
- 28. (0.00396) BD*( 1) B 2- H 8 \r
- ( 51.20%) 0.7156* B 2 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- 0.7067 -0.0243 0.4239 0.0222\r
- ( 48.80%) -0.6985* H 8 s(100.00%)\r
- 1.0000 0.0004\r
- 29. (0.00396) BD*( 1) B 1- H 6 \r
- ( 51.20%) 0.7156* B 1 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- 0.7067 -0.0243 -0.4239 -0.0222\r
- ( 48.80%) -0.6985* H 6 s(100.00%)\r
- 1.0000 0.0004\r
- 30. (0.00396) BD*( 1) B 1- H 7 \r
- ( 51.20%) 0.7156* B 1 s( 31.98%)p 2.13( 68.02%)\r
- -0.0002 0.5655 -0.0061 0.0000 0.0000\r
- -0.7067 0.0243 -0.4239 -0.0222\r
- ( 48.80%) -0.6985* H 7 s(100.00%)\r
- 1.0000 0.0004\r
- \r
- </pre>\r
-<p>\r
- The resulting NBO Lewis structure has improved significantly\r
-[only 0.057e (0.35%) non-Lewis occupancy]. The structure includes\r
-the expected 3-center B-H-B bonds (NBOs 1, 2), each with reasonably\r
-high occupancy (1.9847e). Each 3-c bond is composed of <i>p</i>-rich\r
-(<i>sp</i><sup>4.55</sup>) boron hybrids and the hydrogen 1<i>s</i> NAO,\r
-with about 47.14% of the orbital density on the central hydrogen. Note\r
-that each 3-center bond NBO is associated with <i>two</i> 3-c antibond\r
-NBOs (viz., NBOs 23, 24 for the first 3-c bond, NBO 1), which contribute\r
-in distinct ways to delocalization interactions. Of course, the \r
-accuracy of <i>any</i> molecular Lewis structure might be improved\r
-slightly by extending the NBO search to 3-center bonds (thus\r
-allowing greater variational flexibility to maximize occupancy),\r
-but this example illustrates the kind of <i>qualitative</i> improvement\r
-that indicates when 3-center bonds are needed\r
-in the zeroth-order picture of the bonding.\r
-<p>\r
- Note that\r
-the NBO 3-c label may frequently have the wrong 'connectivity' (as\r
-in the present case, e.g., where "B 1- B 2- H 3" is written\r
-instead of the more reasonable "B 1- H 3- B 2"). This is a\r
-consequence of the fact that the NBO algorithms have no inkling\r
-of the positions of the atoms in space, and thus of which\r
-label is more 'reasonable.'\r
-<p>\r
-<i>B.6.9 NBO Directed Search ($CHOOSE Keylist)</i>\r
-<p>\r
- To illustrate the $CHOOSE keylist for a directed NBO search, we\r
-again make use of the methylamine example (Section A.3). The vicinal\r
-<i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>CH</sub> delocalization, to which attention\r
-has been repeatedly called in the examples,\r
-may be associated, in resonance theory terms,\r
-with the "double-bond, no-bond" resonance structure shown below:\r
-<center>\r
-<img src="nbofig3.gif">\r
-</center>\r
-<p>\r
-To investigate the suitability of this resonance structure\r
-for describing the methylamine wavefunction, we would\r
-specify the $CHOOSE keylist (Section B.4) as follows:\r
- <pre>\r
- $CHOOSE !double-bond, no-bond resonance\r
- LONE 3 1 END\r
- BOND S 1 4 S 1 5 D 1 2 S 2 6 S 2 7 END\r
- $END\r
-\r
-</pre>When this is included in the input file, the NBO program produces\r
-the output shown below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 16.66741 1.33259 2 6 0 1 1 2 0.95\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: NBOs selected via the $CHOOSE keylist\r
-\r
-WARNING: 1 low occupancy (<1.9990e) core orbital found on C 1\r
-\r
---------------------------------------------------------\r
- Core 3.99853 ( 99.963% of 4)\r
- Valence Lewis 12.66888 ( 90.492% of 14)\r
- ================== ============================\r
- Total Lewis 16.66741 ( 92.597% of 18)\r
- -----------------------------------------------------\r
- Valence non-Lewis 1.30491 ( 7.249% of 18)\r
- Rydberg non-Lewis 0.02768 ( 0.154% of 18)\r
- ================== ============================\r
- Total non-Lewis 1.33259 ( 7.403% of 18)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (1.95945) BD ( 1) C 1- N 2 \r
- ( 7.66%) 0.2768* C 1 s( 0.63%)p99.99( 99.37%)\r
- -0.0001 -0.0770 -0.0186 0.5107 -0.0551\r
- 0.8520 -0.0632 0.0000 0.0000\r
- ( 92.34%) 0.9609* N 2 s( 19.31%)p 4.18( 80.69%)\r
- 0.0000 0.4395 -0.0001 -0.1175 -0.0067\r
- 0.8905 -0.0110 0.0000 0.0000\r
- 2. (1.93778) BD ( 2) C 1- N 2 \r
- ( 39.14%) 0.6256* C 1 s( 36.80%)p 1.72( 63.20%)\r
- -0.0004 -0.6055 -0.0371 -0.7047 -0.0632\r
- 0.3594 -0.0471 0.0000 0.0000\r
- ( 60.86%) 0.7801* N 2 s( 19.33%)p 4.17( 80.67%)\r
- -0.0001 -0.4396 0.0011 0.8364 -0.0016\r
- 0.3271 -0.0137 0.0000 0.0000\r
- 3. (1.98365) BD ( 1) C 1- H 4 \r
- ( 61.02%) 0.7811* C 1 s( 31.10%)p 2.22( 68.90%)\r
- 0.0001 0.5577 0.0006 -0.3480 0.0095\r
- 0.2603 0.0094 0.7070 -0.0103\r
- ( 38.98%) 0.6244* H 4 s(100.00%)\r
- 1.0000 0.0008\r
- 4. (1.98365) BD ( 1) C 1- H 5 \r
- ( 61.02%) 0.7811* C 1 s( 31.10%)p 2.22( 68.90%)\r
- 0.0001 0.5577 0.0006 -0.3480 0.0095\r
- 0.2603 0.0094 -0.7070 0.0103\r
- ( 38.98%) 0.6244* H 5 s(100.00%)\r
- 1.0000 0.0008\r
- 5. (1.99491) BD ( 1) N 2- H 6 \r
- ( 68.46%) 0.8274* N 2 s( 30.67%)p 2.26( 69.33%)\r
- 0.0000 0.5538 0.0005 0.3785 0.0165\r
- -0.2232 0.0044 -0.7070 -0.0093\r
- ( 31.54%) 0.5616* H 6 s(100.00%)\r
- 1.0000 0.0031\r
- 6. (1.99491) BD ( 1) N 2- H 7 \r
- ( 68.46%) 0.8274* N 2 s( 30.67%)p 2.26( 69.33%)\r
- 0.0000 0.5538 0.0005 0.3785 0.0165\r
- -0.2232 0.0044 0.7070 0.0093\r
- ( 31.54%) 0.5616* H 7 s(100.00%)\r
- 1.0000 0.0031\r
- 7. (1.99900) CR ( 1) C 1 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0003 0.0000 -0.0001 0.0000\r
- 0.0002 0.0000 0.0000 0.0000\r
- 8. (1.99953) CR ( 1) N 2 s(100.00%)p 0.00( 0.00%)\r
- 1.0000 -0.0001 0.0000 0.0001 0.0000\r
- 0.0000 0.0000 0.0000 0.0000\r
- 9. (0.81453) LP ( 1) H 3 s(100.00%)\r
- 1.0000 0.0000\r
- 10. (0.01893) RY*( 1) C 1 s( 10.61%)p 8.42( 89.39%)\r
- 0.0000 -0.0737 0.3173 -0.0090 0.7223\r
- 0.0971 0.6021 0.0000 0.0000\r
- 11. (0.00034) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0146 0.9999\r
- 12. (0.00025) RY*( 3) C 1 s( 57.37%)p 0.74( 42.63%)\r
- 0.0000 -0.0012 0.7575 -0.0176 0.1886\r
- -0.0071 -0.6248 0.0000 0.0000\r
- 13. (0.00002) RY*( 4) C 1 s( 32.38%)p 2.09( 67.62%)\r
- 14. (0.00117) RY*( 1) N 2 s( 1.48%)p66.74( 98.52%)\r
- 0.0000 -0.0067 0.1213 0.0062 0.0380\r
- 0.0166 0.9917 0.0000 0.0000\r
- 15. (0.00044) RY*( 2) N 2 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 -0.0132 0.9999\r
- 16. (0.00038) RY*( 3) N 2 s( 33.41%)p 1.99( 66.59%)\r
- 0.0000 0.0133 0.5779 0.0087 -0.8150\r
- -0.0120 -0.0392 0.0000 0.0000\r
- 17. (0.00002) RY*( 4) N 2 s( 65.14%)p 0.54( 34.86%)\r
- 18. (0.00177) RY*( 1) H 3 s(100.00%)\r
- 0.0000 1.0000\r
- 19. (0.00096) RY*( 1) H 4 s(100.00%)\r
- -0.0008 1.0000\r
- 20. (0.00096) RY*( 1) H 5 s(100.00%)\r
- -0.0008 1.0000\r
- 21. (0.00122) RY*( 1) H 6 s(100.00%)\r
- -0.0031 1.0000\r
- 22. (0.00122) RY*( 1) H 7 s(100.00%)\r
- -0.0031 1.0000\r
- 23. (1.02290) BD*( 1) C 1- N 2 \r
- ( 92.34%) 0.9609* C 1 s( 0.63%)p99.99( 99.37%)\r
- -0.0001 -0.0770 -0.0186 0.5107 -0.0551\r
- 0.8520 -0.0632 0.0000 0.0000\r
- ( 7.66%) -0.2768* N 2 s( 19.31%)p 4.18( 80.69%)\r
- 0.0000 0.4395 -0.0001 -0.1175 -0.0067\r
- 0.8905 -0.0110 0.0000 0.0000\r
- 24. (0.22583) BD*( 2) C 1- N 2 \r
- ( 60.86%) 0.7801* C 1 s( 36.80%)p 1.72( 63.20%)\r
- -0.0004 -0.6055 -0.0371 -0.7047 -0.0632\r
- 0.3594 -0.0471 0.0000 0.0000\r
- ( 39.14%) -0.6256* N 2 s( 19.33%)p 4.17( 80.67%)\r
- -0.0001 -0.4396 0.0011 0.8364 -0.0016\r
- 0.3271 -0.0137 0.0000 0.0000\r
- 25. (0.01415) BD*( 1) C 1- H 4 \r
- ( 38.98%) 0.6244* C 1 s( 31.10%)p 2.22( 68.90%)\r
- -0.0001 -0.5577 -0.0006 0.3480 -0.0095\r
- -0.2603 -0.0094 -0.7070 0.0103\r
- ( 61.02%) -0.7811* H 4 s(100.00%)\r
- -1.0000 -0.0008\r
- 26. (0.01415) BD*( 1) C 1- H 5 \r
- ( 38.98%) 0.6244* C 1 s( 31.10%)p 2.22( 68.90%)\r
- -0.0001 -0.5577 -0.0006 0.3480 -0.0095\r
- -0.2603 -0.0094 0.7070 -0.0103\r
- ( 61.02%) -0.7811* H 5 s(100.00%)\r
- -1.0000 -0.0008\r
- 27. (0.01394) BD*( 1) N 2- H 6 \r
- ( 31.54%) 0.5616* N 2 s( 30.67%)p 2.26( 69.33%)\r
- 0.0000 -0.5538 -0.0005 -0.3785 -0.0165\r
- 0.2232 -0.0044 0.7070 0.0093\r
- ( 68.46%) -0.8274* H 6 s(100.00%)\r
- -1.0000 -0.0031\r
- 28. (0.01394) BD*( 1) N 2- H 7 \r
- ( 31.54%) 0.5616* N 2 s( 30.67%)p 2.26( 69.33%)\r
- 0.0000 -0.5538 -0.0005 -0.3785 -0.0165\r
- 0.2232 -0.0044 -0.7070 -0.0093\r
- ( 68.46%) -0.8274* H 7 s(100.00%)\r
- -1.0000 -0.0031\r
- \r
- </pre>\r
-<p>\r
- One can see that the $CHOOSE resonance structure is significantly\r
-inferior to the principal resonance structure \r
-found by the default NBO search in \r
-Section A.3. About 1.333e, or 7.4% of the electron density,\r
-is found in non-Lewis NBOs of \r
-the $CHOOSE structure (compared to 0.05e, or 0.3%, for\r
-the principal structure). Particularly defective is the hydride\r
-'lone pair' (NBO 9), which has less than half the \r
-expected occupancy (0.81453e). The C-N <img src=pi.gif> bond (NBO 1) is seen\r
-to be more than 92% polarized toward N, indicative of essential\r
-lone pair character. \r
-<p>\r
- Note that structural elements shared by the two resonance\r
-structures (e.g., the two N-H bonds, which are common to\r
-both structures) need not have identical\r
-forms, since each detail of the NBOs \r
-is optimized with respect to the overall structure.\r
-<p>\r
-<i>B.6.10 NBO Energetic Analysis ($DEL Keylist)</i>\r
-<p>\r
- The NBO energetic analysis with deletions ($DEL keylist) will be\r
-illustrated with two simple examples for RHF/3-21G methylamine\r
-(Section A.3).\r
-<p>\r
- The first example is the "NOSTAR" option (type 4,\r
-Section B.5), requesting deletion\r
-of all non-Lewis orbitals, and hence leading to the energy of the\r
-idealized natural Lewis structure. The $DEL keylist in this case is\r
- <pre>\r
- $DEL NOSTAR $END\r
-\r
-</pre>This leads to the output shown below:\r
-<p>\r
- <pre>\r
-\r
-NOSTAR: Delete all Rydberg/antibond NBOs\r
-Deletion of the following orbitals from the NBO Fock matrix:\r
- 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28\r
-\r
-Occupations of bond orbitals:\r
-\r
- Orbital No deletions This deletion Change\r
-------------------------------------------------------------------------------\r
- 1. BD ( 1) C 1- N 2 1.99858 2.00000 0.00142\r
- 2. BD ( 1) C 1- H 3 1.99860 2.00000 0.00140\r
- 3. BD ( 1) C 1- H 4 1.99399 2.00000 0.00601\r
- 4. BD ( 1) C 1- H 5 1.99399 2.00000 0.00601\r
- 5. BD ( 1) N 2- H 6 1.99442 2.00000 0.00558\r
- 6. BD ( 1) N 2- H 7 1.99442 2.00000 0.00558\r
- 7. CR ( 1) C 1 1.99900 2.00000 0.00100\r
- 8. CR ( 1) N 2 1.99953 2.00000 0.00047\r
- 9. LP ( 1) N 2 1.97795 2.00000 0.02205\r
- 10. RY*( 1) C 1 0.00105 0.00000 -0.00105\r
- 11. RY*( 2) C 1 0.00034 0.00000 -0.00034\r
- 12. RY*( 3) C 1 0.00022 0.00000 -0.00022\r
- 13. RY*( 4) C 1 0.00002 0.00000 -0.00002\r
- 14. RY*( 1) N 2 0.00116 0.00000 -0.00116\r
- 15. RY*( 2) N 2 0.00044 0.00000 -0.00044\r
- 16. RY*( 3) N 2 0.00038 0.00000 -0.00038\r
- 17. RY*( 4) N 2 0.00002 0.00000 -0.00002\r
- 18. RY*( 1) H 3 0.00178 0.00000 -0.00178\r
- 19. RY*( 1) H 4 0.00096 0.00000 -0.00096\r
- 20. RY*( 1) H 5 0.00096 0.00000 -0.00096\r
- 21. RY*( 1) H 6 0.00122 0.00000 -0.00122\r
- 22. RY*( 1) H 7 0.00122 0.00000 -0.00122\r
- 23. BD*( 1) C 1- N 2 0.00016 0.00000 -0.00016\r
- 24. BD*( 1) C 1- H 3 0.01569 0.00000 -0.01569\r
- 25. BD*( 1) C 1- H 4 0.00769 0.00000 -0.00769\r
- 26. BD*( 1) C 1- H 5 0.00769 0.00000 -0.00769\r
- 27. BD*( 1) N 2- H 6 0.00426 0.00000 -0.00426\r
- 28. BD*( 1) N 2- H 7 0.00426 0.00000 -0.00426\r
-\r
-NEXT STEP: Evaluate the energy of the new density matrix\r
- that has been constructed from the deleted NBO\r
- Fock matrix by doing one SCF cycle.\r
-\r
-------------------------------------------------------------------------------\r
- Energy of deletion : -94.618081014\r
- Total SCF energy : -94.679444944\r
- -------------------\r
- Energy change : 0.061364 a.u., 38.506 kcal/mol\r
-\r
- </pre>\r
-<p>\r
- In the output above, the NBO program first enumerates the 19 NBOs\r
-to be deleted by the "NOSTAR" request, then gives the complete list\r
-of NBOs with their occupancies before ("no deletions") and after \r
-("this deletion") deletions, with the\r
-net change for each. For this NOSTAR deletion, each of the\r
-nine Lewis NBOs (1-9) necessarily gets 2.0000 electrons, and each\r
-of the non-Lewis NBOs (10-28) gets occupancy 0.0000. The program\r
-than reports the energy (-94.618081 a.u.) obtained from a single\r
-pass through the SCF evaluator with the modified density matrix. In\r
-this case, deletion of the 19 non-Lewis orbitals led to an energy\r
-change of only 0.061364 a.u. (38.5 kcal/mol), less than 0.07% of the\r
-total energy.\r
-<p>\r
- The next example is a more selective set of deletions between\r
-'chemical fragments' (type 9), selected by the $DEL keylist input\r
-shown below:\r
- <pre>\r
- $DEL \r
- ZERO 2 ATOM BLOCKS\r
- 4 BY 3\r
- 1 3 4 5\r
- 2 6 7\r
- 3 BY 4\r
- 2 6 7\r
- 1 3 4 5\r
- $END\r
-\r
-</pre>This specifies removal of all delocalizing interactions from\r
-Lewis NBOs of the methyl fragment (atoms 1,3,4,5) into non-Lewis\r
-NBOs of the amine fragment (atoms 2,6,7), or vice versa. The\r
-NBO output for this example is shown below:\r
-<p>\r
- <pre>\r
-\r
-Zero delocalization from NBOs localized on atoms:\r
- 1 3 4 5\r
-to NBOs localized on atoms:\r
- 2 6 7\r
- (NBOs in common to the two groups of atoms left out)\r
-Zero delocalization from NBOs localized on atoms:\r
- 2 6 7\r
-to NBOs localized on atoms:\r
- 1 3 4 5\r
- (NBOs in common to the two groups of atoms left out)\r
-Deletion of the NBO Fock matrix elements between orbitals:\r
- 2 3 4 7\r
-and orbitals:\r
- 14 15 16 17 21 22 27 28\r
-Deletion of the NBO Fock matrix elements between orbitals:\r
- 5 6 8 9\r
-and orbitals:\r
- 10 11 12 13 18 19 20 24 25 26\r
-\r
-Occupations of bond orbitals:\r
-\r
- Orbital No deletions This deletion Change\r
-------------------------------------------------------------------------------\r
- 1. BD ( 1) C 1- N 2 1.99858 1.99860 0.00002\r
- 2. BD ( 1) C 1- H 3 1.99860 1.99937 0.00077\r
- 3. BD ( 1) C 1- H 4 1.99399 1.99911 0.00512\r
- 4. BD ( 1) C 1- H 5 1.99399 1.99911 0.00512\r
- 5. BD ( 1) N 2- H 6 1.99442 1.99979 0.00537\r
- 6. BD ( 1) N 2- H 7 1.99442 1.99979 0.00537\r
- 7. CR ( 1) C 1 1.99900 1.99919 0.00019\r
- 8. CR ( 1) N 2 1.99953 1.99974 0.00021\r
- 9. LP ( 1) N 2 1.97795 1.99996 0.02201\r
- 10. RY*( 1) C 1 0.00105 0.00016 -0.00090\r
- 11. RY*( 2) C 1 0.00034 0.00000 -0.00033\r
- 12. RY*( 3) C 1 0.00022 0.00002 -0.00020\r
- 13. RY*( 4) C 1 0.00002 0.00002 0.00000\r
- 14. RY*( 1) N 2 0.00116 0.00004 -0.00112\r
- 15. RY*( 2) N 2 0.00044 0.00000 -0.00044\r
- 16. RY*( 3) N 2 0.00038 0.00003 -0.00035\r
- 17. RY*( 4) N 2 0.00002 0.00001 -0.00001\r
- 18. RY*( 1) H 3 0.00178 0.00088 -0.00090\r
- 19. RY*( 1) H 4 0.00096 0.00057 -0.00038\r
- 20. RY*( 1) H 5 0.00096 0.00057 -0.00038\r
- 21. RY*( 1) H 6 0.00122 0.00057 -0.00065\r
- 22. RY*( 1) H 7 0.00122 0.00057 -0.00065\r
- 23. BD*( 1) C 1- N 2 0.00016 0.00034 0.00018\r
- 24. BD*( 1) C 1- H 3 0.01569 0.00027 -0.01542\r
- 25. BD*( 1) C 1- H 4 0.00769 0.00055 -0.00714\r
- 26. BD*( 1) C 1- H 5 0.00769 0.00055 -0.00714\r
- 27. BD*( 1) N 2- H 6 0.00426 0.00009 -0.00417\r
- 28. BD*( 1) N 2- H 7 0.00426 0.00009 -0.00417\r
-\r
-NEXT STEP: Evaluate the energy of the new density matrix\r
- that has been constructed from the deleted NBO\r
- Fock matrix by doing one SCF cycle.\r
-\r
-------------------------------------------------------------------------------\r
- Energy of deletion : -94.635029232\r
- Total SCF energy : -94.679444944\r
- -------------------\r
- Energy change : 0.044416 a.u., 27.871 kcal/mol\r
-\r
- </pre>\r
-<p>\r
- The output first lists the various orbitals and Fock matrix\r
-elements affected by this deletion, then the 'before' and 'after'\r
-occupancies and net changes for each NBO. In this case, one can\r
-see that the principal effect of the deletion was increased occupancy\r
-(+0.022) of the nitrogen lone pair, NBO 9, and depleted occupancy\r
-(-0.015) of the antiperiplanar <img src=sigma.gif>*<sub>C<sub>1</sub>H<sub>3</sub></sub>\r
-antibond, NBO 24, with somewhat lesser depletion (-0.007)\r
-of the other two C-H antibonds. The total energy change (loss of\r
-delocalization energy) associated with this deletion \r
-was 27.9 kcal/mol.\r
-<p>\r
- To further pinpoint the source of this delocalization, one could\r
-do more selective deletions of individual orbitals or Fock\r
-matrix elements. For example, if one uses \r
-deletion type 2 (deletion of a single\r
-Fock matrix element, Section B.5.2) to delete the \r
-(9,24) element associated with the\r
-<i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>C<sub>1</sub>H<sub>3</sub></sub> interaction, one finds\r
-a deletion energy of 7.06 kcal/mol associated with this \r
-interaction alone. [This value may be compared with the simple second-order\r
-perturbative estimate (8.13 kcal/mol) of the\r
-<i>n</i><sub>N</sub> <img src=rarr.gif> <img src=sigma.gif>*<sub>C<sub>1</sub>H<sub>3</sub></sub> (9<img src=rarr.gif>24) interaction\r
-that was noted in Section A.3.5.]\r
-<p>\r
-<i>B.6.11 Open-Shell UHF Output: Methyl Radical</i>\r
-<p>\r
- Open-shell NBO output will be illustrated with the simple\r
-example of the planar methyl radical (CH<sub>3</sub>), treated at the UHF/6-31G*\r
-level (<i>R</i><sub>CH</sub> = 1.0736 Å). In \r
-the open-shell case, one obtains\r
-two separate NPA and NBO listings, one for the <img src=alpha.gif> and one for \r
-the <img src=beta.gif> spin set, corresponding to the "different Lewis structures\r
-for different spins" description. A portion of the NBO output for\r
-the <img src=alpha.gif> spin manifold is reproduced below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS, alpha spin orbitals:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 0.90 4.99903 0.00097 1 3 0 1 0 0 0.00\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
---------------------------------------------------------\r
- Core 0.99984 ( 99.984% of 1)\r
- Valence Lewis 3.99919 ( 99.980% of 4)\r
- ================== ============================\r
- Total Lewis 4.99903 ( 99.981% of 5)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.00081 ( 0.016% of 5)\r
- Rydberg non-Lewis 0.00016 ( 0.003% of 5)\r
- ================== ============================\r
- Total non-Lewis 0.00097 ( 0.019% of 5)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (0.99973) BD ( 1) C 1- H 2 \r
- ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 0.5772 -0.0070 0.0000 -0.4076\r
- -0.0110 0.7060 0.0191 0.0000 0.0000\r
- -0.0338 0.0000 0.0000 -0.0195 -0.0090\r
- ( 38.86%) 0.6233* H 2 s(100.00%)\r
- 1.0000 0.0080\r
- 2. (0.99973) BD ( 1) C 1- H 3 \r
- ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 0.5772 -0.0070 0.0000 -0.4076\r
- -0.0110 -0.7060 -0.0191 0.0000 0.0000\r
- 0.0338 0.0000 0.0000 -0.0195 -0.0090\r
- ( 38.86%) 0.6233* H 3 s(100.00%)\r
- 1.0000 0.0080\r
- 3. (0.99973) BD ( 1) C 1- H 4 \r
- ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 0.5772 -0.0070 0.0000 0.8153\r
- 0.0221 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0391 -0.0090\r
- ( 38.86%) 0.6233* H 4 s(100.00%)\r
- 1.0000 0.0080\r
- 4. (0.99984) CR ( 1) C 1 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 5. (1.00000) LP ( 1) C 1 s( 0.00%)p 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.9978 -0.0668\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 6. (0.00000) RY*( 1) C 1 s(100.00%)p 0.00( 0.00%)d 0.00( 0.00%)\r
- 7. (0.00000) RY*( 2) C 1 s(100.00%)\r
- 8. (0.00000) RY*( 3) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 9. (0.00000) RY*( 4) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 10. (0.00000) RY*( 5) C 1 s( 0.00%)p 1.00(100.00%)\r
- 11. (0.00000) RY*( 6) C 1 s( 0.00%)p 1.00( 0.23%)d99.99( 99.77%)\r
- 12. (0.00000) RY*( 7) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 13. (0.00000) RY*( 8) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 14. (0.00000) RY*( 9) C 1 s( 0.00%)p 1.00( 0.23%)d99.99( 99.77%)\r
- 15. (0.00000) RY*(10) C 1 s( 0.02%)p 0.00( 0.00%)d99.99( 99.98%)\r
- 16. (0.00005) RY*( 1) H 2 s(100.00%)\r
- 17. (0.00005) RY*( 1) H 3 s(100.00%)\r
- 18. (0.00005) RY*( 1) H 4 s(100.00%)\r
- 19. (0.00027) BD*( 1) C 1- H 2 \r
- ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 -0.5772 0.0070 0.0000 0.4076\r
- 0.0110 -0.7060 -0.0191 0.0000 0.0000\r
- 0.0338 0.0000 0.0000 0.0195 0.0090\r
- ( 61.14%) -0.7819* H 2 s(100.00%)\r
- -1.0000 -0.0080\r
- 20. (0.00027) BD*( 1) C 1- H 3 \r
- ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 -0.5772 0.0070 0.0000 0.4076\r
- 0.0110 0.7060 0.0191 0.0000 0.0000\r
- -0.0338 0.0000 0.0000 0.0195 0.0090\r
- ( 61.14%) -0.7819* H 3 s(100.00%)\r
- -1.0000 -0.0080\r
- 21. (0.00027) BD*( 1) C 1- H 4 \r
- ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%)\r
- 0.0000 -0.5772 0.0070 0.0000 -0.8153\r
- -0.0221 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 -0.0391 0.0090\r
- ( 61.14%) -0.7819* H 4 s(100.00%)\r
- -1.0000 -0.0080\r
-\r
- </pre>\r
-<p>\r
- As can be seen in the output, the NBO spin-orbital \r
-occupancy threshold was set at 0.90 (rather than 1.90), and the\r
-occupancies of <img src=alpha.gif> Lewis spin-NBOs (1-5) are about 1.0000, but\r
-other aspects of the output are familiar. Note the slight admixture\r
-of <i>d</i>-character (0.16%) in the <img src=sigma.gif><sub>CH</sub> bond hybrids \r
-(NBOs 1-3), whereas the out-of-plane radical non-bonded orbital (NBO 5) has\r
-pure <i>p</i>-character.\r
-<p>\r
- The NBO output for the <img src=beta.gif> ('ionized') spin set then follows:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS, beta spin orbitals:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 0.90 3.99981 0.00019 1 3 0 0 0 0 0.00\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
---------------------------------------------------------\r
- Core 0.99985 ( 99.985% of 1)\r
- Valence Lewis 2.99996 ( 99.999% of 3)\r
- ================== ============================\r
- Total Lewis 3.99981 ( 99.995% of 4)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.00002 ( 0.000% of 4)\r
- Rydberg non-Lewis 0.00017 ( 0.004% of 4)\r
- ================== ============================\r
- Total non-Lewis 0.00019 ( 0.005% of 4)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (0.99999) BD ( 1) C 1- H 2 \r
- ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- 0.0000 0.5762 0.0080 0.0000 -0.4076\r
- -0.0125 0.7059 0.0217 0.0000 0.0000\r
- -0.0345 0.0000 0.0000 -0.0199 -0.0350\r
- ( 44.20%) 0.6649* H 2 s(100.00%)\r
- 1.0000 -0.0069\r
- 2. (0.99999) BD ( 1) C 1- H 3 \r
- ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- 0.0000 0.5762 0.0080 0.0000 -0.4076\r
- -0.0125 -0.7059 -0.0217 0.0000 0.0000\r
- 0.0345 0.0000 0.0000 -0.0199 -0.0350\r
- ( 44.20%) 0.6649* H 3 s(100.00%)\r
- 1.0000 -0.0069\r
- 3. (0.99999) BD ( 1) C 1- H 4 \r
- ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- 0.0000 0.5762 0.0080 0.0000 0.8151\r
- 0.0251 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0399 -0.0350\r
- ( 44.20%) 0.6649* H 4 s(100.00%)\r
- 1.0000 -0.0069\r
- 4. (0.99985) CR ( 1) C 1 s(100.00%)\r
- 1.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 5. (0.00002) LP*( 1) C 1 s( 10.35%)p 0.00( 0.00%)d 8.66( 89.65%)\r
- 6. (0.00000) RY*( 1) C 1 s( 98.99%)p 0.00( 0.00%)d 0.01( 1.01%)\r
- 7. (0.00000) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 8. (0.00000) RY*( 3) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 9. (0.00000) RY*( 4) C 1 s( 0.00%)p 1.00(100.00%)\r
- 10. (0.00000) RY*( 5) C 1 s( 0.00%)p 1.00(100.00%)\r
- 11. (0.00000) RY*( 6) C 1 s( 0.00%)p 1.00( 0.24%)d99.99( 99.76%)\r
- 12. (0.00000) RY*( 7) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 13. (0.00000) RY*( 8) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 14. (0.00000) RY*( 9) C 1 s( 0.00%)p 1.00( 0.24%)d99.99( 99.76%)\r
- 15. (0.00000) RY*(10) C 1 s( 91.02%)p 0.00( 0.00%)d 0.10( 8.98%)\r
- 16. (0.00006) RY*( 1) H 2 s(100.00%)\r
- 17. (0.00006) RY*( 1) H 3 s(100.00%)\r
- 18. (0.00006) RY*( 1) H 4 s(100.00%)\r
- 19. (0.00000) BD*( 1) C 1- H 2 \r
- ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- ( 55.80%) -0.7470* H 2 s(100.00%)\r
- 20. (0.00000) BD*( 1) C 1- H 3 \r
- ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- ( 55.80%) -0.7470* H 3 s(100.00%)\r
- 21. (0.00000) BD*( 1) C 1- H 4 \r
- ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%)\r
- ( 55.80%) -0.7470* H 4 s(100.00%)\r
-\r
- </pre>\r
-<p>\r
- The principal difference to be seen is that the radical\r
-orbital (NBO 5) is essentially empty in this spin set, and\r
-the polarization of the <img src=sigma.gif><sub>CH</sub> bonds is somewhat altered\r
-(about 55.8% on the C atom in the <img src=beta.gif> set set, \r
-<i>vs.</i> 61.1% in the <img src=alpha.gif> set). [In other cases, the\r
-<img src=alpha.gif> and <img src=beta.gif> NBO Lewis structures might differ even\r
-in the number and location of 1-c (non-bonding) and 2-c (bond)\r
-structural elements.] Note that the overall quality of the open-shell\r
-natural Lewis structure description (> 99.9%) is\r
-comparable to that of ordinary closed-shell molecules, and the\r
-interpretation of the NBO output follows\r
-familiar lines.\r
-<p>\r
-<center>\r
-<b>WARNING</b>\r
-</center>\r
-<p>\r
-You should not attempt to analyze an open-shell wavefunction with an\r
-ESS method that produces only the "spinless" (spin-averaged) density\r
-matrix, rather than the separate density matrices for <img src=alpha.gif> \r
-and <img src=beta.gif> spin. Although NAOs and their total populations are\r
-calculated correctly from the spinless density matrix, NBOs\r
-and NLMOs are not. NBO analysis of an open-shell \r
-spinless density matrix is a fundamental misuse\r
-of the program.\r
-<p>\r
-<i>B.6.12 Effective Core Potential: Cu<sub>2</sub> Dimer</i>\r
-<p>\r
- To illustrate some of the variations of NBO output associated\r
-with use of effective core potentials (ECP) and inclusion of\r
-<i>d</i> orbitals, we use the example of the copper dimer Cu<sub>2</sub>\r
-(<i>R</i> = 2.2195 Å),\r
-treated at the RHF level with a Hay-Wadt ECP and valence DZ\r
-basis (RHF/LANL1DZ), carried out with\r
-the GAUSSIAN-88 system. (The wavefunction returned by GAUSSIAN-88\r
-in this case corresponds\r
-to an excited state configuration of Cu<sub>2</sub>.) Since the \r
-NBO program communicates directly with\r
-the ESS program for details\r
-about the ECP, no special keywords are necessary.\r
-<p>\r
- Use of an ECP shows up most directly in the NPA portion\r
-of the output, shown below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL POPULATIONS: Natural atomic orbital occupancies \r
- \r
- NAO Atom # lang Type(AO) Occupancy Energy \r
----------------------------------------------------------\r
- 1 Cu 1 s Val( 4s) 0.94240 -0.26321\r
- 2 Cu 1 s Ryd( 5s) 0.00019 0.92165\r
- 3 Cu 1 px Ryd( 4p) 0.99604 -0.06989\r
- 4 Cu 1 px Ryd( 5p) 0.00001 0.09916\r
- 5 Cu 1 py Ryd( 4p) 0.99604 -0.06989\r
- 6 Cu 1 py Ryd( 5p) 0.00001 0.09916\r
- 7 Cu 1 pz Ryd( 5p) 0.05481 1.09062\r
- 8 Cu 1 pz Ryd( 4p) 0.00062 0.52821\r
- 9 Cu 1 dxy Val( 3d) 0.00000 -0.36077\r
- 10 Cu 1 dxy Ryd( 4d) 0.00000 0.72280\r
- 11 Cu 1 dxz Val( 3d) 1.99997 -1.29316\r
- 12 Cu 1 dxz Ryd( 4d) 0.00398 0.75681\r
- 13 Cu 1 dyz Val( 3d) 1.99997 -1.29316\r
- 14 Cu 1 dyz Ryd( 4d) 0.00398 0.75681\r
- 15 Cu 1 dx2y2 Val( 3d) 1.99939 -1.38791\r
- 16 Cu 1 dx2y2 Ryd( 4d) 0.00061 0.67825\r
- 17 Cu 1 dz2 Val( 3d) 1.99890 -1.26114\r
- 18 Cu 1 dz2 Ryd( 4d) 0.00308 1.16392\r
-\r
- 19 Cu 2 s Val( 4s) 0.94240 -0.26321\r
- 20 Cu 2 s Ryd( 5s) 0.00019 0.92165\r
- 21 Cu 2 px Ryd( 4p) 0.99604 -0.06989\r
- 22 Cu 2 px Ryd( 5p) 0.00001 0.09916\r
- 23 Cu 2 py Ryd( 4p) 0.99604 -0.06989\r
- 24 Cu 2 py Ryd( 5p) 0.00001 0.09916\r
- 25 Cu 2 pz Ryd( 5p) 0.05481 1.09062\r
- 26 Cu 2 pz Ryd( 4p) 0.00062 0.52821\r
- 27 Cu 2 dxy Val( 3d) 0.00000 -0.36077\r
- 28 Cu 2 dxy Ryd( 4d) 0.00000 0.72280\r
- 29 Cu 2 dxz Val( 3d) 1.99997 -1.29316\r
- 30 Cu 2 dxz Ryd( 4d) 0.00398 0.75681\r
- 31 Cu 2 dyz Val( 3d) 1.99997 -1.29316\r
- 32 Cu 2 dyz Ryd( 4d) 0.00398 0.75681\r
- 33 Cu 2 dx2y2 Val( 3d) 1.99939 -1.38791\r
- 34 Cu 2 dx2y2 Ryd( 4d) 0.00061 0.67825\r
- 35 Cu 2 dz2 Val( 3d) 1.99890 -1.26114\r
- 36 Cu 2 dz2 Ryd( 4d) 0.00308 1.16392\r
-\r
-[ 36 electrons found in the effective core potential]\r
-\r
-WARNING: Population inversion found on atom Cu 1\r
- Population inversion found on atom Cu 2\r
-\r
-\r
-Summary of Natural Population Analysis: \r
- \r
- Natural Population \r
- Natural -----------------------------------------------\r
- Atom # Charge Core Valence Rydberg Total\r
------------------------------------------------------------------------\r
- Cu 1 0.00000 18.00000 8.94064 2.05936 29.00000\r
- Cu 2 0.00000 18.00000 8.94064 2.05936 29.00000\r
-=======================================================================\r
- * Total * 0.00000 36.00000 17.88127 4.11873 58.00000\r
-\r
- Natural Population \r
---------------------------------------------------------\r
- Effective Core 36.00000\r
- Valence 17.88127 ( 81.2785% of 22)\r
- Natural Minimal Basis 53.88127 ( 92.8987% of 58)\r
- Natural Rydberg Basis 4.11873 ( 7.1013% of 58)\r
---------------------------------------------------------\r
-\r
- Atom # Natural Electron Configuration\r
-----------------------------------------------------------------------------\r
- Cu 1 [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)\r
- Cu 2 [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)\r
- \r
- </pre>\r
-<p>\r
- As noted below the first NPA table, 36 electrons were found\r
-in the ECP, so the labels for NAOs in the table begin with the\r
-designations 4<i>s</i>, 5<i>s</i>, etc. of the presumed extra-core\r
-electrons. The ECP electrons are duly entered in the NPA tables\r
-(labelled as "effective core" in the NPA summary table)\r
-as part of the total Lewis occupancy,\r
-and are taken into proper account in assigning atomic charges. The\r
-NPA output in this case includes a "population inversion" message to\r
-warn that one or more NAO occupancies are not ordered in accordance\r
-with the energy order [e.g., the 3<i>d</i><sub>xy</sub> orbital (NAO 9)\r
-is unoccupied in this excited configuration, although\r
-its energy lies below the occupied 4<i>s</i>, 4<i>p</i><sub>y</sub>, 4<i>p</i><sub>z</sub>\r
-levels.]\r
-<p>\r
-<p>\r
- The main ECP effect in the NBO portion of the output is the\r
-omission of core NBOs, as illustrated below:\r
-<p>\r
- <pre>\r
-\r
-NATURAL BOND ORBITAL ANALYSIS:\r
-\r
- Occupancies Lewis Structure Low High\r
- Occ. ------------------- ----------------- occ occ\r
- Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev\r
-=============================================================================\r
- 1(1) 1.90 57.99970 0.00030 0 3 0 8 0 0 0.00\r
------------------------------------------------------------------------------\r
-\r
-Structure accepted: No low occupancy Lewis orbitals\r
-\r
---------------------------------------------------------\r
- Effective Core 36.00000\r
- Valence Lewis 21.99970 ( 99.999% of 22)\r
- ================== ============================\r
- Total Lewis 57.99970 ( 99.999% of 58)\r
- -----------------------------------------------------\r
- Valence non-Lewis 0.00000 ( 0.000% of 58)\r
- Rydberg non-Lewis 0.00030 ( 0.001% of 58)\r
- ================== ============================\r
- Total non-Lewis 0.00030 ( 0.001% of 58)\r
---------------------------------------------------------\r
-\r
-\r
- (Occupancy) Bond orbital/ Coefficients/ Hybrids\r
--------------------------------------------------------------------------------\r
- 1. (2.00000) BD ( 1)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%)\r
- 0.9702 -0.0003 0.0000 0.0000 0.0000\r
- 0.0000 -0.2340 0.0245 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0225 0.0530\r
- ( 50.00%) 0.7071*Cu 2 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%)\r
- 0.9702 -0.0003 0.0000 0.0000 0.0000\r
- 0.0000 0.2340 -0.0245 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0225 0.0530\r
- 2. (2.00000) BD ( 2)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- 0.0000 0.0000 0.9980 0.0029 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- -0.0035 -0.0630 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000\r
- ( 50.00%) 0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- 0.0000 0.0000 0.9980 0.0029 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0035 0.0630 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000\r
- 3. (2.00000) BD ( 3)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- 0.0000 0.0000 0.0000 0.0000 0.9980\r
- 0.0029 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 -0.0035 -0.0630 0.0000\r
- 0.0000 0.0000 0.0000\r
- ( 50.00%) 0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- 0.0000 0.0000 0.0000 0.0000 0.9980\r
- 0.0029 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0035 0.0630 0.0000\r
- 0.0000 0.0000 0.0000\r
- 4. (2.00000) LP ( 1)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.9998\r
- -0.0175 0.0000 0.0000\r
- 5. (2.00000) LP ( 2)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0037\r
- -0.0010 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 1.0000 0.0026 0.0000\r
- 0.0000 0.0000 0.0000\r
- 6. (2.00000) LP ( 3)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 0.0037 -0.0010 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 1.0000 0.0026 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000\r
- 7. (1.99985) LP ( 4)Cu 1 s( 0.06%)p 0.02( 0.00%)d99.99( 99.94%)\r
- 0.0231 0.0070 0.0000 0.0000 0.0000\r
- 0.0000 -0.0030 -0.0008 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 -0.9996 -0.0115\r
- 8. (2.00000) LP ( 1)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.9998\r
- -0.0175 0.0000 0.0000\r
- 9. (2.00000) LP ( 2)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 0.0000 0.0000 -0.0037\r
- 0.0010 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 1.0000 0.0026 0.0000\r
- 0.0000 0.0000 0.0000\r
- 10. (2.00000) LP ( 3)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 0.0000 0.0000 -0.0037 0.0010 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 1.0000 0.0026 0.0000 0.0000 0.0000\r
- 0.0000 0.0000 0.0000\r
- 11. (1.99985) LP ( 4)Cu 2 s( 0.06%)p 0.02( 0.00%)d99.99( 99.94%)\r
- 0.0231 0.0070 0.0000 0.0000 0.0000\r
- 0.0000 0.0030 0.0008 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 -0.9996 -0.0115\r
- 12. (0.00015) RY*( 1)Cu 1 s( 63.84%)p 0.51( 32.31%)d 0.06( 3.85%)\r
- -0.1106 0.7913 0.0000 0.0000 0.0000\r
- 0.0000 -0.4699 0.3199 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0064 -0.1962\r
- 13. (0.00000) RY*( 2)Cu 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 14. (0.00000) RY*( 3)Cu 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 15. (0.00000) RY*( 4)Cu 1 s( 31.12%)p 2.21( 68.87%)d 0.00( 0.00%)\r
- 16. (0.00000) RY*( 5)Cu 1 s( 7.79%)p11.84( 92.21%)d 0.00( 0.00%)\r
- 17. (0.00000) RY*( 6)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 18. (0.00000) RY*( 7)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 19. (0.00000) RY*( 8)Cu 1 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%)\r
- 20. (0.00000) RY*( 9)Cu 1 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%)\r
- 21. (0.00000) RY*(10)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 22. (0.00000) RY*(11)Cu 1 s( 3.06%)p 0.35( 1.07%)d31.35( 95.87%)\r
- 23. (0.00015) RY*( 1)Cu 2 s( 63.84%)p 0.51( 32.31%)d 0.06( 3.85%)\r
- -0.1106 0.7913 0.0000 0.0000 0.0000\r
- 0.0000 0.4699 -0.3199 0.0000 0.0000\r
- 0.0000 0.0000 0.0000 0.0000 0.0000\r
- 0.0000 0.0064 -0.1962\r
- 24. (0.00000) RY*( 2)Cu 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 25. (0.00000) RY*( 3)Cu 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%)\r
- 26. (0.00000) RY*( 4)Cu 2 s( 31.12%)p 2.21( 68.87%)d 0.00( 0.00%)\r
- 27. (0.00000) RY*( 5)Cu 2 s( 7.79%)p11.84( 92.21%)d 0.00( 0.00%)\r
- 28. (0.00000) RY*( 6)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 29. (0.00000) RY*( 7)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 30. (0.00000) RY*( 8)Cu 2 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%)\r
- 31. (0.00000) RY*( 9)Cu 2 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%)\r
- 32. (0.00000) RY*(10)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%)\r
- 33. (0.00000) RY*(11)Cu 2 s( 3.06%)p 0.35( 1.07%)d31.35( 95.87%)\r
- 34. (0.00000) BD*( 1)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%)\r
- ( 50.00%) -0.7071*Cu 2 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%)\r
- 35. (0.00000) BD*( 2)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- ( 50.00%) -0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- 36. (0.00000) BD*( 3)Cu 1-Cu 2 \r
- ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
- ( 50.00%) -0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%)\r
-\r
-\r
-\r
-\r
-Natural Bond Orbitals (Summary):\r
-\r
- Principal Delocalizations\r
- NBO Occupancy Energy (geminal,vicinal,remote)\r
-===============================================================================\r
-Molecular unit 1 (Cu2)\r
- 1. BD ( 1)Cu 1-Cu 2 2.00000 -0.53276\r
- 2. BD ( 2)Cu 1-Cu 2 2.00000 -0.21503\r
- 3. BD ( 3)Cu 1-Cu 2 2.00000 -0.21503\r
- 4. LP ( 1)Cu 1 2.00000 -1.38854\r
- 5. LP ( 2)Cu 1 2.00000 -1.29317\r
- 6. LP ( 3)Cu 1 2.00000 -1.29317\r
- 7. LP ( 4)Cu 1 1.99985 -1.26133\r
- 8. LP ( 1)Cu 2 2.00000 -1.38854\r
- 9. LP ( 2)Cu 2 2.00000 -1.29317\r
- 10. LP ( 3)Cu 2 2.00000 -1.29317\r
- 11. LP ( 4)Cu 2 1.99985 -1.26133\r
- 12. RY*( 1)Cu 1 0.00015 0.70166\r
- 13. RY*( 2)Cu 1 0.00000 0.09932\r
- 14. RY*( 3)Cu 1 0.00000 0.09932\r
- 15. RY*( 4)Cu 1 0.00000 1.09217\r
- 16. RY*( 5)Cu 1 0.00000 0.44430\r
- 17. RY*( 6)Cu 1 0.00000 -0.36077\r
- 18. RY*( 7)Cu 1 0.00000 0.72280\r
- 19. RY*( 8)Cu 1 0.00000 0.75266\r
- 20. RY*( 9)Cu 1 0.00000 0.75266\r
- 21. RY*(10)Cu 1 0.00000 0.67888\r
- 22. RY*(11)Cu 1 0.00000 1.26372\r
- 23. RY*( 1)Cu 2 0.00015 0.70166\r
- 24. RY*( 2)Cu 2 0.00000 0.09932\r
- 25. RY*( 3)Cu 2 0.00000 0.09932\r
- 26. RY*( 4)Cu 2 0.00000 1.09217\r
- 27. RY*( 5)Cu 2 0.00000 0.44430\r
- 28. RY*( 6)Cu 2 0.00000 -0.36077\r
- 29. RY*( 7)Cu 2 0.00000 0.72280\r
- 30. RY*( 8)Cu 2 0.00000 0.75266\r
- 31. RY*( 9)Cu 2 0.00000 0.75266\r
- 32. RY*(10)Cu 2 0.00000 0.67888\r
- 33. RY*(11)Cu 2 0.00000 1.26372\r
- 34. BD*( 1)Cu 1-Cu 2 0.00000 0.41179\r
- 35. BD*( 2)Cu 1-Cu 2 0.00000 0.08327\r
- 36. BD*( 3)Cu 1-Cu 2 0.00000 0.08327\r
- -------------------------------\r
- Total Lewis 57.99970 ( 99.9995%)\r
- Valence non-Lewis 0.00000 ( 0.0000%)\r
- Rydberg non-Lewis 0.00030 ( 0.0005%)\r
- -------------------------------\r
- Total unit 1 58.00000 (100.0000%)\r
- Charge unit 1 0.00000\r
- \r
- </pre>\r
-<p>\r
- As the output shows, the NBO tables include reference \r
-to only 11 occupied NBOs, rather than\r
-the 29 that would appear in a full calculation. Semi-empirical \r
-methods that neglect core electrons (AMPAC, etc.) are\r
-handled similarly.\r
-<p>\r
- The output for the Cu<sub>2</sub>\r
-example also illustrates some aspects of the inclusion of <i>d</i> orbitals\r
-in the basis set. NBOs 4-7 and 8-11 represent the 3<i>d</i><sup>8</sup>\r
-subshells on each atom, essentially of pure atomic <i>d</i>\r
-character (except for a small admixture\r
-of <i>p</i> character in NBOs 7, 11). Both\r
-the <img src=sigma.gif><sub>CuCu</sub> bond (NBO 1) and the two <img src=pi.gif><sub>CuCu</sub> bonds \r
-(NBOs 2, 3) have very slight admixtures (< 0.4%) of <i>d</i> \r
-character. The remaining orbitals of predominant <i>d</i> \r
-character (NBOs 17-22 and 28-33) are of negligible occupancy. Note\r
-that the abbreviated "<i>sp<sup><img src=lambda.gif></sup>d<sup><img src=mu.gif></sup></i>" designations\r
-can lead to strange variations among hybrids\r
-of essentially similar character; thus, NBO 20 (<i>p<sup>1.0</sup>d<sup>99.9</sup></i>),\r
-NBO 21 (<i>d</i><sup>1.0</sup>), and NBO 22 (<i>s<sup>3.1</sup>p<sup>0.4</sup>d<sup>31.4</sup></i>)\r
-are all of nearly pure (> 95%) <i>d</i> character, the difference in\r
-labelling stemming from \r
-whether there is sufficient\r
-<i>s</i> or <i>p</i> character (in numerical terms) to express the\r
-hybrid ratios in <i>sp<sup><img src=lambda.gif></sup>d<sup><img src=mu.gif></sup></i> form. Consult \r
-the percentages of <i>s</i>-.\r
-<i>p</i>-, and <i>d</i>-character whenever there is doubt about how to\r
-interpret a particular <i>sp<sup><img src=lambda.gif></sup>d<sup><img src=mu.gif></sup></i> designation.\r
-<p>\r
-<b>B.7 FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM</b>\r
-<p>\r
-<i>B.7.1 Introduction</i>\r
-<p>\r
- The general NBO program, GENNBO, is a stand-alone program which is not\r
-directly attached to an ESS program. Rather, information about the\r
-wavefunction is provided to the core NBO routines by a sequential input\r
-file, FILE47, described in this section.\r
-<p>\r
- Some knowledge of FILE47 is useful even if your NBO program is attached\r
-to an ESS package. If requested (see the ARCHIVE option, Section B.2.5),\r
-the NBO program writes out FILE47 which summarizes all information pertaining\r
-to the computed electronic wavefunction. This file can be subsequently\r
-used as input to the GENNBO program (reassigned as LFN 5)\r
-to repeat the analysis of this\r
-wavefunction; simply include the $NBO, $CORE, and $CHOOSE keylists in\r
-FILE47 and execute GENNBO. You need never recompute the wavefunction to\r
-vary its NBO analysis! In fact, generating the FILE47 input file is a\r
-useful way to archive a wavefunction for future use or reference. [Note:\r
-the GENNBO program can not perform the NBO energetic analysis ($DEL keylist)\r
-since this would require access to the formatted one- and two-electron\r
-integrals of the parent ESS package.]\r
-<p>\r
- If you intend to use the NBO program in conjunction with an ESS package\r
-not supported in this distribution (i.e. for which no custom drivers are\r
-provided), you might consider attaching a routine to your ESS program which\r
-would write the proper form of FILE47 for input into the GENNBO program.\r
-Thus, a two-step process would be required to obtain the NBO analysis of\r
-a wavefunction: (i) the initial calculation of the wavefunction with the\r
-ESS package, writing FILE47; (ii) the NBO analysis using the GENNBO program\r
-with FILE47 as input. Alternatively, you may decide to attach the NBO program\r
-directly to your ESS package by writing your own driver routines. See\r
-the Programmer's Guide, Section C.13, for direction.\r
-<p>\r
- Section B.7.2 describes and illustrates the overall\r
-format of FILE47. Sections B.7.3-B.7.7 detail the entries of the\r
-keylists and datalists that compose this file.\r
-<p>\r
-<i>B.7.2 Format of the FILE47 Input File</i>\r
-<p>\r
- The FILE47 input file is composed of a set of keylists and datalists, each\r
-list beginning with a "$" identifier (e.g. "$BASIS") and ending with\r
-"$END",\r
-<p>\r
-<pre> $BASIS entries $END</pre>\r
-<p>\r
-Individual lists are used to specify basis set information ($BASIS),\r
-density matrix elements ($DENSITY), and so forth. The order of the\r
-lists within FILE47 is immaterial. Entries within each datalist are generally\r
-free format, and may be continued on as many lines as desired. An\r
-exclamation point (!) on any line terminates input from the line, and may\r
-be followed by arbitrary comments. The $GENNBO keylist and\r
-the $COORD, $BASIS, $DENSITY, and $OVERLAP datalists \r
-are required, but the other\r
-datalists ($FOCK, $LCAOMO, $CONTRACT, $DIPOLE) or the standard\r
-NBO keylists ($NBO, $CORE, $CHOOSE) are optional, depending on the requested\r
-application. If the $NBO keylist is not present in FILE47, the default\r
-NBO analysis is performed.\r
-<p>\r
- The entries of each keylist or datalist may be keywords, numerical matrix\r
-elements, or other parameters of prescribed form. A sample FILE47 input\r
-file (for the RHF/3-21G methylamine example of Section A.3) is shown below:\r
- <pre>\r
-\r
- $GENNBO NATOMS=7 NBAS=28 UPPER BODM $END\r
- $NBO NAOMO=PVAL $END\r
- $COORD\r
- Methylamine...Pople-Gordon standard geometry...RHF/3-21G \r
- 6 6 -0.74464 -0.03926 0.00000 ! Carbon\r
- 7 7 0.71885 0.09893 0.00000 ! Nitrogen\r
- 1 1 -1.00976 -1.09653 0.00000 ! Hydrogen\r
- 1 1 -1.15467 0.43814 0.88998 ! Hydrogen\r
- 1 1 -1.15467 0.43814 -0.88998 ! Hydrogen\r
- 1 1 1.09878 -0.34343 -0.82466 ! Hydrogen\r
- 1 1 1.09878 -0.34343 0.82466 ! Hydrogen\r
- $END\r
- $BASIS\r
- CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7\r
- LABEL = 1,1,101,102,103,1,101,102,103,1,1,101,102,103,1,101,102,103,\r
- 1,1,1,1,1,1,1,1,1,1\r
- $END\r
- $CONTRACT\r
- NSHELL = 16\r
- NEXP = 21\r
- NCOMP = 1, 4, 4, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 \r
- NPRIM = 3, 2, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 \r
- NPTR = 1, 4, 6, 7, 10, 12, 13, 15, 16, 18, 16, 18, 19, 21, 19, 21 \r
- EXP = 0.1722560E+03, 0.2591090E+02, 0.5533350E+01, 0.3664980E+01,\r
- 0.7705450E+00, 0.1958570E+00, 0.2427660E+03, 0.3648510E+02,\r
- 0.7814490E+01, 0.5425220E+01, 0.1149150E+01, 0.2832050E+00,\r
- 0.5447178E+01, 0.8245472E+00, 0.1831916E+00, 0.5447178E+01,\r
- 0.8245472E+00, 0.1831916E+00, 0.5447178E+01, 0.8245472E+00,\r
- 0.1831916E+00 \r
- CS = 0.2093132E+01, 0.2936751E+01, 0.1801737E+01, -0.7473843E+00,\r
- 0.7126610E+00, 0.2098285E+00, 0.2624092E+01, 0.3734359E+01,\r
- 0.2353454E+01, -0.1047101E+01, 0.9685501E+00, 0.2766851E+00,\r
- 0.3971513E+00, 0.5579200E+00, 0.1995672E+00, 0.3971513E+00,\r
- 0.5579200E+00, 0.1995672E+00, 0.3971513E+00, 0.5579200E+00,\r
- 0.1995672E+00 \r
- CP = 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.1709178E+01,\r
- 0.8856221E+00, 0.1857223E+00, 0.0000000E+00, 0.0000000E+00,\r
- 0.0000000E+00, 0.2808586E+01, 0.1456735E+01, 0.2944871E+00,\r
- 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00,\r
- 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00,\r
- 0.0000000E+00 \r
- $END\r
- $OVERLAP ! Overlap matrix elements in the AO basis\r
- 0.10000000E+01 0.19144744E+00 0.10000000E+01 . . .\r
- $END\r
- $DENSITY ! Bond-order matrix elements in the AO basis\r
- 0.20363224E+01 0.11085239E+00 0.10393086E+00 . . .\r
- $END\r
- $FOCK ! Fock matrix elements in the AO basis\r
- -0.11127777E+02 -0.28589754E+01 -0.89570272E+00 . . .\r
- $END\r
- $LCAOMO ! AO to MO transformation matrix\r
- -0.57428375E-03 -0.23835711E-02 0.17741799E-02 . . .\r
- $END\r
- $DIPOLE ! dipole matrix elements in the AO basis\r
- -0.14071733E+01 -0.26939974E+00 -0.14071733E+01 . . .\r
- $END\r
-\r
- </pre>\r
-<p>\r
-The nine lists of FILE47 are described in turn in\r
-the following sections, making use of this\r
-example for illustration.\r
-<p>\r
-<i>B.7.3 $GENNBO Keylist</i>\r
-<p>\r
- The $GENNBO keylist (required) contains keywords \r
-essential to the proper execution\r
-of the NBO program. The following is the list of keywords recognized\r
-by this keylist:\r
-<p>\r
-<i>KEYWORD</i> <i>OPTION DESCRIPTION</i>\r
-<p>\r
-REUSE Instructs GENNBO to reuse an old NBO direct-access file, FILE48,\r
-rather than create a new FILE48 from the wavefunction information\r
-contained in the FILE47 datalists. Therefore, if the REUSE keyword\r
-is specified, all datalists in FILE47 will be ignored, but the\r
-$NBO, $CORE, and $CHOOSE keylists will still be recognized. This keyword\r
-preempts all other keywords of the $GENNBO keylist.\r
-<p>\r
-NATOMS Number of atoms in the molecule (required).\r
-<p>\r
-NBAS Number of basis functions (required).\r
-<p>\r
-OPEN Designates an open shell wavefunction. GENNBO will subsequently\r
-read in alpha and beta density, Fock, and MO coefficient matrices.\r
-<p>\r
-ORTHO Indicates that the AO basis set is orthogonal (basis\r
-functions are always assumed normalized). If this keyword is\r
-specified, GENNBO will not read the $OVERLAP datalist. This keyword\r
-is incompatible with $NBO keywords for 'pre-orthogonal'\r
-basis sets (SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, AOPNHO, AOPNBO,\r
-AOPNLMO).\r
-<p>\r
-UPPER Indicates that only the upper triangular portions of the overlap,\r
-density, Fock, and dipole matrices are listed in the their respective\r
-datalists. By default, GENNBO assumes that the full matrices are\r
-given.\r
-<p>\r
-BODM Indicates that the $DENSITY datalist contains the\r
-bond-order matrix ("Fock-Dirac density matrix") rather\r
-than the density matrix (i.e., matrix elements of the\r
-density operator). (In orthogonal AO basis sets, the bond-order matrix\r
-and density matrix are identical, but in nonorthogonal basis sets they\r
-must be distinguished.) By default, GENNBO assumes this datalist contains\r
-the density matrix elements. If "BODM" is included, the datalist\r
-elements are transformed with the AO overlap matrix to produce the\r
-true density matrix.\r
-<p>\r
-BOHR Indicates that the atomic coordinates ($COORD) and the dipole\r
-integrals ($DIPOLE) are in atomic units, rather than the default\r
-angstroms.\r
-<p>\r
-EV Indicates that the Fock matrix elements ($FOCK) have units of\r
-electron volts (eV), rather than the default atomic units (Hartrees).\r
-<p>\r
-CUBICF Instructs GENNBO to use the set of seven cubic <i>f</i>-type functions\r
-rather than the ten Cartesian or seven pure <i>f</i> functions\r
-(cf. Section B.7.5).\r
-<p>\r
-The methylamine sample $GENNBO keylist \r
-specifies 7 atoms, 28 basis\r
-functions, upper triangular matrix input, and $DENSITY datalist containing\r
-the bond-order matrix.\r
-<p>\r
-<i>B.7.4 $COORD Datalist</i>\r
-<p>\r
- The $COORD datalist (required, unless REUSE is\r
-specified in $GENNBO) contains the job title and information indicating\r
-the identity and coordinates of each atom, including missing core electrons\r
-or effective core potentials.\r
-<p>\r
- The first line following the $COORD identifier is an arbitrary\r
-job title, up to 80 characters.\r
-<p>\r
- Subsequent lines are used to specify the\r
-atomic number, the nuclear charge, and the (x,y,z) coordinates of each\r
-atom.\r
-[For example, atom 1 in the methylamine sample input is a carbon\r
-atom (atomic number 6) with nuclear charge 6 and coordinates \r
-x = -0.74464,\r
-y = -0.03926, z = 0.00000, in angstroms.]\r
-Coordinates are assumed to be in angstroms unless the BOHR keyword\r
-appears in the $GENNBO keylist, specifying atomic units. The \r
-atomic number and nuclear charge\r
-are generally identical, but if core electrons are neglected (as in most\r
-semi-empirical treatments) or if effective core potentials (ECP) are employed,\r
-the nuclear charge will be less than the atomic number by the number of\r
-electrons neglected on that particular atom. Thus, for an AMPAC calculation,\r
-in which the two 1<i>s</i> core electron of a carbon atom are neglected, the line\r
-following the job title in the methylamine example would read\r
-<p>\r
-<pre> 6 4 -0.74464 -0.03926 0.00000 ! Carbon</pre>\r
-<p>\r
-where "4" is the effective (valence) nuclear charge of the atom.\r
-<p>\r
-<i>B.7.5 $BASIS Datalist</i>\r
-<p>\r
- The $BASIS datalist (required, unless REUSE is specified\r
-in $GENNBO) provides essential information about the AO basis\r
-functions,\r
-specifying the atomic center and the angular symmetry (<i>s</i>, <i>p</i><sub>x</sub>,\r
-<i>p</i><sub>y</sub>, <i>p</i><sub>z</sub>,\r
-etc.) of each AO. This information is contained \r
-in two arrays in this datalist called CENTER and LABEL.\r
-<p>\r
- The atomic center for each AO is \r
-specified by entering "CENTER=" followed\r
-by the serial number of the atom for each AO, separated by commas or spaces.\r
-[For example, the entry\r
-<p>\r
-<pre> CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7</pre>\r
-<p>\r
-of the methylamine sample file indicates that the first 9 AOs (1-9) are\r
-centered on atom 1 (the carbon atom), the next nine AOs (10-18) on center 2,\r
-and so forth.]\r
-<p>\r
- The angular symmetry for each AO is specified by entering "LABEL="\r
-followed by a symmetry label for each AO, separated by commas or \r
-spaces. The NBO program handles <i>s</i>, <i>p</i>, <i>d</i>,\r
-or <i>f</i> (<i>l</i> = 0-3) basis AOs, of either cartesian or pure angular \r
-symmetry types. The label for each AO is a 3-digit integer of the\r
-form <i>l</i>*100 + <i>k</i> + <i>m</i>, where <i>k</i> is 0 (cartesian) or 50 (pure),\r
-and <i>m</i> is a particular component of the <i>l</i>-type symmetry (see\r
-table below). For\r
-<i>s</i> or <i>p</i> AOs,\r
-the cartesian and pure <i>l</i>-symmetry sets are identical, so each AO can be\r
-labelled in two distinct ways, but\r
-the six cartesian <i>d</i> functions can be transformed to the five pure <i>d</i>\r
-functions plus an additional <i>s</i> function, and the ten cartesian <i>f</i>\r
-functions can be transformed to the seven\r
-pure <i>f</i> functions plus three additional <i>p</i> \r
-functions. Two distinct sets of pure <i>f</i>\r
-functions are recognized, the "standard" [default] set and\r
-the "cubic" set, the latter being used whenever the "CUBICF"\r
-keyword is included in the $GENNBO keylist.\r
- \r
- The labels associated\r
-with each allowed AO function type are tabulated below, \r
-where <i>x, y, z</i> refer to the\r
-specified cartesian axis system:\r
-<p>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=6><hr></td></tr>\r
-<tr><td align=center><i>label</i></td><td align=left><i>AO type</i></td><td align=center><i>label</i></td><td align=left><i>AO type</i></td><td align=center><i>label</i></td><td align=left><i>AO type</i></td></tr>\r
-<tr><td colspan=6><hr></td></tr>\r
-<tr><td align=left colspan=2><u>Pure <i>s, p</i> sets:</u> </td><td align=left colspan=2><u>Cartesian <i>f</i> set:</u> </td><td align=left colspan=2><u>Pure <i>f</i> "cubic" set:</u></td></tr>\r
-<tr><td align=center>1 (51)</td><td align=left><i>s</i></td><td align=center>301</td><td align=left><i>f</i><sub>xxx</sub></td><td align=center>351</td><td align=left><i>f</i>(D1): x(5x<sup>2</sup>-3r<sup>2</sup>)</td></tr>\r
-<tr><td align=center>101 (151)</td><td align=left><i>p</i><sub>x</sub></td><td align=center>302</td><td align=left><i>f</i><sub>xxy</sub></td><td align=center>352</td><td align=left><i>f</i>(D2): y(5y<sup>2</sup>-3r<sup>2</sup>)</td></tr>\r
-<tr><td align=center>102 (152)</td><td align=left><i>p</i><sub>y</sub></td><td align=center>303</td><td align=left><i>f</i><sub>xxz</sub></td><td align=center>353</td><td align=left><i>f</i>(D3): z(5z<sup>2</sup>-3r<sup>2</sup>)</td></tr>\r
-<tr><td align=center>103 (153)</td><td align=left><i>p<sub>z</sub></i></td><td align=center>304</td><td align=left><i>f</i><sub>xyy</sub></td><td align=center>354</td><td align=left><i>f</i>(B): xyz</td></tr>\r
-<tr><td align=center> </td><td align=left> </td><td align=center>305</td><td align=left><i>f</i><sub>xyz</sub></td><td align=center>355</td><td align=left><i>f</i>(E1): x(z<sup>2</sup>-y<sup>2</sup>)</td></tr>\r
-<tr><td align=left colspan=2><u>Cartesian <i>d</i> set:</u> </td><td align=center colspan=1>306</td><td align=left colspan=1><i>f</i><sub>xzz</sub></td><td align=center colspan=1>356</td><td align=left colspan=1><i>f</i>(E2): y(z<sup>2</sup>-x<sup>2</sup>)</td></tr>\r
-<tr><td align=center>201</td><td align=left><i>d</i><sub>xx</sub></td><td align=center>307</td><td align=left><i>f</i><sub>yyy</sub></td><td align=center>357</td><td align=left><i>f</i>(E3): z(x<sup>2</sup>-y<sup>2</sup>)</td></tr>\r
-<tr><td align=center colspan=1>202</td><td align=left colspan=1><i>d</i><sub>xy</sub></td><td align=center colspan=1>308</td><td align=left colspan=1><i>f</i><sub>yyz</sub></td></tr>\r
-<tr><td align=center colspan=1>203</td><td align=left colspan=1><i>d</i><sub>xz</sub></td><td align=center colspan=1>309</td><td align=left colspan=1><i>f</i><sub>yzz</sub></td></tr>\r
-<tr><td align=center colspan=1>204</td><td align=left colspan=1><i>d</i><sub>yy</sub></td><td align=center colspan=1>310</td><td align=left colspan=1><i>f</i><sub>zzz</sub></td></tr>\r
-<tr><td align=center colspan=1>205</td><td align=left colspan=1><i>d</i><sub>yz</sub></td><td align=center colspan=1> </td><td align=left colspan=1> </td></tr>\r
-<tr><td align=center colspan=1>206</td><td align=left colspan=1><i>d</i><sub>zz</sub></td><td align=left colspan=2><u>Pure <i>f</i> "standard" set:</u></td></tr>\r
-<tr><td align=center colspan=1> </td><td align=left colspan=1> </td><td align=center colspan=1>351</td><td align=left colspan=1><i>f</i>(0): z(5z<sup>2</sup>-3r<sup>2</sup>)</td></tr>\r
-<tr><td align=left colspan=2><u>Pure <i>d</i> set:</u> </td><td align=center colspan=1>352</td><td align=left colspan=1><i>f</i>(c1): x(5z<sup>2</sup>-r<sup>2</sup>)</td></tr>\r
-<tr><td align=center colspan=1>251</td><td align=left colspan=1><i>d</i><sub>xy</sub></td><td align=center colspan=1>353</td><td align=left colspan=1><i>f</i>(s1): y(5z<sup>2</sup>-r<sup>2</sup>)</td></tr>\r
-<tr><td align=center colspan=1>252</td><td align=left colspan=1><i>d</i><sub>xz</sub></td><td align=center colspan=1>354</td><td align=left colspan=1><i>f</i>(c2): z(x<sup>2</sup>-y<sup>2</sup>)</td></tr>\r
-<tr><td align=center colspan=1>253</td><td align=left colspan=1><i>d</i><sub>yz</sub></td><td align=center colspan=1>355</td><td align=left colspan=1><i>f</i>(s2): xyz</td></tr>\r
-<tr><td align=center colspan=1>254</td><td align=left colspan=1><i>d<sub>x</sub>2<sub>-y</sub>2</i></td><td align=center colspan=1>356</td><td align=left colspan=1><i>f</i>(c3): x(x<sup>2</sup>-3y<sup>2</sup>)</td></tr>\r
-<tr><td align=center colspan=1>255</td><td align=left colspan=1><i>d<sub>z</sub>2</i> = <i>d<sub>3z</sub>2<sub>-r</sub>2</i></td><td align=center colspan=1>357</td><td align=left colspan=1><i>f</i>(s3): y(3x<sup>2</sup>-y<sup>2</sup>)</td></tr>\r
-<tr><td colspan=6><hr></td></tr>\r
-</table>\r
- \r
-[For example, in the methylamine sample input,\r
-the first nine entries of the LABEL array,\r
-<p>\r
-<pre> LABEL = 1,1,101,102,103,1,101,102,103,. . .</pre>\r
-<p>\r
-identify the first 9 AOs (of carbon) as being of <i>s</i>, <i>s</i>, <i>p</i><sub>x</sub>, <i>p</i><sub>y</sub>, <i>p</i><sub>z</sub>,\r
-<i>s</i>, <i>p</i><sub>x</sub>, <i>p</i><sub>y</sub>, <i>p</i><sub>z</sub> type, respectively.]\r
-<p>\r
-<i>B.7.6 $CONTRACT Datalist</i>\r
-<p>\r
- The $CONTRACT datalist (optional)\r
-contains additional information about the contraction coefficients\r
-and orbital exponents of AO basis functions. This information is\r
-not used in the NBO analysis of a wavefunction. However, if the\r
-AOINFO or PLOT keyword is specified in the $NBO keylist (See Section B.2.5),\r
-the GENNBO driver routines write out this information to\r
-an external file (LFN 31) in the proper format for orbital plotting with\r
-the ORBPLOT program. Omit the $CONTRACT datalist if you do not\r
-intend to make orbital plots.\r
-<p>\r
- Two integers must be initially given: NSHELL (the number of shells of\r
-basis functions) and NEXP (the number of orbital exponents).\r
-[In the methylamine example, there are 16 shells of basis functions and 27\r
-orbital exponents.] These integers should precede \r
-the remainder of the basis set information\r
-of this datalist.\r
-<p>\r
- The number of components (basis functions) in each shell is specified in\r
-the NCOMP array. The sum of the components for each shell should equal\r
-the total number of basis functions. This list of components is a\r
-partitioning of the basis function centers and labels (in the $BASIS\r
-datalist) into shells. [For example, in the methylamine sample, the NCOMP array\r
-<p>\r
-<pre> NCOMP = 1,4,4,. . .</pre>\r
-<p>\r
-indicates that the first three shells have a total of 9 (i.e. 1+4+4) basis \r
-functions. These are the 9 AOs (1-9) discussed previously in the $BASIS\r
-datalist.]\r
-<p>\r
- The NPRIM array gives the number of primitive gaussian functions of each\r
-shell. [For the methylamine example, the first three shells of the AO\r
-basis are contractions of\r
-<p>\r
-<pre> NPRIM = 3,2,1,. . .</pre>\r
-<p>\r
-three, two, and one primitives, respectively, corresponding to\r
-the conventional "3-21G" basis set designation.]\r
-<p>\r
- Pointers for each shell are listed in the NPTR array. These pointers\r
-specify the location of the orbital exponents (EXP) and contraction\r
-coefficients (CS, CP, CD, CF) for each shell. [In the sample input file,\r
-<p>\r
-<pre> NPTR = 1,4,6,. . .</pre>\r
-<p>\r
-the orbital exponents and contraction coefficients for the first three\r
-shells begin at elements 1, 4, and 6, respectively.]\r
-<p>\r
- EXP, CS, CP, CD, and CF are free format, real arrays containing the orbital\r
-exponents, and the s, p, d, and f contraction coefficients of the AO basis set.\r
-NEXP elements should appear in each array, and the arrays of contraction\r
-coefficients need only appear if there are basis functions of that particular\r
-symmetry in the basis set. [For example, the 3-21G basis of the sample\r
-methylamine input only has <i>s</i> and <i>p</i> basis functions. Therefore, the\r
-CD and CF arrays are not necessary.]\r
-<p>\r
- The information in the $CONTRACT datalist along with that in the $BASIS\r
-datalist is enough to completely determine the AO basis set. [For example,\r
-the second shell on the methylamine sample contains 4 basis functions\r
-(NCOMP). These are <i>s</i>, <i>p</i><sub>x</sub>, <i>p</i><sub>y</sub>, and <i>p</i><sub>z</sub>\r
-orbitals (LABEL), all centered on atom 1 (CENTER), and each basis function\r
-is a contraction of two primitive gaussians (NPRIM). From NPTR, EXP, CS,\r
-and CP, we find the explicit form of these functions:\r
-<p>\r
-<center>\r
-<img src=phi.gif><sub>s</sub>(<b>r</b>)  = -0.747 e<sup><sup>-3.66 r<sup>2</sup></sup></sup>  + 0.713 e<sup><sup>-0.77 r<sup>2</sup></sup></sup>\r
-<p>\r
-<img src=phi.gif><sub>p<sub>x</sub></sub>(<b>r</b>) = 1.709 x e<sup><sup>-3.66 r<sup>2</sup></sup></sup> + 0.886 x e<sup><sup>-0.77 r<sup>2</sup></sup></sup>\r
-<p>\r
-<img src=phi.gif><sub>p<sub>y</sub></sub>(<b>r</b>) = 1.709 y e<sup><sup>-3.66 r<sup>2</sup></sup></sup> + 0.886 y e<sup><sup>-0.77 r<sup>2</sup></sup></sup>\r
-<p>\r
-<img src=phi.gif><sub>p<sub>z</sub></sub>(<b>r</b>) = 1.709 z e<sup><sup>-3.66 r<sup>2</sup></sup></sup> + 0.886 z e<sup><sup>-0.77 r<sup>2</sup></sup></sup>\r
-<p>\r
-</center>\r
-where <b>r</b>=(x,y,z) is measured in bohr units relative to the cartesian\r
-coordinates of atom 1.]\r
-<p>\r
-<i>B.7.7 Matrix Datalists</i>\r
-<p>\r
- The remaining datalists ($OVERLAP, $DENSITY, $FOCK, $LCAOMO, $DIPOLE)\r
-specify various matrix elements possibly used by the NBO analysis. All \r
-entries in these datalists are free format, with entries separated\r
-by commas or spaces. Only the upper triangular portions of each symmetric\r
-matrix (overlap, density, Fock, dipole) should be provided if the\r
-UPPER keyword is specified in the $GENNBO keylist. The numbering of the\r
-matrix rows and columns must correspond to the ordering of the AOs in \r
-the $BASIS datalist. All three matrices of dipole integrals should appear\r
-in the $DIPOLE datalist, all <i>x</i> integrals before <i>y</i> before <i>z</i>.\r
-<p>\r
- Of the matrix datalists, the $DENSITY datalist is \r
-always required, and\r
-the $OVERLAP datalist is required for all non-orthogonal \r
-AO basis sets, but other datalists are optional (unless implicitly\r
-required by specified keyword options). Nevertheless, it is good practice \r
-to include as many of these datalists\r
-in FILE47 as possible for later use with keyword options which require\r
-them. The following table lists the $NBO keywords that require\r
-each datalist to be included in FILE47:\r
-<p>\r
-<i>Datalist</i> <i>$NBO Keywords Requiring the Datalist</i>\r
-<p>\r
-$OVERLAP SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, \r
-AOPNHO, AOPNBO, AOPNLMO\r
-<p>\r
-$FOCK E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO\r
-<p>\r
-$LCAOMO AOMO, NAOMO, NHOMO, NBOMO, NLMOMO\r
-<p>\r
-$DIPOLE DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE\r
-<p>\r
-$CONTRACT AOINFO, PLOT\r
-<p>\r
- For example, in the methylamine sample input, the keyword "NAOMO=PVAL"\r
-of the $NBO keylist requires that the $LCAOMO datalist be present (in\r
-addition to the $OVERLAP, $DENSITY, and $FOCK datalists used for default\r
-PRINT=2 analysis), but the $DIPOLE datalist might have been omitted in\r
-this case. Inclusion of the $LCAOMO datalist (in addition to the $FOCK\r
-datalist) insures that degenerate MOs will be chosen in a prescribed way\r
-for decomposition in terms of other functions.\r
-<p>\r
-<center>\r
-<h2>Section C: NBO PROGRAMMER'S GUIDE</h2>\r
-</center>\r
-<p>\r
-<b>C.1 INTRODUCTION</b>\r
-<p>\r
- Section C constitutes the\r
-programmer's guide to the NBO.SRC program. It\r
-assumes that the user has a thorough familiarity with Fortran\r
-programming and the operations of the NBO program (Sections\r
-A and B) as well as some familiarity with\r
-published algorithms for NAO/NBO/NLMO\r
-determination. This section is intended for the accomplished\r
-programmer who wishes to inquire into the details of the\r
-NBO numerical methods and find the specific source\r
-code associated with individual steps of the published \r
-NAO/NBO/NLMO algorithms or segments of NBO output.\r
-<p>\r
- The NBO.SRC program consists of about 20000 lines, of which\r
-more than 6000 are comment lines (approximately the length of\r
-this manual!). These comment statements provide the principal\r
-documentation of the steps within each subroutine\r
-or function, and should be consulted on questions pertaining\r
-to individual subprograms. \r
-<p>\r
- In this Programmer's Guide, \r
-we focus on global aspects of program organization \r
-and data structure. Individual subprograms\r
-(about 180 in number) are described in capsule form, in the\r
-order in which they appear in the source listing, to\r
-indicate the relationship to \r
-program tasks and the association with specific segments\r
-of NBO output. The capsule descriptions include mention [in\r
-brackets] of numerical thresholds\r
-or possible dependencies on machine precision that are of particular\r
-concern to the programmer. Throughout the Programmer's Guide,\r
-in referring to individual subprograms, we\r
-use the abbreviation "SR" for "subroutine" and "FN" for \r
-"function".\r
-<p>\r
- Sections C.2-C.4 describe the overall NBO.SRC source layout,\r
-labelled COMMON blocks, and I/O structures (including the\r
-FILE48 direct access file). Sections C.5-C.11 then\r
-follow the layout of the source code in describing the principal\r
-groupings of subprograms, with a brief description of each\r
-subprogram. Section C.12 similarly describes subprograms of\r
-the GENNBO stand-alone program. The final section C.13 provides\r
-guidance on attaching the NBO program to a new ESS package not\r
-supported by this distribution.\r
-<p>\r
-<p>\r
-<b>C.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS</b>\r
-<p>\r
- The NBO.SRC program is organized into seven principal groups\r
-of routines (I-VII), described in Sections C.5-C.11, respectively,\r
-as shown below:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=right>Group</td><td align=left>description</td><td align=center>no.</td><td align=center>Section</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=right>I.</td><td align=left>NAO/NBO/NLMO routines</td><td align=center>61</td><td align=center>C.5</td></tr>\r
-<tr><td align=right>II.</td><td align=left>Energy analysis routines</td><td align=center>6</td><td align=center>C.6</td></tr>\r
-<tr><td align=right>III.</td><td align=left>Direct access file (DAF) routines</td><td align=center>41</td><td align=center>C.7</td></tr>\r
-<tr><td align=right>IV.</td><td align=left>Free format input routines</td><td align=center>7</td><td align=center>C.8</td></tr>\r
-<tr><td align=right>V.</td><td align=left>Other I/O routines</td><td align=center>27</td><td align=center>C.9</td></tr>\r
-<tr><td align=right>VI.</td><td align=left>General utility routines</td><td align=center>31</td><td align=center>C.10</td></tr>\r
-<tr><td align=right>VII.</td><td align=left>System-dependent routines</td><td align=center>(3)</td><td align=center>C.11</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-</table>\r
-The routines of Groups I, II are associated with the two\r
-main tasks of the NBO program: (1) NAO/NBO/NLMO formation, \r
-and (2) NBO energetic analysis. Group II routines generally\r
-require Fock matrix information, and thus are restricted to\r
-RHF and UHF wavefunctions, whereas Group I are \r
-applicable to general wavefunctions. Each of these\r
-groups is controlled by a master subroutine\r
-(NBO and NBOEAN, respectively) of highest precedence, which in turn \r
-calls routines of secondary precedence (such \r
-as NAODRV, NBODRV, etc.) to control the\r
-task. Routines are generally clustered together under the\r
-subroutine of next higher precedence, and within each cluster, the order\r
-of routines generally corresponds to the chronological\r
-sequence in which the routines are called in execution. \r
-<p>\r
- The remaining Groups III-VI 'serve' various routines of Groups\r
-I-II, and are ordered more loosely by function, \r
-or alphabetically. Groups I-VI \r
-are system-independent, whereas Group VII contains the special\r
-drivers (RUNNBO, FEAOIN, DELSCF) for individual ESS programs, whose\r
-generic function is described in Section C.11. Further information\r
-on the ESS-specific forms of the Group VII driver routines is given\r
-in the Appendix. \r
-<p>\r
- A general overview of the subprograms of Groups I and II\r
-is shown in the accompanying flow chart, \r
-indicating the logical relationship of the routines to\r
-be discussed in Sections C.5, C.6. The sequence of execution\r
-is generally from top to bottom and from left to right, \r
-with subprograms of equal precedence shown at an equal vertical level.\r
-<p>\r
-<p>\r
- \r
- \r
- \r
-<center>\r
-<h2>NBO Flow Chart for Group I, II Subprograms</h2>\r
-<p>\r
-<img src="nbofig2.gif">\r
-</center>\r
-<p>\r
-<b>C.3 LABELLED COMMON BLOCKS</b>\r
-<p>\r
- The NBO programs contain eighteen\r
-labelled COMMON blocks \r
-to control information flow between subprograms\r
-(other than through explicit argument\r
-lists). Each COMMON \r
-block name begins with "NB" to minimize\r
-possible conflicts with a linked ESS program. \r
-<p>\r
-The eighteen COMMON blocks can be divided into six 'primary'\r
-and twelve 'secondary' blocks, with regard to claim on the\r
-programmer's attention. The 'primary'\r
-COMMON blocks 1-6 (/NBINFO/, /NBFLAG/, /NBOPT/,\r
-/NBAO/, /NBATOM/, and /NBIO/)\r
-contain variables that must be set by the\r
-ESS-specific driver routine FEAOIN, or by an equivalent interface\r
-provided by the programmer. The remaining 'secondary'\r
-blocks 7-18 are for internal communication\r
-only, and are ordinarily of lesser concern.\r
-<p>\r
-The dimensions of COMMON block arrays are \r
-fixed by PARAMETER declarations of the form\r
- <pre>\r
- PARAMETER(MAXATM = 99,MAXBAS = 500)\r
-\r
-</pre>where MAXATM and MAXBAS are, respectively,\r
-the maximum allowed numbers of atoms and basis \r
-functions. These program limits can therefore be simply \r
-altered. There is no difficulty in <i>decreasing</i> either of these values,\r
-or in increasing MAXBAS (up to 999). However, the program cannot\r
-readily adapt to MAXATM > 99, since this \r
-would result in format overflows in orbital labels throughout the output.\r
-<p>\r
-All entries of a given COMMON block are generally of the same\r
-numeric type (INTEGER, LOGICAL, etc.), as specified below. The names (dummy),\r
-and meaning of variables in each primary COMMON block 1-6 are \r
-described briefly, with an asterisk (*) marking the items\r
-that must be passed from the external ESS program via driver routines:\r
-<p>\r
-<u>1. COMMON/NBINFO/</u> <p>\r
-The INTEGER variables of this block store general information\r
-related to basis set dimensionality, spin manifold, number of atoms,\r
-and energy units:\r
-<p>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>ISPIN</td><td align=left>+2 for <img src=alpha.gif> spin, -2 for <img src=beta.gif> spin</td></tr>\r
-<tr><td align=left>*</td><td align=left>NATOMS</td><td align=left>number of atoms (<img src=le.gif> MAXATM)</td></tr>\r
-<tr><td align=left>*</td><td align=left>NDIM</td><td align=left>declared dimensionality of matrices (overlap, density, etc.)</td></tr>\r
-<tr><td align=left>*</td><td align=left>NBAS</td><td align=left>number of basis AOs (<img src=le.gif> NDIM <img src=le.gif> MAXBAS)</td></tr>\r
-<tr><td align=left> </td><td align=left>MXBO</td><td align=left>maximum number of AOs per 2-c or 3-c NBO</td></tr>\r
-<tr><td align=left> </td><td align=left>MXAO</td><td align=left>maximum AOs per atom</td></tr>\r
-<tr><td align=left> </td><td align=left>MXAOLM</td><td align=left>maximum AOs of the same symmetry per atom</td></tr>\r
-<tr><td align=left>*</td><td align=left>MUNIT</td><td align=left>0 for Hartree energy units, 1 for eV units, 2 for kcal/mol.</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>2. COMMON/NBFLAG/</u> <p>\r
-The LOGICAL variables of this block are set .TRUE. or .FALSE.\r
-depending on whether the "condition" (type of wavefunction, spin\r
-set, etc.) is satisfied:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left> </td><td align=center>variable (FLAG)</td><td align=left>condition that FLAG=.TRUE.</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left>*</td><td align=left>ROHF</td><td align=left>Restricted open-shell Hartree-Fock wavefunction</td></tr>\r
-<tr><td align=left>*</td><td align=left>UHF</td><td align=left>Unrestricted Hartree-Fock wavefunction</td></tr>\r
-<tr><td align=left>*</td><td align=left>CI</td><td align=left>Configuration Interaction wavefunction</td></tr>\r
-<tr><td align=left>*</td><td align=left>OPEN</td><td align=left>open-shell calculation</td></tr>\r
-<tr><td align=left>*</td><td align=left>COMPLX</td><td align=left>complex-valued wavefunction (not currently implemented)</td></tr>\r
-<tr><td align=left> </td><td align=left>ALPHA</td><td align=left><img src=alpha.gif> spin set</td></tr>\r
-<tr><td align=left> </td><td align=left>BETA</td><td align=left><img src=beta.gif> spin set</td></tr>\r
-<tr><td align=left>*</td><td align=left>MCSCF</td><td align=left>Multi-Configuration Self-Consistent-Field wavefunction</td></tr>\r
-<tr><td align=left>*</td><td align=left>AUHF</td><td align=left>Spin-Annihilated UHF wavefunction</td></tr>\r
-<tr><td align=left>*</td><td align=left>ORTHO</td><td align=left>basis set is orthonormal</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-Note (Section B.6.11) that both <img src=alpha.gif> and <img src=beta.gif> spin density matrices\r
-should be available if OPEN is set '.TRUE.' for the open-shell case.\r
-<p>\r
-<p>\r
-<u>3. COMMON/NBOPT/</u> <p>\r
-The INTEGER variables (flags) of this block are used for storing the keyword\r
-options selected by the user in the $NBO keylist. In many cases, a variable\r
-of the form IWOPT ("IW" stands for "I Want") is set to one or zero\r
-(or to some Hollerith content; see below) depending on whether \r
-the "requested option" has been specified or not. The table also \r
-lists the keyword (if any) that requests the option:\r
-<p>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>variable</td><td align=left>keyword</td><td align=left>requested option</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left>*</td><td align=left>IWDM</td><td align=left>BODM</td><td align=left>1 to transform input bond-order matrix, 0 otherwise</td></tr>\r
-<tr><td align=left> </td><td align=left>IW3C</td><td align=left>3CBOND</td><td align=left>3-center bonds</td></tr>\r
-<tr><td align=left> </td><td align=left>IWAPOL</td><td align=left> </td><td align=left>'apolar' bonds, <i>c</i><sub>A</sub> = <i>c</i><sub>B</sub> (not used)</td></tr>\r
-<tr><td align=left> </td><td align=left>IWHYBS</td><td align=left>$NBO</td><td align=left>set equal to JPRINT(5)</td></tr>\r
-<tr><td align=left> </td><td align=left>IWPNAO</td><td align=left>(PAOPNAO)</td><td align=left>PAO<img src=rarr.gif>PNAO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>IWTNAO</td><td align=left>AONAO</td><td align=left>AO<img src=rarr.gif>NAO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>IWTNAB</td><td align=left>NAONBO</td><td align=left>NAO<img src=rarr.gif>NBO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>IWTNBO</td><td align=left>AONBO</td><td align=left>AO<img src=rarr.gif>NBO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>IWFOCK</td><td align=left> </td><td align=left>+1 if Fock matrix available on DAF, 0 otherwise</td></tr>\r
-<tr><td align=left>*</td><td align=left>IWCUBF</td><td align=left>CUBICF</td><td align=left>cubic <i>f</i> functions</td></tr>\r
-<tr><td align=left>*</td><td align=left>IPSEUD</td><td align=left> </td><td align=left>effective core potential</td></tr>\r
-<tr><td align=left> </td><td align=left>KOPT</td><td align=left> </td><td align=left>(not used)</td></tr>\r
-<tr><td align=left> </td><td align=left>IPRINT</td><td align=left>PRINT=n</td><td align=left>print level</td></tr>\r
-<tr><td align=left> </td><td align=left>IWDETL</td><td align=left>DETAIL</td><td align=left>detailed output</td></tr>\r
-<tr><td align=left> </td><td align=left>IWMULP</td><td align=left>MULAT</td><td align=left>Mulliken population analysis</td></tr>\r
-<tr><td align=left> </td><td align=left>ICHOOS</td><td align=left>$CHOOSE</td><td align=left>directed NBO ($CHOOSE) search</td></tr>\r
-<tr><td align=left> </td><td align=left>JCORE</td><td align=left>$CORE</td><td align=left>user-specified core list</td></tr>\r
-<tr><td align=left> </td><td align=left>JPRINT(60)</td><td align=left>various</td><td align=left>printing option flags</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-</table>\r
-<p>\r
-The keyword associated with each element I=1-54 \r
-of the JPRINT array is shown below (55-60 are not currently used):\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td align=left>JPRINT(I) <i>associated keywords:</i></td></tr>\r
-<tr><td><table border=0 width=100%>\r
-<tr><td colspan=8><hr></td></tr>\r
-<tr><td align=center>I</td><td align=left>keyword</td><td align=center>I</td><td align=left>keyword</td><td align=center>I</td><td align=left>keyword</td><td align=center>I</td><td align=left>keyword</td></tr>\r
-<tr><td colspan=8><hr></td></tr>\r
-<tr><td align=center>1</td><td align=left>SKIPBO</td><td align=center>15</td><td align=left>FNLMO</td><td align=center>29</td><td align=left>FNHO</td><td align=center>43</td><td align=left>PLOT</td></tr>\r
-<tr><td align=center>2</td><td align=left>version</td><td align=center>16</td><td align=left>DMNBO</td><td align=center>30</td><td align=left>AOPNHO</td><td align=center>44</td><td align=left>AOPNAO</td></tr>\r
-<tr><td align=center>3</td><td align=left>E2PERT</td><td align=center>17</td><td align=left>DMNLMO</td><td align=center>31</td><td align=left>FNAO</td><td align=center>45</td><td align=left>NBOMO</td></tr>\r
-<tr><td align=center>4</td><td align=left>NPA</td><td align=center>18</td><td align=left>NAONLMO</td><td align=center>32</td><td align=left>(reserved)</td><td align=center>46</td><td align=left>DIPOLE</td></tr>\r
-<tr><td align=center>5</td><td align=left>NBO</td><td align=center>19</td><td align=left>SPNAO</td><td align=center>33</td><td align=left>NAONHO</td><td align=center>47</td><td align=left>NBONLMO</td></tr>\r
-<tr><td align=center>6</td><td align=left>NBOSUM</td><td align=center>20</td><td align=left>SPNHO</td><td align=center>34</td><td align=left>DMNHO</td><td align=center>48</td><td align=left>SPNLMO</td></tr>\r
-<tr><td align=center>7</td><td align=left>ARCHIVE</td><td align=center>21</td><td align=left>SPNBO</td><td align=center>35</td><td align=left>DMNAO</td><td align=center>49</td><td align=left>AOPNLMO</td></tr>\r
-<tr><td align=center>8</td><td align=left>NLMO</td><td align=center>22</td><td align=left>AOINFO</td><td align=center>36</td><td align=left>BEND</td><td align=center>50</td><td align=left>DIAO</td></tr>\r
-<tr><td align=center>9</td><td align=left>NAOMO</td><td align=center>23</td><td align=left>AONLMO</td><td align=center>37</td><td align=left>FNBO</td><td align=center>51</td><td align=left>DINAO</td></tr>\r
-<tr><td align=center>10</td><td align=left>NOBOND</td><td align=center>24</td><td align=left>NHONLMO</td><td align=center>38</td><td align=left>NHOMO</td><td align=center>52</td><td align=left>DINHO</td></tr>\r
-<tr><td align=center>11</td><td align=left>RPNAO</td><td align=center>25</td><td align=left>AOPNBO</td><td align=center>39</td><td align=left>SAO</td><td align=center>53</td><td align=left>DINBO</td></tr>\r
-<tr><td align=center>12</td><td align=left>BNDIDX</td><td align=center>26</td><td align=left>AOMO</td><td align=center>40</td><td align=left>FAO</td><td align=center>54</td><td align=left>DINLMO</td></tr>\r
-<tr><td align=center>13</td><td align=left>NLMOMO</td><td align=center>27</td><td align=left>DMAO</td><td align=center>41</td><td align=left>NHONBO</td><td align=center>55-60</td><td align=left>(not used)</td></tr>\r
-<tr><td align=center>14</td><td align=left>RESONANCE</td><td align=center>28</td><td align=left>AONHO</td><td align=center>42</td><td align=left>BOAO</td><td align=center> </td><td align=left> </td></tr>\r
-<tr><td colspan=8><hr></td></tr>\r
-</td></tr></table>\r
-</table>\r
-In general, if the flag is\r
-set to zero, its associated keyword option has not been specified. However, \r
-if an option is requested, its flag can be set to a variety of\r
-positive, negative, or Hollerith values, depending on the parameters\r
-specified with the keyword option. In particular, the option flags associated\r
-with the matrix output keywords, described in Section B.2.4, are set\r
-according to the following scheme:\r
-<p>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>value</td><td align=left>effect</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>0</td><td align=left>Do nothing</td></tr>\r
-<tr><td align=center>0 < <i>n</i></td><td align=left>Print <i>n</i> columns of the matrix</td></tr>\r
-<tr><td align=center>-1000 < <i>n</i> < 0</td><td align=left>Write matrix to external file |<i>n</i>|</td></tr>\r
-<tr><td align=center>n < -999</td><td align=left>Read matrix from external file |<i>n</i>/1000|</td></tr>\r
-<tr><td align=center>'FULL'</td><td align=left>Print the full matrix to the output file</td></tr>\r
-<tr><td align=center>'VAL'</td><td align=left>Print only core plus valence orbitals</td></tr>\r
-<tr><td align=center>'LEW'</td><td align=left>Print only the occupied (Lewis) orbitals</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>4. COMMON/NBAO/</u> <p>\r
-The INTEGER arrays of this block store information on the\r
-atomic centers and angular symmetry of each AO:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left>*</td><td align=left>LCTR(MAXBAS)</td><td align=left>list of atomic centers of the basis AOs</td></tr>\r
-<tr><td align=left> </td><td align=left> </td><td align=left>(LCTR(3)=2 if AO 3 is on atom 2)</td></tr>\r
-<tr><td align=left>*</td><td align=left>LANG(MAXBAS)</td><td align=left>angular symmetry labels (Sec. B.7.5) of the basis AOs</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>5. COMMON/NBATOM/</u> <p>\r
-The INTEGER arrays of this block store information about the\r
-orbitals on each atomic center:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left>*</td><td align=left>IATNO(MAXATM)</td><td align=left>atomic number for each atom</td></tr>\r
-<tr><td align=left> </td><td align=left>INO(MAXATM)</td><td align=left>number of atomic hybrids on each atom</td></tr>\r
-<tr><td align=left> </td><td align=left>NORBS(MAXATM)</td><td align=left>number of AOs on each atom</td></tr>\r
-<tr><td align=left> </td><td align=left>LL(MAXATM)</td><td align=left>number of the first NAO on each atom</td></tr>\r
-<tr><td align=left> </td><td align=left>LU(MAXATM)</td><td align=left>number of the last NAO on each atom</td></tr>\r
-<tr><td align=left>*</td><td align=left>IZNUC(MAXATM)</td><td align=left>nuclear charge on each atom (<img src=le.gif> IATNO)</td></tr>\r
-<tr><td align=left> </td><td align=left>IATCR(MAXATM)</td><td align=left>atomic core list for modified $CORE table</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>6. COMMON/NBIO/</u> <p>\r
-The INTEGER variables of this block are the\r
-stored default logical file\r
-numbers for I/O operations. The table below identifies\r
-the value (default file assignment) and the\r
-contents of the file associated with each LFN (cf. Section B.2.4):\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left> </td><td align=left>LFN</td><td align=center>value</td><td align=left>file contents</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left>*</td><td align=left>LFNIN</td><td align=center> </td><td align=left>standard ESS input file</td></tr>\r
-<tr><td align=left>*</td><td align=left>LFNPR</td><td align=center> </td><td align=left>standard ESS output (print) file</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNAO</td><td align=center>31</td><td align=left>AO info file</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNPNA</td><td align=center>32</td><td align=left>AO<img src=rarr.gif>PNAO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNNAO</td><td align=center>33</td><td align=left>AO<img src=rarr.gif>NAO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNPNH</td><td align=center>34</td><td align=left>AO<img src=rarr.gif>PNHO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNNHO</td><td align=center>35</td><td align=left>AO<img src=rarr.gif>NHO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNPNB</td><td align=center>36</td><td align=left>AO<img src=rarr.gif>PNBO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNNBO</td><td align=center>37</td><td align=left>AO<img src=rarr.gif>NBO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNPNL</td><td align=center>38</td><td align=left>AO<img src=rarr.gif>PNLMO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNNLM</td><td align=center>39</td><td align=left>AO<img src=rarr.gif>NLMO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNMO</td><td align=center>40</td><td align=left>AO<img src=rarr.gif>MO transformation (LCAO-MO coeffs.)</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNDM</td><td align=center>41</td><td align=left>density matrix in AO basis</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNNAB</td><td align=center>42</td><td align=left>NAO<img src=rarr.gif>NBO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNPPA</td><td align=center>43</td><td align=left>PAO<img src=rarr.gif>PNAO transformation</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNGEN</td><td align=center>47</td><td align=left>'archive' file</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNDAF</td><td align=center>48</td><td align=left>direct access file (DAF)</td></tr>\r
-<tr><td align=left> </td><td align=left>LFNDEF</td><td align=center>49</td><td align=left>'default' for other file output</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-</table>\r
-<p>\r
-The remaining 'secondary' COMMON blocks 7-18 contain variables that\r
-remain wholly within the system-independent code, and thus can be\r
-ignored with respect to interfacing to a new ESS. Blocks 7-13\r
-involve communication with the Group I, II subprograms, whereas\r
-blocks 14-18 are wholly within the 'support' routines of\r
-Groups III-VII.\r
-<p>\r
-<p>\r
-<u>7. COMMON/NBBAS/</u> <p>\r
-The INTEGER arrays of this block generally store information about\r
-the atomic, bond, and molecular units with which the NBOs or NAOs are \r
-associated. The meaning of all entries in COMMON/NBBAS/ <i>changes</i>\r
-between the NAO and NBO segments of the program, so this block\r
-functions virtually as 'scratch storage,' and its entries must be\r
-approached with extreme caution! The following table indicates the meaning\r
-of COMMON/NBBAS/ entries during NBO segments (only!):\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>LABEL(MAXBAS,6)</td><td align=left>NBO label information (lbl; *; bond no.; at1; at2; at3)</td></tr>\r
-<tr><td align=left>NBOUNI(MAXBAS)</td><td align=left>molecular unit of each NBO</td></tr>\r
-<tr><td align=left>NBOTYP(MAXBAS)</td><td align=left>no. centers + 10 (if low-occ LP) + 20 (if BD* or RY*)</td></tr>\r
-<tr><td align=left>LSTOCC(MAXBAS)</td><td align=left>1 (NMB) or 0 (NRB) NAO labels</td></tr>\r
-<tr><td align=left>IBXM(MAXBAS)</td><td align=left>NBO label permutation list</td></tr>\r
-<tr><td align=left>LARC(MAXBAS)</td><td align=left>re-ordering list</td></tr>\r
-<tr><td align=left>LBL(MAXBAS)</td><td align=left>atomic center of AO</td></tr>\r
-<tr><td align=left>LORBC(MAXBAS)</td><td align=left>angular momentum label of AO</td></tr>\r
-<tr><td align=left>LORB(MAXBAS)</td><td align=left>(variable)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>8. COMMON/NBTHR/</u> <p>\r
-The DOUBLE PRECISION variables of this block store the \r
-default values of various\r
-numerical thresholds that can be set by the user:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>THRSET</td><td align=left>NBO occupancy threshold</td></tr>\r
-<tr><td align=left>PRJSET</td><td align=left>projection threshold</td></tr>\r
-<tr><td align=left>ACCTHR</td><td align=left>threshold [0.1] for assigning acceptor orbital NBOTYP</td></tr>\r
-<tr><td align=left>CRTSET</td><td align=left>threshold for core-occupancy warning</td></tr>\r
-<tr><td align=left>E2THR</td><td align=left>minimum E for 2nd-order energy analysis printing</td></tr>\r
-<tr><td align=left>ATHR</td><td align=left>minimum bend angle for BEND printing</td></tr>\r
-<tr><td align=left>PTHR</td><td align=left>minimum % <i>p</i>-character for BEND printing</td></tr>\r
-<tr><td align=left>ETHR</td><td align=left>minimum NBO occupancy for BEND printing</td></tr>\r
-<tr><td align=left>DTHR</td><td align=left>minimum dipole moment for DIPOLE printing</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>9. COMMON/NBLBL/</u> <p>\r
-The INTEGER variables of this block store the number of\r
-orbitals associated with the "LEW" and "VAL" print parameters\r
-(Section B.2.4) and the 10 Hollerith fragments required to compose each of\r
-the 4 possible types of localized orbital labels (AO, NAO, NHO, NBO):\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>NLEW</td><td align=left>number of Lewis NBOs (= number of occupied MOs)</td></tr>\r
-<tr><td align=left>NVAL</td><td align=left>number of minimal basis (NMB) NAOs</td></tr>\r
-<tr><td align=left>LBL(10,MAXBAS,4)</td><td align=left>label fragments (AO; NAO; NHO; NBO)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>10. COMMON/NBNAO/</u> <p>\r
-The INTEGER arrays of this block store information pertaining\r
-to the labelling of NAOs in the NPA output:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>NAOC(MAXBAS)</td><td align=left>atomic center of each NAO</td></tr>\r
-<tr><td align=left>NAOA(MAXBAS)</td><td align=left>angular symmetry label (Sec. B.7.5) of each NAO</td></tr>\r
-<tr><td align=left>LTYP(MAXBAS)</td><td align=left>'Cor', 'Val', or 'Ryd' label for each NAO</td></tr>\r
-<tr><td align=left>IPRIN(MAXBAS)</td><td align=left>principal quantum number (<i>n</i>) of each NAO</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>11. COMMON/NBMOL/</u> <p>\r
-The INTEGER scalars, vectors, and arrays of this block \r
-store information pertaining to "molecular units":\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>NMOLEC</td><td align=left>number of molecular units</td></tr>\r
-<tr><td align=left>MOLAT(MAXATM)</td><td align=left>molecular unit of each atom</td></tr>\r
-<tr><td align=left>MOLEC(MAXATM,MAXATM)</td><td align=left>list of atoms (J) in each molecular unit (I)</td></tr>\r
-<tr><td align=left>NMOLA</td><td align=left>scratch storage for open-shell case</td></tr>\r
-<tr><td align=left>MOLATA(MAXATM)</td><td align=left>scratch storage for open-shell case</td></tr>\r
-<tr><td align=left>MOLECA(MAXATM,MAXATM)</td><td align=left>scratch storage for open-shell case</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>12. COMMON/NBTOPO/</u> <p>\r
-The INTEGER variables of this block contain atom search lists to direct\r
-the search for NBOs and information pertaining\r
-to the 'topology' (bond connectivity) of the molecule: \r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>IORDER(MAXATM)</td><td align=left>permuted atom order for NBO search</td></tr>\r
-<tr><td align=left>JORDER(MAXATM)</td><td align=left>atom ordering for 'best' resonance structure</td></tr>\r
-<tr><td align=left>NTOPO(MAXATM,MAXATM)</td><td align=left>number of bonds between atoms I,J</td></tr>\r
-<tr><td align=left> </td><td align=left>(or number of lone pairs on I, if I = J)</td></tr>\r
-<tr><td align=left>N3CTR</td><td align=left>number of 3-center bonds (<img src=le.gif> 10)</td></tr>\r
-<tr><td align=left>IC3TR(10,3)</td><td align=left>the 3 atoms of each 3-c bond</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>13. COMMON/NBDXYZ/</u> <p>\r
-The DOUBLE PRECISION variables of this block store \r
-information pertaining to the molecular dipole moment and charge\r
-distribution:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>XDIP</td><td align=left><i>x</i>-component of molecular dipole moment (<img src=alpha.gif> spin)</td></tr>\r
-<tr><td align=left>YDIP</td><td align=left><i>y</i>-component of molecular dipole moment (<img src=alpha.gif> spin)</td></tr>\r
-<tr><td align=left>ZDIP</td><td align=left><i>z</i>-component of molecular dipole moment (<img src=alpha.gif> spin)</td></tr>\r
-<tr><td align=left>CHARGE(MAXATM)</td><td align=left>list of 'uncompensated' nuclear charges (dipole loops)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>14. COMMON/NBCRD1/</u> <p>\r
-The INTEGER variables of this block store general information\r
-related to the 'card image' (line) being processed\r
-by the free-format input routines:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>ICD(80)</td><td align=left>array of Hollerith characters (<img src=le.gif> 80) of the input line</td></tr>\r
-<tr><td align=left>LOOK(80)</td><td align=left>scratch buffer for card image</td></tr>\r
-<tr><td align=left>LENGTH</td><td align=left>length of the non-blank string in LOOK</td></tr>\r
-<tr><td align=left>IPT</td><td align=left>pointer to current location in ICD</td></tr>\r
-<tr><td align=left>LFN</td><td align=left>input file assignment</td></tr>\r
-<tr><td align=left>NEXP</td><td align=left>exponent of a number in exponential format</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>15. COMMON/NBCRD2/</u> <p>\r
-The LOGICAL variables of this block store information\r
-related to the current line being read\r
-by the free-format input routines. In each case, the\r
-variable is set .TRUE. if the specified condition is met:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>condition that variable is .TRUE.</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>POINT</td><td align=left>a number containing a decimal point is present</td></tr>\r
-<tr><td align=left>END</td><td align=left>word 'END' or EOF has been encountered</td></tr>\r
-<tr><td align=left>NEXT</td><td align=left>ready for reading next word in line (ICD)</td></tr>\r
-<tr><td align=left>EXP</td><td align=left>a number in exponential notation is present</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>16. COMMON/NBODAF/</u> <p>\r
-The INTEGER variables of this block store information\r
-related to the NBO direct access file (FILE48). The PARAMETER statement\r
- <pre>\r
- PARAMETER (NBDAR = 100)\r
-\r
-</pre>sets the maximum number of logical records accessible in FILE48:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>INBO</td><td align=left>logical file number [48] for DAF</td></tr>\r
-<tr><td align=left>NAV</td><td align=left>last-accessed physical record of DAF</td></tr>\r
-<tr><td align=left>IONBO(NBDAR)</td><td align=left>mapping of physical and logical record numbers</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>17. COMMON/NBONAV/</u> <p>\r
-The INTEGER variables of this block provide scratch storage\r
-for writing to the NBO direct access file (FILE48). The PARAMETER statement\r
- <pre>\r
- PARAMETER (ISINGL = 2, LENGTH = 256)\r
-\r
-</pre>sets the FILE48 physical record LENGTH to 256 longwords \r
-(1024 bytes):\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>meaning</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>IXDNBO(LENGTH)</td><td align=left>scratch array for DAF writes</td></tr>\r
-<tr><td align=left>NBNAV</td><td align=left>number of physical records in IXDNBO</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<u>18. COMMON/NBGEN/</u> <p>\r
-The LOGICAL variables of this block store information related\r
-to running the GENNBO program in stand-alone mode. In each case, the\r
-variable is set .TRUE. if the specified condition is met:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>variable</td><td align=left>condition that variable is .TRUE.</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>REUSE</td><td align=left>"REUSE" keyword requests use of an existing DAF</td></tr>\r
-<tr><td align=left>UPPER</td><td align=left>"UPPER" keyword specifies upper-triangular matrices</td></tr>\r
-<tr><td align=left>BOHR</td><td align=left>"BOHR" keyword specifies atomic units of length</td></tr>\r
-<tr><td align=left>DENOP</td><td align=left>density matrix is provided (i.e., "BODM" not set)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<b>C.4 DIRECT ACCESS FILE AND OTHER I/O</b>\r
-<p>\r
- The principal I/O routines of Groups III-V are described in\r
-Sections C.7-C.9. The <i>input</i> to the NBO programs is primarily\r
-from the standard ESS input file (LFN 5), \r
-and the <i>output</i> is primarily to the\r
-standard ESS output file (LFN 6). Other "matrix output" \r
-(read/write) I/O is by default assigned to LFNs 31-49 (see\r
-Table of Section B.2.4), or to a user-selectable LFN, based\r
-on keyword entries in the $NBO keylist. \r
-<p>\r
- The remaining two files that are routinely created or modified\r
-by the NBO programs are the FILE48 direct access file (LFN 48)\r
-and the FILE47 'archive' file\r
-(LFN 47, described in Section B.7). The latter file can also serve \r
-as the main input file (reassigned as LFN 5) when the NBO program is run in\r
-stand-alone GENNBO mode.\r
-<p>\r
- From the programmer's viewpoint, the most important information\r
-concerns the organization of the FILE48 direct access file. The\r
-records of this file are assigned as shown in the following \r
-table. The items marked with an asterisk (*) must be provided\r
-from the ESS program (e.g., through the FEAOIN driver), and hence\r
-are of particular importance to the programmer:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=center>record</td><td align=center> </td><td align=left>content</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=center> 1 </td><td align=center> </td><td align=left>NBODAF common block</td></tr>\r
-<tr><td align=center> 2 </td><td align=center>*</td><td align=left>Job title</td></tr>\r
-<tr><td align=center> 3 </td><td align=center>*</td><td align=left>NATOMS,NDIM,NBAS,MUNIT,wavefunction flags</td></tr>\r
-<tr><td align=center> 4 </td><td align=center>*</td><td align=left>IATNO,IZNUC,LCTR,LANG</td></tr>\r
-<tr><td align=center> 5 </td><td align=center>*</td><td align=left>AO basis set info</td></tr>\r
-<tr><td align=center> 8 </td><td align=center>*</td><td align=left>Deletion energy, total energy</td></tr>\r
-<tr><td align=center> 9 </td><td align=center>*</td><td align=left>Atomic coordinates</td></tr>\r
-<tr><td align=center> 10 </td><td align=center>*</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center> 11 </td><td align=center> </td><td align=left>PNAO overlap matrix</td></tr>\r
-<tr><td align=center> 20 </td><td align=center>*</td><td align=left>AO density matrix (alpha)</td></tr>\r
-<tr><td align=center> 21 </td><td align=center>*</td><td align=left>AO density matrix (beta)</td></tr>\r
-<tr><td align=center> 22 </td><td align=center> </td><td align=left>Pure AO density matrix</td></tr>\r
-<tr><td align=center> 23 </td><td align=center> </td><td align=left>NAO density matrix (alpha)</td></tr>\r
-<tr><td align=center> 24 </td><td align=center> </td><td align=left>NAO density matrix (beta)</td></tr>\r
-<tr><td align=center> 25 </td><td align=center> </td><td align=left>AO density matrix with NBO deletions (alpha)</td></tr>\r
-<tr><td align=center> 26 </td><td align=center> </td><td align=left>AO density matrix with NBO deletions (beta)</td></tr>\r
-<tr><td align=center> 27 </td><td align=center> </td><td align=left>NBO occupancies (alpha)</td></tr>\r
-<tr><td align=center> 28 </td><td align=center> </td><td align=left>NBO occupancies (beta)</td></tr>\r
-<tr><td align=center> 30 </td><td align=center>*</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center> 31 </td><td align=center>*</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td align=center> 32 </td><td align=center> </td><td align=left>NAO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center> 33 </td><td align=center> </td><td align=left>NAO Fock matrix (beta)</td></tr>\r
-<tr><td align=center> 34 </td><td align=center> </td><td align=left>NBO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center> 35 </td><td align=center> </td><td align=left>NBO Fock matrix (beta)</td></tr>\r
-<tr><td align=center> 40 </td><td align=center>*</td><td align=left>AO to MO transformation matrix (alpha)</td></tr>\r
-<tr><td align=center> 41 </td><td align=center>*</td><td align=left>AO to MO transformation matrix (beta)</td></tr>\r
-<tr><td align=center> 42 </td><td align=center> </td><td align=left>AO to PNAO transformation matrix</td></tr>\r
-<tr><td align=center> 43 </td><td align=center> </td><td align=left>AO to NAO transformation matrix</td></tr>\r
-<tr><td align=center> 44 </td><td align=center> </td><td align=left>AO to NBO transformation matrix (alpha)</td></tr>\r
-<tr><td align=center> 45 </td><td align=center> </td><td align=left>AO to NBO transformation matrix (beta)</td></tr>\r
-<tr><td align=center> 46 </td><td align=center> </td><td align=left>AO to NLMO transformation matrix</td></tr>\r
-<tr><td align=center> 47 </td><td align=center> </td><td align=left>NAO to NHO transformation matrix</td></tr>\r
-<tr><td align=center> 48 </td><td align=center> </td><td align=left>NAO to NBO transformation matrix</td></tr>\r
-<tr><td align=center> 49 </td><td align=center> </td><td align=left>NBO to NLMO transformation matrix</td></tr>\r
-<tr><td align=center> 50 </td><td align=center>*</td><td align=left>X dipole integrals</td></tr>\r
-<tr><td align=center> 51 </td><td align=center>*</td><td align=left>Y dipole integrals</td></tr>\r
-<tr><td align=center> 52 </td><td align=center>*</td><td align=left>Z dipole integrals</td></tr>\r
-<tr><td align=center> 60 </td><td align=center> </td><td align=left>NBO labels (alpha)</td></tr>\r
-<tr><td align=center> 61 </td><td align=center> </td><td align=left>NBO labels (beta)</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-[Cartesian coordinates (record 9) and dipole integrals\r
-(records 50-52) should be in angstrom units.]\r
-<p>\r
- The direct access file serves as \r
-a principal medium of communication between\r
-all segments of the NBO program. Input received from the ESS\r
-program (Section C.11) is immediately saved in the direct access file\r
-and subsequently fetched by other subprograms, using\r
-the fetch/save I/O routines of Section C.7. Further information on\r
-the structure of the direct access file is specified in COMMON\r
-blocks 16, 17 of Section C.3.\r
-<p>\r
-<p>\r
-<b>C.5 NAO/NBO/NLMO ROUTINES (GROUP I)</b>\r
-<p>\r
-<i>C.5.1 SR NBO Master Subroutine</i>\r
-<p>\r
- The subroutine of highest precedence in the core NBO program is\r
-SR NBO. This routine initially requests that the input file be searched for\r
-the $NBO keylist (See NBOINP, Section C.9). If found, SR NBO continues by\r
-calling three main clusters of programs, as shown below:\r
-<p>\r
-<pre> SR NBO(CORE,MEMORY,NBOOPT)</pre>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td align=center>Job Initialization</td><td align=center>NAO Formation</td><td align=center>NBO/NLMO Formation</td></tr>\r
-<tr><td align=center>Routines</td><td align=center>Routines</td><td align=center>Routines</td></tr>\r
-<tr><td align=center>(Sec. C.5.2)</td><td align=center>(Sec. C.5.3)</td><td align=center>(Sec. C.5.4)</td></tr>\r
-</table>\r
-In addition, SR NBO creates a new NBO direct access file (DAF) each time\r
-it is called, and closes this file upon completion (See NBOPEN and NBCLOS,\r
-Section C.9).\r
-<p>\r
- SR NBO is provided a memory vector, CORE, which is\r
-'MEMORY' double precision words in length. For modest-sized calculations\r
-(e.g. 10 heavy atoms with a double-zeta basis set), a vector\r
-of 50,000 words should be adequate. Although SR NBO performs an initial\r
-partitioning of this memory vector, the majority of the dynamic memory\r
-allocation occurs in the NAO and NBO/NLMO formation routines, described\r
-in Sections C.5.3 and C.5.4.\r
-<p>\r
- An array of job options, NBOOPT(10), is also passed to SR NBO.\r
-These job options identify the current version of the NBO program\r
-(i.e., the identity of the ESS calling program),\r
-control program input and execution,\r
-and determine several of the default options of the NBO analysis, as\r
-summarized in the following table. [Entries marked with an asterisk (*)\r
-contain information pertaining to the identity or job options of the\r
-calling ESS program, and thus are of special concern to the\r
-programmer.]\r
-<p>\r
-<p>\r
-<i>OPTION</i> <br><i>ENTRY</i> <i>DESCRIPTION</i>\r
-<p>\r
-* <br>NBOOPT(1) <br>-2 Do nothing (return control to calling program)\r
-<br>-1 Perform Natural Population Analysis (NPA) only\r
-<br>0 Perform NPA/NBO/NLMO analyses, normal program run\r
-<br>1 Perform NPA/NBO/NLMO analyses, don't read $NBO keylist\r
-<br>2 Initiate energetic analysis, read one deletion from $DEL\r
-<br>3 Complete energetic analysis, print the energy change\r
-<p>\r
-* <br>NBOOPT(2) <br>0 SCF density\r
-<br>1 MP first order density\r
-<br>3 MP2 density\r
-<br>4 MP3 density\r
-<br>5 MP4 density\r
-<br>6 CI one-particle density\r
-<br>7 CI density\r
-<br>8 QCI/CC density\r
-<br>9 Density correct to second order\r
-<p>\r
-NBOOPT(3) <br>1 Perform the NBO/NLMO dipole analysis\r
-(force the DIPOLE keyword)\r
-<p>\r
-NBOOPT(4) <br>1 Allow strongly delocalized Lewis structures\r
-(force the RESONANCE keyword)\r
-<p>\r
-NBOOPT(5) <br>1 Spin-annihilated UHF (AUHF) wavefunction (unused)\r
-<p>\r
-NBOOPT(6-9) (unused)\r
-<p>\r
-* <br>NBOOPT(10) <br>0 General version of the NBO program (GENNBO)\r
-<br>1 AMPAC version\r
-<br>6 GAMESS version\r
-<br>7 HONDO version\r
-<br>8x GAUSSIAN-8x version\r
-<p>\r
-These options are read by job\r
-initialization routines (Section C.5.2) and stored in COMMON/NBOPT/,\r
-where they control events throughout the program. [Note that NBOOPT(2)\r
-is only used by the Gaussian versions.]\r
-<p>\r
-<p>\r
-<i>C.5.2 Job Initialization Routines</i>\r
-<p>\r
- The routines of this section initialize the default options\r
-and parameters, read and store the user's $NBO keyword options:\r
-<p>\r
-<p>\r
-This routine sets default option flags\r
-(COMMON/NBOPT/), default logical file numbers (COMMON/NBIO/), and\r
-default thresholds (COMMON/NBTHR/) for the NBO program. In addition,\r
-SR NBOSET interprets the NBOOPT array, setting\r
-option flags appropriately.\r
-<p>\r
-<p>\r
-This routine is primarily responsible for reading and setting\r
-option flags (COMMON/NBOPT/)\r
-according to the keywords specified in the $NBO keylist. It reads\r
-the $NBO keywords using the free format routines described in Section C.8,\r
-continuing until the word "$END" terminates the keylist. Options which\r
-are incompatible with the chosen wavefunction or program version are 'shut\r
-off', and other options are 'turned on' in accord with the requested print\r
-level ($NBO keyword PRINT). All keywords which are selected in the $NBO\r
-keylist are echoed in the output file.\r
-<p>\r
-<p>\r
- \r
-Determines the scratch memory\r
-requirements of the NBO program, as determined by the options selected\r
-in the $NBO keylist. Program execution halts if the memory requirements\r
-exceed the available memory.\r
-<p>\r
-<p>\r
-<i>C.5.3 NAO Formation Routines</i>\r
-<p>\r
- The principal task of this cluster of routines is to control the formation\r
-of the NAOs from the input AO basis. In addition, these routines\r
-are responsible for the writing (to an external file) or printing (to the\r
-output file) of a variety of matrices in the AO, PNAO, and NAO basis sets,\r
-according to job options requested in the $NBO keylist. The first set of\r
-routines are called by SR NBO:\r
-<p>\r
-<p>\r
-<u></u><pre>SR NAODRV(DM,T,A)</pre> \r
-This is the principal controller routine for non-orthogonal basis sets.\r
-The scratch vector A is partitioned within this routine according to the\r
-memory requirements of the NAO subprograms.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NAOSIM(DM,T,A)</pre> \r
-This routine 'simulates' SR NAODRV in the case of a semi-empirical\r
-calculation, where the (orthonormal) basis AOs are the presumed\r
-effective valence shell atomic orbitals, and no NAO transformation is\r
-needed.\r
-<p>\r
-<p>\r
-<u></u><pre>SR DMNAO(DM,T,A)</pre> \r
-Performs the transformation and analysis of the open-shell AO density\r
-matrix (alpha or beta spin) to the NAO basis. This routine employs the\r
-AO to NAO transformation, T, determined by SR NAODRV:\r
-<p>\r
-<p>\r
-<u></u><pre>SR DMSIM(DM,T,A)</pre> \r
-Simulates SR DMNAO for the open-shell semi-empirical case, when no\r
-transformation is required.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBODRV(DM,T,A)</pre> <p>\r
-Principal driver program for NBO formation; Section C.5.4.\r
-<p>\r
-The next set of routines are called by the main NAO driver,\r
-SR NAODRV. They include the principal subroutine, SR NAO,\r
-which generates the NAOs:\r
-<p>\r
-<p>\r
-<u></u><pre>SR SIMTRM(A,S,V,NDIM,N,IWMULP,IWCUBF)</pre>>> \r
-Performs the similarity transformation S<sup>t</sup>*A*S leading to\r
-Mulliken populations, with S = overlap matrix, A = bond-order matrix.\r
-<p>\r
-<p>\r
-<u></u><pre>SR MULANA(BS,VMAYER,BMAYER,IWMULP,IWCUBF)</pre> \r
-Evaluates Mulliken gross populations and performs Mayer-Mulliken\r
-bond-order analysis (requires bond order matrix).\r
-<p>\r
-<p>\r
-<u></u><pre>SR DFGORB(RENORM,DM,T,ITRAN,IWCUBF,ITOPT,LFNPR)</pre> \r
-Performs the decomposition of 'raw' cartesian <i>d</i>, <i>f</i>, or <i>g</i>\r
-AO sets to pure angular symmetry AOs (e.g., 6 cartesian <i>d</i> <img src=rarr.gif>\r
-5 pure <i>d</i> + 1 <i>s</i>); cf. Section B.7.5.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NAO(T,S,OCC,BLK,SBLK,EVAL,C,EVECT,EVAL2,LISTAO,NBLOCK)</pre> \r
-This is the principal routine for formation of NAOs, following\r
-closely the algorithm described by A. E. Reed, R. B. Weinstock, and\r
-F. Weinhold, <i>J. Chem. Phys. <b>83</b></i>, 735-746 (1985).\r
-<p>\r
-<p>\r
-<u></u><pre>SR NAOANL(DM,SPNAO,BINDEX,BINDT,OVPOP,F,ENAO)</pre> \r
-This is the principal routine for performing and printing out natural\r
-population analysis (NPA). The routine assigns orbital labels\r
-and energies and writes out the NPA, natural electron configuration (NEC),\r
-NAO-Wiberg bond index and overlap-weighted bond population tables.\r
-[Thresholds TEST, TEST2, ALLOW, ALLOW2 test for numerical conservation of\r
-an integer number of electrons.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR FRMTMO(T,TMO,C,SCR,INDEX,NCOL)</pre> <p>\r
-Forms and outputs NCOL columns of the transformation matrix to MOs\r
-from a chosen localized set, specified by INDEX = 2 (NAO), 3 (NHO),\r
-4 (NBO), or 5 (NLMO). Input matrix T is the transformation from AOs\r
-to the basis set specified by INDEX, and matrices TMO, C, and SCR are\r
-scratch arrays employed by this routine.\r
-<p>\r
-The remaining routines of this section are auxiliary subroutines\r
-called by SR NAO to perform individual steps of the NAO algorithm:\r
-<p>\r
-<p>\r
-<u></u><pre>SR LOADAV(LISTAO,NL,M,S,NDIM,A,B,MXAOLM)</pre> \r
-Averages the AO density matrix elements over the 2<i>l</i> + 1 components\r
-of <i>l</i> for a particular atom, and loads the density matrix and\r
-overlap integrals for the orbitals of LISTAO into \r
-matrices A, B, respectively.\r
-<p>\r
-<p>\r
-<u></u><pre>SR ATDIAG(N,A,B,EVAL,C)</pre> \r
-Solves the generalized eigenvalue problem (A - EVAL*B)*C = 0\r
-to diagonalize an atomic block.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SETBAS(LSTOCC,LSTEMT,NOCC,NEMT,IAT,L,NL,NF,NDIM)</pre> \r
-Selects the 'occupied' NAOs to be included in the natural minimal basis\r
-set for a particular atom (up to Z = 105) and angular\r
-momentum symmetry type (L), and stores them in LSTOCC.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NEWWTS(S,T,WT)</pre> <p>\r
-Recomputes symmetry-averaged occupancy weights for PNAOs. This routine is\r
-only used in conjunction with the 'PAOPNAO=R' keyword.\r
-<p>\r
-<p>\r
-<u></u><pre>SR WORTH(S,T,BLK,LIST,NDIM,NBAS,N,OCC,EVAL,BIGBLK)</pre> \r
-This subroutine implements the occupancy-weighted symmetric\r
-orthogonalization (OWSO), a key feature of the NAO algorithm. [Note\r
-that BLK and BIGBLK share the same storage area, though they\r
-are dimensioned differently. The routine includes three\r
-numerical thresholds, WTTHR (10<sup>-3</sup>) for occupancy weight,\r
-DIAGTH (10<sup>-12</sup>) for Jacobi diagonalization, and DANGER (10<sup>3</sup>)\r
-for linear dependence difficulties.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR SHMDT(T,S,NDIM,NBAS,NOCC,LSTOCC,NEMT,LSTEMT,SBLK)</pre> \r
-Schmidt orthogonalization of column vectors of T.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NEWRYD(T,S,TPNAO,DMBLK,SBLK,EVECT,OCC,EVAL,EVAL2,LIST,IRPNAO)</pre> <p>\r
-Computes new Rydberg NAOs after Schmidt orthogonalization of\r
-the Rydberg space to the NMB set.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RYDIAG(T,S,TPNAO,DMBLK,SBLK,OCC,EVAL,EVECT,EVAL2,</pre> <p>\r
-IORB,NC,NM,NSTART,NRYDC,LARC,LIST,IRPNAO) \r
-Diagonalizes an atomic Rydberg block and updates the PNAO\r
-transformation matrix.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RYDSEL(LSTEMT,NEMT,NSEL1,LIST1,NSEL2,LIST2,WT)</pre> \r
-Partitions Rydbergs into 'significantly occupied' (> WTTHR)\r
-and 'negligibly occupied' (<img src=le.gif> WTTHR) sets, assigning the\r
-latter to have equal (non-zero) occupancy weighting. This\r
-avoids numerical singularities associated with the OWSO occupancy\r
-weighting for orbitals of negligible occupancy, effectively\r
-replacing OWSO by ordinary Löwdin-orthogonalization\r
-of these 'residual' Rydbergs among themselves. [Threshold \r
-WTTHR (10<sup>-4</sup>) controls singularities of the inverse\r
-square-root weighting matrix.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR REDIAG(DM,T,TPNAO,EVAL,BLK,C,IRANK,IRPNAO)</pre> \r
-Rediagonalizes the atomic density matrix blocks after symmetry\r
-averaging.\r
-<p>\r
-<p>\r
-<u></u><pre>SR REDBLK(T,TPNAO,IL,DM,BLK,EVAL,C,NF,IORB,NC,IRANK,IRPNAO)</pre> \r
-Finds the rediagonalization transformation for a specific\r
-<i>l</i>-symmetry atomic subblock of the density matrix.\r
-<p>\r
-<p>\r
-<i>C.5.4 NBO/NLMO Formation Routines</i>\r
-<p>\r
- The master routine of this cluster is\r
-SR  NBODRV(DM,T,A), which partitions the scratch storage\r
-vector (A) according to the memory requirements of the NBO formation\r
-and analysis subprograms and controls the calculation of the\r
-transformation (T) from NAOs to NBOs using the NAO density matrix (DM).\r
-SR NBODRV calls either SR NATHYB (for the default NBO search) or SR CHSDRV\r
-(for the $CHOOSE directed NBO search) to form the NBOs. It\r
-also calls the NLMO\r
-formation routine (SR NLMO) and dipole analysis routine (SR DIPANL).\r
-According to job options selected in the $NBO keylist, SR NBODRV also\r
-transforms and outputs a variety of matrices in the PNHO, NHO, PNBO, NBO,\r
-PNLMO, and NLMO basis sets. [Note that the first NATOMS*NATOMS\r
-elements of the A vector store the Wiberg bond index elements\r
-determined in the NAO routines; these should not be destroyed until\r
-calculation of NBOs is complete.]\r
-<p>\r
-<p>\r
- The following routines are called by SR NBODRV:\r
-<p>\r
-<u></u><pre>SR NATHYB(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,</pre> <p>\r
-P,TA,HYB,VA,VB,TOPO) \r
-This routine performs the basic NBO search, the central task of\r
-NBO analysis, closely following the description given by\r
-J. P. Foster and F. Weinhold, <i>J. Am. Chem. Soc. <b>102</b></i>, \r
-7211-7218 (1980). The routine constructs the \r
-orthogonal matrix (T) for the NAO to NBO\r
-transformation from the input NAO density matrix (DM). The efficiency\r
-of the search procedure is enhanced by using the \r
-NAO-Wiberg bond index as a 'GUIDE' to order the NBO search.\r
-<p>\r
-[Beware the IBXM bond orbital permutation list (!), which reorders the\r
-LABEL array of COMMON/NBBAS/. The occupancy threshold, THRESH, determines\r
-whether an NBO is accepted during the search for bond orbitals (cf. SR CYCLES).\r
-Two numerical thresholds\r
-(PRJTHR, PRJINC) control possible linear dependencies: In\r
-the main loops over 1-c, 2-c (and 3-c) functions, each prospective\r
-NBO is checked for possible redundancy with previous NHOs by\r
-the PRJEXP (projection operator expectation value) test. The\r
-threshold PRJTHR for a 'new' hybrid is initially set\r
-conservatively low (0.20),\r
-but will be auto-incremented by PRJINC (0.05) as needed to prevent\r
-linear dependency; any numerical singularity triggers IALARM and\r
-causes PRJTHR to be incremented and the entire NBO search repeated.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR CHSDRV(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,</pre> <p>\r
-P,TA,HYB,VA,VB,TOPO) \r
-This routine, the "$CHOOSE driver," reads the $CHOOSE keylist,\r
-setting up the arrays NTOPO and I3CTR of COMMON/NBTOPO/ which will\r
-control the directed NBO search of SR CHOOSE.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CHOOSE(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,</pre> <p>\r
-P,TA,HYB,VA,VB,TOPO,IFLG) \r
-This routine is essentially similar to SR NATHYB, but the search\r
-loops are directed by the $CHOOSE specification.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SRTNBO(T,BNDOCC)</pre> \r
-Reorders (dangerous!) the NBOs according to bond type and constituent atomic\r
-centers. NBOs are ordered BD (and 3C), CR, LP, LP*, RY*, BD* (and 3C*).\r
-Note that this step is not required for the proper execution of any of the\r
-NBO analysis or NLMO formation routines, but it leads to more readable\r
-output.\r
-<p>\r
-<p>\r
-<u></u><pre>SR XCITED(DM,T,HYB,THYB,S,OCC,SCR,ISCR)</pre> \r
-Examines PNHO overlaps to determine whether NBOs were properly labelled\r
-as 'bonds' (unstarred, Lewis) or 'antibonds' (starred, non-Lewis)\r
-in the NBO formation routines (SR NATHYB and SR CHOOSE). If incorrect\r
-nodal character is recognized in a bond or antibond (generally indicative\r
-of an excited state), a warning is printed\r
-and the orbital is relabelled. Note that this will probably mix the\r
-NBO ordering set by SR SRTNBO.\r
-<p>\r
-<p>\r
-<u></u><pre>SR ANLYZE(T,BNDOCC,HYB,HYCOEF,THYB)</pre> \r
-Prints out the principal table (Section A.3.3) \r
-of NBO analysis [using the IBXM ordering!],\r
-expressing each NHO in <i>sp<sup><img src=lambda.gif></sup></i> form.\r
- \r
-<p>\r
-<br><u></u><pre>SR HTYPE(HYB,LTYP,MXAO,NH,COEF,PCT,NL,ISGN)</pre> <p>\r
-Analyzes input hybrid for polarization coefficient and percentages\r
-of each angular momentum component (accepts up to <i>g</i> orbitals).\r
-<p>\r
-<p>\r
-<u></u><pre>SR FRMHYB(HYB,THYB,COEFF,HYCLEF,KL,KU,NHYB)</pre> <p>\r
-Forms the NAO to NHO transformation (THYB) and saves it on the DAF.\r
-<p>\r
-<p>\r
-<u></u><pre>SR HYBDIR(BNDOCC,ATCOOR,THYB,TBND,SCR)</pre> \r
-Computes hybrid directionality and bond bending angles as determined from\r
-percentage <i>p</i>-character for selected\r
-NBOs, and prints the BEND table \r
-(Section A.3.4). [Keyword-selectable thresholds\r
-ATHR (angular deviation), PTHR (% <i>p</i>-character), and ETHR (occupancy)\r
-control printing.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR HYBCMP(XYZ,PCENT,IHYB,JCTR,HYB)</pre> \r
-Finds direction and percentage <i>p</i>-character of a given hybrid.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FNDMOL(IATOMS)</pre> \r
-Finds 'molecular units' from NBO connectivity.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBOCLA(BNDOCC,ACCTHR)</pre> \r
-Classifies NBOs according to donor/acceptor type, number of atomic centers,\r
-and parent molecular unit.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FNBOAN(BNDOCC,F,MOLNBO)</pre> \r
-Performs the 2nd-order perturbation theory energy analysis of\r
-the NBO Fock matrix and prints the table (Section A.3.5). [Thresholds ETHR1\r
-(intramolecular) and ETHR2 (intermolecular) control printing.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBOSUM(F,BNDOCC,LIST,LISTA,SCR)</pre> \r
-Prepares and prints the NBO summary table (Section A.3.6).\r
-<p>\r
-<p>\r
-<u></u><pre>SR GETDEL(IBO,OCC,THR1,THR2,NL,LIST,DEL,DELOC,IFLG)</pre> <p>\r
-Assembles the delocalization list, LIST(NL), for the IBO<sup>th</sup> \r
-NBO. Only intramolecular and intermolecular delocalizations which are\r
-stronger than THR1 and THR2 (in kcal mol<sup>-1</sup>), respectively,\r
-are included in the list.\r
-<p>\r
-<p>\r
-<u></u><pre>SR BLDSTR(IBO,IL,NL,LIST,ML,ISTR)</pre> \r
-Builds a character string containing delocalization information for the\r
-NBO summary table.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NLMO(N,A,EVAL,EVEC,TSYM,RESON,NOCC,IALARM)</pre> <p>\r
-This is the main routine for determination of the NLMOs, following\r
-closely the description given by A. E. Reed and F. Weinhold,\r
-<i>J. Chem. Phys. <b>83</b></i>, 1736-1740 (1985). [Numerical thresholds\r
-DIFFER (10<sup>-5</sup>), DONE (10<sup>-10</sup>), and EPS (10<sup>-11</sup>)\r
-control the modified Jacobi diagonalizations.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR LMOANL(T,S,RESON,OCC,TS,BORDER,OWBORD,ATLMO,SIAB,NOCC,NAB)</pre> <p>\r
-Prints out details of the NAO<img src=rarr.gif>NLMO transformation and\r
-the NAO/NLMO bond order table (Section B.6.2).\r
-<p>\r
-<p>\r
-<u></u><pre>SR DIPANL(DM,T,C,TNBO,DX,DY,DZ,SCR,INDEX)</pre> \r
-Calculates and prints out the DIPOLE analysis table (Section B.6.3).\r
-<p>\r
-<p>\r
-<u></u><pre>SR DIPELE(DXYZ,C,T,SCR,ETA,TOANG,NOCC,INDEX)</pre> \r
-Evaluates the <i>x,y,z</i> (INDEX = 1,2,3) electronic dipole moment\r
-contributions, including delocalization contributions, for each\r
-occupied NBO.\r
-<p>\r
-<p>\r
-<u></u><pre>SR DIPNUC(DX,DY,DZ,ATCOOR,ETA,NOCC)</pre> <p>\r
-Evaluates the nuclear contributions (DX, DY, DZ) to the molecular\r
-dipole moment.\r
-<p>\r
-<p>\r
-The following routines are called by SR NATHYB and SR CHOOSE \r
-in calculating the NBOs. Overall supervision\r
-of this set of routines is exercised by SR CYCLES. Other routines\r
-are associated with specific steps of the NBO algorithm:\r
-<p>\r
-<p>\r
-<u></u><pre>SR CORE(DM,T,BORB,POL,Q,HYB,BNDOCC,IBD,DETAIL,LFNPR)</pre> <p>\r
-Performs the first step in the search for NBOs. This routine identifies\r
-core orbitals and depletes the NAO density matrix of their contributions.\r
-<p>\r
-<p>\r
-<u></u><pre>FN IWPRJ(NCTR)</pre> \r
-This function returns zero (no projection wanted)\r
-if still on the same atomic center, or one (projection operator should\r
-be formed) if this is a new center.\r
-<p>\r
-<p>\r
-<u></u><pre>SR DEPLET(DM,T,Q,POL,BORB,BNDOCC,NBD)</pre> \r
-'Depletes' density matrix of contribution from bond orbital (BORB), by\r
-subtracting its diagonal contribution from the spectral expansion of\r
-the density operator. This insures that the same electron pair will\r
-not be found twice in the NBO loops.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LOAD(DM,IAT1,IAT2,IAT3,BLK,NB)</pre> \r
-Loads the appropriate atomic blocks of the density matrix\r
-into the local (2-c, 3-c) density matrix subblock (BLK), in\r
-preparation for diagonalization.\r
-<p>\r
-<p>\r
-<u></u><pre>SR PRJEXP(BORB,IAT1,IAT2,IAT3,Q,P,PK,HYB,VA,VB,HYBEXP)</pre> <p>\r
-Determines how much of a prospective bond orbital (BORB) is composed\r
-of hybrids already used. The projection operator onto the space of\r
-previously accepted hybrids is used to evaluate the expectation\r
-value of each hybrid component of BORB.\r
-<p>\r
-<p>\r
-<u></u><pre>SR STASH(BORB,IBD,IAT1,IAT2,IAT3,POL,Q,HYB)</pre> <p>\r
-Decomposes bond orbital (BORB) into constituent normalized hybrids\r
-and stores them in the hybrid array (Q).\r
-<p>\r
-<p>\r
-<u></u><pre>SR ORTHYB(Q,S,TA,EVAL,C,IALARM,IFLG)</pre> <p>\r
-Performs symmetric (Löwdin) orthogonalization on occupied\r
-atomic hybrids (PNHOs) to give final NHOs. [Threshold TOOSML\r
-(10<sup>-4</sup>) turns on the alarm (IALARM) to warn of numerical\r
-instabilities due to linear dependence.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR FRMPRJ(P,IA,Q,NK,PK,VK,PI)</pre> <p>\r
-Forms projection matrix to annihilate components of the occupied\r
-atomic hybrids on a given center.\r
-<p>\r
-<p>\r
-<u></u><pre>SR AUGMNT(P,BLK,C,EVAL,DM,TA,BORB,V,LARC,IA,NOCC,NORB)</pre> <p>\r
-This routine augments the set of occupied atomic hybrids on a center\r
-with a sufficient number of Rydberg AOs (in order of occupancy) to\r
-complete the span of the basis set on that atom. \r
-<p>\r
-<p>\r
-<u></u><pre>SR REPOL(DM,Q,POL,BLK,EVAL,C,NBD)</pre> <p>\r
-Diagonalizes each 2x2 block of the density matrix in the basis of\r
-final NHOs to get the optimal polarization coefficients for each NBO. \r
-<p>\r
-<p>\r
-<u></u><pre>SR FORMT(T,Q,POL)</pre> \r
-Constructs the final NAO to NBO transformation matrix (T) from\r
-the final array of NHOs (Q) and polarization coefficients (POL).\r
-<p>\r
-<p>\r
-<u></u><pre>SR CYCLES(ITER,THRESH,GUIDE,BNDOCC,TOPO,ICONT)</pre> <p>\r
-Controls the overall search for an acceptable resonance structure,\r
-including the lowering of the occupancy threshold (THRESH) for the\r
-RESONANCE keyword. Decides whether a structure is acceptable,\r
-initiates reordered searches over atoms for alternative resonance structures,\r
-and returns with the best overall structure. Prints the \r
-initial table (Section A.3.3) of the NBO output.\r
-<p>\r
-The final routines of this group are auxiliary to the formation\r
-of NLMOs, called by SR NLMO:\r
-<p>\r
-<p>\r
-<u></u><pre>SR SYMUNI(TSYM,A,COS,SIN,OVLP,BLK,EVAL,NROT,NIUNIQ,NJUNIQ,ILIST,</pre> <p>\r
-JLIST,NOFF,IOFF,JOFF,NDIM) <p>\r
-Symmetrizes the unitary transformation matrix (TSYM) to preserve\r
-symmetries inherent in the density matrix, using symmetric\r
-orthogonalization of columns (if necessary) to preserve unitarity.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SYMORT(S,T,BLK,NDIM,N,EVAL)</pre> \r
-Symmetric orthogonalization of a set of column vectors (T). [Thresholds\r
-DIAGTH (10<sup>-12</sup>) for off-diagonal Jacobi diagonalization\r
-and DANGER (10<sup>3</sup>) to detect singularities of the overlap matrix;\r
-all eigenvalues of S must be less than DIAGTH*DANGER.]\r
-<p>\r
-<b>C.6 ENERGY ANALYSIS ROUTINES (GROUP II)</b>\r
-<p>\r
-The small set of routines in this group carry out the second main\r
-task of NBO analysis, the NBO Energetic Analysis ("deletions,"\r
-associated with inclusion of a $DEL keylist; Section B.5). These routines\r
-depend on the presence of a Fock matrix, and are bypassed in\r
-any non-SCF calculation.\r
-<p>\r
-Overall control of Group II routines is with SR NBOEAN, which in turn\r
-calls the remaining programs of this group:\r
-<p>\r
-<u></u><pre>SR NBOEAN(A,MEMORY,NBOOPT,IDONE)</pre> <p>\r
-The task performed by this subroutine is dependent of the value of\r
-NBOOPT(1). If set to 2, this routine initiates (by calling SR NBODEL)\r
-the calculation of the next NBO deletion of the $DEL keylist. If set\r
-to 3, this routine completes the NBO deletion by computing the energy\r
-for the deletion. INTEGER variable IDONE is set to 1 if no additional\r
-deletions are found in the $DEL keylist.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBODEL(A,MEMORY,IDONE)</pre> \r
-Controls the calculation of the new AO density matrix from the requested\r
-deletion in the $DEL keylist. A modified NBO Fock matrix is created\r
-(SR DELETE) and diagonalized (SR JACOBI), leading to a new AO density\r
-matrix (SR NEWDM). This routine also prints the NBO deletions table\r
-(Section B.6.10).\r
-<p>\r
-<p>\r
-<u></u><pre>SR DELETE(F,TRF,NDIM,IDEL,LEN,ITYPE,NDEL,NTRUNC,DONE,ISPIN)</pre> <p>\r
-Reads the $DEL list for the next deletion, deletes (sets \r
-to zero) the appropriate\r
-elements from the Fock matrix, and prints out the deletion specification\r
-Section B.6.10).\r
-<p>\r
-<p>\r
-<u></u><pre>SR NEWDM(DM,U,EIG,NDIM,IDEL,LEN,NDEL,ITYPE,NMOOCC,ISPIN)</pre> \r
-Constructs a new density matrix corresponding to the deleted Fock matrix.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RNKEIG(RANK,EIG,N,NDIM,ARCRNK)</pre> <p>\r
-Ranks the eigenvalues found in vector EIG (lowest eigenvalue having\r
-first rank). I = ARCRNK(N) is the entry whose rank is N.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SIMLTR(N,NDIM,F,U,R,S,KNTROL)</pre> <p>\r
-Performs the similarity transform U<sup>t</sup>*F*U on a packed\r
-upper-triangular matrix F.\r
-<p>\r
-<b>C.7 DIRECT ACCESS FILE ROUTINES (GROUP III)</b>\r
-<p>\r
- The routines of Group III are involved in communication between\r
-the NBO programs and the FILE48\r
-direct access file (DAF), whose contents\r
-are described in Section C.4. Two levels of I/O routines are employed.\r
-<p>\r
- The higher-level 'fetch/save' routines are called directly by the NBO\r
-subroutines.\r
-In most cases, the\r
-function of the fetch/save routines can be recognized by its name or argument\r
-list; e.g., "FETITL(TITLE)" fetches\r
-the job title line, "FEFAO(F,IWFOCK)" fetches \r
-the AO Fock matrix (FAO),\r
-and so forth. Each routine can also be associated with a\r
-logical record number (IDAR) of the direct access file (Section C.4),\r
-where the I/O item is stored. We list these \r
-routines in order of appearance, together with the associated\r
-direct access file record number(s) IDAR, without further description:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left>routine</td><td align=center>IDAR</td><td align=left>routine</td><td align=center>IDAR</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-<tr><td align=left>SR FETITL(TITLE)</td><td align=center>2</td><td align=left>SR SVTLMO(T)</td><td align=center>49</td></tr>\r
-<tr><td align=left>SR FEE0(EDEL,ETOT)</td><td align=center>8</td><td align=left>SR FETLMO</td><td align=center>49</td></tr>\r
-<tr><td align=left>SR SVE0(EDEL)</td><td align=center>8</td><td align=left>SR SVTNHO</td><td align=center>47</td></tr>\r
-<tr><td align=left>SR FECOOR(ATCOOR)</td><td align=center>9</td><td align=left>SR FETNHO</td><td align=center>47</td></tr>\r
-<tr><td align=left>SR FESRAW(S)</td><td align=center>10</td><td align=left>SR SVPPAO(DM)</td><td align=center>22</td></tr>\r
-<tr><td align=left>SR FEDRAW(DM,SCR)</td><td align=center>20,21</td><td align=left>SR FEPPAO(DM)</td><td align=center>22</td></tr>\r
-<tr><td align=left>SR FEFAO(F,IWFOCK)</td><td align=center>30,31</td><td align=left>SR SVTNAO(T)</td><td align=center>43</td></tr>\r
-<tr><td align=left>SR FEAOMO(T,IT)</td><td align=center>40,41</td><td align=left>SR FETNAO(T)</td><td align=center>43</td></tr>\r
-<tr><td align=left>SR FEDXYZ(DXYZ,I)</td><td align=center>50-52</td><td align=left>SR SVNLMO(T)</td><td align=center>46</td></tr>\r
-<tr><td align=left>SR SVNBO(T,OCC,ISCR)</td><td align=center>44,45</td><td align=left>SR FENLMO(T)</td><td align=center>46</td></tr>\r
-<tr><td align=left>SR FENBO(T,OCC,ISCR,NELEC)</td><td align=center>44,45</td><td align=left>SR SVDNAO(DM)</td><td align=center>23,24</td></tr>\r
-<tr><td align=left>SR FETNBO(T)</td><td align=center>44,45</td><td align=left>SR FEDNAO(DM)</td><td align=center>23,24</td></tr>\r
-<tr><td align=left>SR SVPNAO(T)</td><td align=center>42</td><td align=left>SR SVFNBO(F)</td><td align=center>34,35</td></tr>\r
-<tr><td align=left>SR FEPNAO(T)</td><td align=center>42</td><td align=left>SR FEFNBO(F)</td><td align=center>34,35</td></tr>\r
-<tr><td align=left>SR SVSNAO(S)</td><td align=center>11</td><td align=left>SR SVNEWD(DM)</td><td align=center>25,26</td></tr>\r
-<tr><td align=left>SR FESNAO(S)</td><td align=center>11</td><td align=left>SR FENEWD(DM)</td><td align=center>25,26</td></tr>\r
-<tr><td align=left>SR SVTNAB(T)</td><td align=center>48</td><td align=left>SR FEINFO(ICORE,ISWEAN)</td><td align=center>3</td></tr>\r
-<tr><td align=left>SR FETNAB(T)</td><td align=center>48</td><td align=left>SR FEBAS(NSHELL,NEXP,ISCR)</td><td align=center>5</td></tr>\r
-<tr><td colspan=4><hr></td></tr>\r
-</table>\r
- In turn, the fetch/save routines call the following lower-level,\r
-primitive subprograms,\r
-which open, close, read, write, and test the contents of the DAF\r
-(these are heavily modified versions of the direct\r
-access file subroutines of HONDO):\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBOPEN(NEW,ERROR)</pre> <p>\r
-Opens a new or existing unformatted DAF depending in the value of logical\r
-variable NEW. Record lengths are currently set at 256 (LENGTH) single\r
-precision words (1024 bytes), and\r
-up to 100 (NBDAR) logical records can be written. Note that logical records\r
-and physical records of the DAF are not equivalent; single logical records\r
-can span several physical records and need not be ordered sequentially.\r
-The array IONBO (in COMMON/NBODAF/) maps each logical record with its\r
-associated physical records. The first physical record of the DAF is\r
-reserved for COMMON/NBODAF/. [Note: Some machines may require \r
-that you alter the parameters LENGTH (the chosen\r
-record length) and ISINGL (a record length scaling factor).]\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBWRIT(IX,NX,IDAR)</pre> <p>\r
-Writes NX double precision words of array IX to logical record number IDAR\r
-of the NBO DAF.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBREAD(IX,NX,IDAR)</pre> \r
-Reads NX double precision words of the logical record number IDAR of the \r
-NBO DAF.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBCLOS</pre> \r
-Rewrites common block /NBODAF/ on the first physical record of the DAF, and\r
-closes the file.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBINQR(IDAR)</pre> <p>\r
-Inquires whether information has been stored in logical record IDAR of\r
-the direct access file, and sets IDAR=0 if the record is empty.\r
-<p>\r
-<b>C.8 FREE FORMAT INPUT ROUTINES (GROUP IV)</b>\r
-<p>\r
- The routines of Group IV are the small set of system-independent\r
-free-format input routines that are used in reading the various\r
-keylists and datalists of the input \r
-file. The routines of this group are the\r
-'primitives' that read and interpret individual keywords or\r
-entries of a keylist. They are called by higher-level\r
-I/O routines (such as SR JOBOPT of Group I) throughout the NBO program.\r
-<p>\r
-The free-format input primitive routines are:\r
-<p>\r
-<u></u><pre>SR STRTIN(LFNIN)</pre> <p>\r
-Initializes input from the LFNIN input file.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RDCARD</pre> <p>\r
-Reads the next 'card' (line) of the input file, and stores this line in\r
-the integer array ICD in COMMON/NBCRD1/ with all lower case characters\r
-converted\r
-to upper case. Logical variable END in COMMON/NBCRD2/ is set to .TRUE. if\r
-the end-of-file is encountered.\r
-<p>\r
-<p>\r
-<u></u><pre>SR IFLD(INT,ERROR)</pre> <p>\r
-Searches input file LFNIN for the next string of non-blank characters,\r
-and checks to see if they form an integer. If so, the numerical value\r
-of the integer is placed in INT. If not, the logical variable ERROR is\r
-set to .TRUE. and INT is set positive (indicating an "END" terminating\r
-mark or end-of-file was encountered) or negative (indicating that the\r
-character string is not an integer).\r
-<p>\r
-<p>\r
-<u></u><pre>SR RFLD(REAL,ERROR)</pre> <p>\r
-Similar to SR IFLD, but for a real number REAL. This routine will accept\r
-real numbers in a variety of different formats. For example, 1000 can be\r
-represented by 1000, 1000.0, 1.0E3, D3, 1+3, etc.\r
-<p>\r
-<p>\r
-<u></u><pre>SR HFLD(KEYWD,LENG,ENDD)</pre> <p>\r
-Similar to SR IFLD and RFLD, but for a Hollerith array KEYWD(LENG).\r
-The logical variable ENDD is set to .TRUE. if the "END" terminating\r
-mark or the\r
-end-of-file is encountered. On return to the calling subroutine, LENG\r
-is set to the length of the string in KEYWD or to zero if the end-of-file\r
-is encountered.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FNDFLD</pre> <p>\r
-Searches for the next non-blank field on the input file, reading\r
-additional lines if necessary. Commas and equal signs are treated as\r
-blanks, and any character string which follows an exclamation point\r
-is treated as an arbitrary comment, and is ignored.\r
-The contents of this field are stored\r
-in the integer array LOOK of length LENGTH in COMMON/NBCRD1/.\r
- \r
-<br><u></u><pre>FN EQUAL(IA,IB,L)</pre> <p>\r
-This logical function tests the equivalence of the first 'L' elements of\r
-the Hollerith strings IA and IB.\r
-<p>\r
-<b>C.9 OTHER SYSTEM-INDEPENDENT I/O ROUTINES (GROUP V)</b>\r
-<p>\r
- This section summarizes the I/O routines of Group V. These routines\r
-perform a variety of auxiliary I/O tasks, such as the reading\r
-or writing of matrices, or perform functions closely related to I/O.\r
-<p>\r
- The first set of programs in this group are responsible for\r
-searching for the $GENNBO, $NBO, $CORE, $CHOOSE, and $DEL identifiers\r
-of the job input file LFNIN:\r
-<p>\r
-<p>\r
-<u></u><pre>SR GENINP(NEWDAF)</pre> <p>\r
-Searches for the $GENNBO identifier. In addition, this routine\r
-reads in the keywords of the $GENNBO keylist (see Section B.7),\r
-setting the option flags of COMMON/NBOPT/ and COMMON/NBGEN/ appropriately.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NBOINP(NBOOPT,IDONE)</pre> <p>\r
-Searches for the $NBO identifier according to the program version number,\r
-NBOOPT(10). The integer variable IDONE is\r
-set to 0 if this identifier is located, or 1 otherwise.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CORINP(IESS,ICOR)</pre> <p>\r
-Searches for the $CORE identifier according to the program version number,\r
-IESS. The integer variable ICOR is\r
-set to 1 if this identifier is located, or 0 otherwise.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CHSINP(IESS,ICHS)</pre> <p>\r
-Searches for the $CHOOSE identifier according to the program version number,\r
-IESS. The integer variable ICHS is\r
-set to 1 if this identifier is located, or 0 otherwise.\r
-<p>\r
-<p>\r
-<u></u><pre>SR DELINP(NBOOPT,IDONE)</pre> <p>\r
-Searches for the $DEL identifier according to the program version number,\r
-NBOOPT(10). The integer variable IDONE is\r
-set to 0 if this identifier is located, or 1 otherwise.\r
-<p>\r
- The remaining routines of this group perform miscellaneous I/O functions:\r
-<p>\r
-<p>\r
-<u></u><pre>SR RDCORE(JCORE)</pre> <p>\r
-Initializes the atomic core array (IATCR on COMMON/NBATOM/), and reads\r
-the entries of the $CORE keylist.\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRPPNA(T,OCC,IFLG)</pre> <p>\r
-Writes the transformation from 'pure'\r
-AOs to PNAOs, the NAO labels (NAOCTR, NAOL, and LSTOCC from COMMON/NBBAS/),\r
-and PNAO occupancies (diagonal PNAO density matrix elements) to an external\r
-file (LFN = -IFLG). Pure AOs (PAOs) are obtained\r
-from 'raw' cartesian AOs by the transformations of SR DFGORB.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RDPPNA(T,OCC,IFLG)</pre> <p>\r
-Reads the transformation from 'pure' AOs (PAOs) to PNAOs, NAO labels, and\r
-PNAO occupancies from an external file (LFN = -IFLG/1000) (cf.\r
-SR WRPPNA).\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRTNAO(T,IFLG)</pre> <p>\r
-Writes the AO to NAO transformation (fetched from the DAF), NAO labels, and\r
-the PNAO overlap matrix (also fetched from the DAF) to an external file\r
-(LFN = -IFLG). Note that T is the PNAO overlap matrix when control is\r
-returned to the calling routine.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RDTNAO(DM,T,SCR,IFLG)</pre> <p>\r
-Reads the AO to NAO transformation, NAO labels, and PNAO overlap matrix from an\r
-external file (LFN = -IFLG/1000). The transformation and overlap\r
-matrices are saved on the\r
-DAF, and the input AO density matrix is transformed to the NAO basis. Note\r
-that T is the PNAO overlap matrix on return to the calling routine\r
-(cf. SR WRTNAO).\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRTNAB(T,IFLG)</pre> \r
-Writes the NAO to NBO transformation and NBO info (LABELS and IBXM arrays of\r
-COMMON/NBBAS/) to an external file (LFN = -IFLG).\r
-<p>\r
-<p>\r
-<u></u><pre>SR RDTNAB(T,DM,BNDOCC,SCR,IFLG)</pre> <p>\r
-Reads the NAO to NBO transformation and NBO info from an external\r
-disk file (LFN = -IFLG/1000). The input NAO density matrix is also\r
-transformed to the NBO basis, and the NBO occupancies are stored in\r
-BNDOCC (cf. WRTNAB).\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRTNBO(T,BNDOCC,ISCR,IFLG)</pre> <p>\r
-Writes the AO to NBO transformation, the NBO occupancies, and additional\r
-NBO info (NBOUNI, NBOTYP, LABEL, IBXM, and IATNO arrays) to an external\r
-disk file (LFN = -IFLG).\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRNLMO(T,DM,ISCR,IFLG)</pre> <p>\r
-Similar to SR WRTNBO but for NLMOs. Note that the NLMO labels are\r
-identical to the NBO labels.\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRBAS(SCR,ISCR,LFN)</pre> <p>\r
-Writes the atomic coordinates and AO basis set information to the 'AOINFO'\r
-file LFN. The information contained in this file is identical to that of the\r
-$COORD, $BASIS, and $CONTRACT datalists of the GENNBO input file (see Section\r
-B.7). For more information on the file format, see the subroutine source code.\r
-<p>\r
-<p>\r
-<u></u><pre>SR WRARC(SCR,ISCR,LFN)</pre> <p>\r
-Writes the 'ARCHIVE' file LFN (see Section B.7).\r
-<p>\r
-<p>\r
-<u></u><pre>SR AOUT(A,MR,NR,NC,TITLE,INDEX,IFLG)</pre> <p>\r
-General utility to write matrix A(MR,1) to an external file (LFN = -IFLG)\r
-or print it to the output file (IFLG = number of columns to print, 'FULL',\r
-'VAL', or 'LEW'). TITLE is a CHARACTER*80 matrix label, and the\r
-rows of A are labelled according to the value of INDEX = 0 (atoms), 1 (AOs),\r
-2 (NAOs), 3 (NHOs), 4 (NBOs), or 5 (NLMOs). This routine calls SR APRINT or\r
-SR AWRITE.\r
-<p>\r
-<p>\r
-<u></u><pre>SR APRINT(A,MR,NR,NC,TITLE,INDEX,MCOL)</pre> <p>\r
-Prints MCOL columns of matrix A to the output file. The format of the\r
-matrix is chosen according to the magnitude of the largest matrix element\r
-in A (cf. SR AOUT).\r
-<p>\r
-<p>\r
-<u></u><pre>SR AWRITE(A,MR,NR,NC,TITLE,LFN)</pre> <p>\r
-Writes matrix A to external disk file LFN (cf. SR AOUT).\r
-<p>\r
-<p>\r
-<u></u><pre>SR AREAD(A,MR,NR,NC,JOB,LFN,ERROR)</pre> <p>\r
-Reads NC columns of the matrix A(MR,1) from the external file LFN.\r
-The job title in the external file is returned to the calling subroutine\r
-in the Hollerith array, JOB(20), and the LOGICAL \r
-variable ERROR is set to .TRUE. if an error occurred while reading.\r
-<p>\r
-<p>\r
-<u></u><pre>SR OUTPUT(A,MR,MC,NR,NC)</pre> \r
-Prints the matrix A(MR,MC) to the standard output file. This routine is\r
-called only when the print formats of SR APRINT are unsuitable for matrix A.\r
-<p>\r
-<p>\r
-<u></u><pre>SR INTERP(STRING,LEN,IFLG,LFN,READ,ERROR)</pre> <p>\r
-Interprets the Hollerith array STRING(LEN), storing the result in IFLG. The\r
-contents of STRING can be any of the read/write/print parameters\r
-such as 'W38', 'PVAL', 'R43', etc., described in Section B.2.4,\r
-and the resulting value of IFLG is determined according to the \r
-discussion of COMMON/NBOPT/ in\r
-Section C.3. When this routine is called, IFLG should be set to its\r
-default value,\r
-LFN should be the default file for writing or reading, and LOGICAL variable\r
-READ should be set to .TRUE. if reading from an external file is allowed. \r
-The LOGICAL variable ERROR is set to .TRUE. if STRING is uninterpretable.\r
-<p>\r
-<p>\r
-<u></u><pre>FN IOINQR(IFLG)</pre> <p>\r
-Interprets IFLG as to whether the I/O item should be printed (IOINQR = 'PRNT'),\r
-read (IOINQR = 'READ'), or written out (IOINQR = 'WRIT') to an external file.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LBLAO</pre> <p>\r
-Forms labels for AOs and stores them in COMMON/NBLBL/.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LBLNAO</pre> <p>\r
-Forms labels for NAOs and stores them in COMMON/NBLBL/.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LBLNBO</pre> <p>\r
-Forms labels for NBOs and stores them in COMMON/NBLBL/.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LBLNHO(INHO,INBO,ICTR,NCTR)</pre> <p>\r
-Forms labels for NHOs and stores them in COMMON/NBLBL/.\r
-<p>\r
-<p>\r
-<b>C.10 GENERAL UTILITY ROUTINES (GROUP VI)</b>\r
-<p>\r
-The utility routines of Group VI perform a variety of mathematical\r
-and other general tasks (such as solving sets of linear\r
-equations), and are called from routines\r
-throughout the NBO program. They are grouped in alphabetical\r
-order (except for the final group of routines controlled by\r
-the SR LINEQ driver):\r
-<p>\r
-<p>\r
-<u></u><pre>SR ANGLES(X,Y,Z,THETA,PHI)</pre> <p>\r
-Converts cartesian coordinates (X,Y,Z) to corresponding polar\r
-angle THETA and azimuthal angle PHI in spherical polar coordinates.\r
-<p>\r
-<p>\r
-<u></u><pre>FN BDFIND(IAT,JAT)</pre> <p>\r
-LOGICAL function BDFIND is set to .TRUE. if there is at least one bond\r
-between atoms IAT, JAT.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CHEM(NAT,NATOMS,LISTA,NL,ISTR)</pre> <p>\r
-Builds a 'chemical formula' for the list of atoms in LISTA having\r
-been identified as belonging to a particular 'molecular unit'. The\r
-chemical formula is stored in the Hollerith array ISTR(NL). \r
-<p>\r
-<p>\r
-<u></u><pre>SR CONSOL(AUT,ALT,NDIM,N)</pre> <p>\r
-Consolidates an upper-triangular (AUT) and lower-triangular (ALT)\r
-matrix in a single matrix, stored in AUT. \r
-<p>\r
-<p>\r
-Converts the Hollerith array IJ(LEN) into an integer IK. This is the \r
-inverse of SR IDIGIT.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CONVRT(N,NC1,NC2)</pre> \r
-Converts a 2-digit integer N to two Hollerith characters NC1, NC2.\r
-<p>\r
-<p>\r
-<u></u><pre>SR COPY(A,B,NDIM,NR,NC)</pre> \r
-Copies matrix A to matrix B.\r
-<p>\r
-<p>\r
-<u></u><pre>SR CORTBL(IAT,ICORE,IECP)</pre> \r
-Stores the nominal "core table," giving the number of core\r
-<i>s</i>, <i>p</i>, <i>d</i>, <i>f</i> orbitals for elements 1-105 (H to Lw,\r
-and elements 104, 105). This table controls the number of\r
-high-occupancy unhybridized NAOs that will be isolated and\r
-removed as core NBOs (taking account also of any effective\r
-core potential).\r
-<p>\r
-<p>\r
-<u></u><pre>SR DEBYTE(I,IBYTE)</pre> <p>\r
-Decomposes a Hollerith variable I into its four individual\r
-Hollerith 'bytes' IBYTE(4).\r
-<p>\r
-<p>\r
-<u></u><pre>SR HALT(WORD)</pre> <p>\r
-Halts the execution of the NBO program if an unrecognizable keyword\r
-is found in the $NBO keylist.\r
-<p>\r
-<p>\r
-<u></u><pre>SR IDIGIT(KINT,IK,ND,MAXD)</pre> <p>\r
-Converts the INTEGER variable KINT in the first ND elements of the\r
-Hollerith array IK(MAXD). This is the inverse of SR CONVIN.\r
-<p>\r
-<p>\r
-<u></u><pre>FN IHTYP(IBO,JBO)</pre> \r
-This Hollerith function determines whether the IBO<img src=rarr.gif>JBO delocalization\r
-is vicinal ('v'), geminal ('g'), or remote ('r'), based on the derived NBO\r
-connectivity.\r
-<p>\r
-<p>\r
-<u></u><pre>SR JACOBI(N,A,EIVU,EIVR,NDIM,NVDIM,ICONTR)</pre> <p>\r
-Diagonalizes a real symmetric matrix by the Jacobi rotations\r
-method. If ICONTR=0, a standard Jacobi diagonalization (unconstrained\r
-2x2 rotations) is carried out. If ICONTR=1, the algorithm is\r
-prevented from mixing orbitals that are degenerate within 'DIFFER'\r
-if the off-diagonal element connecting them is less \r
-than 'DIFFER'. [Threshold DIFFER (10<sup>-5</sup>) controls\r
-degenerate mixing, DONE (10<sup>-13</sup>) is the maximum allowed\r
-off-diagonal element, and EPS (0.5x10<sup>-13</sup>) is a number\r
-between DONE and the machine precision.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR LIMTRN(T,M,A,B,NDIM,NBAS,NCDIM,NC,IOPT)</pre> <p>\r
-This routine carries out a 'limited' transformation of a matrix (T),\r
-using only the rows and columns specified by vector M. The\r
-operations performed are T*A, A<sup>t</sup>*T*A, or A<sup>t</sup>*T\r
-according to the value of IOPT.\r
-<p>\r
-<p>\r
-<u></u><pre>SR MATMLT(A,B,V,NDIM,N)</pre> \r
-Multiplies square matrices A*B (using scratch vector V) and\r
-stores result in A.\r
-<p>\r
-<p>\r
-<u></u><pre>SR MATML2(A,B,V,NDIM,N)</pre> <p>\r
-Multiplies A<sup>t</sup>*B (using scratch vector V) and stores the\r
-result in B. The algorithm assumes that A*B is a symmetric,\r
-so about half the work is saved. [SR MATML2 is typically the second step\r
-in a similarity transform of B by A, where B (and thus \r
-A<sup>t</sup>*B*A) is symmetric.]\r
-<p>\r
-<p>\r
-<u></u><pre>FN NAMEAT(IZ)</pre> <p>\r
-Returns the (Hollerith) atomic symbol for\r
-atomic number IZ <img src=le.gif> 103.\r
-<p>\r
-<p>\r
-<u></u><pre>SR NORMLZ(A,S,M,N)</pre> \r
-Normalizes the columns of A using the overlap matrix S.\r
-<p>\r
-<p>\r
-<u></u><pre>SR ORDER(RANK,LIST,N,NDIM,ARCRNK)</pre> <p>\r
-Ranks the positive elements of integer LIST(N), lowest values first. [RANK\r
-and ARCRNK are integer vectors, with I = ARCRNK(N) if LIST(I) is the\r
-element of rank N.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR PACK(T,NDIM,NBAS,L2)</pre> \r
-Packs the upper-triangular portion of the symmetric matrix T(NBAS,NBAS)\r
-the first L2 elements of T.\r
-<p>\r
-<p>\r
-<u></u><pre>SR RANK(EIG,N,NDIM,ARCRNK)</pre> <p>\r
-Orders the entries of vector EIG, highest values first. ARCRNK(I)\r
-is the old location of the I<sup>th</sup> highest value in EIG. On return,\r
-EIG(I) is the I<sup>th</sup> highest value. [Entries are not switched\r
-unless they differ by more than a DIFFER (5x10<sup>-8</sup>) \r
-threshold.]\r
-<p>\r
-<p>\r
-<u></u><pre>SR SIMTRN(A,T,V,NDIM,N)</pre> <p>\r
-Performs the general similarity transform T<sup>t</sup>*A*T of A by T, using\r
-scratch vector V.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SIMTRS(A,S,V,NDIM,N)</pre> <p>\r
-Performs the 'fast' similarity transform S<sup>t</sup>*A*S, assuming the\r
-result is symmetric.\r
-<p>\r
-<p>\r
-<u></u><pre>SR TRANSP(A,NDIM,N)</pre> \r
-Transposes the matrix A: A<img src=rarr.gif>A<sup>t</sup>.\r
-<p>\r
-<p>\r
-<u></u><pre>SR UNPACK(T,NDIM,NBAS,L2)</pre> \r
-Unpacks an upper triangular matrix (vector of length L2) into a\r
-symmetric matrix T(NBAS,NBAS).\r
-<p>\r
-<p>\r
-<u></u><pre>SR VALTBL(IAT,IVAL)</pre> <p>\r
-Specifies the nominal "valence table," giving the number of valence\r
-AOs of each symmetry type for elements 1-105.\r
-<p>\r
-<p>\r
-<u></u><pre>FN VECLEN(X,N,NDIM)</pre> <p>\r
-Evaluates Euclidean length of vector X.\r
-<p>\r
-<p>\r
-<u></u><pre>SR LINEQ(A,X,B,SCR,N,M,NDIM,MDIM,ZERTOL,EPS,MAXIT,LFNPR,IERR)</pre> <p>\r
-This and the three following routines constitute\r
-the linear equations package for solving the system\r
-A*X = B for matrix X by the method of Gaussian elimination.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FACTOR(A,W,D,IPIVOT,N,NDIM,ZERTOL,IFLAG)</pre> <p>\r
-Supports SR LINEQ.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FNDSOL(A,X,B,W,R,E,IPIVOT,N,NDIM,EPS,MAXIT,LFNPR,IERR)</pre> <p>\r
-Supports SR LINEQ.\r
-<p>\r
-<p>\r
-<u></u><pre>SR SUBST(X,W,B,IPIVOT,N,NDIM)</pre> <p>\r
-Supports SR LINEQ.\r
-<p>\r
-<b>C.11 SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)</b>\r
-<p>\r
- The routines of Group VII comprise the set of ESS-dependent\r
-driver routines which initiate the NBO and NBO energetic analyses and\r
-provide the NBO program with a variety of information about the\r
-electronic wavefunction. This section provides a brief, generic description of\r
-each of the driver routines. If you intend to write a set of routines\r
-for an ESS program not supported by this distribution, refer to the\r
-driver source code\r
-for additional guidance. Also, see Section C.13 for helpful\r
-hints for attaching the NBO program to an ESS package.\r
-<p>\r
- The driver routines are grouped together at the end of the NBO source\r
-code. Since multiple versions of each driver are provided (one for each\r
-supported ESS package and GENNBO), all of the executable lines in these\r
-routines are 'commented out' with an asterisk in the first column. In\r
-addition, every line of the drivers has an identifier '<i>XXX</i>DRV' in\r
-columns 73-78, where '<i>XXX</i>' is a 3-letter identifier for the associated\r
-ESS package. It is the responsibility of the program ENABLE to 'uncomment'\r
-the appropriate lines of the code for the requested program version\r
-(see Section A.2).\r
-<p>\r
- The system-dependent driver routines are:\r
-<p>\r
-<p>\r
-<u></u><pre>SR RUNNBO</pre> <p>\r
-Determines the\r
-logical file numbers for the input and output files (LFNIN and LFNPR)\r
-of the parent program, initializes the NBOOPT job option array \r
-Section C.5.1),\r
-and initiates the NBO analysis (SR NBO) and energetic analysis\r
-(SR NBOEAN). This routine is the only routine \r
-of the NBO program called directly\r
-by the parent ESS package.\r
-<p>\r
-<p>\r
-<u></u><pre>SR FEAOIN(CORE,ICORE,NBOOPT)</pre> <p>\r
-Interrogates the scratch files and COMMON blocks of the parent program,\r
-providing the NBO program with required information of the electronic\r
-wavefunction via the NBO COMMON blocks and FILE48 direct access file.\r
-(Note that for GENNBO, this routine directs the input of information\r
-from the GENNBO input file, FILE47.) The NBO COMMON blocks and FILE48\r
-records which must be initialized by SR FEAOIN are discussed in Sections\r
-C.3, C.4. Additional information on the COMMON blocks and scratch files\r
-of the parent ESS package is provided in the Appendices.\r
-<p>\r
-<p>\r
-<u></u><pre>SR DELSCF(CORE,ICORE,NBOOPT)</pre> <p>\r
-Performs one of two tasks, depending of the value of NBOOPT(1). If\r
-NBOOPT(1) is set to 2, SR DELSCF provides the parent ESS program with\r
-the modified density matrix generated by the NBO energetic analysis\r
-routines. The parent program will then compute the "deletion energy"\r
-for this modified wavefunction. If NBOOPT(1) is set to 3, SR DELSCF\r
-fetches the deletion energy from the parent program and writes it to\r
-the FILE48 direct access file. (The NBOOPT array is discussed in\r
-Section C.5.1).\r
-<p>\r
-<p>\r
-<b>C.12 GENNBO AUXILIARY ROUTINES</b>\r
-<p>\r
- An additional set of routines is provided for the GENNBO stand-alone\r
-program. These routines are called by the GENNBO driver routine FEAOIN\r
-and are responsible for reading the datalists of the GENNBO input file.\r
-Each of these routines rewinds the input file before searching sequentially\r
-for its associated datalist. Thus, the order of datalists (as well as\r
-keylists) in the input file is immaterial. Each routine also checks\r
-that all required information in the datalist is given and stores\r
-this information on the FILE48 direct access file or in the NBO COMMON blocks.\r
-<p>\r
- Below we list each GENNBO auxiliary routine, indicating its associated\r
-datalist, but without furthur explanation:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left><i>Datalist</i></td><td align=left>Auxiliary routine to read datalist</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>$COORD</td><td align=left>SR CRDINP(TITLE,ATCOOR,BOHR)</td></tr>\r
-<tr><td align=left>$BASIS</td><td align=left>SR BASINP</td></tr>\r
-<tr><td align=left>$CONTRACT</td><td align=left>SR CONINP(CORE,ICORE)</td></tr>\r
-<tr><td align=left>$OVERLAP</td><td align=left>SR SINP(CORE,UPPER)</td></tr>\r
-<tr><td align=left>$DENSITY</td><td align=left>SR DMINP(CORE,UPPER)</td></tr>\r
-<tr><td align=left>$FOCK</td><td align=left>SR FINP(CORE,UPPER,END)</td></tr>\r
-<tr><td align=left>$LCAOMO</td><td align=left>SR TINP(CORE)</td></tr>\r
-<tr><td align=left>$DIPOLE</td><td align=left>SR DIPINP(CORE,UPPER,BOHR)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<p>\r
-<b>C.13 ATTACHING NBO TO A NEW ESS PROGRAM</b>\r
-<p>\r
-This section briefly outlines the steps to be considered\r
-when attaching the NBO program to a new ESS package that is not supported\r
-by this distribution. \r
-<p>\r
-In general, you should try to identify the supported\r
-ESS package that is most similar to the ESS package you wish to use,\r
-and try to create driver routines modelled as closely as\r
-possible on those provided for the ESS. [In fact, examining the source code\r
-for driver routines of <i>all</i> supported ESS packages is\r
-good preparation for writing your own drivers.]\r
-<p>\r
-1. Decide where in the parent ESS package you wish to perform the NBO\r
-analysis. This will necessarily be placed after the calculation of the\r
-wavefunction (and the associated density matrix), usually near \r
-the wavefunction analysis routines (e.g., the perennial\r
-"Mulliken population\r
-analysis" section) or wavefunction properties \r
-section of the code. If possible,\r
-restrict the modification of your ESS source code to insertion of \r
-a single "CALL RUNNBO" statement at some point where\r
-the information required for NBO analysis is known to be available.\r
-<p>\r
-2. Check carefully for possible conflicts between the parent ESS program and\r
-the NBO program in (1) function or subroutine names, (2) COMMON\r
-block names, and (3) logical file assignments (LFNs) for I/O. NBO \r
-common block names all begin with /NB.../, and default\r
-LFN assignments are in the range 31-49. (Duplicate FN or SR names\r
-are detected by a linker.)\r
-<p>\r
-3. Create new driver (interfacing) subroutines RUNNBO, FEAOIN,\r
-and DELSCF to perform the functions briefly described in Section\r
-C.11, using the drivers provided with this\r
-distribution as templates insofar as possible. The following \r
-are a few helpful hints for each driver:\r
-<p>\r
-a. The RUNNBO routine should be relatively straightforward to write, following\r
-an analogous example provided in this distribution. Note that you\r
-can simply omit the calls to SR NBOEAN and SR DELSCF from RUNNBO if\r
-you do not plan to use the NBO energetic analysis (for example, because\r
-the DELSCF driver is unmanageable).\r
-<p>\r
-If your parent program is quite different from any of those supported by this\r
-distribution, choose an alternate version number [NBOOPT(10)], and carefully\r
-consider step 4 below.\r
-<p>\r
-b. Routine FEAOIN should fetch information about the electronic wavefunction\r
-from your ESS package and load it into the NBO COMMON blocks and FILE48\r
-direct access file. This requires intimate knowledge of where these items\r
-are stored in the ESS program, so the FEAOIN examples of the\r
-distribution may provide little direct guidance. See Sections \r
-C.3, C.4 for description of the NBO\r
-COMMON blocks and file records which must be initialized by this routine.\r
-<p>\r
-Note that the NBO analysis will perform properly without the information\r
-stored on logical records 2, 5, 9, 30, 31, 40, 41, and 50-52 of the\r
-direct access file. If information is not provided on these records, the\r
-NBO program will simply shut off (with warnings) any requested keyword\r
-options which are thereby incompatible. In addition, the overlap matrix\r
-of record 10 need not be provided if the input basis set is orthogonal,\r
-and the energies of record 8 are not required if the NBO energetic analysis\r
-is not implemented for your ESS package.\r
-<p>\r
-c. Creating routine DELSCF will require intimate knowledge of the SCF routines\r
-in the parent ESS program; again, versions of DELSCF\r
-provided with this distribution may only be of minimal \r
-assistance. As described in Section C.11, SR DELSCF is\r
-responsible for providing a modified AO density matrix to an SCF energy\r
-evaluator (one pass throught the SCF routines) and returning this\r
-new energy to the NBO deletion routines via the FILE48 direct access \r
-file. If you do not intend to employ the NBO\r
-energetic analysis, you need not provide this routine to the \r
-NBO program. [Note that the 2nd-order perturbation theory energy analysis\r
-will be carried out (provided the Fock matrix is available)\r
-even if you do not include the NBOEAN and DELSCF\r
-energy analysis routines.]\r
-<p>\r
-4. In addition to the explicitly system-dependent subroutines \r
-RUNNBO, FEAOIN, and DELSCF, there are\r
-a few routines within the NBO program which can be considered\r
-<i>quasi</i>-system dependent, and might, therefore, require modification.\r
-These are SR NBOSET (Section C.5.2) and the 'INP' routines NBOINP, CORINP,\r
-CHSINP, and DELINP (Section C.9):\r
-<p>\r
-a. SR NBOSET assigns the logical file\r
-numbers (LFNs) 31-49 to be used by the NBO program. As mentioned\r
-above, if these are in conflict\r
-with the files employed by the parent ESS program, the conflicting \r
-LFNs will have to be reassigned in this subroutine.\r
-<p>\r
-b. The 'INP' routines may have to be modified according to\r
-the manner in which the input file of the parent program should be processed by\r
-the NBO program. More specifically, these routines either \r
-rewind the input file before searching\r
-for their associated keylist identifier, or they simply begin searching\r
-the input file sequentially at the point where the parent program left off,\r
-depending on the version number specified in NBOOPT(10). Be sure this\r
-parameter is consistent with the way you wish to modify the\r
-ESS input file for NBO input.\r
-<p>\r
-<center>\r
-<h2>Section D: APPENDIX</h2>\r
-</center>\r
-<p>\r
-<b>D.1 INTRODUCTION</b>\r
-<p>\r
- This Appendix contains system-dependent information about NBO input\r
-and source code for the ESS (electronic structure system) packages supported\r
-by this distribution. We assume that the user has basic familiarity with\r
-the ESS program of interest.\r
-<p>\r
- The Appendix is organized according to the ESS packages supported,\r
-which are described in Sections D.2-D.7, as shown below:\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>ESS package</td><td align=center>Section</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=left>GAUSSIAN 88</td><td align=center>D.2</td></tr>\r
-<tr><td align=left>GAUSSIAN 86</td><td align=center>D.3</td></tr>\r
-<tr><td align=left>GAUSSIAN 82</td><td align=center>D.4</td></tr>\r
-<tr><td align=left>GAMESS</td><td align=center>D.5</td></tr>\r
-<tr><td align=left>HONDO</td><td align=center>D.6</td></tr>\r
-<tr><td align=left>AMPAC</td><td align=center>D.7</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
- Each ESS section contains information on:\r
-<p>\r
-1. Sample input file for RHF/3-21G methylamine\r
-<p>\r
-2. NBO program installation\r
-<p>\r
-3. Communication between the NBO drivers and the ESS program\r
-<p>\r
- For most users, only the first section(s) on sample input file will\r
-be required reading. For the programmer responsible for attaching the NBO\r
-program to an ESS package, the final section on NBO drivers will be\r
-important only if the available ESS version differs significantly from\r
-that assumed in the installation instructions.\r
-<p>\r
- In the Appendix we use "SR" and "FN" to denote subroutines\r
-and functions, respectively.\r
-<p>\r
-<p>\r
-<b>D.2 GAUSSIAN 88 VERSION</b>\r
-<p>\r
-<i>D.2.1 GAUSSIAN 88 sample input</i>\r
-<p>\r
- A sample GAUSSIAN 88 input file to\r
-recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)\r
-output displayed in Section A.3 is shown below:\r
-<p>\r
-<p>\r
- <pre>\r
-\r
-# RHF/3-21G\r
-\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
-\r
- 0 1\r
- C\r
- N 1 CN\r
- H 1 CH 2 tet\r
- H 1 CH 2 tet 3 120. 0\r
- H 1 CH 2 tet 3 240. 0\r
- H 2 NH 1 tet 3 60. 0\r
- H 2 NH 1 tet 3 300. 0\r
-\r
- CN 1.47\r
- CH 1.09\r
- NH 1.01\r
- tet 109.4712\r
-\r
-$NBO $END\r
-\r
- </pre>The keylists of the NBO program should always appear at the bottom of the\r
-GAUSSIAN 88 input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL.\r
-NBO job options are selected by inserting their\r
-associated keywords (Section B.2) into the $NBO keylist. All NBO keywords\r
-are applicable to the electronic wavefunctions computed by the GAUSSIAN 88\r
-programs.\r
-<p>\r
- If the NBO program \r
-encounters the end-of-file while searching for a keylist, the input file\r
-is rewound and the search for the keylist is continued. This is particularly\r
-useful for jobs which call the NBO analysis several times. For example, an\r
-MP2 calculation with the GAUSSIAN 88 option DENSITY=ALL causes Link 601 to\r
-loop over three densities (SCF, Rho2, and MP2), and hence, the NBO analysis\r
-is called three times, once for each density. A single $NBO keylist\r
-(and $CORE and $CHOOSE keylists) will suffice as input for all three analyses.\r
-Alternatively, separate $NBO keylists, one for each density, could be inserted\r
-at the bottom of the GAUSSIAN 88 input file.\r
-<p>\r
- The IOp parameters 40-43 of Link 601 exert additional control over the\r
-NBO program, as listed below:\r
-<p>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left>parameter</td><td align=center>value</td><td align=left>effect</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-<tr><td align=left>IOp(40)</td><td align=center>-2</td><td align=left>skip the NBO analysis</td></tr>\r
-<tr><td align=left> </td><td align=center>-1</td><td align=left>perform the NPA only</td></tr>\r
-<tr><td align=left> </td><td align=center>0</td><td align=left>perform the NBO analysis</td></tr>\r
-<tr><td align=left> </td><td align=center> </td><td align=left>(read keywords in $NBO)</td></tr>\r
-<tr><td align=left> </td><td align=center>1</td><td align=left>perform the default NBO analysis</td></tr>\r
-<tr><td align=left> </td><td align=center> </td><td align=left>(do not read keywords in $NBO)</td></tr>\r
-<tr><td align=left> </td><td align=center>2</td><td align=left>initiate NBO energetic analysis</td></tr>\r
-<tr><td align=left> </td><td align=center>3</td><td align=left>complete NBO energetic analysis</td></tr>\r
-<tr><td align=left>IOp(41)</td><td align=center>0</td><td align=left>SCF density</td></tr>\r
-<tr><td align=left> </td><td align=center>1</td><td align=left>MP first order density</td></tr>\r
-<tr><td align=left> </td><td align=center>2</td><td align=left>MP2 density</td></tr>\r
-<tr><td align=left> </td><td align=center>3</td><td align=left>MP3 density</td></tr>\r
-<tr><td align=left> </td><td align=center>4</td><td align=left>MP4 density</td></tr>\r
-<tr><td align=left> </td><td align=center>5</td><td align=left>CI one-particle density</td></tr>\r
-<tr><td align=left> </td><td align=center>6</td><td align=left>CI density</td></tr>\r
-<tr><td align=left> </td><td align=center>7</td><td align=left>QCI/CC density</td></tr>\r
-<tr><td align=left> </td><td align=center>8</td><td align=left>density correct to second order</td></tr>\r
-<tr><td align=left>IOp(42)</td><td align=center>1</td><td align=left>perform the dipole analysis</td></tr>\r
-<tr><td align=left> </td><td align=center> </td><td align=left>(force the DIPOLE keyword)</td></tr>\r
-<tr><td align=left>IOp(43)</td><td align=center>1</td><td align=left>allow strongly delocalized structures</td></tr>\r
-<tr><td align=left> </td><td align=center> </td><td align=left>(force the RESONANCE keyword)</td></tr>\r
-<tr><td colspan=3><hr></td></tr>\r
-</table>\r
-For example, to restrict the NBO output to the Natural Population\r
-analysis (NPA) only, set IOp(40) to -1 in all\r
-Link 601 entries of a GAUSSIAN 88 non-standard route, as shown below:\r
-<p>\r
-<pre> 6/40=-1/1;\r
-\r
-</pre>By default, the NBO analysis will be performed, reading keywords from\r
-the $NBO keylist [IOp(40)=0], on the density matrix for the current\r
-wavefunction. The DIPOLE and RESONANCE keywords are generally activated\r
-through the $NBO keylist rather than via the IOp parameters.\r
-<p>\r
-<i>D.2.2 NBO energetic analysis</i>\r
-<p>\r
- Due to the overlay structure of the GAUSSIAN 88 programs, a non-standard\r
-route must be employed to perform the NBO energetic analysis. The following\r
-table lists and describes the tasks of the GAUSSIAN 88 links in the order that\r
-they appear in the non-standard route:\r
-<p>\r
-<p>\r
-<i>LINK</i> <i>DESCRIPTION</i>\r
-<p>\r
-6/7=2,8=2,9=2,10=2,19=1/1; Perform the normal NBO analysis, storing information about the NBOs for\r
-the NBO energetic analysis on the FILE48 direct access file.\r
-<p>\r
-6/40=2/1(1); Read the next deletion listed in the $DEL keylist. If there are no more\r
-deletions, move to the next link. Otherwise, compute the modified density\r
-matrix, store it on the read-write files, and skip the next link in the\r
-non-standard route.\r
-<p>\r
-99/5=1,9=1/99; Finish GAUSSIAN 88 execution.\r
-<p>\r
-5/7=1,13=1/1,2; Using the modified density matrix, compute the deletion energy by\r
-a single pass through the SCF energy evaluator. Store the deletion energy\r
-on the read-write files.\r
-<p>\r
-6/40=3/1(-3); Read the deletion energy from the read-write files and complete the energetic\r
-analysis. Step backwards, in the non-standard route, three links.\r
-<p>\r
- The following is a GAUSSIAN 88 input file\r
-that will generate, in addition to the default NBO output, the NLMO\r
-(Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic\r
-(Section B.6.10) analyses of methylamine:\r
-<p>\r
- <pre>\r
-\r
-# NONSTD\r
-1//1;\r
-2//2;\r
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;\r
-4/7=1/1;\r
-5//1;\r
-6/7=2,8=2,9=2,10=2,19=1/1;\r
-6/40=2/1(1);\r
-99/5=1,9=1/99;\r
-5/7=1,13=1/1;\r
-6/40=3/1(-3);\r
-\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
-\r
- 0 1\r
- C\r
- N 1 CN\r
- H 1 CH 2 tet\r
- H 1 CH 2 tet 3 120. 0\r
- H 1 CH 2 tet 3 240. 0\r
- H 2 NH 1 tet 3 60. 0\r
- H 2 NH 1 tet 3 300. 0\r
-\r
- CN 1.47\r
- CH 1.09\r
- NH 1.01\r
- tet 109.4712\r
-\r
-$NBO NLMO DIPOLE $END\r
-$DEL NOSTAR\r
- ZERO 2 ATOM BLOCKS 4 BY 3\r
- 1 3 4 5\r
- 2 6 7\r
- 3 BY 4\r
- 2 6 7\r
- 1 3 4 5\r
-$END\r
-\r
- </pre>Note that for the GAUSSIAN 88 version of the NBO program, each deletion\r
-in the $DEL keylist must begin on a new line of the input file (the first\r
-deletion can follow the "$DEL" keylist identifier, as shown above). The\r
-"$END" keylist terminator must also appear on its own line.\r
-<p>\r
-<i>D.2.3 Geometry reoptimization with NBO deletions</i>\r
-<p>\r
- The structural effects of electron delocalization can be examined\r
-by coupling the NBO energetic analysis to the Fletcher-Powell (numerical)\r
-geometry optimization routines of the GAUSSIAN 88 package. The\r
-following GAUSSIAN 88 input file will reoptimize selected internal\r
-coordinates of RHF/3-21G methylamine in the absence of its strong\r
-<i>n</i><sub>N</sub><img src=rarr.gif><img src=sigma.gif><sup>*</sup><sub>CH</sub> hyperconjugative interaction:\r
-<p>\r
- <pre>\r
-\r
-#NONSTD\r
-1//1,2;\r
-2//2;\r
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;\r
-4/7=1/1;\r
-5//1;\r
-6/7=2,8=2,9=2,10=2,19=1/1;\r
-6/40=2/1(2);\r
-1//2(3);\r
-99/9=1/99;\r
-5/7=1,13=1/1;\r
-6/40=3/1(-4);\r
-2//2;\r
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;\r
-4/5=5,7=1,16=2/1;\r
-5//1;\r
-6/7=2,8=2,9=2,10=2,19=1/1;\r
-6/40=2/1(3);\r
-1//2(-6);\r
-2//2;\r
-99/9=1/99;\r
-5/7=1,13=1/1;\r
-6/40=3/1(-5);\r
-\r
-Methylamine...RHF/3-21G optimization with deletions\r
-\r
- 0 1\r
- C\r
- N 1 CN\r
- H 1 CHa 2 alfa\r
- H 1 CHb 2 beta 3 dlta 0\r
- H 1 CHb 2 beta 3 -dlta 0\r
- H 2 NH 1 gama 3 epsn 0\r
- H 2 NH 1 gama 3 -epsn 0\r
-\r
- CN 1.4713\r
- CHa 1.0901\r
- alfa 114.7843\r
-\r
- CHb 1.0825\r
- NH 1.0035\r
- beta 108.9484\r
- gama 113.6544\r
- dlta 121.4265\r
- epsn 64.2369\r
-\r
-$NBO PRINT=0 NBO $END ! Request reduced NBO output\r
-$DEL\r
- DELETE 1 ELEMENT 9 24\r
-$END\r
-\r
- </pre>Reoptimization of the internal coordinates specified in this example\r
-leads to lengthening of the C-N bond (1.513 Å) and closing of\r
-the H-C-N bond angle (108.3 °), as expected from\r
-lone pair/antibond overlap arguments. The C-H bond length contracts\r
-(1.075 Å) due to the removal of electron density from its antibond.\r
-<p>\r
- Note that the numerical optimization routines of the GAUSSIAN 88 program\r
-must be employed since analytic gradients are not available for the modified\r
-wavefunction of the NBO energetic analysis. Hence, these optimizations are\r
-time-consuming, generally requiring 8<i>n</i>-12<i>n</i> single point\r
-calculations (<i>n</i> = number of symmetry unique internal coordinates) before\r
-convergence of the gradients is obtained (the example requires 28 single\r
-point calculations before convergence). Careful selection of the coordinates\r
-to be optimized is recommended.\r
-<p>\r
-<i>D.2.4 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided\r
-in this distribution were written for the Revision C version of\r
-GAUSSIAN 88, dated 19-AUG-1988.\r
-Section D.2.5 lists the GAUSSIAN 88\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the GAUSSIAN 88 programs.\r
-<p>\r
- Three modifications to SR MulDrv of Link 601 are required to run the\r
-NBO analysis:\r
-<p>\r
- <pre>\r
-\r
-*Deck MulDrv\r
- Subroutine MulDrv(Core)\r
-\r
- .\r
- .\r
- .\r
-\r
- IEnd1 = IScr2 + NBasis - 1\r
- Call GetSCM(-1,Core,NGot,6hMulDrv,0)\r
-C\r
-C <<< Beginning of first NBO insert >>\r
-C\r
-C Run the NBO energetic analysis.\r
-C\r
- If(IOp(40).ge.2) then\r
- IDens = 0 ! SCF density for deletion runs\r
- IOp(41) = IDens\r
- Call RunNBO(Core,NGot,IOp,IContr)\r
- go to 999\r
- endIf\r
-C\r
-C <<< End of first NBO insert >>\r
-C\r
-C Put density matrices first.\r
-C\r
- IPA = IEnd1 + 1\r
-\r
- .\r
- .\r
- .\r
-\r
- Call ElEner(IOut,ISelfE,SCFDen,ISCF,IROHF,NAE,NBE,NBasis,\r
- $ Core(IPA),Core(IV),MDV)\r
-C\r
-C <<< Beginning of second NBO insert >>>\r
-C\r
-C Run the NBO analysis.\r
-C\r
- If(IOp(40).ne.-2) then\r
- IOp(41) = IDens\r
- Call RunNBO(Core,NGot,IOp,IContr)\r
- endIf\r
-C\r
-C <<< End of second NBO insert >>>\r
-C\r
- else if(IDens1.eq.IDSt.and.IDens1.eq.IDEnd) then\r
-\r
- .\r
- .\r
- .\r
-\r
- Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,\r
- $ Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))\r
-C\r
-C <<< Beginning of third NBO insert >>>\r
-C\r
-C The following line has been changed from "Call ChainX(0)" in\r
-C order to exit the NBO deletion loop after the deletions are done:\r
-C\r
- 999 Call ChainX(IContr)\r
-C\r
-C <<< End of third NBO insert >>>\r
-C\r
- Return\r
- End\r
-\r
- </pre>The first NBO insert initiates the NBO energetic analysis of\r
-SCF wavefunctions. The second insert lies within a loop over densities,\r
-and thus, the NBO program is called once for each density matrix analyzed\r
-by this link. The third insert allows the NBO energetic analysis to exit\r
-from the loop in the non-standard route.\r
-<p>\r
-The NBO program installation should continue as discussed in Section A.2.\r
-<p>\r
-<i>D.2.5 NBO communication with GAUSSIAN 88</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-GAUSSIAN 88 routines, read-write files, and COMMON blocks:\r
-<p>\r
-<u>GAUSSIAN 88 routines:</u><pre>\r
-\r
- SR CharPn(IString)\r
- SR DENGET(IOut,IODens,IMeth,LenDen,GotIt,P)\r
- FN ILSW(IOPER,WHERE,WHAT)\r
- FN InToWP(Nints)\r
- FN ITqry(Ifile)\r
- SR TRead(IARN,X,M,N,MM,NN,K)\r
- SR TWrite(IARN,X,M,N,MM,NN,K)\r
-\r
-</pre><u>GAUSSIAN 88 read-write files:</u>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>file</td><td align=left>contents</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>501</td><td align=left>Total energy</td></tr>\r
-<tr><td align=center>502</td><td align=left>Job title</td></tr>\r
-<tr><td align=center>506</td><td align=left>Basis set information</td></tr>\r
-<tr><td align=center>512</td><td align=left>Effective core potential information</td></tr>\r
-<tr><td align=center>514</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center>518</td><td align=left>AO dipole integrals</td></tr>\r
-<tr><td align=center>524</td><td align=left>MO coefficients (alpha)</td></tr>\r
-<tr><td align=center>526</td><td align=left>MO coefficients (beta)</td></tr>\r
-<tr><td align=center>528</td><td align=left>SCF density matrix (alpha)</td></tr>\r
-<tr><td align=center>530</td><td align=left>SCF density matrix (beta)</td></tr>\r
-<tr><td align=center>536</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center>538</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td align=center>603</td><td align=left>AO density matrix</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<u>GAUSSIAN 88 COMMON blocks:</u><pre>\r
-\r
- COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),\r
- + ATMCHG(400),C(1200)\r
- COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),\r
- + KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)\r
- COMMON/B/EXX(6000),C1(6000),C2(6000),C3(6000),X(2000),Y(2000),\r
- + Z(2000),JAN(2000),SHELLA(2000),SHELLN(2000),SHELLT(2000),\r
- + SHELLC(2000),AOS(2000),AON(2000),NSHELL,MAXTYP\r
- INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON\r
- DIMENSION C4(2000),SHLADF(2000)\r
- EQUIVALENCE(C4(1),C3(2001)),(SHLADF(1),C3(4001))\r
- </pre>\r
-<p>\r
-<b>D.3 GAUSSIAN 86 VERSION</b>\r
-<p>\r
-<i>D.3.1 GAUSSIAN 86 sample input</i>\r
-<p>\r
- See Section D.2.1. Note that the NBO IOp parameters of Link 601\r
-are set to 40-43 (changed from 20-23 in previous distributions of the NBO\r
-program).\r
-<p>\r
-<i>D.3.2 NBO energetic analysis</i>\r
-<p>\r
- See Section D.2.2.\r
-<p>\r
-<i>D.3.3 Geometry reoptimization with NBO deletions</i>\r
-<p>\r
- See Section D.2.3.\r
-<p>\r
-<i>D.3.4 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided\r
-in this distribution were written for the Revision C version of\r
-GAUSSIAN 86, dated 30-APR-1986.\r
-Section D.3.5 lists the GAUSSIAN 86\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the GAUSSIAN 86 programs.\r
-<p>\r
- Two modifications to SR MulDrv of Link 601 are required to run the\r
-NBO analysis:\r
-<p>\r
- <pre>\r
-\r
-*Deck MulDrv\r
- Subroutine MulDrv(Core)\r
- .\r
- .\r
- .\r
-\r
- If(NGot.lt.IEnd1) Write(IOut,2002) IEnd1, NGot\r
- Len2 = (NGot-I2A+1)/NTT\r
-C\r
-C <<< Beginning of first NBO insert >>>\r
-C\r
- IF(IOp(40).GE.2.OR.IOp(41).NE.0) GO TO 999\r
-C\r
-C <<< End of first NBO insert >>>\r
-C\r
-C Do population analysis.\r
-C\r
- CALL MULPOP(MaxAtm,IOP,IROHF,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,\r
-\r
- .\r
- .\r
- .\r
-\r
- Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,\r
- $ Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))\r
-C\r
-C <<< Beginning of second NBO insert >>>\r
-C\r
- 999 Call GetSCM(-1,Core(1),NGot,3HNBO,0)\r
- Call RunNBO(Core,NGot,IOp,IContr)\r
-C\r
-C The following line has been changed from "999 Call ChainX(0)" in\r
-C order to exit the NBO deletion loop after deletions are complete.\r
-C\r
- Call ChainX(IContr)\r
-C\r
-C <<< End of second NBO insert >>>\r
-C\r
- Return\r
- End\r
-\r
- </pre>The first NBO insert allows Link 601 to by-pass the Mulliken\r
-Population and electric moment analysis routines if the NBO energetic\r
-analysis is to be performed or if a correlated wavefunction is being\r
-analyzed. The second insert requests all available memory be allocated\r
-for the NBO program and initiates the NBO analysis. Note that the call\r
-to SR ChainX has been altered from the original code.\r
-<p>\r
-The NBO program installation should continue as discussed in Section A.2.\r
-<p>\r
-<i>D.3.5 NBO communication with GAUSSIAN 86</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-GAUSSIAN 86 routines, read-write files, and COMMON blocks:\r
-<p>\r
-<u>GAUSSIAN 86 routines:</u><pre>\r
-\r
- SR CharPn(IString)\r
- FN ILSW(IOPER,WHERE,WHAT)\r
- FN InToWP(Nints)\r
- FN ITqry(Ifile)\r
- SR TRead(IARN,X,M,N,MM,NN,K)\r
- SR TWrite(IARN,X,M,N,MM,NN,K)\r
-\r
-</pre><u>GAUSSIAN 86 read-write files:</u>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>file</td><td align=left>contents</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>203</td><td align=left>CI density matrix (alpha)</td></tr>\r
-<tr><td align=center>204</td><td align=left>CI density matrix (beta)</td></tr>\r
-<tr><td align=center>501</td><td align=left>Total energy</td></tr>\r
-<tr><td align=center>502</td><td align=left>Job title</td></tr>\r
-<tr><td align=center>506</td><td align=left>Basis set information</td></tr>\r
-<tr><td align=center>512</td><td align=left>Effective core potential information</td></tr>\r
-<tr><td align=center>514</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center>518</td><td align=left>AO dipole integrals</td></tr>\r
-<tr><td align=center>524</td><td align=left>MO coefficients (alpha)</td></tr>\r
-<tr><td align=center>526</td><td align=left>MO coefficients (beta)</td></tr>\r
-<tr><td align=center>528</td><td align=left>SCF density matrix (alpha)</td></tr>\r
-<tr><td align=center>530</td><td align=left>SCF density matrix (beta)</td></tr>\r
-<tr><td align=center>536</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center>538</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<u>GAUSSIAN 86 COMMON blocks:</u><pre>\r
-\r
- COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),\r
- + ATMCHG(400),C(1200)\r
- COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),\r
- + KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)\r
- COMMON/B/EXX(1200),C1(1200),C2(1200),C3(1200),X(400),Y(400),\r
- + Z(400),JAN(400),SHELLA(400),SHELLN(400),SHELLT(400),\r
- + SHELLC(400),AOS(400),AON(400),NSHELL,MAXTYP\r
- INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON\r
- DIMENSION C4(400),SHLADF(400)\r
- EQUIVALENCE(C4(1),C3(401)),(SHLADF(1),C3(801))\r
- </pre>\r
-<p>\r
-<b>D.4 GAUSSIAN 82 VERSION</b>\r
-<p>\r
-<i>D.4.1 GAUSSIAN 82 sample input</i>\r
-<p>\r
- See Section D.2.1. Note that the NBO IOp parameters of Link 601\r
-are set to 40-43 (changed from 20-23 in previous distributions of the NBO\r
-program).\r
-<p>\r
-<i>D.4.2 NBO energetic analysis</i>\r
-<p>\r
- See Section D.2.2.\r
-<p>\r
-<i>D.4.3 Geometry reoptimization with NBO deletions</i>\r
-<p>\r
- See Section D.2.3.\r
-<p>\r
-<i>D.4.4 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided\r
-in this distribution were written for the Revision H version of\r
-GAUSSIAN 82, dated 28-NOV-1983.\r
-Section D.4.5 lists the GAUSSIAN 82\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the GAUSSIAN 82 programs.\r
-<p>\r
- Two modifications to SR MulDrv of Link 601 are required to run the\r
-NBO analysis:\r
-<p>\r
- <pre>\r
-\r
-*Deck MulDrv\r
- Subroutine MulDrv(Core)\r
-\r
- .\r
- .\r
- .\r
-\r
- IF(IPRINT.NE.0)\r
- $WRITE(IOUT,2001)I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,IEND\r
-C\r
-C <<< Beginning of first NBO insert >>>\r
-C\r
-C The following line has been changed from "CALL GETSCM(IEND,...)",\r
-C in order to ask for all available memory.\r
-C\r
- CALL GETSCM(-1,CORE(1),JJJMEM,6HMULDRV,0)\r
-C\r
- IF(IOP(40).GE.2.OR.IOP(41).NE.0) GO TO 100\r
-C\r
-C <<< End of first NBO insert >>>\r
-C\r
-C DO THE POPULATION ANALYSIS.\r
- CALL MULPOP(IOP,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,IAN,AtmChg,\r
- $ C,Core(I1),CORE(I2),CORE(I3),CORE(I4),CORE(I5),\r
- $ CORE(I6),CORE(I7),CORE(I8),CORE(I9),CORE(I10))\r
-C\r
-C <<< Beginning of second NBO insert >>>\r
-C\r
- 100 CALL RUNNBO(CORE,JJJMEM,IOP,ICONTR)\r
-C\r
-C The following line has been changed from "CALL CHAINX(0)" in\r
-C order to exit the NBO deletion loop after deletions are complete.\r
-C\r
- CALL CHAINX(ICONTR)\r
-C\r
-C <<< End of second NBO insert >>>\r
-C\r
- RETURN\r
- END\r
-\r
- </pre>The first NBO insert allows Link 601 to by-pass the Mulliken\r
-Population analysis routines if the NBO energetic\r
-analysis is to be performed or if a correlated wavefunction is being\r
-analyzed. The second insert initiates the NBO analysis. Note that the calls\r
-to routines GETSCM and CHAINX have been altered from the original code.\r
-<p>\r
-The NBO program installation should continue as discussed in Section A.2.\r
-<p>\r
-<i>D.4.5 NBO communication with GAUSSIAN 82</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-GAUSSIAN 82 routines, read-write files, and COMMON blocks:\r
-<p>\r
-<u>GAUSSIAN 82 routines:</u><pre>\r
-\r
- SR CharPn(IString)\r
- FN ILSW(IOPER,WHERE,WHAT)\r
- FN InToWP(Nints)\r
- FN ITqry(Ifile)\r
- SR TRead(IARN,X,M,N,MM,NN,K)\r
- SR TWrite(IARN,X,M,N,MM,NN,K)\r
-\r
-</pre><u>GAUSSIAN 82 read-write files:</u>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>file</td><td align=left>contents</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>203</td><td align=left>CI density matrix (alpha)</td></tr>\r
-<tr><td align=center>204</td><td align=left>CI density matrix (beta)</td></tr>\r
-<tr><td align=center>501</td><td align=left>Total energy</td></tr>\r
-<tr><td align=center>502</td><td align=left>Job title</td></tr>\r
-<tr><td align=center>506</td><td align=left>Basis set information</td></tr>\r
-<tr><td align=center>512</td><td align=left>Effective core potential information</td></tr>\r
-<tr><td align=center>514</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center>518</td><td align=left><i>x</i> dipole integrals</td></tr>\r
-<tr><td align=center>519</td><td align=left><i>y</i> dipole integrals</td></tr>\r
-<tr><td align=center>520</td><td align=left><i>z</i> dipole integrals</td></tr>\r
-<tr><td align=center>524</td><td align=left>MO coefficients (alpha)</td></tr>\r
-<tr><td align=center>526</td><td align=left>MO coefficients (beta)</td></tr>\r
-<tr><td align=center>528</td><td align=left>SCF density matrix (alpha)</td></tr>\r
-<tr><td align=center>530</td><td align=left>SCF density matrix (beta)</td></tr>\r
-<tr><td align=center>536</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center>538</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<u>GAUSSIAN 82 COMMON blocks:</u><pre>\r
-\r
- COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(101),\r
- + ATMCHG(100),C(300)\r
- COMMON/LP2/NLP(400),CLP(400),ZLP(400),KFIRST(100,5),\r
- + KLAST(100,5),LMAX(100),LPSKIP(100),NFroz(100)\r
- COMMON/B/EXX(240),C1(240),C2(240),C3(240),X(80),Y(80),\r
- + Z(80),JAN(80),SHELLA(80),SHELLN(80),SHELLT(80),\r
- + SHELLC(80),AOS(80),AON(80),NSHELL,MAXTYP\r
- INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON\r
- DIMENSION C4(80),SHLADF(80)\r
- EQUIVALENCE(C4(1),C3(81)),(SHLADF(1),C3(161))\r
- </pre>\r
-<p>\r
-<b>D.5 GAMESS VERSION</b>\r
-<p>\r
-<i>D.5.1 GAMESS sample input</i>\r
-<p>\r
- A sample GAMESS input file to\r
-recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)\r
-output displayed in Section A.3 is shown below:\r
-<p>\r
- <pre>\r
-\r
- $CONTRL SCFTYP=RHF RUNTYP=ENERGY $END\r
- $DATA\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
-CS 0\r
-\r
-Carbon 6. -0.713673 -0.014253 0.000000\r
- 1 SV 3 N21\r
-\r
-Nitrogen 7. 0.749817 0.123940 0.000000\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. -0.978788 -1.071520 0.000000\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. -1.123702 0.463146 -0.889982\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. 1.129752 -0.318420 0.824662\r
- 1 SV 3 N21\r
-\r
- $END\r
- $GUESS GUESS=EXTGUESS $END\r
- $NBO $END\r
-\r
- </pre>NBO job options are selected by inserting their associated keywords\r
-(Section B.2) into the $NBO keylist. All NBO keywords are applicable to the\r
-electronic wavefunctions computed by GAMESS.\r
-<p>\r
- The following is a modified GAMESS input file that will generate, in\r
-addition to the default NBO output, the NLMO (Section B.6.2), the dipole\r
-moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of\r
-methylamine:\r
-<p>\r
- <pre>\r
-\r
- $CONTRL SCFTYP=RHF RUNTYP=ENERGY $END\r
- $DATA\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
-CS 0\r
-\r
-Carbon 6. -0.713673 -0.014253 0.000000\r
- 1 SV 3 N21\r
-\r
-Nitrogen 7. 0.749817 0.123940 0.000000\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. -0.978788 -1.071520 0.000000\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. -1.123702 0.463146 -0.889982\r
- 1 SV 3 N21\r
-\r
-Hydrogen 1. 1.129752 -0.318420 0.824662\r
- 1 SV 3 N21\r
-\r
- $END\r
- $GUESS GUESS=EXTGUESS $END\r
- $NBO NLMO DIPOLE $END\r
- $DEL NOSTAR\r
- ZERO 2 ATOM BLOCKS 4 BY 3\r
- 1 3 4 5\r
- 2 6 7\r
- 3 BY 4\r
- 2 6 7\r
- 1 3 4 5\r
- $END\r
-\r
- </pre>In general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted\r
-in any order within the GAMESS input file; the NBO program rewinds the\r
-input file each time it searches for a keylist.\r
-<p>\r
-<i>D.5.2 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided in this\r
-distribution were written for the GAMESS program dated 6-DEC-1989.\r
-Section D.5.3 lists the GAMESS\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the GAMESS program.\r
-<p>\r
- Only one command line is added to the GAMESS source code to run the\r
-NBO analysis. A call ("IF(RHO) CALL RUNNBO") should be inserted at the\r
-end of the GAMESS properties package (SR HFPROP in module PRPLIB),\r
-as shown below:\r
-<p>\r
- <pre>\r
-\r
-C*MODULE PRPLIB *DECK HFPROP\r
- SUBROUTINE HFPROP(SCFTYP)\r
-\r
- .\r
- .\r
- .\r
-\r
-C\r
-C ----- SELECT DESIRED ELECTROSTATIC PROPERTIES -----\r
-C\r
- CALL PRSELC(SCFTYP)\r
-C\r
- WRITE(IW,FMT='(" ...... END OF PROPERTY EVALUATION ......")')\r
- CALL TIMIT(1)\r
-C\r
-C <<< BEGINNING OF NBO INSERT >>>\r
-C\r
- IF(RHO) CALL RUNNBO\r
-C\r
-C <<< END OF NBO INSERT >>>\r
-C\r
- RETURN\r
- END\r
-\r
- </pre>If the density matrix is available (RHO = .TRUE.), the NBO analysis\r
-is performed each time the properties package is called within GAMESS.\r
-For example, the NBO analysis of the computed wavefunction will be performed\r
-for every single point calculation and for both the\r
-initial and final points of a geometry optimization. The NBO output will\r
-appear immediately after the Mulliken Population Analysis and the electric\r
-properties in the GAMESS output file.\r
-<p>\r
- The NBO program installation should continue as discussed in Section A.2.\r
-<i>D.5.3 NBO communication with GAMESS</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-GAMESS routines, records of the dictionary file, and COMMON blocks:\r
-<p>\r
-<u>GAMESS routines:</u><pre>\r
-\r
- SR DAREAD(IDAF,IODA,V,LEN,NREC,NAV)\r
- FN ENUC(N,Z,C)\r
- ENTRY GOTFM(IPAR)\r
- SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)\r
- SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)\r
- SR SYMH(F,H,IA)\r
- FN TRACEP(A,B,N)\r
- SR VADD(A,I,B,J,C,K,N)\r
- ENTRY VALFM(IPAR)\r
- \r
-<u></pre>GAMESS dictionary file:</u>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>record</td><td align=left>contents</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>2</td><td align=left>total energy</td></tr>\r
-<tr><td align=center>12</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center>14</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center>15</td><td align=left>AO to MO transformation matrix (alpha)</td></tr>\r
-<tr><td align=center>16</td><td align=left>AO density matrix (alpha bond-order matrix)</td></tr>\r
-<tr><td align=center>18</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td align=center>19</td><td align=left>AO to MO transformation matrix (beta)</td></tr>\r
-<tr><td align=center>20</td><td align=left>AO density matrix (beta bond-order matrix)</td></tr>\r
-<tr><td align=center>23</td><td align=left><i>x</i> dipole integrals</td></tr>\r
-<tr><td align=center>24</td><td align=left><i>y</i> dipole integrals</td></tr>\r
-<tr><td align=center>25</td><td align=left><i>z</i> dipole integrals</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<u>GAMESS COMMON blocks:</u><pre>\r
-\r
- PARAMETER (MXGTOT=5000, MXSH=1000, MXATM=50) \r
- COMMON /ECP2 / CLP(400),ZLP(400),NLP(400),KFIRST(MXATM,6), \r
- + KLAST(MXATM,6),LMAX(MXATM),LPSKIP(MXATM), \r
- + IZCORE(MXATM) \r
- COMMON /FMCOM / CORE(1)\r
- COMMON /INFOA / NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(MXATM),C(3,MXATM) \r
- COMMON /INTFIL/ NINTMX,NHEX,NTUPL,PACK2E,INTG76\r
- COMMON /IOFILE/ IR,IW,IP,IS,IPK,IDAF,NAV,IODA(99)\r
- COMMON /NSHEL / EX(MXGTOT),CS(MXGTOT),CP(MXGTOT),CD(MXGTOT), \r
- + KSTART(MXSH),KATOM(MXSH),KTYPE(MXSH),KNG(MXSH), \r
- + KLOC(MXSH),KMIN(MXSH),KMAX(MXSH),NSHELL \r
- COMMON /OUTPUT/ NPRINT,ITOL,ICUT,NORMF,NORMP,NOPK\r
- COMMON /RUNLAB/ TITLE(10),A(MXATM),B(MXATM),BFLAB(2047)\r
- COMMON /SCFOPT/ SCFTYP,BLKTYP,MAXIT,MCONV,NCONV,NPUNCH\r
- COMMON /XYZPRP/ X(3)\r
-</pre><b>D.6 HONDO VERSION</b>\r
-<p>\r
-<i>D.6.1 HONDO sample input</i>\r
-<p>\r
- A sample HONDO input file to\r
-recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry)\r
-output displayed in Section A.3 is shown below:\r
-<p>\r
- <pre>\r
-\r
- $CNTRL RUNFLG=0 $END\r
- $BASIS\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
- 0 0 15 1 N21\r
-CS 0\r
-\r
-Carbon 6. -0.713673 -0.014253 0.000000\r
-Nitrogen 7. 0.749817 0.123940 0.000000\r
-Hydrogen 1. -0.978788 -1.071520 0.000000\r
-Hydrogen 1. -1.123702 0.463146 -0.889982\r
-Hydrogen 1. 1.129752 -0.318420 0.824662\r
- $END\r
- $GUESS NGUESS=4 $END\r
- $INTGRL $END\r
- $WFN WFNFLG=0 $END\r
- $SCF NCO=9 $END\r
- $NBO $END\r
-\r
- </pre>NBO job options are selected by inserting their associated keywords\r
-(Section B.2) into the $NBO keylist. All NBO keywords are applicable to the\r
-electronic wavefunctions computed by HONDO.\r
-<p>\r
- The following is a modified HONDO input file that will generate, in\r
-addition to the default NBO output, the NLMO (Section B.6.2), the dipole\r
-moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of\r
-methylamine:\r
-<p>\r
- <pre>\r
-\r
- $CNTRL RUNFLG=0 $END\r
- $BASIS\r
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry\r
- 0 0 15 1 N21\r
-CS 0\r
-\r
-Carbon 6. -0.713673 -0.014253 0.000000\r
-Nitrogen 7. 0.749817 0.123940 0.000000\r
-Hydrogen 1. -0.978788 -1.071520 0.000000\r
-Hydrogen 1. -1.123702 0.463146 -0.889982\r
-Hydrogen 1. 1.129752 -0.318420 0.824662\r
- $END\r
- $GUESS NGUESS=4 $END\r
- $INTGRL $END\r
- $WFN WFNFLG=0 $END\r
- $SCF NCO=9 $END\r
- $NBO NLMO DIPOLE $END\r
- $DEL NOSTAR\r
- ZERO 2 ATOM BLOCKS 4 BY 3\r
- 1 3 4 5\r
- 2 6 7\r
- 3 BY 4\r
- 2 6 7\r
- 1 3 4 5\r
- $END\r
-\r
- </pre>In general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted\r
-in any order within the HONDO input file; the NBO program rewinds the\r
-input file each time it searches for a keylist.\r
-<p>\r
-<i>D.6.2 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided in this\r
-distribution were written for HONDO 7.0, dated 18-JAN-1988.\r
-Section D.6.3 lists the HONDO\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the HONDO program.\r
-<p>\r
- Only one command line is added to the HONDO source code to run the\r
-NBO analysis. A call ("CALL RUNNBO") should be inserted at the\r
-end of the HONDO properties package (SR PROPTY in module PRP),\r
-as shown below:\r
-<p>\r
- <pre>\r
-\r
- SUBROUTINE PROPTY\r
-\r
- .\r
- .\r
- .\r
-\r
-C\r
-C ----- ELECTRON AND SPIN DENSITIES -----\r
-C\r
- IF(NODEN.EQ.0) CALL ELDENS\r
-C\r
-C <<< BEGINNING OF NBO INSERT >>>\r
-C\r
- CALL RUNNBO\r
-C\r
-C <<< END OF NBO INSERT >>>\r
-C\r
- NCALL=0\r
- IF(SOME) NCALL=1\r
- CALL TIMIT(NCALL)\r
- RETURN\r
-\r
- .\r
- .\r
- .\r
-\r
- END\r
-\r
- </pre>The NBO analysis\r
-is performed each time the properties package is called within HONDO.\r
-For example, the NBO analysis of the computed wavefunction will be performed\r
-(unless NOPROP=1 in the $CONTRL namelist) for every single point calculation,\r
-for each point on a scan of a potential energy surface, and for both the\r
-initial and final points of a geometry optimization. The NBO output will\r
-appear immediately after the Mulliken Population Analysis and the electric\r
-properties in the HONDO output file.\r
-<p>\r
- The NBO program installation should continue as discussed in Section A.2.\r
-<i>D.6.3 NBO communication with HONDO</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-HONDO routines, records of the dictionary file, and COMMON blocks:\r
-<p>\r
-<u>HONDO routines:</u><pre>\r
-\r
- SR DAREAD(IDAF,IODA,IX,NX,IDAR)\r
- SR DIPAMS(BMASS,NCALL,NCODE,SOME)\r
- FN DOTTRI(A,B,N)\r
- FN ENUC(N,Z,C)\r
- SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)\r
- SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)\r
- SR SYMFCK(F,H,IA)\r
- \r
-<u></pre>HONDO dictionary file:</u>\r
-<p>\r
-<table border=0 width=100%>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>record</td><td align=left>contents</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-<tr><td align=center>2</td><td align=left>total energy</td></tr>\r
-<tr><td align=center>12</td><td align=left>AO overlap matrix</td></tr>\r
-<tr><td align=center>14</td><td align=left>AO Fock matrix (alpha)</td></tr>\r
-<tr><td align=center>15</td><td align=left>AO to MO transformation matrix (alpha)</td></tr>\r
-<tr><td align=center>16</td><td align=left>AO density matrix (alpha bond-order matrix)</td></tr>\r
-<tr><td align=center>18</td><td align=left>AO Fock matrix (beta)</td></tr>\r
-<tr><td align=center>19</td><td align=left>AO to MO transformation matrix (beta)</td></tr>\r
-<tr><td align=center>20</td><td align=left>AO density matrix (beta bond-order matrix)</td></tr>\r
-<tr><td align=center>33</td><td align=left><i>x</i> dipole integrals</td></tr>\r
-<tr><td align=center>34</td><td align=left><i>y</i> dipole integrals</td></tr>\r
-<tr><td align=center>35</td><td align=left><i>z</i> dipole integrals</td></tr>\r
-<tr><td colspan=2><hr></td></tr>\r
-</table>\r
-<u>HONDO COMMON blocks:</u><pre>\r
-\r
- COMMON/IJPAIR/IA(1)\r
- COMMON/INFOA/NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(50),C(3,50)\r
- COMMON/INTFIL/NOPK,NOK,NOSQUR,NINTMX,NHEX,NTUPL,PACK2E\r
- COMMON/IOFILE/IR,IW,IP,IJK,IPK,IDAF,NAV,IODA(99)\r
- COMMON/MEMORY/MAXCOR,MAXLCM\r
- COMMON/MOLNUC/NUC(50)\r
- COMMON/NSHEL/EX(440),CS(440),CP(440),CD(440),CF(440),CG(440),\r
- + KSTART(120),KATOM(120),KTYPE(120),KNG(120),\r
- + KLOC(120),KMIN(120),KMAX(120),NSHELL\r
- COMMON/RUNLAB/TITLE(10),ANAM(50),BNAM(50),BFLAB(512)\r
- COMMON/SCFOPT/SCFTYP\r
- COMMON/SCM/CORE(1)\r
- COMMON/WFNOPT/WFNTYP\r
- </pre>\r
-<p>\r
-<b>D.7 AMPAC VERSION</b>\r
-<p>\r
-<i>D.7.1 AMPAC sample input</i>\r
-<p>\r
- A sample AMPAC input file that will create default methylamine\r
-(AM1 at Pople-Gordon idealized geometry) output similar to the\r
-<i>ab initio</i> output displayed in Section A.3 is shown below:\r
-<p>\r
- <pre>\r
-\r
-AM1\r
-\r
-CH3NH2...AM1//Pople-Gordon standard geometry\r
- C 0.000000 0 0.000000 0 0.000000 0 0 0 0\r
- N 1.470000 0 0.000000 0 0.000000 0 1 0 0\r
- H 1.090000 0 109.471230 0 0.000000 0 1 2 0\r
- H 1.090000 0 109.471230 0 120.000000 0 1 2 3\r
- H 1.090000 0 109.471230 0 240.000000 0 1 2 3\r
- H 1.010000 0 109.471230 0 60.000000 0 2 1 3\r
- H 1.010000 0 109.471230 0 300.000000 0 2 1 3\r
-\r
-$NBO $END\r
-\r
-\r
- </pre>The keylists of the NBO program should always appear at the bottom of the\r
-AMPAC input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL.\r
-NBO job options are selected by inserting their associated keywords\r
-(Section B.2) into the $NBO keylist.\r
-<p>\r
- Due to the implicit orthogonality of the basis functions, the\r
-following NBO keywords are not applicable to the wavefunctions\r
-computed by AMPAC (or other semi-empirical packages):\r
- <pre>\r
- AOPNAO AOPNLMO NAONHO SPNAO\r
- AONAO DINAO NAONLMO SPNHO\r
- AOPNHO DMNAO NAOMO SPNBO\r
- AOPNBO FNAO SAO SPNLMO\r
-\r
-</pre>In addition, the NBO keywords that require access to the AO dipole\r
-integrals (DIPOLE, DIAO, DINAO, DINHO, DINBO, DINLMO) are not applicable\r
-with AMPAC, since these integrals are unavailable to the NBO program.\r
-<p>\r
- The following is a modified AMPAC input file that will generate, in\r
-addition to the default NBO output, the NLMO and the\r
-NBO energetic analyses of methylamine:\r
-<p>\r
- <pre>\r
-\r
-AM1\r
-\r
-CH3NH2...AM1//Pople-Gordon standard geometry\r
- C 0.000000 0 0.000000 0 0.000000 0 0 0 0\r
- N 1.470000 0 0.000000 0 0.000000 0 1 0 0\r
- H 1.090000 0 109.471230 0 0.000000 0 1 2 0\r
- H 1.090000 0 109.471230 0 120.000000 0 1 2 3\r
- H 1.090000 0 109.471230 0 240.000000 0 1 2 3\r
- H 1.010000 0 109.471230 0 60.000000 0 2 1 3\r
- H 1.010000 0 109.471230 0 300.000000 0 2 1 3\r
-\r
-$NBO NLMO $END\r
-$DEL NOSTAR\r
- ZERO 2 ATOM BLOCKS 3 BY 4\r
- 1 3 4 5\r
- 2 6 7\r
- 4 BY 3\r
- 2 6 7\r
- 1 3 4 5\r
-$END\r
-\r
-<i>D.7.2 Sample NBO output for AMPAC wavefunctions</i></pre>\r
-<p>\r
- Since the AMPAC output differs in significant respects from the\r
-<i>ab initio</i> examples presented in Sections A,B, we present\r
-some excerpts from the NBO output and a\r
-brief discussion of the NBO analysis of the AM1 wavefunction for\r
-methylamine (Pople-Gordon idealized geometry). The numerical values\r
-in these exerpts (summary tables) should be adequate for checking\r
-purposes.\r
-<p>\r
- The summary of the Natural Population Analysis (NPA)\r
-for methylamine is shown below:\r
- <pre>\r
-\r
-Summary of Natural Population Analysis: \r
- \r
- Natural Population \r
- Natural -----------------------------------------------\r
- Atom # Charge Core Valence Rydberg Total\r
------------------------------------------------------------------------\r
- C 1 -0.13281 2.00000 4.13281 0.00000 6.13281\r
- N 2 -0.34739 2.00000 5.34739 0.00000 7.34739\r
- H 3 0.03346 0.00000 0.96654 0.00000 0.96654\r
- H 4 0.08488 0.00000 0.91512 0.00000 0.91512\r
- H 5 0.08488 0.00000 0.91512 0.00000 0.91512\r
- H 6 0.13849 0.00000 0.86151 0.00000 0.86151\r
- H 7 0.13849 0.00000 0.86151 0.00000 0.86151\r
-=======================================================================\r
- * Total * 0.00000 4.00000 14.00000 0.00000 18.00000\r
-\r
- </pre>Note that the core electrons of all heavy atoms (neglected in the\r
-semi-empirical AMPAC procedure) are incorporated into the NPA, along the\r
-lines of the treatment of effective core potentials (Section B.6.12).\r
-Note also that the numerical values of AM1 natural charges (and other\r
-quantities) differ significantly from those presented in Section A.3.2,\r
-reflecting a tendency toward somewhat reduced bond polarities in AM1\r
-wavefunctions.\r
-<p>\r
-The NBO summary table is shown below:\r
- <pre>\r
-\r
-Natural Bond Orbitals (Summary):\r
-\r
- Principal Delocalizations\r
- NBO Occupancy Energy (geminal,vicinal,remote)\r
-===============================================================================\r
-Molecular unit 1 (CH5N)\r
- 1. BD ( 1) C 1- N 2 1.99095 -20.60408 9(g),10(g),11(g),12(g),13(g)\r
- 2. BD ( 1) C 1- H 3 1.99184 -17.81012 8(g),10(g),11(g),9(g)\r
- 3. BD ( 1) C 1- H 4 1.98864 -17.75195 12(v),9(g),11(g),8(g)\r
- 4. BD ( 1) C 1- H 5 1.98864 -17.75195 13(v),9(g),10(g),8(g)\r
- 5. BD ( 1) N 2- H 6 1.98916 -19.74256 13(g),8(g),10(v)\r
- 6. BD ( 1) N 2- H 7 1.98916 -19.74256 12(g),8(g),11(v)\r
- 7. LP ( 1) N 2 1.98489 -15.52775 9(v)\r
- 8. BD*( 1) C 1- N 2 0.01048 4.75597\r
- 9. BD*( 1) C 1- H 3 0.02306 4.29359\r
- 10. BD*( 1) C 1- H 4 0.01070 4.57248\r
- 11. BD*( 1) C 1- H 5 0.01070 4.57248\r
- 12. BD*( 1) N 2- H 6 0.01090 5.27834\r
- 13. BD*( 1) N 2- H 7 0.01090 5.27834\r
- -------------------------------\r
- Total Lewis 17.92328 ( 99.5738%)\r
- Valence non-Lewis 0.07672 ( 0.4262%)\r
- Rydberg non-Lewis 0.00000 ( 0.0000%)\r
- -------------------------------\r
- Total unit 1 18.00000 (100.0000%)\r
- Charge unit 1 0.00000\r
-\r
- </pre>Note that in this case the orbital energies and other matrix elements\r
-of the Fock operator are printed in electron volts, the energy units of the\r
-AMPAC package. Note also that the physical pattern of delocalization effects\r
-differs significantly from that shown in Section A.3.6, the AM1 results\r
-portraying numerous strong <i>geminal</i> interactions that are not present\r
-in the <i>ab initio</i> output. Other differences between the AM1 and\r
-<i>ab initio</i> wavefunctions will be evident throughout the NBO output.\r
-<p>\r
- Finally, we include the output segment showing the NBO energetic analysis\r
-of methylamine:\r
- <pre>\r
-\r
-NOSTAR: Delete all Rydberg/antibond NBOs\r
-Deletion of the following orbitals from the NBO Fock matrix:\r
- 8 9 10 11 12 13\r
-\r
-Occupations of bond orbitals:\r
-\r
- Orbital No deletions This deletion Change\r
-------------------------------------------------------------------------------\r
- 1. BD ( 1) C 1- N 2 1.99095 2.00000 0.00905\r
- 2. BD ( 1) C 1- H 3 1.99184 2.00000 0.00816\r
- 3. BD ( 1) C 1- H 4 1.98864 2.00000 0.01136\r
- 4. BD ( 1) C 1- H 5 1.98864 2.00000 0.01136\r
- 5. BD ( 1) N 2- H 6 1.98916 2.00000 0.01084\r
- 6. BD ( 1) N 2- H 7 1.98916 2.00000 0.01084\r
- 7. LP ( 1) N 2 1.98489 2.00000 0.01511\r
- 8. BD*( 1) C 1- N 2 0.01048 0.00000 -0.01048\r
- 9. BD*( 1) C 1- H 3 0.02306 0.00000 -0.02306\r
- 10. BD*( 1) C 1- H 4 0.01070 0.00000 -0.01070\r
- 11. BD*( 1) C 1- H 5 0.01070 0.00000 -0.01070\r
- 12. BD*( 1) N 2- H 6 0.01090 0.00000 -0.01090\r
- 13. BD*( 1) N 2- H 7 0.01090 0.00000 -0.01090\r
-\r
-NEXT STEP: Evaluate the energy of the new density matrix\r
- that has been constructed from the deleted NBO\r
- Fock matrix by doing one SCF cycle.\r
-\r
-------------------------------------------------------------------------------\r
- Energy of deletion : 22.024\r
- Total SCF energy : -5.051\r
- -------------------\r
- Energy change : 27.075 kcal/mol, 27.075 kcal/mol\r
-------------------------------------------------------------------------------\r
-\r
- </pre>Note that the "energy of deletion" (22.0 kcal/mol), "total SCF\r
-energy" (-5.1 kcal/mol) and "energy change" (27.1 kcal/mol) are all\r
-given in terms of heats of formation, the standard AM1 form of expressing\r
-molecular energies.\r
-<p>\r
-<i>D.7.3 NBO program installation</i>\r
-<p>\r
- The NBO interfacing (driver) routines provided in this\r
-distribution were written for AMPAC, version 1.00.\r
-Section D.7.4 lists the AMPAC\r
-dependent elements of the NBO driver routines that may need slight\r
-modification for other versions of the AMPAC program.\r
-<p>\r
- Only one command line is added to the AMPAC source code to run the\r
-NBO analysis. A command "CALL RUNNBO" should be inserted in the\r
-AMPAC properties package (SR WRITE in module WRITE), as shown below:\r
-<p>\r
- <pre>\r
-\r
- SUBROUTINE WRITE(TIME0,FUNCT)\r
-\r
- .\r
- .\r
- .\r
-\r
- X=MECI(EIGS,C,CBETA,EIGB, NORBS,NMOS,NCIS, .TRUE.)\r
- ENDIF\r
-C\r
-C <<< BEGINNING OF NBO INSERT >>>\r
-C\r
- CALL RUNNBO\r
-C\r
-C <<< END OF NBO INSERT >>>\r
-C\r
- IF (INDEX(KEYWRD,'MULLIK') +INDEX(KEYWRD,'GRAPH') .NE. 0) THEN\r
- IF (INDEX(KEYWRD,'MULLIK') .NE. 0) THEN\r
-\r
- .\r
- .\r
- .\r
-\r
- </pre>The NBO analysis is performed each time SR WRITE is called.\r
-For example, the NBO analysis of the computed wavefunction will be performed\r
-for every single point calculation and at the end of geometry optimizations.\r
-The NBO output will appear immediately after the Mulliken Population Analysis\r
-in the AMPAC output file.\r
-<p>\r
- The NBO program installation should continue as discussed in Section A.2.\r
-<i>D.7.4 NBO communication with AMPAC</i>\r
-<p>\r
- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following\r
-AMPAC routines and COMMON blocks:\r
-<p>\r
-<u>AMPAC routines:</u><pre>\r
-\r
- SR GMETRY(GEO,COORD)\r
- SR HCORE(COORD,H,W,WJ,WK,ENUCLR)\r
- SR FOCK2(F,PTOT,P,W,WJ,WK,NUMAT,NFIRST,NMIDLE,NLAST)\r
- SR FOCK1(F,PTOT,PA,PB)\r
- FN HELECT(N,P,H,F)\r
- \r
-<u></pre>AMPAC COMMON blocks:</u><pre>\r
-\r
- INCLUDE 'SIZES'\r
- COMMON /ATHEAT/ ATHEAT\r
- COMMON /DENSTY/ P(MPACK),PA(MPACK),PB(MPACK)\r
- COMMON /ENUCLR/ ENUCLR\r
- COMMON /FOKMAT/ F(MPACK),FB(MPACK)\r
- COMMON /GEOKST/ NATOM,LABELS(NUMATM),NA(NUMATM),NB(NUMATM),\r
- + NC(NUMATM)\r
- COMMON /GEOM / GEO(3,NUMATM)\r
- COMMON /HMATRX/ H(MPACK)\r
- COMMON /KEYWRD/ KEYWRD\r
- COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),\r
- + NLAST(NUMATM),NORBS,NELECS,NALPHA,NBETA,NCLOSE,\r
- + NOPEN,NDUMY,FRACT\r
- COMMON /NATORB/ NATORB(107)\r
- COMMON /TITLES/ COMENT(10),TITLE(10)\r
- COMMON /VECTOR/ C(MORB2),EIGS(MAXORB),CBETA(MORB2),EIGB(MAXORB)\r
- COMMON /WMATRX/ WJ(N2ELEC),WK(N2ELEC)\r
- </pre>\r
-<p>\r
-<center>\r
-<h2>INDEX</h2>\r
-</center>\r
-<p>\r
-<pre>\r
- Acceptor orbital,A21\r
- ACS Software,A11\r
- AMPAC version,A2,A7,A8,B66,C17\r
- Angular symmetry labels,A5,<i>B68</i>,C7\r
- Antiperiplanar interaction,A19,A23,B50\r
- Archive file (FILE47),A5,\r
- <i>B62-71</i>,C8,C14,C31,C36\r
- Arrays\r
- IBXM,C9,C22,C23\r
- JPRINT,C6\r
- NBOOPT,C16,<i>C17</i>,C18,\r
- C26,C30,C36,C39\r
- Atom-centered basis functions,A1\r
- Atomic charge,A14\r
- Atomic orbitals,A1,A5,A6,B67-68\r
- Contracted gaussian,A6,B69-70\r
- Pure (PAO),<i>B11</i>,B67-68,C19,C30\r
- Slater-type,A6\r
- <i>see</i> Atomic shell\r
- <i>see</i> Core orbitals\r
- <i>see</i> Pre-orthogonal orbitals\r
- Atomic shell\r
- Core,A7,A8,A13,A14,A16,C24\r
- Rydberg,A2,A8,A13,A14,A16,C25\r
- Valence,A8,A13,A14,A16\r
- Atomic units,A13,B65,C4,C13\r
- Attaching NBO to ESS program,\r
- A10-11,C36,C38-39\r
- AUHF method\r
- <i>see</i> Wavefunction type\r
- Azimuthal angle (<img src=phi.gif>),A20,C33\r
- \r
- Basis set\r
- <i>see</i> Atomic orbitals\r
- Benzene (C<sub>6</sub>H<sub>6</sub>),B3,B32-36\r
- Bond bending,A8,A20\r
- <i>see</i> Hybrid direction\r
- BONDO program,A7\r
- Bond order,B29-31\r
- Matrix,B11,B65,C19\r
- Boys LMOs,B3\r
- Brunck, T. K.,A7\r
- \r
- Canonical MOs,B6,B27-28,B71,C20\r
- Carpenter, J. E.,A7\r
- Chemical fragment,<i>B16</i>,B19\r
-<p>\r
- $CHOOSE list\r
- <i>see</i> Keylists\r
- Comments (!),B1,B63,C29\r
- Comment statements,C1\r
- COMMON blocks\r
- /NBAO/,C7\r
- /NBATOM/,C7\r
- /NBBAS/,C9,C22,C31,C30\r
- /NBCRD1/,C11,C29\r
- /NBCRD2/,C12,C29\r
- /NBDAF/,C12,C27,C28\r
- /NBDXYZ/,C11\r
- /NBFLAG/,C5\r
- /NBGEN/,C13,C30\r
- /NBINFO/,C4\r
- /NBIO/,C8,C18\r
- /NBLBL/,C10,C32\r
- /NBMOL/,C10\r
- /NBNAO/,C10\r
- /NBONAV/,C12\r
- /NBOPT/,C6-7,C18,C30\r
- /NBTHR/,C9,C18\r
- /NBTOPO/,C11,C22\r
- Contour plotting program,A8,B9,B69\r
- Contracted gaussian orbitals\r
- <i>see</i> Atomic orbitals\r
- Copper dimer (Cu<sub>2</sub>),B56-61\r
- $CORE list\r
- <i>see</i> Keylists\r
- Core orbitals,A6,A7,A8,A16,\r
- B12-13,B56-61,B66,C24,C30,C33\r
- Core polarization,A8,B12\r
- Core table,B12,C33\r
-<p>\r
- DAF\r
- <i>see</i> Direct access file\r
- Datalists,B63-64\r
- $BASIS,<i>B67-68</i>,B71,C31,C37\r
- $CONTRACT,<i>B69-70</i>,C31,C37\r
- $COORD,B63,B65,<i>B66</i>,C31,C37\r
- $DENSITY,B71\r
- $DIPOLE,B65,B71,C37\r
- $FOCK,B65,B71,C37\r
- $LCAOMO,B71,C37\r
- Matrix,B71\r
- $OVERLAP,B65,B71,C37\r
- <i>d</i>-orbitals,B53,B56,B61\r
- Default output,A12,B10\r
- Deletion types,B17-19\r
-<p>\r
- $DEL (deletions) list\r
- <i>see</i> Keylists\r
- Delocalization,A1,A2,A21,B3,B32,B51\r
- Delocalization tail,A22,B23\r
-<p>\r
- Density matrix,A1,A5,A6,B6-7,C13\r
- <i>see</i> Bond-order matrix\r
- <i>see</i> Spin density matrices\r
- Depletion of density matrix,C24\r
- Diborane (B<sub>2</sub>H<sub>6</sub>),B40-43\r
- Dictionary file,A4\r
- Different Lewis structures for\r
- different spin\r
- <i>see</i> Open-shell calculation\r
- Dimension specification,C4\r
- Dipole moment,A5,A6,A8,B5,B6-7,\r
- <i>B24-25</i>,B65,B71,C11,C15,C24\r
-<p>\r
- Direct access file (FILE48),A3,A4,A5,\r
- B9,B65,C12,<i>C14-15</i>,C16,C27,\r
- C28,C36-39\r
- Directed NBO search\r
- <i>see</i> Keylists, $CHOOSE\r
- Directional analysis\r
- <i>see</i> Hybrid direction\r
- Distribution tape,A10\r
- Donor orbital,A21,A22\r
- Double-bond, no-bond resonance,B44-47\r
- Driver routines,A3\r
- <i>see</i> Subroutines RUNNBO, etc.\r
- \r
- Edmiston-Ruedenberg LMOs,B3\r
- Effective core potential (ECP),\r
- A8,<i>B56-61</i>,B66\r
- Electronic structure system (ESS),A3\r
- Common blocks,A4\r
- Connection to NBO program,A3,A4,A7,\r
- A10-11,B56,B62,C36,C38-39\r
- Input file,A5,A11,A12\r
- Output file,A5,A12\r
- Scratch files,A4\r
- <i>see</i> AMPAC, GAUSSIAN-8X, <i>etc.</i>\r
- ENABLE program,A10,C36\r
- Energetic analysis,A3,A5,<i>B16-19</i>,\r
- C2,C26,C38,C39\r
- <i>see</i> Perturbation theory...\r
- Excited state,A6,A8,A15,B56,C23\r
- \r
-<p>\r
- <i>f</i>-orbitals\r
- <i>see</i> Angular symmetry labels\r
- <i>see</i> Keyword CUBICF\r
-<p>\r
- Fenske-Hall method\r
- <i>see</i> MEDVL \r
- Fetch/Save routines,C15,C27\r
-<p>\r
- FILE48\r
- <i>see</i> Direct access file\r
-<p>\r
- FILE47 \r
- <i>see</i> Archive file\r
- Flow chart,A4,C3,C16\r
- Fock matrix,A2,A5,A6,A8,A14,A21,\r
- B6,B16-20,B26,B48-51,B65,B71,\r
- C2,C23,C26,C39\r
- Fortran 77,A6,A10\r
- Foster, J.P.,C22\r
- Free format,B1,C29\r
- Freezing a transformation,B8\r
- Functions\r
- EQUAL,C29\r
- IHTYP,C34\r
- IOINQR,C32\r
- IWPRJ,C24\r
- NAMEAT,C34\r
- VECLEN,C35\r
- \r
- GAMESS version,A1,A2,A7,A10,A12,C17\r
- Gaussian elimination,C35\r
- GAUSSIAN-8X version,A2,A7,\r
- A10,B56,C17\r
- Geminal interaction,A22,B18,C33\r
- Generalized eigenvalue problem,C20\r
-<p>\r
- GENNBO input file \r
- <i>see</i> Archive file\r
-<p>\r
- GENNBO stand-alone program\r
- A10,B9,B62-71,C13,C36,C37,C38\r
- Geometry,B66\r
- Glendening, E. D.,A7\r
- Groups of routines\r
- I (NAO/NBO/NLMO),C2,C16-25\r
- II (energy analysis),C2,C26\r
- III (direct access file),C2,C27-28\r
- IV (free format input),C2,C29\r
- V (other I/O),C2,C30-32\r
- VI (general utility),C2,C33-35\r
- VII (system-dependent),C2,C36\r
- GUGA formalism,A1\r
- GVB method\r
- <i>see</i> Wavefunction type\r
- \r
- Hay-Wadt ECP,B56\r
- HONDO version,A2,A10,C17,C27\r
- Hybrid composition,A19,B23\r
- Hybrid direction,A8,<i>A20</i>,B4,C23\r
- Hydrogen fluoride (HF),B37-39\r
- \r
- I/O routines\r
- <i>see</i> Groups of routines\r
- INP routines,C30,C39\r
- Input file,A5,B62,C14\r
- Installation procedure,A10-11\r
- Ionic hybrids,B37-39\r
- \r
- Job control keywords,B2,B3\r
- Job initialization routines,C16,C18\r
- Job threshold keywords,B2,B4-5\r
- \r
- Kekulée structure,B36\r
- Keylist,A5,A11,A12,<i>B1</i>\r
-<p>\r
- Keylists\r
- $CHOOSE,B1,B2,B12,<i>B14-15</i>,<i>B44-47</i>,\r
- B62,B63,B65,C6,C22,C30\r
- $CORE,B1,B2,<i>B12-B13</i>,\r
- B62,B63,B65,C3,C6-7,C30\r
- $DEL,B1,B2,B12,<i>B16-20</i>,\r
- <i>B48-51</i>,B62,C17,C26,C30\r
- $GENNBO,<i>B65</i>,B66,C30\r
- $NBO,B1,<i>B2-11</i>,B21-43,B62,B63,\r
- B65,B69,C6,C17,C18,C22,C30\r
- Keyword names (matrix output),B6-7\r
- Keyword parameters (matrix output),B7-8\r
- Keywords\r
- AOINFO,B2,<i>B9</i>,B69,B71,C6,C31\r
- AOMO,B2,B6,B71,C6\r
- AONAO,B2,B6,C6,C30-31\r
- AONBO,B2,B6,C6,C31\r
- AONHO,B2,B6,C6\r
- AONLMO,B2,B3,B6,C6,C31\r
- AOPNAO,B2,B6,B71,C6\r
- AOPNBO,B2,B6,B71,C6\r
- AOPNHO,B2,B6,B71,C6\r
- AOPNLMO,B2,B6,B71,C6\r
- ARCHIVE,B2,<i>B9</i>,<i>B62-71</i>,C6,C31\r
- BEND,A8,<i>A20</i>,B2,<i>B4</i>,B5,B10,C6,C23\r
- BNDIDX,B2,<i>B9</i>,B10,B21,\r
- <i>B29-B31</i>,C6\r
- BOAO,B11,C6\r
- BODM,<i>B65</i>,C6,C13\r
- BOHR,<i>B65</i>,B66,,C13\r
- CUBICF,<i>B65</i>,B68,C6\r
- DESTAR,B18\r
- DETAIL,B2,<i>B9</i>,C6\r
- DIAO,B2,B7,B71,C6\r
- DINAO,B2,B7,B71,C6\r
- DINBO,B2,B7,B71,C6\r
- DINHO,B2,B7,B71,C6\r
- DINLMO,B2,B6,B7,B71,C6\r
- DIPOLE,A8,B2,B3,<i>B5</i>,B10,B21,\r
- <i>B24-25</i>,B71,C6,C17,C24\r
- DMAO,B2,B7,C6\r
- DMNAO,B2,B7,C6\r
- DMNBO,B2,B7,C6\r
- DMNHO,B2,B7,C6\r
- DMNLMO,B2,B7,C6\r
- E2PERT,<i>A21</i>,B2,<i>B4</i>,B5,B10,B71,C6\r
- EV,B65\r
- FAO,B2,B7,B71,C6\r
- FNAO,B2,B7,B71,C6\r
- FNBO,B2,B6-8,B7,B71,C6\r
- FNHO,B2,B7,<i>B26</i>,B71,C6\r
- FNLMO,B2,B7,B71,C6\r
- LFNPR,B2,<i>B9</i>,C8\r
- Matrix output,B6-8,B26-28\r
- MULAT,B11,C6\r
- MULORB,B11\r
- NAOMO,B2,B6-8,B71,C6\r
- NAONBO,B6-8,C6\r
- NAONHO,B6-8,C6\r
- NAONLMO,B6-8,C6\r
- NATOMS,B65\r
- NBAS,B65\r
- NBODAF,B2,B9\r
- NBO,<i>A16-19</i>,B2,<i>B3</i>,B10,C6\r
- NBOMO,B2,B6-8,<i>B27-28</i>,B71,C6\r
- NBONLMO,B2,B6-8,C6\r
- NBOSUM,<i>A22-23</i>,B2,<i>B3</i>,B10,C6,C23\r
- NHOMO,B2,B6-8,B71,C6\r
- NHONBO,B2,B6-8,C6\r
- NHONLMO,B2,B6-8,C6\r
- NLMO,B2,<i>B3</i>,B5,B10,<i>B22-23</i>,C6\r
- NLMOMO,B2,B6-8,B71,C6\r
- NOBOND,B2,<i>B3</i>,B21,<i>B37-39</i>,C6\r
- NOGEM,B18\r
- NOSTAR,B18,<i>B48-49</i>\r
- NOVIC,B18\r
- NPA,<i>A13-15</i>,B2,<i>B3</i>,B10,C6,C20\r
- OPEN,B65\r
- ORTHO,B65\r
- PAOPNAO,B11,C6\r
- PLOT,A8,B2,<i>B9</i>,B69,B71,C6\r
- PRINT,B2,B5,<i>B10</i>,B71,C18,C6\r
- PRJTHR,B11\r
- RESONANCE,A16,B2,<i>B3</i>,B21,\r
- <i>B32-36</i>,C6,C17,C25\r
- REUSE,<i>B65</i>,B66,B67,C13\r
- RPNAO,B11,C6\r
- SAO,B2,B7,B71,C6\r
- SKIPBO,B2,<i>B3</i>,B10,C6\r
- SPNAO,B2,B6-8,B7,B71,C6\r
- SPNBO,B2,B7,B71,C6\r
- SPNHO,B2,B7,B71,C6\r
- SPNLMO,B2,B3,B7,B71,C6\r
- 3CBOND,B2,<i>B3</i>,B14,B21,<i>B40-43</i>,C6\r
- THRESH,B11\r
- UPPER,B65,B71,C13\r
- ZERO,B19,<i>B49-51</i>\r
-<p>\r
- Kinks\r
- <i>see</i> Hybrid direction, Bond bending\r
- \r
-<p>\r
- Labelled COMMON blocks,A3,A6,C4-13\r
- <i>see</i> COMMON blocks\r
-<p>\r
- Lewis orbitals\r
- <i>see</i> Natural bond orbitals\r
- Linear equations package,C35\r
- Linear independence,A1,C22,C24\r
- Logical file number (LFN),C8,C38,C39\r
- Löwdin, P.-O.,A1\r
- Löwdin orthogonalization,C21\r
- \r
- Matrix multiplication,C34\r
-<p>\r
- Matrix output keywords,\r
- B2,<i>B6-8</i>,B9,<i>B26-28</i>,C7\r
- Mayer-Mulliken bond-order,C19\r
- MCSCF method\r
- <i>see</i> Wavefunction type\r
- MEDVL version,A10\r
- Memory allocation,\r
- A6,A12,C16,C18,C19,C22\r
- Methylamine (CH<sub>3</sub>NH<sub>2</sub>),\r
- A12-23,B21-31,B44-51,B63-71\r
- Methyl radical (CH<sub>3</sub>),B52-55\r
- Molecular units,<i>B16</i>,B18,B19,C10,C23\r
- Møller-Plesset method\r
- <i>see</i> Wavefunction type\r
- MOPAC version,A10\r
-<p>\r
- Mulliken population analysis,\r
- A10,B11,C19,C38\r
- Multiple bonds,A19,B14,B44-47,B56-61\r
- \r
- Naaman, R.,A7\r
- NAO formation routines,C16,C19-21\r
-<p>\r
- Natural atomic orbital (NAO)\r
- Formation,A1,A7,C16,C19-21\r
- Labels,A13-14,C10\r
- Listing,A13,C10\r
- Summary table,A7\r
- <i>see</i> Natural population analysis\r
-<p>\r
- Natural bond orbital (NBO)\r
- Analysis,A1-2,A16-19\r
- Formalism,A1-A2,A7\r
- Labels,A8,A19,B27-28,B43,C9,C10,C32\r
- Lewis,A2,A16,A19,A21,A23,B48-51,B17\r
- Listing,<i>A17-19</i>,B2\r
- Non-Lewis,A2,A16,A19,\r
- A21,A23,B17,B18,B48-51\r
- Summary table,<i>A22-23</i>,C23\r
- 3-center,A16,<i>B40-43</i>\r
- <i>see</i> Perturbation theory...\r
- <i>see</i> NBO/NLMO formation routines\r
-<p>\r
- Natural electron configuration (NEC),\r
- A7,<i>A15</i>,C20\r
-<p>\r
- Natural hybrid orbital (NHO)\r
- Directional analysis,A20\r
- Formation,A1-2\r
- Labels,B26,C10\r
- Listing,A-19\r
- <i>see</i> Natural bond orbitals\r
- <i>see</i> Hybrid direction\r
-<p>\r
- Natural Lewis structure,A1-2,A16,\r
- A19,B3,B18,B48,B49\r
- Energy,B18,B48\r
-<p>\r
- Natural localized molecular orbital (NLMO)\r
- Formation,A7,B3,C25\r
- Listing,B3,<i>B22-23</i>\r
- Natural minimal basis (NMB) set,A2,A14\r
- Natural population analysis (NPA),\r
- A3,A6,A7,<i>A13-14</i>,B3,\r
- B10,B21,B56-57,C20\r
- Natural Rydberg basis (NRB) set,A2,A18\r
- NBO direct access file\r
- <i>see</i> Direct access file\r
- $NBO keylist\r
- <i>see</i> Keylists\r
- NBO energetic analysis\r
- <i>see</i> Energetic analysis\r
- <i>see</i> Perturbation theory...\r
- NBO.MAN file,A10,A11\r
- NBO/NLMO formation routines,\r
- C16,C22-25\r
- NBO program,Section C\r
- I/O,A5,A12,C27-32\r
- Installation,A10-11\r
- Organization,A3-4,C2-4\r
- Restrictions,A6\r
- <i>see</i> Electronic structure system\r
- NBO.SRC file,A10,C1,C2\r
- NBO summary table,<i>A22-23</i>,C23\r
- NLMO/NPA bond order,B30-31\r
- Non-Lewis orbitals\r
- <i>see</i> Natural Bond Orbital\r
- \r
- Open-shell calculation,\r
- A1,A5,B14,B25,<i>B52-55</i>,B65,C5\r
- <i>see</i> Wavefunction type\r
- Orbital contour plotting program,\r
- A8,B9,B69\r
- Orthogonalization,C20\r
- Löwdin (symmetric),C24\r
- Occupancy-weighted (OWSO),C20,C21\r
- Schmidt,C20\r
- Output control keywords,B2,<i>B9-10</i>\r
- Output file,A8,A12,C1\r
-<p>\r
- Overlap matrix,A5,A6,A8,B6,B71,C38\r
- singularities,C25\r
- Overlap-weighted NAO bond order,B30\r
- \r
-<p>\r
- Perturbation theory energy analysis,\r
- A8,<i>A21</i>,B3,B4,C23,C39\r
- Phi,A20,C33\r
-<p>\r
- PNAO, PNBO, PNHO, PNLMO\r
- <i>see</i> Pre-orthogonal orbitals\r
- Polar angle (<img src=theta.gif>),A20,C33\r
- Polarization coefficients,A2,A19,C25\r
- Pople-Gordon geometry,A12,A20,B21,B32\r
-<p>\r
- Population analysis\r
- <i>see</i> Mulliken population analysis\r
- <i>see</i> Natural population analysis\r
- Population inversion,A14,B57\r
-<p>\r
- Pre-orthogonal orbitals,\r
- A1-2,A6,A8,B6,B65,B71\r
-<p>\r
- Print parameters,B2,<i>B7-8</i>,\r
- B11,B27-28,C7,C10\r
-<p>\r
- Program groups,C2\r
- <i>see</i> Groups of routines\r
-<p>\r
- Program limits\r
- Atoms,A6,C4\r
- Basis functions,A6,C4\r
- Program precedence,C2,C3\r
- Pseudopotential\r
- <i>see</i> Effective core potential\r
- Pure AOs,B11\r
- <i>see</i> Atomic orbital\r
- \r
- QCPE,A7,A8\r
- \r
- Read (R) parameter\r
- <i>see</i> Print parameters\r
- Read-write file,A4\r
- Reed, A. E.,A7,B11,B31,C19\r
- References,A7\r
- Remote interaction,A22,C33\r
- Resonance structures,A9,B14-15,B32-33,\r
- B38,B39,B44-47,C11,C25\r
- Rewind input file,C39\r
- RHF method\r
- <i>see</i> Wavefunction type\r
- Rives, A. B.,A7\r
- ROHF method\r
- <i>see</i> Wavefunction type\r
- \r
- Schleyer, P. v.R.,B31\r
- 2nd-order perturbation theory analysis\r
- <i>see</i> Perturbation theory energy...\r
- Semi-documented keywords,B2,<i>B11</i>\r
- Similarity transformation,C19,C26,C34\r
-<p>\r
- Slater-type orbitals\r
- <i>see</i> AO basis functions\r
-<p>\r
- Spin\r
- <i>see</i> Open-shell calculations\r
-<p>\r
- Spin-annihilated UHF (AUHF) method\r
- <i>see</i> Wavefunction type\r
- Spin density matrices,A1,B52-55,C5\r
-<p>\r
- Storage\r
- <i>see</i> Memory allocation\r
-<p>\r
- Subroutines,C2,C3\r
- ANGLES,C33\r
- ANLYZE,C23\r
- AOUT,C31\r
- APRINT,C31,C32\r
- AREAD,C31\r
- ATDIAG,C20\r
- AUGMNT,C25\r
- AWRITE,C31\r
- BDFIND,C33\r
- BLDSTR,C23\r
- CHEM,C33\r
- CHOOSE,C22,C23,C24\r
- CHSDRV,C22\r
- CHSINP,C30\r
- CONSOL,C33\r
- CONVIN,C33\r
- CONVRT,C33\r
- COPY,C33\r
- CORE,C24\r
- CORINP,C30\r
- CORTBL,C33\r
- CYCLES,C22,C25\r
- DEBYTE,C33\r
- DELETE,C26\r
- DELINP,C30\r
- DELSCF,A3,A4,A5,C2,<i>C36</i>,C38,C39\r
- DEPLET,C24\r
- DFGORB,C19,C30\r
- DIPANL,A6,C22,C24\r
- DIPELE,C24\r
- DIPNUC,C24\r
- DMNAO,C19\r
- DMSIM,C19\r
- FACTOR,C35\r
- FEAOIN,A3,A4,A5,C2,C6,\r
- C14,<i>C36</i>,C38,C39\r
- FEAOMO,C27\r
- FEAOM,C27\r
- FEBAS,C27\r
- FECOOR,C27\r
- FEDNAO,C27\r
- FEDRAW,C27\r
- FEDXYZ,C27\r
- FEE0,C27\r
- FEFAO,C27\r
- FEFNBO,C27\r
- FEINFO,C27\r
- FENBO,C27\r
- Subroutines (<i>continued</i>)\r
- FENEWD,C27\r
- FENLMO,C27\r
- FEPNAO,C27\r
- FEPPAO,C27\r
- FESNAO,C27\r
- FESRAW,C27\r
- FETITL,C27\r
- FETLMO,C27\r
- FETNAB,C27\r
- FETNAO,C27\r
- FETNBO,C27\r
- FETNHO,C27\r
- FNBOAN,C23\r
- FNDFLD,C29\r
- FNDMOL,C23\r
- FNDSOL,C35\r
- FORMT,C25\r
- FRMHYB,C23\r
- FRMPRJ,C25\r
- FRMTMO,C20\r
- GENINP,C30\r
- GETDEL,C23\r
- HALT,C33\r
- HFLD,C29\r
- HTYPE,C23\r
- HYBCMP,C23\r
- HYBDIR,C23\r
- IDIGIT,C33\r
- IFLD,C29\r
- INTERP,C32\r
- JACOBI,C25,C34\r
- JOBOPT,C18,C29\r
- LBLAO,C32\r
- LBLNAO,C32\r
- LBLNBO,C32\r
- LBLNHO,C32\r
- LIMTRN,C34\r
- LINEQ,C33,C35\r
- LMOANL,C24\r
- LOADAV,C20\r
- LOAD,C24\r
- MATML2,C34\r
- MATMLT,C34\r
- MULANA,C19\r
- NAOANL,C21\r
- NAODRV,C2,C19\r
- NAOSIM,C19\r
- NAO,C19\r
- NATHYB,C22,C23,C24\r
- NBCLOS,C16,C28\r
- NBINQR,C28\r
- NBOCLA,C23\r
- NBODEL,C26\r
- NBODIM,C18\r
- NBODRV,C2,C19,C22\r
- NBOEAN,A3,A4,A6,C3,C26,C36,C39\r
- NBOINP,C30\r
- NBOPEN,C16,C27\r
- NBOSET,C18,C39\r
- NBO,A3,A4,C2,C16,C36\r
- NBOSUM,C23\r
- NBREAD,C28\r
- NBWRIT,C28\r
- NEWDM,C26\r
- NEWRYD,C20\r
- NEWWTS,C20\r
- NLMO,C22,C24\r
- NORMLZ,C34\r
- ORDER,C34\r
- ORTHYB,C24\r
- OUTPUT,C32\r
- PACK,C34\r
- PRJEXP,C24\r
- RANK,C34\r
- RDCARD,C29\r
- RDCORE,C30\r
- RDPPNA,C30\r
- RDTNAB,C31\r
- RDTNAO,C31\r
- REDBLK,C21\r
- REDIAG,C21\r
- REPOL,C25\r
- RFLD,C29\r
- RNKEIG,C26\r
- RUNNBO,A3,A4,<i>C36</i>,C38,C39\r
- RYDIAG,C20\r
- RYDSEL,C21\r
- SETBAS,C20\r
- SHMDT,C20\r
- SIMLTR,C26\r
- SIMTRM,C19\r
- SIMTRN,C34\r
- SIMTRS,C34\r
- SRTNBO,C22\r
- STASH,C24\r
- STRTIN,C29\r
- SUBST,C35\r
- SVDNAO,C27\r
- SVE0,C27\r
- SVFNBO,C27\r
- SVNBO,C27\r
- SVNEWD,C27\r
- SVNLMO,C27\r
- SVPNAO,C27\r
- SVPPAO,C27\r
- SVSNAO,C27\r
- SVTLMO,C27\r
- Subroutines (<i>continued</i>)\r
- SVTNAB,C27\r
- SVTNAO,C27\r
- SVTNHO,C27\r
- SYMORT,C25\r
- SYMUNI,C25\r
- TRANSP,C34\r
- UNPACK,C35\r
- VALTBL,C35\r
- WRARC,C31\r
- WRBAS,C31\r
- WRMLMO,C31\r
- WRPPNA,C30\r
- WRTNAB,C31\r
- WRTNAO,C30,C31\r
- WRTNBO,C312\r
- XCITED,C23\r
- Symmetric orthogonalization,C24,C25\r
- Symmetry,B16\r
- System-dependent driver routines,C36\r
- \r
- TechSet,A11,A20\r
- Theta,A20,C33\r
- 3-center bonds\r
- <i>see</i> Natural bond orbitals\r
- Thresholds,C9\r
- ALLOW2,C20\r
- ALLOW,C20\r
- ANG,B4\r
- ATHR,C23\r
- DANGER,C20,C25\r
- DIAGTH,C20,C25\r
- DIFFER,C24,C34,C34\r
- DONE,C34\r
- DVAL,B5,B25\r
- EPS,C24,C34\r
- ETHR1,C23\r
- ETHR2,C23\r
- ETHR,C23\r
- EVAL,B4\r
- OCC,B4\r
- PCT,B4\r
- PRJINC,C22\r
- PRJTHR,B11,C22\r
- PTHR,C23\r
- TEST2,C20\r
- TEST,C20\r
- THRESH,C22\r
- THR1,C23\r
- THR2,C23\r
- THRESH,B11,C25\r
- TOOSML,C24\r
- WORTH,C20\r
- WTTHR,C20,C21\r
- 2e-stabilization,A21\r
- \r
-<p>\r
- UHF method\r
- <i>see</i> Wavefunction type\r
-<p>\r
- Upper triangular matrix,\r
- B65,B71,C13,C33,C34\r
- \r
- Vager, Z.,A7\r
-<p>\r
- Valency index\r
- <i>see</i> Bond order\r
- Versions, previous,<i>A7</i>,A9,B13\r
-<p>\r
- Vicinal interaction,A22-23,B18,\r
- B23,B25,B51,C33\r
- \r
- Warnings,B16,B17,B36,B55\r
-<p>\r
- Wavefunction type\r
- AUHF,C5,C17\r
- CI,A6,C5,C17\r
- Complex,A6,C5\r
- Correlated,B25\r
- GVB,A6\r
- MCSCF,A1,A6,C5\r
- Møller-Plesset,A6,C17\r
- RHF,A6,A12,B16,B56,C2\r
- ROHF,A6,C5\r
- SCF,A6,B16,B25,C17\r
- Semi-empirical,A7,A8,B66\r
- UHF,A6,B16,B20,B52-55,C2,C5\r
- Weinhold, F.,A7,B11,C19,C22\r
- Weinstock, R. B.,A7,B11,C19\r
- Wiberg bond index,A16,B9,B29,C20,C22\r
- Write (W) parameter\r
- <i>see</i> Print parameters\r
-</body>\r
-</html>\r
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