From fcf5c29bd3a129b4b08f734a9940341d05a770b7 Mon Sep 17 00:00:00 2001 From: toshinagata1964 Date: Fri, 28 Mar 2014 06:45:19 +0000 Subject: [PATCH] Document is updated; the Japanese version of GPL text is now in html format. git-svn-id: svn+ssh://svn.sourceforge.jp/svnroot/molby/trunk@519 a2be9bc6-48de-4e38-9406-05402d4bc13c --- Documents/etc/gpl.ja.html | 428 ++ Documents/etc/gpl.ja.txt | 416 -- Documents/etc/mopac6_manual.pdf | Bin 748406 -> 0 bytes Documents/etc/nbo/alpha.gif | Bin 70 -> 0 bytes Documents/etc/nbo/beta.gif | Bin 75 -> 0 bytes Documents/etc/nbo/ca.gif | Bin 66 -> 0 bytes Documents/etc/nbo/chi.gif | Bin 72 -> 0 bytes Documents/etc/nbo/delta.gif | Bin 72 -> 0 bytes Documents/etc/nbo/epsilon.gif | Bin 63 -> 0 bytes Documents/etc/nbo/ge.gif | Bin 65 -> 0 bytes Documents/etc/nbo/index.html | 8893 --------------------------------------- Documents/etc/nbo/lambda.gif | Bin 71 -> 0 bytes Documents/etc/nbo/le.gif | Bin 64 -> 0 bytes Documents/etc/nbo/mu.gif | Bin 70 -> 0 bytes Documents/etc/nbo/nbofig1.gif | Bin 4178 -> 0 bytes Documents/etc/nbo/nbofig2.gif | Bin 6890 -> 0 bytes Documents/etc/nbo/nbofig3.gif | Bin 657 -> 0 bytes Documents/etc/nbo/phi.gif | Bin 73 -> 0 bytes Documents/etc/nbo/pi.gif | Bin 66 -> 0 bytes Documents/etc/nbo/rarr.gif | Bin 68 -> 0 bytes Documents/etc/nbo/sigma.gif | Bin 67 -> 0 bytes Documents/etc/nbo/sum.gif | Bin 70 -> 0 bytes Documents/etc/nbo/theta.gif | Bin 70 -> 0 bytes Documents/src/doc_source.html | 2 +- 24 files changed, 429 insertions(+), 9310 deletions(-) create mode 100644 Documents/etc/gpl.ja.html delete mode 100644 Documents/etc/gpl.ja.txt delete mode 100644 Documents/etc/mopac6_manual.pdf delete mode 100644 Documents/etc/nbo/alpha.gif delete mode 100644 Documents/etc/nbo/beta.gif delete mode 100644 Documents/etc/nbo/ca.gif delete mode 100644 Documents/etc/nbo/chi.gif delete mode 100644 Documents/etc/nbo/delta.gif delete mode 100644 Documents/etc/nbo/epsilon.gif delete mode 100644 Documents/etc/nbo/ge.gif delete mode 100644 Documents/etc/nbo/index.html delete mode 100644 Documents/etc/nbo/lambda.gif delete mode 100644 Documents/etc/nbo/le.gif delete mode 100644 Documents/etc/nbo/mu.gif delete mode 100644 Documents/etc/nbo/nbofig1.gif delete mode 100644 Documents/etc/nbo/nbofig2.gif delete mode 100644 Documents/etc/nbo/nbofig3.gif delete mode 100644 Documents/etc/nbo/phi.gif delete mode 100644 Documents/etc/nbo/pi.gif delete mode 100644 Documents/etc/nbo/rarr.gif delete mode 100644 Documents/etc/nbo/sigma.gif delete mode 100644 Documents/etc/nbo/sum.gif delete mode 100644 Documents/etc/nbo/theta.gif diff --git a/Documents/etc/gpl.ja.html b/Documents/etc/gpl.ja.html new file mode 100644 index 0000000..686be2b --- /dev/null +++ b/Documents/etc/gpl.ja.html @@ -0,0 +1,428 @@ + + + + + +GNU 一般公衆利用許諾契約書 + + + +
+                    GNU 一般公衆利用許諾契約書
+                       バージョン2、1991年6月
+                       日本語訳、2002年5月20日
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+                       59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ この利用許諾契約書を、一字一句そのままに複製し頒布することは許可する。
+ しかし変更は認めない。
+
+ This is an unofficial translation of the GNU General Public License
+ into Japanese.  It was not published by the Free Software Foundation,
+ and does not legally state the distribution terms for software that
+ uses the GNU GPL--only the original English text of the GNU GPL does
+ that. However, we hope that this translation will help Japanese
+ speakers understand the GNU GPL better.
+
+ (訳: 以下はGNU General Public Licenseの非公式な日本語訳です。これはフ
+ リーソフトウェア財団(the Free Software Foundataion)によって発表された
+ ものではなく、GNU GPLを適用したソフトウェアの頒布条件を法的に有効な形
+ で述べたものではありません。頒布条件としてはGNU GPLの英語版テキストで
+ 指定されているもののみが有効です。しかしながら、私たちはこの翻訳が、
+ 日本語を使用する人々にとってGNU GPLをより良く理解する助けとなることを
+ 望んでいます。)
+
+ 翻訳は 八田真行<mhatta@gnu.org>が行った。原文は
+ http://www.gnu.org/licenses/gpl.txtである。誤訳の指摘や改善案を歓迎す
+ る。
+                            はじめに
+
+ソフトウェア向けライセンスの大半は、あなたがそのソフトウェアを共有した
+り変更したりする自由を奪うように設計されています。対照的に、GNU 一般公
+衆利用許諾契約書は、あなたがフリーソフトウェアを共有したり変更したりす
+る自由を保証する--すなわち、ソフトウェアがそのユーザすべてにとってフリー
+であることを保証することを目的としています。この一般公衆利用許諾契約書
+はフリーソフトウェア財団のソフトウェアのほとんどに適用されており、また
+GNU GPLを適用すると決めたフリーソフトウェア財団以外の作者によるプログ
+ラムにも適用されています(いくつかのフリーソフトウェア財団のソフトウェ
+アには、GNU GPLではなくGNU ライブラリ一般公衆利用許諾契約書が適用され
+ていることもあります)。あなたもまた、ご自分のプログラムにGNU GPLを適用
+することが可能です。
+
+私たちがフリーソフトウェアと言うとき、それは利用の自由について言及して
+いるのであって、価格は問題にしていません。私たちの一般公衆利用許諾契約
+書は、あなたがフリーソフトウェアの複製物を頒布する自由を保証するよう設
+計されています(希望に応じてその種のサービスに手数料を課す自由も保証さ
+れます)。また、あなたがソースコードを受け取るか、あるいは望めばそれを
+入手することが可能であるということ、あなたがソフトウェアを変更し、その
+一部を新たなフリーのプログラムで利用できるということ、そして、以上で述
+べたようなことができるということがあなたに知らされるということも保証さ
+れます。
+
+あなたの権利を守るため、私たちは誰かがあなたの有するこれらの権利を否定
+することや、これらの権利を放棄するよう要求することを禁止するという制限
+を加える必要があります。よって、あなたがソフトウェアの複製物を頒布した
+りそれを変更したりする場合には、これらの制限のためにあなたにある種の責
+任が発生することになります。
+
+例えば、あなたがフリーなプログラムの複製物を頒布する場合、有料か無料に
+関わらず、あなたは自分が有する権利を全て受領者に与えなければなりません。
+また、あなたは彼らもソースコードを受け取るか手に入れることができるよう
+保証しなければなりません。そして、あなたは彼らに対して以下で述べる条件
+を示し、彼らに自らの持つ権利について知らしめるようにしなければなりませ
+ん。
+
+私たちはあなたの権利を二段階の手順を踏んで保護します。(1) まずソフトウェ
+アに対して著作権を主張し、そして (2) あなたに対して、ソフトウェアの複
+製や頒布または改変についての法的な許可を与えるこの契約書を提示します。
+
+また、各作者や私たちを保護するため、私たちはこのフリーソフトウェアには
+何の保証も無いということを誰もが確実に理解するようにし、またソフトウェ
+アが誰か他人によって改変され、それが次々と頒布されていったとしても、そ
+の受領者は彼らが手に入れたソフトウェアがオリジナルのバージョンでは無い
+こと、そして原作者の名声は他人によって持ち込まれた可能性のある問題によっ
+て影響されることがないということを周知させたいと思います。
+
+最後に、ソフトウェア特許がいかなるフリーのプログラムの存在にも不断の脅
+威を投げかけていますが、私たちは、フリーなプログラムの再頒布者が個々に
+特許ライセンスを取得することによって、事実上プログラムを独占的にしてし
+まうという危険を避けたいと思います。こういった事態を予防するため、私た
+ちはいかなる特許も誰もが自由に利用できるようライセンスされるか、全くラ
+イセンスされないかのどちらかでなければならないことを明確にしました。
+
+(訳注: 本契約書で「独占的(proprietary)」とは、ソフトウェアの利用や再頒
+布、改変が禁止されているか、許可を得ることが必要とされているか、あるい
+は厳しい制限が課せられていて自由にそうすることが事実上できなくなってい
+る状態のことを指す。詳しくは
+http://www.gnu.org/philosophy/categories.ja.html#ProprietarySoftwareを
+参照せよ。)
+
+複製や頒布、改変についての正確な条件と制約を以下で述べていきます。
+
+                    GNU 一般公衆利用許諾契約書
+                 複製、頒布、改変に関する条件と制約
+
+0. この利用許諾契約書は、そのプログラム(またはその他の著作物)をこの一
+般公衆利用許諾契約書の定める条件の下で頒布できるという告知が著作権者に
+よって記載されたプログラムまたはその他の著作物全般に適用される。以下で
+は、「『プログラム』」とはそのようにしてこの契約書が適用されたプログラ
+ムや著作物全般を意味し、また「『プログラム』を基にした著作物」とは『プ
+ログラム』やその他著作権法の下で派生物と見なされるもの全般を指す。すな
+わち、『プログラム』かその一部を、全く同一のままか、改変を加えたか、あ
+るいは他の言語に翻訳された形で含む著作物のことである(「改変」という語
+の本来の意味からはずれるが、以下では翻訳も改変の一種と見なす)。それぞ
+れの契約者は「あなた」と表現される。
+
+複製や頒布、改変以外の活動はこの契約書ではカバーされない。それらはこの
+契約書の対象外である。『プログラム』を実行する行為自体に制限はない。ま
+た、そのような『プログラム』の出力結果は、その内容が『プログラム』を基
+にした著作物を構成する場合のみこの契約書によって保護される(『プログラ
+ム』を実行したことによって作成されたということとは無関係である)。この
+ような線引きの妥当性は、『プログラム』が何をするのかに依存する。
+
+1. それぞれの複製物において適切な著作権表示と保証の否認声明(disclaimer
+of warranty)を目立つよう適切に掲載し、またこの契約書および一切の保証の
+不在に触れた告知すべてをそのまま残し、そしてこの契約書の複製物を『プロ
+グラム』のいかなる受領者にも『プログラム』と共に頒布する限り、あなたは
+『プログラム』のソースコードの複製物を、あなたが受け取った通りの形で複
+製または頒布することができる。媒体は問わない。
+
+あなたは、物理的に複製物を譲渡するという行為に関して手数料を課しても良
+いし、希望によっては手数料を取って交換における保護の保証を提供しても良
+い。
+
+2. あなたは自分の『プログラム』の複製物かその一部を改変して『プログラ
+ム』を基にした著作物を形成し、そのような改変点や著作物を上記第1節の定
+める条件の下で複製または頒布することができる。ただし、そのためには以下
+の条件すべてを満たしていなければならない:
+
+    a) あなたがそれらのファイルを変更したということと変更した日時が良
+    く分かるよう、改変されたファイルに告示しなければならない。
+
+    b) 『プログラム』またはその一部を含む著作物、あるいは『プログラム』
+    かその一部から派生した著作物を頒布あるいは発表する場合には、その全
+    体をこの契約書の条件に従って第三者へ無償で利用許諾しなければならな
+    い。
+
+    c) 改変されたプログラムが、通常実行する際に対話的にコマンドを読む
+    ようになっているならば、そのプログラムを最も一般的な方法で対話的に
+    実行する際、適切な著作権表示、無保証であること(あるいはあなたが保
+    証を提供するということ)、ユーザがプログラムをこの契約書で述べた条
+    件の下で頒布することができるということ、そしてこの契約書の複製物を
+    閲覧するにはどうしたらよいかというユーザへの説明を含む告知が印刷さ
+    れるか、あるいは画面に表示されるようにしなければならない(例外とし
+    て、『プログラム』そのものは対話的であっても通常そのような告知を印
+    刷しない場合には、『プログラム』を基にしたあなたの著作物にそのよう
+    な告知を印刷させる必要はない)。
+
+以上の必要条件は全体としての改変された著作物に適用される。著作物の一部
+が『プログラム』から派生したものではないと確認でき、それら自身別の独立
+した著作物であると合理的に考えられるならば、あなたがそれらを別の著作物
+として分けて頒布する場合、そういった部分にはこの契約書とその条件は
+適用されない。しかし、あなたが同じ部分を『プログラム』を基にした著作物
+全体の一部として頒布するならば、全体としての頒布物は、この契約書が
+課す条件に従わなければならない。というのは、この契約書が他の契約者
+に与える許可は『プログラム』丸ごと全体に及び、誰が書いたかは関係なく各
+部分のすべてを保護するからである。
+
+よって、すべてあなたによって書かれた著作物に対し、権利を主張したりあな
+たの権利に異議を申し立てることはこの節の意図するところではない。むしろ、
+その趣旨は『プログラム』を基にした派生物ないし集合著作物の頒布を管理す
+る権利を行使するということにある。
+
+また、『プログラム』を基にしていないその他の著作物を『プログラム』(あ
+るいは『プログラム』を基にした著作物)と一緒に集めただけのものを一巻の
+保管装置ないし頒布媒体に収めても、その他の著作物までこの契約書が保
+護する対象になるということにはならない。
+
+3. あなたは上記第1節および2節の条件に従い、『プログラム』(あるいは第2
+節における派生物)をオブジェクトコードないし実行形式で複製または頒布す
+ることができる。ただし、その場合あなたは以下のうちどれか一つを実施しな
+ければならない:
+
+    a) 著作物に、『プログラム』に対応した完全かつ機械で読み取り可能な
+    ソースコードを添付する。ただし、ソースコードは上記第1節および2節の
+    条件に従いソフトウェアの交換で習慣的に使われる媒体で頒布しなければ
+    ならない。あるいは、
+
+    b) 著作物に、いかなる第三者に対しても、『プログラム』に対応した完
+    全かつ機械で読み取り可能なソースコードを、頒布に要する物理的コスト
+    を上回らない程度の手数料と引き換えに提供する旨述べた少なくとも3年
+    間は有効な書面になった申し出を添える。ただし、ソースコードは上記第
+    1節および2節の条件に従いソフトウェアの交換で習慣的に使われる媒体で
+    頒布しなければならない。あるいは、
+
+    c) 対応するソースコード頒布の申し出に際して、あなたが得た情報を一
+    緒に引き渡す(この選択肢は、営利を目的としない頒布であって、かつあ
+    なたが上記小節bで指定されているような申し出と共にオブジェクトコー
+    ドあるいは実行形式のプログラムしか入手していない場合に限り許可され
+    る)。
+
+著作物のソースコードとは、それに対して改変を加える上で好ましいとされる
+著作物の形式を意味する。ある実行形式の著作物にとって完全なソースコード
+とは、それが含むモジュールすべてのソースコード全部に加え、関連するイン
+ターフェース定義ファイルのすべてとライブラリのコンパイルやインストール
+を制御するために使われるスクリプトをも加えたものを意味する。しかし特別
+な例外として、そのコンポーネント自体が実行形式に付随するのでは無い限り、
+頒布されるものの中に、実行形式が実行されるオペレーティングシステムの主
+要なコンポーネント(コンパイラやカーネル等)と通常一緒に(ソースかバイナ
+リ形式のどちらかで)頒布されるものを含んでいる必要はないとする。
+
+実行形式またはオブジェクトコードの頒布が、指定された場所からコピーする
+ためのアクセス手段を提供することで為されるとして、その上でソースコード
+も同等のアクセス手段によって同じ場所からコピーできるようになっているな
+らば、第三者がオブジェクトコードと一緒にソースも強制的にコピーさせられ
+るようになっていなくてもソースコード頒布の条件を満たしているものとする。
+
+4. あなたは『プログラム』を、この契約書において明確に提示された行
+為を除き複製や改変、サブライセンス、あるいは頒布してはならない。他に
+『プログラム』を複製や改変、サブライセンス、あるいは頒布する企てはすべ
+て無効であり、この契約書の下でのあなたの権利を自動的に終結させるこ
+とになろう。しかし、複製物や権利をこの契約書に従ってあなたから得た
+人々に関しては、そのような人々がこの契約書に完全に従っている限り彼
+らのライセンスまで終結することはない。
+
+5. あなたはこの契約書を受諾する必要は無い。というのは、あなたはこ
+れに署名していないからである。しかし、この契約書以外にあなたに対し
+て『プログラム』やその派生物を変更、頒布する許可を与えるものは存在しな
+い。これらの行為は、あなたがこの契約書を受け入れない限り法によって
+禁じられている。そこで、『プログラム』(あるいは『プログラム』を基にし
+た著作物のすべて)を改変ないし頒布することにより、あなたは自分がそのよ
+うな行為を行うためにこの契約書を受諾したということ、そして『プログ
+ラム』とそれに基づく著作物の複製や頒布、改変についてこの契約書が課
+す制約と条件をすべて受け入れたということを示したものと見なす。
+
+6. あなたが『プログラム』(または『プログラム』を基にした著作物全般)を
+再頒布するたびに、その受領者は元々のライセンス許可者から、この契約書で
+指定された条件と制約の下で『プログラム』を複製や頒布、あるいは改変する
+許可を自動的に得るものとする。あなたは、受領者がここで認められた権利を
+行使することに関してこれ以上他のいかなる制限も課すことができない。あな
+たには、第三者がこの契約書に従うことを強制する責任はない。
+
+7. 特許侵害あるいはその他の理由(特許関係に限らない)から、裁判所の判決
+あるいは申し立ての結果としてあなたに(裁判所命令や契約などにより)この契
+約書の条件と矛盾する制約が課された場合でも、あなたがこの契約書の条件を
+免除されるわけではない。もしこの契約書の下であなたに課せられた責任と他
+の関連する責任を同時に満たすような形で頒布できないならば、結果としてあ
+なたは『プログラム』を頒布することが全くできないということである。例え
+ば特許ライセンスが、あなたから直接間接を問わずコピーを受け取った人が誰
+でも『プログラム』を使用料無料で再頒布することを認めていない場合、あな
+たがその制約とこの契約書を両方とも満たすには『プログラム』の頒布を完全
+に中止するしかないだろう。
+
+この節の一部分が特定の状況の下で無効ないし実施不可能な場合でも、節の残
+りの部分は適用されるよう意図されている。その他の状況では節が全体として
+適用されるよう意図されている。
+
+特許やその他の財産権を侵害したり、そのような権利の主張の効力に異議を唱
+えたりするようあなたを誘惑することがこの節の目的ではない。この節には、
+人々によってライセンス慣行として実現されてきた、フリーソフトウェア頒布
+のシステムの完全性を護るという目的しかない。多くの人々が、フリーソフト
+ウェアの頒布システムが首尾一貫して適用されているという信頼に基づき、こ
+のシステムを通じて頒布される多様なソフトウェアに寛大な貢献をしてきたの
+は事実であるが、人がどのようなシステムを通じてソフトウェアを頒布したい
+と思うかはあくまでも作者/寄与者次第であり、あなたが選択を押しつけるこ
+とはできない。
+
+この節は、この契約書のこの節以外の部分の一帰結になると考えられるケー
+スを徹底的に明らかにすることを目的としている。
+
+8. 『プログラム』の頒布や利用が、ある国においては特許または著作権が主
+張されたインターフェースのいずれかによって制限されている場合、『プログ
+ラム』にこの契約書を適用した元の著作権者は、そういった国々を排除し
+た明確な地理的頒布制限を加え、そこで排除されていない国の中やそれらの国々
+の間でのみ頒布が許可されるようにしても構わない。その場合、そのような制
+限はこの契約書本文で書かれているのと同様に見なされる。
+
+9. フリーソフトウェア財団は、時によって改訂または新版の一般公衆利用許
+諾書を発表することができる。そのような新版は現在のバージョンとその精神
+においては似たものになるだろうが、新たな問題や懸念を解決するため細部で
+は異なる可能性がある。
+
+それぞれのバージョンには、見分けが付くようにバージョン番号が振られてい
+る。『プログラム』においてそれに適用されるこの契約書のバージョン番号が
+指定されていて、更に「それ以降のいかなるバージョン」も適用して良いとなっ
+ていた場合、あなたは従う条件と制約として、指定のバージョンか、フリーソ
+フトウェア財団によって発行された指定のバージョン以降の版のどれか一つの
+どちらかを選ぶことが出来る。『プログラム』でライセンスのバージョン番号
+が指定されていないならば、あなたは今までにフリーソフトウェア財団から発
+行されたバージョンの中から好きに選んで構わない。
+
+10. もしあなたが『プログラム』の一部を、その頒布条件がこの契約書と
+異なる他のフリーなプログラムと統合したいならば、作者に連絡して許可を求
+めよ。フリーソフトウェア財団が著作権を保有するソフトウェアについては、
+フリーソフトウェア財団に連絡せよ。私たちは、このような場合のために特別
+な例外を設けることもある。私たちが決定を下すにあたっては、私たちのフリー
+ソフトウェアの派生物すべてがフリーな状態に保たれるということと、一般的
+にソフトウェアの共有と再利用を促進するという二つの目標を規準に検討され
+るであろう。
+                            無保証について
+
+11. 『プログラム』は代価無しに利用が許可されるので、適切な法が認める限
+りにおいて、『プログラム』に関するいかなる保証も存在しない。書面で別に
+述べる場合を除いて、著作権者、またはその他の団体は、『プログラム』を、
+表明されたか言外にかは問わず、商業的適性を保証するほのめかしやある特定
+の目的への適合性(に限られない)を含む一切の保証無しに「あるがまま」で提
+供する。『プログラム』の質と性能に関するリスクのすべてはあなたに帰属す
+る。『プログラム』に欠陥があると判明した場合、あなたは必要な保守点検や
+補修、修正に要するコストのすべてを引き受けることになる。
+
+12. 適切な法か書面での同意によって命ぜられない限り、著作権者、または上
+記で許可されている通りに『プログラム』を改変または再頒布したその他の団
+体は、あなたに対して『プログラム』の利用ないし利用不能で生じた一般的、
+特別的、偶然的、必然的な損害(データの消失や不正確な処理、あなたか第三
+者が被った損失、あるいは『プログラム』が他のソフトウェアと一緒に動作し
+ないという不具合などを含むがそれらに限らない)に一切の責任を負わない。
+そのような損害が生ずる可能性について彼らが忠告されていたとしても同様で
+ある。
+
+                          条件と制約終わり
+
+            以上の条項をあなたの新しいプログラムに適用する方法
+
+あなたが新しいプログラムを開発したとして、公衆によってそれが利用される
+可能性を最大にしたいなら、そのプログラムをこの契約書の条項に従って
+誰でも再頒布あるいは変更できるようフリーソフトウェアにするのが最善です。
+
+そのためには、プログラムに以下のような表示を添付してください。その場合、
+保証が排除されているということを最も効果的に伝えるために、それぞれのソー
+スファイルの冒頭に表示を添付すれば最も安全です。少なくとも、「著作権表
+示」という行と全文がある場所へのポインタだけは各ファイルに含めて置いて
+ください。
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program; if not, write to the Free Software
+    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+    (訳:
+
+    <プログラムの名前と、それが何をするかについての簡単な説明。>
+    Copyright (C) <西暦年>  <作者の名前>
+
+    このプログラムはフリーソフトウェアです。あなたはこれを、フリーソフ
+    トウェア財団によって発行された GNU 一般公衆利用許諾契約書(バージョ
+    ン2か、希望によってはそれ以降のバージョンのうちどれか)の定める条件
+    の下で再頒布または改変することができます。
+
+    このプログラムは有用であることを願って頒布されますが、*全くの無保
+    証* です。商業可能性の保証や特定の目的への適合性は、言外に示された
+    ものも含め全く存在しません。詳しくはGNU 一般公衆利用許諾契約書をご
+    覧ください。
+
+    あなたはこのプログラムと共に、GNU 一般公衆利用許諾契約書の複製物を
+    一部受け取ったはずです。もし受け取っていなければ、フリーソフトウェ
+    ア財団まで請求してください(宛先は the Free Software Foundation,
+    Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA)。
+
+    )
+
+電子ないし紙のメールであなたに問い合わせる方法についての情報も書き加え
+ましょう。
+
+プログラムが対話的なものならば、対話モードで起動した際に出力として以下
+のような短い告知が表示されるようにしてください:
+
+    Gnomovision version 69, Copyright (C) year name of author
+    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+    (訳:
+
+    Gnomovision バージョン 69, Copyright (C) 年 作者の名前
+    Gnomovision は*全くの無保証*で提供されます。詳しくは「show w」
+    とタイプして下さい。これはフリーソフトウェアであり、ある条件の下で
+    再頒布することが奨励されています。詳しくは「show c」とタイプして下
+    さい。
+
+    )
+
+ここで、仮想的なコマンド「show w」と「show c」は一般公衆利用許諾契約書
+の適切な部分を表示するようになっていなければなりません。もちろん、あな
+たが使うコマンドを「show w」や「show c」と呼ぶ必然性はありませんので、
+あなたのプログラムに合わせてマウスのクリックやメニューのアイテムにして
+も結構です。
+
+またあなたは、必要ならば(プログラマーとして働いていたら)あなたの雇用主、
+あるいは場合によっては学校から、そのプログラムに関する「著作権放棄声明
+(copyright disclaimer)」に署名してもらうべきです。以下は例ですので、名
+前を変えてください:
+
+  Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+  `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+  <signature of Ty Coon>, 1 April 1989
+  Ty Coon, President of Vice
+
+  (訳:
+
+  Yoyodyne社はここに、James Hackerによって書かれたプログラム
+  「Gnomovision」(コンパイラへ通すプログラム)に関する一切の著作権の利
+  益を放棄します。
+
+   <Ty Coon氏の署名>、1989年4月1日
+   Ty Coon、副社長
+
+  )
+
+この一般公衆利用許諾契約書では、あなたのプログラムを独占的なプログラム
+に統合することを認めていません。あなたのプログラムがサブルーチンライブ
+ラリならば、独占的なアプリケーションとあなたのライブラリをリンクするこ
+とを許可したほうがより便利であると考えるかもしれません。もしこれがあな
+たの望むことならば、この契約書の代わりにGNU ライブラリ一般公衆利用許諾
+契約書を適用してください。
+
+ diff --git a/Documents/etc/gpl.ja.txt b/Documents/etc/gpl.ja.txt deleted file mode 100644 index cb6d419..0000000 --- a/Documents/etc/gpl.ja.txt +++ /dev/null @@ -1,416 +0,0 @@ - GNU °ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ - ¥Ð¡¼¥¸¥ç¥ó2¡¢1991ǯ6·î - ÆüËܸìÌõ¡¢2002ǯ5·î20Æü - - Copyright (C) 1989, 1991 Free Software Foundation, Inc. - 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA - ¤³¤ÎÍøÍѵöÂú·ÀÌó½ñ¤ò¡¢°ì»ú°ì¶ç¤½¤Î¤Þ¤Þ¤ËÊ£À½¤·ÈÒÉÛ¤¹¤ë¤³¤È¤Ïµö²Ä¤¹¤ë¡£ - ¤·¤«¤·Êѹ¹¤Ïǧ¤á¤Ê¤¤¡£ - - This is an unofficial translation of the GNU General Public License - into Japanese. It was not published by the Free Software Foundation, - and does not legally state the distribution terms for software that - uses the GNU GPL--only the original English text of the GNU GPL does - that. 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See the - GNU General Public License for more details. - - You should have received a copy of the GNU General Public License - along with this program; if not, write to the Free Software - Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA - - (Ìõ: - - <¥×¥í¥°¥é¥à¤Î̾Á°¤È¡¢¤½¤ì¤¬²¿¤ò¤¹¤ë¤«¤Ë¤Ä¤¤¤Æ¤Î´Êñ¤ÊÀâÌÀ¡£> - Copyright (C) <À¾Îñǯ> <ºî¼Ô¤Î̾Á°> - - ¤³¤Î¥×¥í¥°¥é¥à¤Ï¥Õ¥ê¡¼¥½¥Õ¥È¥¦¥§¥¢¤Ç¤¹¡£¤¢¤Ê¤¿¤Ï¤³¤ì¤ò¡¢¥Õ¥ê¡¼¥½¥Õ - ¥È¥¦¥§¥¢ºâÃĤˤè¤Ã¤Æȯ¹Ô¤µ¤ì¤¿ GNU °ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ(¥Ð¡¼¥¸¥ç - ¥ó2¤«¡¢´õ˾¤Ë¤è¤Ã¤Æ¤Ï¤½¤ì°Ê¹ß¤Î¥Ð¡¼¥¸¥ç¥ó¤Î¤¦¤Á¤É¤ì¤«)¤ÎÄê¤á¤ë¾ò·ï - ¤Î²¼¤ÇºÆÈÒÉÛ¤Þ¤¿¤Ï²þÊѤ¹¤ë¤³¤È¤¬¤Ç¤­¤Þ¤¹¡£ - - ¤³¤Î¥×¥í¥°¥é¥à¤ÏÍ­ÍѤǤ¢¤ë¤³¤È¤ò´ê¤Ã¤ÆÈÒÉÛ¤µ¤ì¤Þ¤¹¤¬¡¢*Á´¤¯¤Î̵ÊÝ - ¾Ú* ¤Ç¤¹¡£¾¦¶È²ÄǽÀ­¤ÎÊݾڤäÆÃÄê¤ÎÌÜŪ¤Ø¤ÎŬ¹çÀ­¤Ï¡¢¸À³°¤Ë¼¨¤µ¤ì¤¿ - ¤â¤Î¤â´Þ¤áÁ´¤¯Â¸ºß¤·¤Þ¤»¤ó¡£¾Ü¤·¤¯¤ÏGNU °ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ¤ò¤´ - Í÷¤¯¤À¤µ¤¤¡£ - - ¤¢¤Ê¤¿¤Ï¤³¤Î¥×¥í¥°¥é¥à¤È¶¦¤Ë¡¢GNU °ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ¤ÎÊ£À½Êª¤ò - °ìÉô¼õ¤±¼è¤Ã¤¿¤Ï¤º¤Ç¤¹¡£¤â¤·¼õ¤±¼è¤Ã¤Æ¤¤¤Ê¤±¤ì¤Ð¡¢¥Õ¥ê¡¼¥½¥Õ¥È¥¦¥§ - ¥¢ºâÃĤޤÇÀÁµá¤·¤Æ¤¯¤À¤µ¤¤(°¸Àè¤Ï the Free Software Foundation, - Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA)¡£ - - ) - -ÅŻҤʤ¤¤·»æ¤Î¥á¡¼¥ë¤Ç¤¢¤Ê¤¿¤ËÌ䤤¹ç¤ï¤»¤ëÊýË¡¤Ë¤Ä¤¤¤Æ¤Î¾ðÊó¤â½ñ¤­²Ã¤¨ -¤Þ¤·¤ç¤¦¡£ - -¥×¥í¥°¥é¥à¤¬ÂÐÏÃŪ¤Ê¤â¤Î¤Ê¤é¤Ð¡¢ÂÐÏå⡼¥É¤Çµ¯Æ°¤·¤¿ºÝ¤Ë½ÐÎϤȤ·¤Æ°Ê²¼ -¤Î¤è¤¦¤Êû¤¤¹ðÃΤ¬É½¼¨¤µ¤ì¤ë¤è¤¦¤Ë¤·¤Æ¤¯¤À¤µ¤¤: - - Gnomovision version 69, Copyright (C) year name of author - Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. - This is free software, and you are welcome to redistribute it - under certain conditions; type `show c' for details. - - (Ìõ: - - Gnomovision ¥Ð¡¼¥¸¥ç¥ó 69, Copyright (C) ǯ ºî¼Ô¤Î̾Á° - Gnomovision ¤Ï*Á´¤¯¤Î̵ÊݾÚ*¤ÇÄ󶡤µ¤ì¤Þ¤¹¡£¾Ü¤·¤¯¤Ï¡Öshow w¡× - ¤È¥¿¥¤¥×¤·¤Æ²¼¤µ¤¤¡£¤³¤ì¤Ï¥Õ¥ê¡¼¥½¥Õ¥È¥¦¥§¥¢¤Ç¤¢¤ê¡¢¤¢¤ë¾ò·ï¤Î²¼¤Ç - ºÆÈÒÉÛ¤¹¤ë¤³¤È¤¬¾©Î夵¤ì¤Æ¤¤¤Þ¤¹¡£¾Ü¤·¤¯¤Ï¡Öshow c¡×¤È¥¿¥¤¥×¤·¤Æ²¼ - ¤µ¤¤¡£ - - ) - -¤³¤³¤Ç¡¢²¾ÁÛŪ¤Ê¥³¥Þ¥ó¥É¡Öshow w¡×¤È¡Öshow c¡×¤Ï°ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ -¤ÎŬÀÚ¤ÊÉôʬ¤òɽ¼¨¤¹¤ë¤è¤¦¤Ë¤Ê¤Ã¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤ê¤Þ¤»¤ó¡£¤â¤Á¤í¤ó¡¢¤¢¤Ê -¤¿¤¬»È¤¦¥³¥Þ¥ó¥É¤ò¡Öshow w¡×¤ä¡Öshow c¡×¤È¸Æ¤ÖɬÁ³À­¤Ï¤¢¤ê¤Þ¤»¤ó¤Î¤Ç¡¢ -¤¢¤Ê¤¿¤Î¥×¥í¥°¥é¥à¤Ë¹ç¤ï¤»¤Æ¥Þ¥¦¥¹¤Î¥¯¥ê¥Ã¥¯¤ä¥á¥Ë¥å¡¼¤Î¥¢¥¤¥Æ¥à¤Ë¤·¤Æ -¤â·ë¹½¤Ç¤¹¡£ - -¤Þ¤¿¤¢¤Ê¤¿¤Ï¡¢É¬Íפʤé¤Ð(¥×¥í¥°¥é¥Þ¡¼¤È¤·¤ÆƯ¤¤¤Æ¤¤¤¿¤é)¤¢¤Ê¤¿¤Î¸ÛÍѼ硢 -¤¢¤ë¤¤¤Ï¾ì¹ç¤Ë¤è¤Ã¤Æ¤Ï³Ø¹»¤«¤é¡¢¤½¤Î¥×¥í¥°¥é¥à¤Ë´Ø¤¹¤ë¡ÖÃøºî¸¢Êü´þÀ¼ÌÀ -(copyright disclaimer)¡×¤Ë½ð̾¤·¤Æ¤â¤é¤¦¤Ù¤­¤Ç¤¹¡£°Ê²¼¤ÏÎã¤Ç¤¹¤Î¤Ç¡¢Ì¾ -Á°¤òÊѤ¨¤Æ¤¯¤À¤µ¤¤: - - Yoyodyne, Inc., hereby disclaims all copyright interest in the program - `Gnomovision' (which makes passes at compilers) written by James Hacker. - - , 1 April 1989 - Ty Coon, President of Vice - - (Ìõ: - - Yoyodyne¼Ò¤Ï¤³¤³¤Ë¡¢James Hacker¤Ë¤è¤Ã¤Æ½ñ¤«¤ì¤¿¥×¥í¥°¥é¥à - ¡ÖGnomovision¡×(¥³¥ó¥Ñ¥¤¥é¤ØÄ̤¹¥×¥í¥°¥é¥à)¤Ë´Ø¤¹¤ë°ìÀÚ¤ÎÃøºî¸¢¤ÎÍø - ±×¤òÊü´þ¤·¤Þ¤¹¡£ - - ¡¢1989ǯ4·î1Æü - Ty Coon¡¢Éû¼ÒĹ - - ) - -¤³¤Î°ìÈ̸ø½°ÍøÍѵöÂú·ÀÌó½ñ¤Ç¤Ï¡¢¤¢¤Ê¤¿¤Î¥×¥í¥°¥é¥à¤òÆÈÀêŪ¤Ê¥×¥í¥°¥é¥à -¤ËÅý¹ç¤¹¤ë¤³¤È¤òǧ¤á¤Æ¤¤¤Þ¤»¤ó¡£¤¢¤Ê¤¿¤Î¥×¥í¥°¥é¥à¤¬¥µ¥Ö¥ë¡¼¥Á¥ó¥é¥¤¥Ö -¥é¥ê¤Ê¤é¤Ð¡¢ÆÈÀêŪ¤Ê¥¢¥×¥ê¥±¡¼¥·¥ç¥ó¤È¤¢¤Ê¤¿¤Î¥é¥¤¥Ö¥é¥ê¤ò¥ê¥ó¥¯¤¹¤ë¤³ 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-

-

NBO 3.0 Program Manual

-

-(Natural Bond Orbital / Natural Population Analysis / -Natural Localized Molecular Orbital Programs) -

-E. D. Glendening, A. E. Reed,* J. E. Carpenter,** and F. Weinhold -

-Theoretical Chemistry Institute and Department of Chemistry, -University of Wisconsin, Madison, Wisconsin 53706 -

-

-* Present address: Bayer AG, Abteilung AV-IM-AM, -5090 Leverkusen, Bayerwerk, Federal Republic of Germany. -

-** Present address: Department of Chemistry, University of -California-Irvine, Irvine, California 92717. -

-

-

Table of Contents

-
-

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Table of Contentsi
Preface: HOW TO USE THIS MANUALiii

A.

GENERAL INTRODUCTION AND INSTALLATION
A.1INTRODUCTION TO THE NBO PROGRAMA-1
A.1.1What does the NBO Program Do?A-1
A.1.2Structure of the NBO ProgramA-3
A.1.3Input and OutputA-5
A.1.4General Capabilities and RestrictionsA-6
A.1.5References and Relationship to Previous VersionsA-7
A.2INSTALLING THE NBO PROGRAMA-10
A.3TUTORIAL EXAMPLE FOR METHYLAMINEA-12
A.3.1Running the ExampleA-12
A.3.2Natural Population AnalysisA-13
A.3.3Natural Bond Orbital AnalysisA-16
A.3.4NHO Directional AnalysisA-20
A.3.5Perturbation Theory Energy AnalysisA-21
A.3.6NBO SummaryA-22

B.

NBO USER'S GUIDE
B.1INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTSB-1
B.2THE $NBO KEYLISTB-2
B.2.1Overview of $NBO KeywordsB-2
B.2.2Job Control KeywordsB-3
B.2.3Job Threshold KeywordsB-4
B.2.4Matrix Output KeywordsB-6
B.2.5Other Output Control KeywordsB-9
B.2.6Print Level KeywordsB-10
B.2.7Semi-Documented Additional KeywordsB-11
B.3THE $CORE LISTB-12
B.4THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)B-14
B.5THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)B-16
B.5.1Introduction to NBO Energetic AnalysisB-16
B.5.2The Nine Deletion TypesB-17
B.5.3Input for UHF AnalysisB-20
B.6NBO KEYLIST ILLUSTRATIONSB-21
B.6.1IntroductionB-21
B.6.2NLMO KeywordB-22
B.6.3DIPOLE KeywordB-24
B.6.4Matrix Output KeywordsB-26
B.6.5BNDIDX KeywordB-29
B.6.6RESONANCE Keyword: BenzeneB-32
B.6.7NOBOND Keyword: Hydrogen FluorideB-37
B.6.83CBOND Keyword: DiboraneB-40
B.6.9NBO Directed Search ($CHOOSE Keylist)B-44
B.6.10NBO Energetic Analysis ($DEL Keylist)B-48
B.6.11Open-Shell UHF Output: Methyl RadicalB-52
B.6.12Effective Core Potential: Cu2 DimerB-56
B.7FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAMB-62
B.7.1IntroductionB-62
B.7.2Format of the FILE47 Input FileB-63
B.7.3$GENNBO KeylistB-65
B.7.4$COORD KeylistB-66
B.7.5$BASIS DatalistB-67
B.7.6$CONTRACT DatalistB-69
B.7.7Matrix DatalistsB-71

C.

NBO PROGRAMMER'S GUIDE
C.1INTRODUCTIONC-1
C.2OVERVIEW OF NBO.SRC SOURCE PROGRAM GROUPSC-2
C.3LABELLED COMMON BLOCKSC-4
C.4DIRECT ACCESS FILE AND OTHER I/OC-14
C.5NAO/NBO/NLMO ROUTINES (GROUP I)C-16
C.5.1SR NBO Master RoutineC-16
C.5.2Job Initialization RoutinesC-18
C.5.3NAO Formation RoutinesC-19
C.5.4NBO/NLMO Formation RoutinesC-22
C.6ENERGY ANALYSIS ROUTINES (GROUP II)C-26
C.7DIRECT ACCESS FILE (DAF) ROUTINES (GROUP III)C-27
C.8FREE FORMAT INPUT ROUTINES (GROUP IV)C-29
C.9OTHER SYSTEM INDEPENDENT I/O ROUTINES (GROUP V)C-30
C.10GENERAL UTILITY ROUTINES (GROUP VI)C-33
C.11SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)C-36
C.12GENNBO AUXILLIARY ROUTINESC-37
C.13ATTACHING NBO TO A NEW ESS PROGRAMC-38
APPENDIX: Specific ESS Versions
INDEX
-

-

PREFACE: HOW TO USE THIS MANUAL

-

- The NBO manual is divided into three major sections: -

- Section A ("General Introduction and Installation") -contains general introductory and 'one-time' information -for the novice user: what the program does, program structure and -relationship to driver electronic structure package, initial installation, -'quick start' sample input data, and a brief tutorial on sample output. -

- Section B ("NBO User's Guide") -is for the intermediate user who has an installed program -and general familiarity with the standard (default) options of the NBO -program. This section documents the list of keywords that can be used -to alter the standard NBO job options, -with examples of the resulting output. This -section is mandatory for users who wish to use -the program to its full potential, to 'turn off' or -'turn on' various NBO options for their specialized applications. -

- Section C ("NBO Programmer's Guide") -is for accomplished programmers who -are interested in program logic and the detailed layout of -the source code. This section describes the relationship of the -source code subprograms -to the published algorithms for NAO, NBO, and NLMO determination, -providing documentation at the level of individual -common blocks, functions, and subroutines. This in turn serves as a -bridge to the 'micro-documentation' included -as comment statements within the source code. Section C also -provides guidelines for constructing 'driver' routines to attach -the NBO programs to new electronic structure packages. -

-

-

Section A: GENERAL INTRODUCTION AND INSTALLATION

-
-

-

-A.1 INTRODUCTION TO THE NBO PROGRAM -

-A.1.1 What Does the NBO Program Do? -

- The NBO program performs the analysis of a many-electron -molecular wavefunction in terms of localized electron-pair -'bonding' units. The program carries out the determination of -natural atomic orbitals (NAOs), natural hybrid orbitals (NHOs), -natural bond orbitals (NBOs), and natural localized molecular -orbitals (NLMOs), and uses these to perform natural population -analysis (NPA), NBO energetic analysis, and other tasks pertaining -to localized analysis of wavefunction properties. The NBO -method makes use of only the first-order -reduced density matrix of the wavefunction, and hence is applicable -to wavefunctions of general mathematical form; in the open-shell -case, the analysis is performed in terms of "different NBOs for -different spins," based on distinct density matrices for -and spin.* This -section provides a brief introduction to NBO algorithms and -nomenclature. -

- NBO analysis is based -on a method for optimally transforming a given wavefunction into -localized form, corresponding to the one-center ("lone pair") -and two-center ("bond") elements of the chemist's Lewis structure -picture. The NBOs are obtained as local block eigenfunctions -of the one-electron density matrix, and are hence "natural" in the sense -of Löwdin, having optimal convergence properties for describing the -electron density. The set of high-occupancy NBOs, each taken doubly -occupied, is said to represent the "natural Lewis structure" of -the molecule. Delocalization effects appear as weak departures -from this idealized localized picture. -

- The various natural localized sets -can be considered to result -from a sequence of transformations of the input atomic orbital basis set -{i},** - -_______________ -

-*Note, however, -that some electronic structure packages do not make provision -for calculating the spin density matrices for some types of -open-shell wavefunctions (e.g., MCSCF wavefunctions calculated -by the GUGA formalism in the GAMESS system), so that NBO analysis -cannot be applied in these cases. -

-**If the wavefunction is not calculated in an atom-centered -basis set, it would be necessary to first compute a wavefunction -for each isolated atom of the molecule (in the actual basis set -and geometry of the molecular calculation), then select the -most highly occupied natural orbitals of each atomic wavefunction -to compose a final set of linearly independent atom-centered basis -functions of the required dimensionality. Since atom-centered -basis functions are the nearly universal choice for molecular -calculations, the current NBO program makes no provision for -this step. -

- -

-

-input basis NAOs NHOs NBOs NLMOs -
-

-Each natural localized set forms a complete orthonormal -set of one-electron functions -for expanding the delocalized molecular -orbitals (MOs) or forming matrix representations of one-electron -operators. The overlap of associated "pre-orthogonal" -NAOs (PNAOs), lacking only the interatomic orthogonalization -step of the NAO procedure, can be used to estimate the strength -of orbital interactions in the usual way. -

- The optimal condensation of occupancy in the natural -localized orbitals leads to partitioning into high- and -low-occupancy orbital types (reduction in dimensionality -of the orbitals having significant occupancy), as reflected -in the orbital labelling. The small set of most -highly-occupied NAOs, having a close -correspondence with the effective minimal basis set of semi-empirical -quantum chemistry, is referred to as the "natural minimal basis" -(NMB) set. The NMB (core + valence) functions are -distinguished from the weakly occupied "Rydberg" -(extra-valence-shell) functions that complete the span of the NAO space, -but typically make little contribution to molecular properties. Similarly -in the NBO space, -the highly occupied NBOs of the natural Lewis structure -can be distinguished from the "non-Lewis" antibond and Rydberg -orbitals that complete the span of the NBO space. Each pair of valence hybrids -hA, hB in the NHO basis give rise to a bond (AB) and antibond (*AB) -in the NBO basis, -

-

-AB = cAhA + cBhB -

-*AB = cBhA - cAhB -

-

-the former a Lewis (L) and the latter a non-Lewis (NL) orbital. The -antibonds (valence shell non-Lewis orbitals) typically play the primary -role in departures (delocalization) from the idealized Lewis structure. -

- The NBO program also makes extensive provision for energetic -analysis of NBO interactions, based on the availability of a 1-electron -effective energy operator (Fock matrix) for the system. Estimates -of energy effects are -based on second-order perturbation theory, -or on the effect of deleting certain orbitals or matrix elements and -recalculating the total energy. NBO energy analysis is dependent -on the specific ESS to which the NBO program -is attached, as described in the Appendix. -

- The program is provided in a core set of NBO routines that can be -attached to an electronic structure system of the user's choice. In -addition, specific 'driver' routines are provided that facilitate -the attachment to popular ab initio and -semi-empirical packages (GAUSSIAN-8X, GAMESS, HONDO, AMPAC, -etc.). These versions are described in -individual Appendices. -

-

-A.1.2 Structure of the NBO Program -

- The overall logical structure of the NBO program and its attachment -to an electronic structure system (ESS) are -illustrated in the block diagram, Fig. 1. This figure illustrates how -the ESS and its scratch -files (in the upper part of the diagram) communicate through -the interface routines RUNNBO, FEAOIN, and DELSCF -with the main NBO modules and associated direct access file (in -the lower part). -

- The main NBO program is represented by modules labelled "NBO" -and "NBOEAN." These refer to the construction of NBOs (including -natural population analysis, construction of NAOs, NLMOs, etc.) and to -NBO energy analysis, respectively. Each module consists -of subroutines and functions that perform the required -operations. These two modules communicate with the -direct-access disk file NBODAF (LFN 48, labelled "FILE48" -elsewhere in this manual) that is created and -maintained by the -NBO routines. Details of the NBO and NBOEAN -modules, common blocks, and direct-access file are described -in the Programmer's Guide, -Section C. -

- The NBO program blocks communicate with the attached -ESS through three system-dependent 'driver' subroutines -(RUNNBO, FEAOIN, DELSCF). The purpose of these drivers -is to load needed information about the wavefunction and -various matrices into the FILE48 direct access file -and NBO common blocks. Although the ESS -is usually thought of as 'driving' the NBO program, -from the point of view of the NBO program the -ESS is merely a 'device' that provides -initial input (e.g., a density matrix and label information) or -other feedback (a calculated energy value) upon -request. Each such ESS device therefore requires special drivers -to make this feedback possible. Versions of the driver subroutines are -included for several popular packages. The driver routines are -described in more detail in the Programmer's Guide, Section C. -

-

- -
-

-Figure 1: Schematic diagram depicting flow of information -between the electronic -structure system (ESS) and the NBO program, -and the communication lines connecting these programs to -the ESS scratch file -(called the "dictionary file," "read-write file," -etc., in various systems) and the NBO direct access file (NBODAF). Heavier -box borders mark the ESS-specific driver -routines (RUNNBO, FEAOIN, -DELSCF) that directly interface the ESS program. The heavy dashed -lines denote calls from the NBO program 'backward' to the ESS program -for information needed to carry out its tasks. Otherwise, the sequential -flow of program control is generally from top to bottom -and from left to right in the diagram. -

-

-A.1.3 Input and Output -

- From the user's point of view, the input to the NBO program -attached to an ESS program consists simply of one or -more keywords (an NBO keylist) included in the ESS input -file. In effect, the NBO program reads these keywords to set -various job options, then interrogates the ESS program through -the DELSCF and FEAOIN drivers for additional information -concerning the wavefunction. The general form of NBO keylists and -the specific functions associated with each keyword are detailed -in the User's Guide, Section B. The method of -including NBO keylists in the input file for each -ESS is detailed in the specific Appendix for the ESS. -

- The following information is passed from -the ESS to the NBO program (transparent to the user): -

-1. The one-electron density matrix D (or density matrices in the -open-shell case) in the chosen atomic orbital (AO) basis set; -

-2. The AO overlap matrix S, and label information identifying the -symmetry (angular momentum type) and location (number of the atom -to which affixed) for each AO; -

-3. Atomic number (nuclear charge) of each atom. -

-Certain additional information is written on the FILE48 direct -access file and may be used -in response to specific job -options, -such as the AO Fock matrix F, if energy analysis is requested; the -AO dipole matrix M, if dipole moment analysis is requested; or -information concerning the mathematical form of the AOs (orbital -exponents, contraction coefficients, etc.), if orbital plotting -information is requested -to be saved as input for a contour plotting program. -

- The principal output from the NBO program -consists of the tables and summaries describing -the results of NBO analysis, included in the ESS output -file. Sample NBO output is described in Section A.2.4 -below. If requested, the NBO program may also write out transformation -matrices or other data to disk files. The NBO program also -creates or updates two files, the direct-access -file (FILE48) and the 'archive' file (FILE47) that -can be used to repeat NBO analysis with different options, -without running the ESS program to recalculate the -wavefunction. Necessary details of these files are given -in Section B.7 and the Programmer's Guide, -Section C. -

-

-A.1.4 General Capabilities and Restrictions -

- Principal capabilities of the NBO program are: -

-1. Natural population, natural bond orbital, and natural localized -molecular orbital analysis of SCF, MCSCF, CI, and Møller-Plesset -wavefunctions (main subroutine: NBO); -

-2. For RHF closed-shell and UHF wavefunctions only, -energetic analysis of the wavefunction in terms of the interactions -(Fock matrix elements) between NBOs (main subroutine: NBOEAN); -

-3. Localized analysis of molecular dipole moment in terms of NLMO -and NBO bond moments and their interactions (main subroutine: DIPANL). -

- A highly transportable subset of standard FORTRAN 77 is employed, -with no special compiler extensions of any vendor, -and all variable names of six characters or less. Common -abbreviations used in naming subprograms, variables, and keywords are: -

-S = overlap matrix -
DM = density matrix (or D) -
F = Fock matrix -
DI = dipole matrix (or DXYZ, or DX, DY, DZ) -
NPA = Natural Population Analysis -
NAO = Natural Atomic Orbital -
NBO = Natural Bond Orbital -
NLMO = Natural Localized Molecular Orbital -
PNAO = pre-orthogonal NAO (i.e., omit interatomic orthogonalization) -
PNHO, PNBO, PNLMO = pre-orthogonal NHO, etc. (formed from PNAOs)   -

- Most of the NBO storage is allocated dynamically, to conform to -the minimum required for the molecular system under study. However, -certain NBO common blocks of fixed dimensionality are used for -integer storage. These are currently dimensioned to accomodate -up to 99 atoms and 500 basis functions. Section C.3 describes how -these restrictions can be altered. The program is not set up to -handle complex wavefunctions, but can treat any real RHF, ROHF, UHF, MCSCF -(including GVB), CI, or Møller-Plesset-type wavefunction -(i.e., any form of wavefunction for which the requisite density -matrices are available) for ground or excited states of general -open- or closed-shell molecules. Effective core potentials -("pseudopotentials") can be handled, including complete neglect -of core electrons as assumed in semi-empirical treatments. The -atomic orbital basis functions (up to f orbitals in angular -symmetry) may be of general Slater-type, contracted Gaussian-type, -or other general composition, -including the "effective" orthonormal valence-shell AOs of -semi-empirical treatments. AO basis functions are -assumed to be normalized, but in general non-orthogonal. -

-

-A.1.5 References and Relationship to Previous Versions -

- This program ("version 3.0") is an extension of previous versions of the -NBO method incorporated in the semi-empirical program BONDO -[F. Weinhold, Quantum Chemistry Program Exchange No. 408 -(1980); "version 1.0"] -and in a GAUSSIAN-82 implementation [A. E. Reed and F. Weinhold, QCPE -Bull. 5, 141 (1985); "version 2.0"], and should be considered to supplant -those versions. Version 3.0 also supplants the various specific versions -("the GAMESS version," "the AMPAC version," etc.) -that have been informally created and distributed to individual users outside -the QCPE framework. -

-Principal contributors to the development of -the NBO methods and programs (1975-1990) are -

- - - - - -
T. K. BrunckA. E. Reed
J. P. FosterJ. E. Carpenter
A. B. RivesE. D. Glendening
R. B. WeinstockF. Weinhold
-Principal references to the development and applications of NAO/NBO/NLMO -methods are: -

-Natural Bond Orbitals:

-J. P. Foster and F. Weinhold, J. Am. Chem. Soc. 102, 7211-7218 -(1980). -

-Natural Atomic Orbitals and Natural Population Analysis:

-A. E. Reed and F. Weinhold, J. Chem. Phys. 78, 4066-4073 (1983); -A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. 83, -735-746 (1985). -

-Natural Localized Molecular Orbitals:

- A. E. Reed and F. Weinhold, J. Chem. Phys. 83, 1736-1740 (1985). -

-Open-Shell NBO:

-J. E. Carpenter and F. Weinhold, J. Molec. Struct. (Theochem) 169, -41-62 (1988); J. E. Carpenter, Ph. D. Thesis, University of Wisconsin, -Madison, 1987. -

-Review Articles:

-A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev. 88, -899-926 (1988); F. Weinhold and J. E. Carpenter, in, R. Naaman -and Z. Vager (eds.), "The Structure of Small Molecules and -Ions," (Plenum, New York, 1988), pp. 227-236. -

- The principal enhancements of version 3.0 include: -

-1. Generalized Program Interface. -Overall program organization (Fig. 1) has been modified to -standardize communication with the main ESS program. This -insures that all special ESS "versions" of the NBO program -now have consistent options and capabilities -(as long as the option is meaningful in the context of the ESS), and enables -the program to be offered in a greater number of specialized ESS versions -than were previously available. -

-2. NAO/NPA Summary Table. -New tables give improved display of NAOs and -natural populations, including -the "natural electron configuration" of -each atom (i.e., the occupancy and type of NAOs describing -the atomic electron configuration of each atom). The new NAO -summary tables (Section A.3.2) -include an SCF atomic orbital energy (if available), -a conventional atomic orbital label (1s, -2s, 2p, etc., in accordance with the labelling -in isolated atoms), and a shell designation (Cor = core, Val = valence, -or Ryd = Rydberg) to aid characterization of the NAO. -

-3. NBO Summary Table. -A new NBO summary table (Section A.3.6) has been -provided to summarize the energetics -and delocalization patterns of the principal NBOs. This succinctly -combines the most important information from the full NBO table, diagonal -NBO Fock matrix elements, and -2nd-order energy analysis. -

-4. Bond Bending Analysis. -The program includes a new analysis of hydrid directionality -and bond "bending" (keyword BEND, Section A.3.4). -

-5. Dipole Moment Analysis. -The program includes new optional provision (keyword DIPOLE, Section -B.6.3) for -analysis of the molecular dipole moment in terms of localized -NLMOs and NBOs. -

-6. Print options. -The program offers new structured printing options (Section B.2.4) that give -greater convenience and flexibility in controlling printed output, -with improved provision for printing matrices or -basis transformations involving general NAO, NHO, NBO, NLMO or -pre-orthogonal (PNAO, PNHO, PNBO, PNLMO) basis sets. -

-7. Orbital Contour Info. -The program makes optional provision (keyword PLOT, Section B.2.5) for -writing out files that can be used by an orbital plotting -program (available separately through QCPE) to -draw contour diagrams of the NBOs or -other natural localized orbitals. -

-8. Effective Core Potentials. -The program now handles effective core potentials (pseudopotentials), -or the complete neglect of core levels characteristic of semi-empirical -wavefunctions (Section B.6.12). -

-The program also includes three changes to -correct problems of the previous version (which may have -affected a small number of users): -

-9. Unpolarized Cores. -NAOs identified as "core" orbitals are now automatically carried over -as unhybridized 1-center core NBOs -(Section B.3). This has virtually no effect on -the form or occupancy of a core NBO, but averts the (rare) problem of -unphysical mixing between core and -valence lone pairs when the occupancies are 'accidentally' -degenerate (usually, both very close to 2.000...) -within the numerical machine precision. A warning message -is printed when the core occupancy is less than 1.9990, indicating -a possible "core polarization" effect of physical significance. -

-10. Excited State Antibond Labels. -The program now directly investigates the nodal structure of an NBO (by -examining the overlap matrix in the PNHO basis) before assigning it a -label as a "bond" (unstarred) or "antibond" (starred) NBO. In previous -versions, these labels were assigned on the basis of the presumed higher -occupancy of the in-phase bond combination, which -was generally true for ground -states, but not for excited states. The program now -prints a warning message whenever it encounters the "anomalous" -situation of an out-of-phase antibond NBO having higher occupancy than -the corresponding in-phase bond NBO, indicative of an excited-state -configuration. [WARNING: the overlap test cannot be applied to -semi-empirical methods with orthogonal AOs (e.g., AMPAC), -so antibond labels for these methods are assigned, as in previous -versions, on the basis of occupancy.] -

-11. Alternative Resonance Structures. The program now institutes a -search for alternative Lewis ('resonance') structures when two or -more structures may be competitive, and returns the -structure of lowest non-Lewis occupancy. This corrects a possible -dependence on atomic numbering in cases of strong delocalization. -

-Despite these changes and extensions, version 3.0 has been -designed to be upward compatible with v. 2.0, as nearly as -possible. Previous users of NBO 2.0 should find that their jobs -run similarly (i.e., most keywords -continue to function -as in previous versions). Thus, experienced -NBO users should find little difficulty -in adapting to, and experimenting with, -the new capabilities of the program. -

-

-A.2 INSTALLING THE NBO PROGRAM -

- The NBO programs and manual are provided on a distribution tape. The -tape contains three files: the TechSet code of this -manual (file NBO.MAN), a file containing the core NBO source routines -and supporting driver routines (file NBO.SRC), and the Fortran -"enabler" program (file ENABLE.FOR). -

- In overview, the installation procedure involves the following steps -(the details of each step being dependent on your operating system): -

-1. Enabling the NBO routines. Copy the contents of the distribution -tape onto your system. Using your system Fortran 77 compiler, compile -and link the enabler program to create the ENABLE.EXE executable; -for example, the VMS commands to create ENABLE.EXE are - 

-     FOR ENABLE
-     LINK ENABLE
-
-
Now, run the ENABLE program (e.g., type "RUN ENABLE" in -a VMS system), and -answer the prompt - 
-     NBO program version to enable?
-
-
by selecting from the available offerings. Each ESS package is -associated with a 3-letter identifier -("G88" for GAUSSIAN-88, "GMS" for GAMESS, -"AMP" for AMPAC, etc.). The ENABLE program will create -a file XXXNBO.FOR (where 'XXX' is the identifier) -that incorporates the appropriate drivers for -your ESS. -

-2. Compiling the NBO routines. Using your system Fortran 77 compiler, -compile the XXXNBO.FOR file to an object code file (say, -XXXNBO.OBJ). [Compiler -errors (if any) should be fixed before proceeding. Please notify the -authors if you encounter undue difficulties in this step.] -

-3. Modifying the ESS routines. In general, the ESS source Fortran code -must be modified to call the NBO routines near the -point where the ESS performs Mulliken Population Analysis or evaluates -properties of the final wavefunction. The modification generally -consists of inserting a single statement (viz., "CALL RUNNBO") in -one subroutine of your ESS system. See the appropriate Appendix -of this Manual for detailed information on exactly how to modify -the ESS code for your chosen system. -

-4. Rebuilding the integrated ESS/NBO program. Re-compile your modified -ESS programs and link the resulting object file (say, ESS.OBJ) with -the XXXNBO.OBJ file to form the -final ESS.EXE executable. In general, this -step will closely follow the initial installation procedure for -your ESS, with the exception that the XXXNBO.OBJ file must be included -in the link statement (or deposited in one of the libraries accessed -by the linker, etc.). -

-Note that installation of the NBO programs into your ESS system in no way -affects the way your system processes standard input files. The only -change involves enabling the reading of NBO keylists -(if detected in your input -file), performance of the tasks requested in the keylist, and return -of control to the parent ESS program in the state in which the -NBO call was encountered. -

- If you are interfacing the NBO programs to a new ESS package (not -represented in the driver routines provided with this distribution), -see Section C for guidance on how to create drivers for your ESS -to provide the necessary information. Alternatively, see -Section B.7 for a description of the input file to GENNBO, -the stand-alone version of the NBO program. -

- The TechSet-coded version of this manual, NBO.MAN, can be -printed on an HP LaserJet printer -('F' cartridge) with the TECHSET -technical typesetting program [ACS Software, American Chemical Society, -Marketing Communications -Dept., 1155 Sixteenth Street, N.W., Washington, D.C. 20036]. -

-

-A.3 TUTORIAL EXAMPLE FOR METHYLAMINE -

-A.3.1 Running the Example -

- This section provides an introductory 'quick start' tutorial -on running a simple NBO job and interpreting the output. The example -chosen is that of methylamine (CH3NH2) in -Pople-Gordon idealized geometry, treated at the ab initio -RHF/3-21G level. This simple split-valence -basis set consists of 28 AOs (nine each -on C and N, two on each H), extended by 13 AOs beyond -the minimal basis level. -

- Input files to run this job (or its nearest equivalent) with -each ESS are given in the Appendix. (The output shown below was -created with the GAMESS system.) In most cases, you can modify -the standard ESS input file to produce NBO output by -simply including the line - 

-     $NBO $END
-
-
at the end of the file. This is an 'empty' NBO keylist, specifying -that NBO analysis should be carried out at the default level. -

- The default NBO output produced by this example is shown below, -just as it appears in your output file. The -start of the NBO section is marked -by a standard header and storage info: -

- 

-*******************************************************************************
-            N A T U R A L   A T O M I C   O R B I T A L   A N D
-         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
-*******************************************************************************
-
-Job title:  Methylamine...RHF/3-21G//Pople-Gordon standard geometry             
-
-Storage needed:  2505 in NPA,  2569 in NBO ( 750000 available)
-
-
Note that all NBO output is formatted to a maximum 80-character -width for convenient display on a computer terminal. The NBO heading -echoes any requested keywords (none for the present default case) -and shows an estimate of the memory requirements -(in double precision words) for the separate -steps of the NBO process, compared -to the total allocated memory available through your ESS -process. Increase the memory allocated to your -ESS process if the estimated NBO requests exceed the available storage. -

-A.3.2 Natural Population Analysis -

- The next four NBO output segments -summarize the results of natural population -analysis (NPA). The first segment is the main NAO table, as shown -below: -

- 

-NATURAL POPULATIONS:  Natural atomic orbital occupancies 
-                                                         
- NAO Atom #  lang   Type(AO)    Occupancy      Energy    
----------------------------------------------------------
-  1    C  1  s      Cor( 1s)     1.99900     -11.04184
-  2    C  1  s      Val( 2s)     1.09038      -0.28186
-  3    C  1  s      Ryd( 3s)     0.00068       1.95506
-  4    C  1  px     Val( 2p)     0.89085      -0.01645
-  5    C  1  px     Ryd( 3p)     0.00137       0.93125
-  6    C  1  py     Val( 2p)     1.21211      -0.07191
-  7    C  1  py     Ryd( 3p)     0.00068       1.03027
-  8    C  1  pz     Val( 2p)     1.24514      -0.08862
-  9    C  1  pz     Ryd( 3p)     0.00057       1.01801
-
- 10    N  2  s      Cor( 1s)     1.99953     -15.25950
- 11    N  2  s      Val( 2s)     1.42608      -0.71700
- 12    N  2  s      Ryd( 3s)     0.00016       2.75771
- 13    N  2  px     Val( 2p)     1.28262      -0.18042
- 14    N  2  px     Ryd( 3p)     0.00109       1.57018
- 15    N  2  py     Val( 2p)     1.83295      -0.33858
- 16    N  2  py     Ryd( 3p)     0.00190       1.48447
- 17    N  2  pz     Val( 2p)     1.35214      -0.19175
- 18    N  2  pz     Ryd( 3p)     0.00069       1.59492
-
- 19    H  3  s      Val( 1s)     0.81453       0.13283
- 20    H  3  s      Ryd( 2s)     0.00177       0.95067
-
- 21    H  4  s      Val( 1s)     0.78192       0.15354
- 22    H  4  s      Ryd( 2s)     0.00096       0.94521
-
- 23    H  5  s      Val( 1s)     0.78192       0.15354
- 24    H  5  s      Ryd( 2s)     0.00096       0.94521
-
- 25    H  6  s      Val( 1s)     0.63879       0.20572
- 26    H  6  s      Ryd( 2s)     0.00122       0.99883
-
- 27    H  7  s      Val( 1s)     0.63879       0.20572
- 28    H  7  s      Ryd( 2s)     0.00122       0.99883
-
-
For each -of the 28 NAO functions, this table lists the atom -to which NAO is attached (in the numbering scheme of the ESS program), -the angular momentum type 'lang' (s, px, etc., in the coordinate -system of the ESS program), the orbital type (whether core, valence, or -Rydberg, and a conventional -hydrogenic-type label), the orbital occupancy (number of -electrons, or 'natural -population' of the orbital), and the orbital energy (in the favored units -of the ESS program, in this case atomic units: 1 a.u. = 627.5 -kcal/mol). [For example, NAO 4 (the highest energy C orbital of the -NMB set) is the valence shell 2px orbital on carbon, occupied -by 0.8909 electrons, whereas NAO 5 is a Rydberg -3px orbital with only 0.0014 electrons.] Note that the -occupancies of the Rydberg (Ryd) NAOs are -typically much lower than those of the core (Cor) plus -valence (Val) -NAOs of the natural minimum basis set, reflecting -the dominant role of the NMB orbitals -in describing molecular properties. -

- The principal quantum numbers for the -NAO labels (1s, 2s, 3s, etc.) are assigned on the -basis of the energy order if a Fock matrix is available, or on the -basis of occupancy otherwise. A message is printed warning of -a 'population inversion' if the occupancy and energy -ordering do not coincide. -

-

-The next segment is an atomic summary showing the -natural atomic charges (nuclear -charge minus summed -natural populations of NAOs on the atom) and total -core, valence, and Rydberg populations on each atom: -

- 

-Summary of Natural Population Analysis:                  
-                                                         
-                                      Natural Population 
-              Natural   -----------------------------------------------
-   Atom #     Charge        Core      Valence    Rydberg      Total
------------------------------------------------------------------------
-     C  1   -0.44079      1.99900     4.43848    0.00331     6.44079
-     N  2   -0.89715      1.99953     5.89378    0.00384     7.89715
-     H  3    0.18370      0.00000     0.81453    0.00177     0.81630
-     H  4    0.21713      0.00000     0.78192    0.00096     0.78287
-     H  5    0.21713      0.00000     0.78192    0.00096     0.78287
-     H  6    0.35999      0.00000     0.63879    0.00122     0.64001
-     H  7    0.35999      0.00000     0.63879    0.00122     0.64001
-=======================================================================
-  * Total *  0.00000      3.99853    13.98820    0.01328    18.00000
-
-
This table succinctly describes the molecular -charge distribution in terms of NPA charges. [For example, -the carbon atom of methylamine is assigned a net NPA -charge of -0.441 -at this level; note also the slightly less positive charge -on H(3) than on the other two methyl hydrogens: +0.184 vs. +0.217.] -

-

-Next follows a summary of the NMB and NRB populations -for the composite -system, summed over atoms: -

- 

-                                Natural Population      
---------------------------------------------------------
-  Core                       3.99853 ( 99.9632% of   4)
-  Valence                   13.98820 ( 99.9157% of  14)
-  Natural Minimal Basis     17.98672 ( 99.9262% of  18)
-  Natural Rydberg Basis      0.01328 (  0.0738% of  18)
---------------------------------------------------------
-
-
This exhibits the high percentage contribution (typically, > 99%) -of the NMB set to the molecular charge distribution. [In the present -case, for example, the 13 Rydberg orbitals of the -NRB set contribute only 0.07% -of the electron density, whereas the 15 NMB functions account -for 99.93% of the total.] -

-

-Finally, the natural populations are summarized as an effective -valence electron configuration ("natural electron configuration") -for each atom: -

- 

-   Atom #          Natural Electron Configuration
-----------------------------------------------------------------------------
-     C  1      [core]2s( 1.09)2p( 3.35)
-     N  2      [core]2s( 1.43)2p( 4.47)
-     H  3            1s( 0.81)
-     H  4            1s( 0.78)
-     H  5            1s( 0.78)
-     H  6            1s( 0.64)
-     H  7            1s( 0.64)
-
-
Although the occupancies of the atomic orbitals are non-integer -in the molecular environment, the effective atomic configurations -can be related to idealized atomic states in -'promoted' configurations. [For example, the carbon atom in -the above table is most nearly described by an idealized -1s22s12p3 electron configuration.] -

-

-A.3.3 Natural Bond Orbital Analysis -

- The next segments of the output summarize the results -of NBO analysis. The first segment reports on details of the search for -an NBO natural Lewis structure: -

- 

-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    17.95048   0.04952      2   6   0   1     0      0    0.02
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
-
Normally, there is but one cycle of the NBO search (cf. the -"RESONANCE" keyword, Section B.6.6). The table summarizes -a variety of information for each cycle: -the occupancy threshold for a 'good' pair in the NBO search; -the total populations of Lewis and non-Lewis -NBOs; the number of core (CR), 2-center bond (BD), -3-center bond (3C), and lone pair (LP) NBOs in -the natural Lewis structure; the number of low-occupancy Lewis (L) -and 'high-occupancy' (> 0.1e) non-Lewis (NL) orbitals; and the -maximum deviation ('Dev') of any formal bond order from a -nominal estimate (NAO Wiberg bond index) for the structure. [If -the latter exceeds 0.1, additional NBO searches are initiated -(indicated by the parenthesized number under 'Cycle') for alternative -Lewis structures.] The Lewis -structure is accepted if all orbitals of the formal Lewis structure -exceed the occupancy threshold (default, 1.90 electrons). -

-

- Next follows a more detailed breakdown of the Lewis and non-Lewis -occupancies into core, valence, and Rydberg shell contributions: -

- 

-WARNING:  1 low occupancy (<1.9990e) core orbital  found on  C 1
-
---------------------------------------------------------
-  Core                      3.99853 ( 99.963% of   4)
-  Valence Lewis            13.95195 ( 99.657% of  14)
- ==================       ============================
-  Total Lewis              17.95048 ( 99.725% of  18)
- -----------------------------------------------------
-  Valence non-Lewis         0.03977 (  0.221% of  18)
-  Rydberg non-Lewis         0.00975 (  0.054% of  18)
- ==================       ============================
-  Total non-Lewis           0.04952 (  0.275% of  18)
---------------------------------------------------------
-
-
This shows the general quality of the natural Lewis structure -description in terms of the percentage of the total electron -density (e.g., in the above case, about 99.7%). The table also -exhibits the relatively important role of the valence non-Lewis -orbitals (i.e., the six valence antibonds, NBOs 23-28) relative to -the extra-valence orbitals (the 13 Rydberg NBOs 10-22) in the -slight departures from a localized Lewis structure model. (In -this case, the table also includes a warning about a carbon core -orbital with slightly less than double occupancy.) -

-

-Next follows the main listing of NBOs, displaying the form and occupancy -of the complete set of NBOs that span the input AO space: - 

-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (1.99858) BD ( 1) C 1- N 2      
-               ( 40.07%)   0.6330* C 1 s( 21.71%)p 3.61( 78.29%)
-                                       -0.0003 -0.4653 -0.0238 -0.8808 -0.0291
-                                       -0.0786 -0.0110  0.0000  0.0000
-               ( 59.93%)   0.7742* N 2 s( 30.88%)p 2.24( 69.12%)
-                                       -0.0001 -0.5557  0.0011  0.8302  0.0004
-                                        0.0443 -0.0098  0.0000  0.0000
-  2. (1.99860) BD ( 1) C 1- H 3      
-               ( 59.71%)   0.7727* C 1 s( 25.78%)p 2.88( 74.22%)
-                                       -0.0002 -0.5077  0.0069  0.1928  0.0098
-                                        0.8396 -0.0046  0.0000  0.0000
-               ( 40.29%)   0.6347* H 3 s(100.00%)
-                                       -1.0000 -0.0030
-  3. (1.99399) BD ( 1) C 1- H 4      
-               ( 61.02%)   0.7812* C 1 s( 26.28%)p 2.80( 73.72%)
-                                        0.0001  0.5127 -0.0038 -0.3046 -0.0015
-                                        0.3800 -0.0017  0.7070 -0.0103
-               ( 38.98%)   0.6243* H 4 s(100.00%)
-                                        1.0000  0.0008
-  4. (1.99399) BD ( 1) C 1- H 5      
-               ( 61.02%)   0.7812* C 1 s( 26.28%)p 2.80( 73.72%)
-                                        0.0001  0.5127 -0.0038 -0.3046 -0.0015
-                                        0.3800 -0.0017 -0.7070  0.0103
-               ( 38.98%)   0.6243* H 5 s(100.00%)
-                                        1.0000  0.0008
-  5. (1.99442) BD ( 1) N 2- H 6      
-               ( 68.12%)   0.8253* N 2 s( 25.62%)p 2.90( 74.38%)
-                                        0.0000  0.5062  0.0005  0.3571  0.0171
-                                       -0.3405  0.0069 -0.7070 -0.0093
-               ( 31.88%)   0.5646* H 6 s(100.00%)
-                                        1.0000  0.0020
-  6. (1.99442) BD ( 1) N 2- H 7      
-               ( 68.12%)   0.8253* N 2 s( 25.62%)p 2.90( 74.38%)
-                                        0.0000  0.5062  0.0005  0.3571  0.0171
-                                       -0.3405  0.0069  0.7070  0.0093
-               ( 31.88%)   0.5646* H 7 s(100.00%)
-                                        1.0000  0.0020
-  7. (1.99900) CR ( 1) C 1             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0003  0.0000 -0.0002  0.0000
-                                        0.0001  0.0000  0.0000  0.0000
-  8. (1.99953) CR ( 1) N 2             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0001  0.0000  0.0001  0.0000
-                                        0.0000  0.0000  0.0000  0.0000
-  9. (1.97795) LP ( 1) N 2             s( 17.85%)p 4.60( 82.15%)
-                                        0.0000  0.4225  0.0002  0.2360 -0.0027
-                                        0.8749 -0.0162  0.0000  0.0000
- 10. (0.00105) RY*( 1) C 1             s(  1.57%)p62.84( 98.43%)
-                                        0.0000 -0.0095  0.1248 -0.0305  0.7302
-                                       -0.0046  0.6710  0.0000  0.0000
- 11. (0.00034) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0146  0.9999
- 12. (0.00022) RY*( 3) C 1             s( 56.51%)p 0.77( 43.49%)
-                                        0.0000 -0.0023  0.7517 -0.0237  0.3710
-                                       -0.0094 -0.5447  0.0000  0.0000
- 13. (0.00002) RY*( 4) C 1             s( 41.87%)p 1.39( 58.13%)
- 14. (0.00116) RY*( 1) N 2             s(  1.50%)p65.53( 98.50%)
-                                        0.0000 -0.0062  0.1224  0.0063  0.0371
-                                        0.0197  0.9915  0.0000  0.0000
- 15. (0.00044) RY*( 2) N 2             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000 -0.0132  0.9999
- 16. (0.00038) RY*( 3) N 2             s( 33.38%)p 2.00( 66.62%)
-                                        0.0000  0.0133  0.5776  0.0087 -0.8150
-                                       -0.0121 -0.0405  0.0000  0.0000
- 17. (0.00002) RY*( 4) N 2             s( 65.14%)p 0.54( 34.86%)
- 18. (0.00178) RY*( 1) H 3             s(100.00%)
-                                       -0.0030  1.0000
- 19. (0.00096) RY*( 1) H 4             s(100.00%)
-                                       -0.0008  1.0000
- 20. (0.00096) RY*( 1) H 5             s(100.00%)
-                                       -0.0008  1.0000
- 21. (0.00122) RY*( 1) H 6             s(100.00%)
-                                       -0.0020  1.0000
- 22. (0.00122) RY*( 1) H 7             s(100.00%)
-                                       -0.0020  1.0000
- 23. (0.00016) BD*( 1) C 1- N 2      
-               ( 59.93%)   0.7742* C 1 s( 21.71%)p 3.61( 78.29%)
-                                       -0.0003 -0.4653 -0.0238 -0.8808 -0.0291
-                                       -0.0786 -0.0110  0.0000  0.0000
-               ( 40.07%)  -0.6330* N 2 s( 30.88%)p 2.24( 69.12%)
-                                       -0.0001 -0.5557  0.0011  0.8302  0.0004
-                                        0.0443 -0.0098  0.0000  0.0000
- 24. (0.01569) BD*( 1) C 1- H 3      
-               ( 40.29%)   0.6347* C 1 s( 25.78%)p 2.88( 74.22%)
-                                        0.0002  0.5077 -0.0069 -0.1928 -0.0098
-                                       -0.8396  0.0046  0.0000  0.0000
-               ( 59.71%)  -0.7727* H 3 s(100.00%)
-                                        1.0000  0.0030
- 25. (0.00769) BD*( 1) C 1- H 4      
-               ( 38.98%)   0.6243* C 1 s( 26.28%)p 2.80( 73.72%)
-                                       -0.0001 -0.5127  0.0038  0.3046  0.0015
-                                       -0.3800  0.0017 -0.7070  0.0103
-               ( 61.02%)  -0.7812* H 4 s(100.00%)
-                                       -1.0000 -0.0008
- 26. (0.00769) BD*( 1) C 1- H 5      
-               ( 38.98%)   0.6243* C 1 s( 26.28%)p 2.80( 73.72%)
-                                       -0.0001 -0.5127  0.0038  0.3046  0.0015
-                                       -0.3800  0.0017  0.7070 -0.0103
-               ( 61.02%)  -0.7812* H 5 s(100.00%)
-                                       -1.0000 -0.0008
- 27. (0.00426) BD*( 1) N 2- H 6      
-               ( 31.88%)   0.5646* N 2 s( 25.62%)p 2.90( 74.38%)
-                                        0.0000 -0.5062 -0.0005 -0.3571 -0.0171
-                                        0.3405 -0.0069  0.7070  0.0093
-               ( 68.12%)  -0.8253* H 6 s(100.00%)
-                                       -1.0000 -0.0020
- 28. (0.00426) BD*( 1) N 2- H 7      
-               ( 31.88%)   0.5646* N 2 s( 25.62%)p 2.90( 74.38%)
-                                        0.0000 -0.5062 -0.0005 -0.3571 -0.0171
-                                        0.3405 -0.0069 -0.7070 -0.0093
-               ( 68.12%)  -0.8253* H 7 s(100.00%)
-                                       -1.0000 -0.0020
-
-
For each NBO (1-28), the -first line of printout -shows the occupancy (between 0 and 2.0000 electrons) and unique label -of the NBO. This -label gives the type -("BD" for 2-center bond, "CR" for 1-center core pair, "LP" for 1-center -valence lone pair, "RY*" for 1-center Rydberg, and "BD*" for 2-center -antibond, the unstarred and starred labels corresponding to Lewis -and non-Lewis NBOs, respectively), a serial number (1, 2,... if there is a -single, double,... bond between the pair of atoms), and the atom(s) to -which the NBO is affixed. [For example, the first NBO in the sample -output is the 2-center bond (with 1.99858 electrons) -between carbon (atom 1) and nitrogen (atom 2), the CN -bond.] The next lines summarize -the natural atomic hybrids hA -of which the NBO is composed, giving the -percentage (100|cA|2) of the NBO on each hybrid (in parentheses), -the polarization coefficient cA, the atom label, and a hybrid -label showing the sp composition -(percentage s-character, p-character, etc.) of -each hA. [For example, the CN NBO -is formed from an sp3.61 hybrid (78.3% -p-character) on carbon interacting with an sp2.24 hybrid -(69.1% p-character) on nitrogen, -

-

-CN = 0.633(sp3.61)C + 0.774(sp2.24)N -
-

-corresponding roughly to the qualitative concept -of interacting sp3 hybrids (75% p-character) and the higher -electronegativity (larger polarization coefficient) of N.] Below -each NHO label is the set of -coefficients that specify how the NHO is written explicitly as a linear -combination of NAOs on the atom. The order of NAO coefficients follows -the numbering of the NAO tables. [For example, in the first NBO entry, -the carbon hybrid hC -of the CN bond has largest coefficients for the 2nd -and 4th NAOs, corresponding to the approximate description -

-

-hC -0.4653(2s)C - 0.8808(2px)C -
-

-in terms of the valence NAOs of the carbon atom.] In -the CH3NH2 example, the NBO search -finds the C-N bond (NBO 1), three C-H bonds (NBOs 2, 3, 4), two N-H -bonds (NBOs 5, 6), N lone pair (NBO 9), and C and N -core pairs (NBOs 7, 8) of the expected Lewis structure. NBOs 10-28 -represent the residual non-Lewis NBOs of low occupancy. In this -example, it is also interesting to note the slight asymmetry of the three -CH NBOs, and the slightly higher occupancy -(0.01569 vs. 0.0077 -electrons) in the *C1H3 antibond -(NBO 24) lying trans to the -nitrogen lone pair. -

-A.3.4 NHO Directional Analysis -

- The next segment of output -summarizes the angular properties of -the natural hybrid orbitals: -

- 

-NHO Directionality and "Bond Bending" (deviations from line of nuclear centers)
-
-        [Thresholds for printing:  angular deviation  >  1.0 degree]
-                                   hybrid p-character > 25.0%
-                                   orbital occupancy  >  0.10e
-
-                      Line of Centers        Hybrid 1              Hybrid 2
-                      ---------------  -------------------   ------------------
-          NBO           Theta   Phi    Theta   Phi    Dev    Theta   Phi    Dev
-===============================================================================
-  1. BD ( 1) C 1- N 2    90.0    5.4     --     --    --      90.0  182.4   3.0
-  3. BD ( 1) C 1- H 4    35.3  130.7    34.9  129.0   1.0      --     --    --
-  4. BD ( 1) C 1- H 5   144.7  130.7   145.1  129.0   1.0      --     --    --
-  5. BD ( 1) N 2- H 6   144.7  310.7   145.0  318.3   4.4      --     --    --
-  6. BD ( 1) N 2- H 7    35.3  310.7    35.0  318.3   4.4      --     --    --
-  9. LP ( 1) N 2          --     --     90.0   74.8   --       --     --    --
-
-
The 'direction' of a hybrid is specified -in terms of the polar () and -azimuthal () angles (in the ESS coordinate system) of the vector -describing its p-component. The hybrid direction is -compared with the direction of the line of centers between the two -nuclei to determine the 'bending' of the bond, expressed as -the deviation angle ("Dev," in degrees) between these two directions. For -example, in the CH3NH2 case shown above, the nitrogen NHO -of the CN bond (NBO 1) is bent away -from the line of C-N -centers by 3.0°, whereas the carbon NHO is approximately -aligned with the C-N axis (within the 1.0° threshold for -printing). The N-H bonds (NBOs 5, 6) are -bent even further (4.4°). The information in this table -is often useful in anticipating the direction of geometry changes -resulting from geometry optimization (viz., likely reduced pyramidalization -of the -NH2 group to relieve the nitrogen bond 'kinks' found -in the tetrahedral Pople-Gordon geometry). -

-

-A.3.5 Perturbation Theory Energy Analysis -

- The next segment summarizes the second-order perturbative estimates -of 'donor-acceptor' (bond-antibond) interactions in the NBO basis: -

- 

-Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis
-
-    Threshold for printing:   0.50 kcal/mol
-                                                         E(2)  E(j)-E(i) F(i,j)
-     Donor NBO (i)              Acceptor NBO (j)       kcal/mol   a.u.    a.u. 
-===============================================================================
-
-within unit  1
-  2. BD ( 1) C 1- H 3     / 14. RY*( 1) N 2              0.84    2.18    0.038
-  3. BD ( 1) C 1- H 4     / 26. BD*( 1) C 1- H 5         0.52    1.39    0.024
-  3. BD ( 1) C 1- H 4     / 27. BD*( 1) N 2- H 6         3.03    1.37    0.057
-  4. BD ( 1) C 1- H 5     / 25. BD*( 1) C 1- H 4         0.52    1.39    0.024
-  4. BD ( 1) C 1- H 5     / 28. BD*( 1) N 2- H 7         3.03    1.37    0.057
-  5. BD ( 1) N 2- H 6     / 10. RY*( 1) C 1              0.56    1.78    0.028
-  5. BD ( 1) N 2- H 6     / 25. BD*( 1) C 1- H 4         2.85    1.51    0.059
-  6. BD ( 1) N 2- H 7     / 10. RY*( 1) C 1              0.56    1.78    0.028
-  6. BD ( 1) N 2- H 7     / 26. BD*( 1) C 1- H 5         2.85    1.51    0.059
-  7. CR ( 1) C 1          / 16. RY*( 3) N 2              0.61   13.11    0.080
-  7. CR ( 1) C 1          / 18. RY*( 1) H 3              1.40   11.99    0.116
-  7. CR ( 1) C 1          / 19. RY*( 1) H 4              1.55   11.99    0.122
-  7. CR ( 1) C 1          / 20. RY*( 1) H 5              1.55   11.99    0.122
-  8. CR ( 1) N 2          / 10. RY*( 1) C 1              1.51   16.23    0.140
-  8. CR ( 1) N 2          / 12. RY*( 3) C 1              0.84   16.77    0.106
-  8. CR ( 1) N 2          / 21. RY*( 1) H 6              0.61   16.26    0.089
-  8. CR ( 1) N 2          / 22. RY*( 1) H 7              0.61   16.26    0.089
-  9. LP ( 1) N 2          / 24. BD*( 1) C 1- H 3         8.13    1.13    0.086
-  9. LP ( 1) N 2          / 25. BD*( 1) C 1- H 4         1.46    1.14    0.037
-  9. LP ( 1) N 2          / 26. BD*( 1) C 1- H 5         1.46    1.14    0.037
-
-
This is carried out by examining all possible -interactions between -'filled' (donor) Lewis-type NBOs and 'empty' (acceptor) non-Lewis -NBOs, and estimating their energetic importance by 2nd-order perturbation -theory. Since these interactions lead to loss of occupancy from the -localized NBOs of the idealized Lewis structure into -the empty non-Lewis orbitals (and thus, to departures from the -idealized Lewis structure description), they are referred to -as 'delocalization' corrections to the zeroth-order natural Lewis -structure. For each donor NBO (i) and acceptor NBO (j), -the stabilization energy E(2) associated with delocalization -("2e-stabilization") i j is estimated as -

-

-E(2) = Eij = qi (F(i,j)2)/(j - i) -
-

-where qi is the donor orbital occupancy, -i, j are diagonal elements (orbital energies) -and F(i,j) is the off-diagonal NBO Fock matrix element. [In the example -above, the nN *CH interaction between the -nitrogen lone pair (NBO 8) and the antiperiplanar C1-H3 antibond -(NBO 24) is seen to give the strongest -stabilization, 8.13 kcal/mol.] As the heading -indicates, entries are included in this table only when the interaction -energy exceeds a default threshold of 0.5 kcal/mol. -

-A.3.6 NBO Summary -

- Next appears a condensed summary of the principal NBOs, showing the -occupancy, orbital energy, and the qualitative pattern of delocalization -interactions associated with each: -

- 

-Natural Bond Orbitals (Summary):
-
-                                                    Principal Delocalizations
-          NBO              Occupancy    Energy      (geminal,vicinal,remote)
-===============================================================================
-Molecular unit  1  (CH5N)
-  1. BD ( 1) C 1- N 2       1.99858    -0.89908
-  2. BD ( 1) C 1- H 3       1.99860    -0.69181    14(v)
-  3. BD ( 1) C 1- H 4       1.99399    -0.68892    27(v),26(g)
-  4. BD ( 1) C 1- H 5       1.99399    -0.68892    28(v),25(g)
-  5. BD ( 1) N 2- H 6       1.99442    -0.80951    25(v),10(v)
-  6. BD ( 1) N 2- H 7       1.99442    -0.80951    26(v),10(v)
-  7. CR ( 1) C 1            1.99900   -11.04131    19(v),20(v),18(v),16(v)
-  8. CR ( 1) N 2            1.99953   -15.25927    10(v),12(v),21(v),22(v)
-  9. LP ( 1) N 2            1.97795    -0.44592    24(v),25(v),26(v)
- 10. RY*( 1) C 1            0.00105     0.97105
- 11. RY*( 2) C 1            0.00034     1.02120
- 12. RY*( 3) C 1            0.00022     1.51414
- 13. RY*( 4) C 1            0.00002     1.42223
- 14. RY*( 1) N 2            0.00116     1.48790
- 15. RY*( 2) N 2            0.00044     1.59323
- 16. RY*( 3) N 2            0.00038     2.06475
- 17. RY*( 4) N 2            0.00002     2.25932
- 18. RY*( 1) H 3            0.00178     0.94860
- 19. RY*( 1) H 4            0.00096     0.94464
- 20. RY*( 1) H 5            0.00096     0.94464
- 21. RY*( 1) H 6            0.00122     0.99735
- 22. RY*( 1) H 7            0.00122     0.99735
- 23. BD*( 1) C 1- N 2       0.00016     0.57000
- 24. BD*( 1) C 1- H 3       0.01569     0.68735
- 25. BD*( 1) C 1- H 4       0.00769     0.69640
- 26. BD*( 1) C 1- H 5       0.00769     0.69640
- 27. BD*( 1) N 2- H 6       0.00426     0.68086
- 28. BD*( 1) N 2- H 7       0.00426     0.68086
-      -------------------------------
-             Total Lewis   17.95048  ( 99.7249%)
-       Valence non-Lewis    0.03977  (  0.2209%)
-       Rydberg non-Lewis    0.00975  (  0.0542%)
-      -------------------------------
-           Total unit  1   18.00000  (100.0000%)
-          Charge unit  1    0.00000
-
-
This table allows one to quickly identify the principal delocalizing -acceptor orbitals associated with each donor NBO, and their -topological relationship to this NBO, i.e., whether attached to the same -atom (geminal, "g"), to an adjacent bonded atom (vicinal, "v"), or -to a more remote ("r") site. These acceptor NBOs will generally -correspond to the principal 'delocalization tails' of the NLMO -associated with the parent donor NBO. [For example, in the table above, -the nitrogen lone pair (NBO 9) is seen to be the lowest-occupancy -(1.97795 electrons) and highest-energy -(-0.44592 a.u.) Lewis NBO, and to -be primarily -delocalized into antibonds 24, 25, 26 (the vicinal *CH -NBOs). The summary at the bottom of the table shows that the -Lewis NBOs 1-9 describe about 99.7% of the total electron density, -with the remaining non-Lewis density found primarily in the -valence-shell antibonds (particularly, NBO 24).] -

-

-

Section B: NBO USER'S GUIDE

-
-

-B.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS -

- Section B constitutes the general -user's guide to the NBO program. It -assumes that the user has an installed -electronic structure system (ESS) with attached NBO program, -a general idea of what the -NBO method is about, and some -acquaintance with standard NBO terminology and output data. If you are -completely inexperienced in these areas, read Section A -(General Introduction and Installation) for the necessary background -to this Section. -

- The User's Guide describes how to use the NBO program -by modifying your input file to the ESS program -to get some NBO output. The modification consists of adding a list -of keywords in a prescribed keylist format. Four distinct -keylist ($KEY) types are recognized ($NBO, $CORE, $CHOOSE, and $DEL), and -these will be described in turn in Sections B.2-B.5. Some of the details -of inserting NBO keylists into the input file depend on the details -of your ESS method, and are described in the appropriate Appendix for -the ESS. However, the general form of NBO keylists and the meaning and -function of each keyword are identical for all versions (insofar as the -option is meaningful for the ESS), and are described herein. -

- The four keylist types have common rules of syntax: Keylist -delimiters are identified by a "$" prefix. Each keylist -begins with the parent keylist name (e.g., "$NBO"), followed -by any number of keywords, and ended -with the word "$END"; for example, - 

-     $NBO   keyword1   keyword2   . . .   $END      !comment
-
-
(The allowed keyword entries for each type of keylist are described -in Sections B.2-B.5.) The keylist is "free format," with keywords -separated by commas or any number of spaces. An NBO option is -activated by simply including its keyword in the appropriate keylist. The -order of keywords in the principal $NBO keylist -does not matter, but multiple keylists must be given -in the order (1) $NBO, (2) $CORE, (3) $CHOOSE, (4) $DEL of presentation -in Sections B.2-B.5. Keywords may be typed in upper or lower case, -and will be echoed near the top of the NBO output. A $KEY list can -be continued to any number of lines, but all the entries of a $KEY list must -appear in a distinct set of lines, starting with the $KEY name on the -first line and ending with the closing $END on the last line (i.e., -no two $KEY lists should share parts of the same line). As the -above example -indicates, any line in the keylist input may terminate with an exclamation -point (!) followed by 'comment' of your choice; the "!" is -considered to terminate -the line, and the trailing 'comment' is ignored by the program. -

-

-B.2 THE $NBO KEYLIST -

-B.2.1 Overview of $NBO keywords -

- The $NBO keylist is the principal means of specifying NBO -job options and controlling output, and must precede -any other keylist ($CORE, $CHOOSE, -or $DEL) in your input file. The allowed keywords that can -appear in a $NBO keylist are grouped as follows: -

-

-Job Control Keywords: - - - -
NPANBOSUMNOBONDSKIPBO
NBORESONANCE3CBONDNLMO
-Job Threshold Keywords: - - - - -
BEND(=ang,pct,occ)
E2PERT(=val)
DIPOLE(=val)
-

-Matrix Output Keywords: - - - - - - - - - - - - -
AONAONAONHONHONBONBONLMONLMOMO
AONHONAONBONHONLMONBOMO
AONBONAONLMONHOMO
AONLMONAOMO
AOMO
AOPNAOAOPNHOAOPNBOAOPNLMO
DMAOFAODIAOSAO
DMNAOFNAODINAOSPNAO
DMNHOFNHODINHOSPNHO
DMNBOFNBODINBOSPNBO
DMNLMOFNLMODINLMOSPNLMO
-

-Other Output Control Keywords: - - - -
LFNPRDETAILBNDIDXAOINFO
PLOTARCHIVENBODAF
-

-Print Level Control: -PRINT=n -

-Keywords are first listed and described according to these formal -groupings in Sections B.2.2-B.2.6. Section B.6 illustrates -the effect of commonly used $NBO -keywords (as well as other $KEY lists) on the -successive stages of NAO/NBO/NLMO transformation and subsequent -energy or dipole analysis, with sample output for these keyword -options. -

- Some keywords of the $NBO keylist -require (or allow) numerical values or other parameters -to specify their exact function. In this -case, the numerical value or parameter must immediately follow the keyword -after an equal sign (=) or any number of blank spaces. Examples: - 

-     E2PERT=2.5   LFNPR 16  NBOMO=W25
-
-
(The equal sign is recommended, and will be used in the remaining -examples.) -

-[ Although the general user's interaction with the NBO programs is usually -through the documented keywords of Sections B.2.2-B.2.6, some additional -'semi-documented' keywords are listed in Section B.2.7 which may be of -interest to the specialist.] -

-B.2.2 Job Control Keywords -

- The keywords in this group activate or deactivate -basic tasks to be performed by -the NBO programs, or change the way the NBO search is conducted. Each -keyword is described in terms of the option it activates (together with an -indication of where the option is useful): -

-KEYWORD OPTION DESCRIPTION -

-NPA Request Natural Population Analysis and printing of NPA summary -tables (Section A.3.2). This keyword also activates calculation -of NAOs, except for semi-empirical ESS methods. -

-NBO Request calculation of NBOs and printing of the main NBO table -(Section A.3.3). -

-NBOSUM Request printing of the NBO summary table (Section A.3.6). This -combines elements of the NBO table and 2nd-order perturbation -theory analysis table (see below) in a convenient form for recognizing -the principal delocalization patterns. -

-RESONANCE Request search for highly delocalized structures -(Section B.6.6). The NBO search -normally aborts when one or more Lewis NBOs has less -than the default occupancy threshold of -1.90 electrons for a 'good' electron -pair. When the RESONANCE keyword is activated, this threshold -is successively lowered in 0.10 decrements to 1.50, -and the NBO search repeated to find the best Lewis structure -within each occupancy threshold. The program returns with the best -overall Lewis structure (lowest total non-Lewis occupancy) found -in these searches. (Useful for benzene and other highly -delocalized molecules.) -

-NOBOND Request that no bonds (2-center NBOs) are to be formed in the -NBO procedure (Section B.6.7). The -resulting NBOs will then simply be 1-center -atomic hybrids. (Useful for highly ionic species.) -

-3CBOND Request search for 3-center bonds (Section B.6.8). The normal -default is to search -for only 1- and 2-center NBOs. (Useful for diborane and other -electron-deficient 'bridged' species.) -

-SKIPBO Skip the computation of NBOs, i.e., only determine NAOs and -perform natural population analysis. (Useful when only NPA is -desired.) -

-NLMO Compute and print out the summary table of Natural Localized -Molecular Orbitals (Section B.6.2). NLMOs are similar to Boys or -Edmiston-Ruedenberg LMOs, but more efficiently calculated. (Useful -for 'semi-localized' description of an SCF or correlated -wavefunction.) Activated automatically by all keywords that pertain -to NLMOs (e.g., AONLMO, SPNLMO, DIPOLE). -

-Note that the SKIPBO keyword has higher precedence than other -keywords in this list, so that keywords with which it is -implicitly in conflict (e.g., NBO, 3CBOND, NLMO) will be ignored -if SKIPBO is included in the $NBO keylist. -

-B.2.3 Job Threshold Keywords -

- The keywords in this group also activate new tasks to be -performed by the NBO program, but these keywords may be modified -by one or more parameters (thresholds) that control the precise -action to be taken. (In each case the keywords may also be used -without parameters, accepting the default values [in brackets].) -

-KEYWORD parameter(s) OPTION DESCRIPTION -

-BEND ang, pct, occ Request the NHO Directional Analysis table (Section A.3.4). The -three parameters [and default values] have the following -significance: -

-= threshold angular deviation for printing -
pct [25] = threshold percentage p-character for printing -
occ [0.1] = threshold NBO occupancy for printing -

-Parameter values may be separated by a space or a comma. -

- Example:

     BEND=2,10,1.9
-
-
This example specifies that the bond-bending table should -only include entries for angular deviations of at least 2° (ang), -hybrids of at least 10% p-character (pct), and NBOs of occupancy -at least 1.9 electrons (occ). -

-

-E2PERT eval Request the Perturbation Theory Energy Analysis -table (Section A.3.5), where -

-eval [0.5] = threshold energy (in kcal/mol) for printing -

-Entries will be printed for NBO donor-acceptor interaction energies -that exceed the 'eval' threshold. -

- Example:

     E2PERT=5.0
-
-
This example would print only interactions of at least 5 kcal/mol -(i.e., only the single entry for the 8.13 kcal/mol -nN *CH interaction in the output -of Section A.3.5). -

-

-DIPOLE dval Request the Molecular Dipole Moment Analysis table (Section B.6.3), where -

-dval [0.02] = threshold dipole moment (Debye) for printing -

-The program will carry out a decomposition of the total molecular -dipole moment in terms of localized NLMO and NBO -contributions, including all terms whose contribution (in vector norm) -exceeds the 'dval' threshold. -

- Example:

     DIPOLE=0.1
-
-
This example would print out dipole contributions of all NBOs (and -their delocalization interactions) of magnitude 0.1 D. -

-Both the BEND and E2PERT keywords are activated by default -at the standard PRINT level option (see Section B.2.6); to get an -example of dipole moment analysis, include the keylist - 

-     $NBO  DIPOLE  $END
-
-
in your input file. Note that the DIPOLE keyword leads to an -analysis in terms of both NBOs and NLMOs, so that the NLMO keyword -(Section B.2.2) is automatically activated in this case. -

-B.2.4 Matrix Output Keywords -

- The keywords in this group activate the printing of various -matrices to the output file, or their writing -to (or reading from) external disk files. The large number -of keywords in this group provide great flexibility in printing -out the details of the successive transformations, -

-

-input AOs (PNAOs) NAOs NHOs NBOs NLMOs canonical MOs -
-

-or the matrices of various operators in the natural -localized basis sets. This ordered sequence of transformations -forms the basis for naming the keywords. -

-Keyword Names -

- The keyword for printing the matrix for a particular basis -transformation, IN OUT, is constructed from the -corresponding acronymns -for the two sets in the generic form "INOUT". For example, -the transformation AO NBO is keyed as "AONBO", -while that from NBOs to -NLMOs is correspondingly "NBONLMO". The transformations are -always specified in the ordered sequence shown above (i.e., "AONBO" -is allowed, but "NBOAO" is an unrecognized 'backward' -keyword). Keywords are recognized for all possible transformations -from the input AOs to other sets -(NAO, NHO, NBO, NLMO, MO, or the pre-orthogonal PNAO, PNHO, PNBO, -PNLMO sets) in the -overall sequence leading to canonical MOs, i.e., -

-AO basis: AONAO AONHO AONBO AONLMO AOMO -AOPNAO AOPNHO AOPNBO AOPNLMO -

-and from each of the orthonormal natural localized sets to sets -lying to the right in the sequence, i.e., -

-

-NAONHO NAONBO NAONLMO NAOMO -

-NHONBO NHONLMO NHOMO -

-NBONLMO NBOMO -

-NLMOMO -

-The matrix TIN,OUT for a specified IN OUT transform has -rows labelled by the IN set and columns labelled by the OUT set. -

- One can also print out the matrix representations of the Fock -matrix (F), density matrix (DM), or dipole moment matrix (DI) -in the input AO set or any of the natural localized sets (NAO, -NHO, NBO, or NLMO). The corresponding keyword is constructed by -combining the abbreviation (M) for the operator with that -for the set (SET) in the generic form "MSET". For example, -to print the Fock matrix (F) in the NBO set, use the -keyword "FNBO", or to print the dipole matrix in the NLMO -basis, use "DINLMO". (For the dipole matrix keywords, all -three vector components will be printed.) One can also print -out elements of the overlap matrix (S) in the input AO basis -or any of the 'pre-orthogonal' sets -(PNAO, PNHO, PNBO, or PNLMO), using, e.g., "SPNAO" for the -overlap matrix in the PNAO basis. The complete set of allowed -keywords for operator matrices is: -

-

-FAO FNAO FNHO FNBO FNLMO -

-DMAO DMNAO DMNHO DMNBO DMNLMO -

-DIAO DINAO DINHO DINBO DINLMO -

-SAO SPNAO SPNHO SPNBO SPNLMO -

-Other desired transformations -can be readily obtained from the keyword transformations -by matrix multiplication. -

-

-Keyword Parameters -

- Each generic matrix keyword ("MATKEY") can include -a parameter that specifies the output operation to -be performed on the matrix. The allowed MATKEY parameters -are of two types (three for AONAO, NAONBO; see below): - -
MATKEY=P[c] (print out the matrix in the standard output file, 'c' columns) -

-MATKEY=W[n] (write out the matrix to disk file n) -

-The first (P[c]) parameter is used to control output to the standard -output file. When the MATKEY keyword is inserted in the $NBO keylist with -no parameters, the matrix is by default printed (in its -entirety) in the standard output file. Thus, "MATKEY=P" -would be equivalent to "MATKEY", with no parameters. The complete -'P[c]' form of the print parameter serves to truncate the -printed matrix output -to a specified number of columns [c]. For example, to print out -only the first 16 columns of a matrix, use the form - 

-     MATKEY=P16         (print 16 columns)
-
-
For certain matrices, one can also restrict -printing to only the valence (VAL) or -Lewis (LEW) columns with modified '[c]' -specifiers. For the transformations -to MOs, use the form - 
-     MATKEY=PVAL        (print core + valence MO columns only)
-
-
where "MATKEY" is AOMO, NAOMO, NHOMO, NBOMO, or NLMOMO (only). This -will print out only the occupied MOs -and the lowest few unoccupied MOs, e.g., the six lowest virtual MOs of -the methylamine example (Section A.3), though -not necessarily those with predominant valence character. Similarly, -for the transformations to NBOs or NLMOs, use the form - 
-     MATKEY=PLEW        (print Lewis orbital columns only)
-
-
where "MATKEY" is AONBO, NHONBO, NAONBO, AONLMO, NAONLMO, -NHONLMO, NBONLMO (or AOMO, NAOMO, NHOMO, NBOMO, NLMOMO). This -prints out the Lewis NBOs or occupied MOs only, e.g., only the nine -occupied NBOs or MOs of the methylamine example. Judicious use of -these print parameters keeps printed -output within reasonable bounds -in calculations with large basis sets. -

-The second type of MATKEY parameter (W[n]) is used to -write the matrix (in its entirety) to a specified disk -file [n]. By default, each keyword transformation matrix is associated with -a particular logical file number (LFN) in the range 31-49, as shown in -the table below: -

- - - - - - - - - - - - - - - - - -
default default default
matrixLFNmatrixLFNmatrixLFN
___
AONAO33NHONBO49DMNHO49
AONHO35NHONLMO49DMNBO49
AONBO37NHOMO49DMNLMO49
AONLMO39NBONLMO49DIAO49
AOMO40NBOMO49DINAO49
AOPNAO32NLMOMO49DINHO49
AOPNHO34FAO49DINBO49
AOPNBO36FNAO49DINLMO49
AOPNLMO38FNHO49SAO49
NAONHO49FNBO49SPNAO49
NAONBO42FNLMO49SPNHO49
NAONLMO49DMAO41SPNBO49
NAOMO49DMNAO49SPNLMO49
-When the "MATKEY=Wn" keyword is inserted in the $NBO keylist with -no 'n' specifier, the matrix is by default written out (in its -entirety) to this LFN. Thus, "MATKEY=W" -is equivalent to "MATKEY=Wn" if "n" is the default LFN for -that keyword. Use the "Wn" parameter to direct output to -any non-default LFN disk file. For example, the keyword - 

-     AONBO=W22
-
-
would write out the AO NBO transformation to LFN = 22 (rather -than the default LFN = 37). -

- The format of the printed output under the print 'P' parameter -differs from that written to an external file under -the 'W' parameter. The 'P' output (intended for a human reader) -includes an identifying label for each row, and gives the -numerical entries to somewhat lesser precision (F8.4 format) than -the corresponding 'W' output (F15.9 format), which is usually -intended as input to another program. Use the "MATKEY=W6" -keyword to route the more precise 'W' form of the matrix to -the standard output file, LFN 6. -

- For the AONAO, NAONBO matrices (only), one can also include a -read parameter (R), - 

-     AONAO=Rn
-     NAONBO=Rn
-
-
which causes the matrix to be input to the -program from LFN n. This -parameter has the -effect of 'freezing' orbitals to a -set prescribed in the input file (thus -bypassing the NBO optimization of these orbitals for the molecular -system). For example, the keyword "NAONBO=R44" would have the -effect of freezing the NAO NBO -transformation coefficients to the form specified in LFN 44 (perhaps -written with the "NAONBO=W44" keyword in a previous calculation -on isolated molecules, and now to be used in a calculation on a -molecular complex). Similarly, the keyword "AONAO=R45" could -be used to force the analysis of an excited state to be -carried out in terms of the NAOs of the ground state (previously -written out with the "AONAO=W45" -keyword). -

-B.2.5 Other Output Control Keywords -

- The keywords in this group also help to control -the I/O produced -by a specified set of job options, and thus supplement the -keywords of the previous section. However, the keywords -of this section 'steer' the flow of information that is -routinely produced by the NBO program (or can be passed through -from the ESS program) without materially affecting the actual -jobs performed by the NBO program. The options associated with -each keyword are tabulated below: -

-KEYWORD OPTION DESCRIPTION -

-LFNPR=n Set the logical file number (LFN) for NBO program output. The default -LFN is n = 6, the usual LFN for output from the ESS program. This -option can be used to steer the NBO section of the job output to a -desired file. - - Example:

  LFNPR=25   (re-direct NBO output to LFN 25)
-
-
DETAIL Request additional details of the NBO search. This option (primarily -for programming and debugging purposes) records details of the -NBO loops over atoms -and atom pairs, enroute to the final NBOs. -

-BNDIDX Request print-out of the NAO-Wiberg Bond Index -array and related valency indices (Section B.6.5). The elements of -this array are the sums of squares of off-diagonal density matrix -elements between pairs of atoms in the NAO basis, and are the NAO -counterpart of the Wiberg bond index [K. Wiberg, Tetrahedron 24, -1083-1096 (1968)]. (This bond index is routinely used -to 'screen' atom pairs for possible bonding in the NBO -search, but the values -are not printed unless the BNDIDX keyword is activated.) -

-AOINFO Request writing of information concerning the AO basis set (geometrical -positions, orbital exponents, contraction coefficients, etc.) to an -external file, LFN 31. This is a portion of the information needed -by the ORBPLOT orbital contour plotting programs (cf. "PLOT" -keyword below.) -

-

-PLOT Request writing of all files required by orbital contour plotting -programs ORBPLOT. This activates the AOINFO keyword, as well -as all the necessary matrix output keywords (AONBO=W37, etc.) -that could be required for ORBPLOT. -

-ARCHIVE=n Request writing the FILE47 'archive' file to external disk -file LFN = n (or, if "=n" is not present, to the default -LFN = 47). This file can serve as the input file to run the -GENNBO program in stand-alone mode, to repeat the NBO analysis -(possibly with new job options) without repeating the calculation -of the wavefunction (Section B.7). -

-NBODAF=n Request writing the NBO direct access file (DAF) to external -disk file LFN = n (or, if "=n" is not present, to the -default LFN =48). -

-B.2.6 Print Level Keywords -

- The keyword "PRINT=n" (n = 0-4) can be used to give -convenient, flexible control of all NBO output in terms of -a specified print level n. This keyword -activates groups of keywords in a heirarchical manner, and -thus incrementally increases the volume of output, ranging -from no NBO output (PRINT=0) to a considerable volume of -detail (PRINT=4). The keywords associated with each -print level are tabulated below [default value, PRINT=2]: -

- - - - - - - - -
print leveladditional output or activated keywords
__
0suppress all output from the NBO program
1activate NPA and NBO keywords
[2]activate BEND, NBOSUM, and E2PERT keywords
3activate NLMO, DIPOLE, and BNDIDX keywords
4activate all(!) keywords
-For each print level n, the NBO output will include items activated -by the listed keywords, as well as all items from lower -print levels. -

- When additional keywords -are included with a "PRINT=n" keyword -in the $NBO keylist, the NBO output includes the additional keyword -items as well as those implied by the print level. This can be used -to tailor the NBO output to virtually any selection of output -items. For example, the keylist - 

-     $NBO  PRINT=2  NLMO  FNBO=P  NAOMO=P11  $END
-
-
would add to the standard methylamine output file of Section A.3 -an NLMO summary table, the Fock matrix in -the NBO basis, and the transformation coefficients -for the first 11 molecular orbitals in terms of NAOs. Similarly, -to produce the NPA listing only, one could use - 
-     $NBO  PRINT=1  SKIPBO  $END
-
-
or - 
-     $NBO  PRINT=0  NPA  $END
-
-
[There is actually a slight difference between -the two examples: The -NBOs are determined by default (once the $NBO keylist is encountered), -even if all output is suppressed with PRINT=0; in the first example, -the keyword SKIPBO bypasses NBO determination, whereas in -the second example the NBOs are still determined 'in background.'] -

-B.2.7 Semi-Documented Additional Keywords -

- Some additional keywords are listed below that may of use -to specialists or program developers: -

-KEYWORD OPTION DESCRIPTION -

-THRESH=val Set the threshold of orbital occupancy desired for bond -orbital selection. If this is not included, the default -occupancy [1.90] will be used (or values decreasing from 1.90 -to 1.50 by 0.10 steps, -if the RESONANCE keyword is included). -

-PRJTHR=val Set the projection threshold [default 0.20] to determine if -a 'new' hybrid orbital has too high overlap with hybrids -previously found. -

-MULAT Print total gross Mulliken populations by atom. -

-MULORB Print gross Mulliken populations, by orbital and atom. -

-RPNAO Revises PAO to PNAO transformation matrix by post-multiplying -by TRyd and Tred [see the NPA paper: -A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. 83, -735-746 (1985)]. -

-PAOPNAO Input or output of pure AO (PAO) to pre-NAO (PNAO) transformation. The -PAOs are AOs of pure angular momentum symmetry (rather than -cartesian gaussians). This keyword can be used with read ('R'), -write ('W', default LFN 43) or print ('P') parameters. -

-BOAO Print out the bond-order matrix (Fock-Dirac density matrix) in the -basis set of input AOs. This keyword can be used with write -('W', default LFN 49) or print ('P') parameters. -

-

-B.3 THE $CORE LIST -

- In the Lewis structure picture, the inner 'core' electron pairs -are pictured as occupying orbitals having essentially -isolated atomic orbital character. In NBO parlance, these core orbitals -correspond to 1-center unhybridized NAOs of near-maximum occupancy, -which are isolated on each center before the main NBO search -begins for localized valence electron pairs. A warning message -is printed if the occupancy of a presumed closed-shell -core NBO falls below 1.9990 electrons (or 0.9990 in the open-shell -case), indicative of a possible core-valence mixing effect of -physical significance. -

- [In previous versions -of the NBO program, core orbitals having the expected pure atomic -character are found in essentially all -cases, except where an 'accidental' degeneracy in occupancy of -core and valence lone pairs leads to undesirable core-valence -mixing; the present version explicitly isolates core pairs -as unhybridized NAOs prior -to the main NBO search to prevent this unphysical effect.] -

- The NBO program contains a table giving the nominal number of -core orbitals to be isolated on each type of atom (e.g., 1s for -first-row atoms Li-Ne, 1s, 2s, 2p for second-row atoms -Na-Ar, etc.). At times, however, it is interesting to examine the -effect of allowing core orbitals to mix into the bonding hybrids, or -to hybridize (polarize) among themselves. This can be accomplished -by including a $CORE keylist to specify the number of core -orbitals to be isolated on each atomic center, thus modifying -the nominal core table. Unlike other NBO keylists, the $CORE list -includes only integers (rather than keywords) to specify the -core modifications, but the rules -are otherwise similar to those for -other keylists. The $CORE list (if included) must follow the $NBO -keylist and precede the $CHOOSE or $DEL keylists. -

-

- The format of the $CORE modification list is: -

-first line: The keyword "$CORE" -

-next lines: Pairs of integers, one pair for each center. The first integer -indicates the atomic center (in the numbering of the main ESS) -and the second is the number of core orbitals to be isolated on -that atom. Note that atomic centers not included in the CORE list -are assigned default cores. -

-last line: The keyword "$END", to indicate the end of core input. -

-The entire list may also be condensed to a single line, -but the word "$CORE" must occur as the first word of the line -and "$END" as -the last word; that is, the core -modification keylist cannot continue on a line that contains other -keylist information. -

- The core orbitals are isolated by occupancy, the most occupied NAOs -being first selected, and full subshells are isolated at a time. Thus, -for example, to select the five orbitals of the -n = 1 and n = 2 shells -as core orbitals, it would make no difference -to select "3" or "4" (instead -of "5"), since all three of these -choices would specify a core containing a 1s, 2s, and -all three 2p orbitals. The $CORE modification list -is read only once, and applies to both - and spin manifolds in an open-shell calculation. -

-

-An example, appropriate for Ni(1)-C(2)-O(3) with the indicated numbering -of atoms, is shown below: - 

-     $CORE
-       1   5
-     $END
-
-
This would direct the NBO program to isolate only 5 core orbitals -on Nickel (atom 1), rather than the nominal 9 core orbitals. In -other words, only 1s, 2s, and 2p orbitals will be considered -as core orbitals in the search for NBOs of NiCO, allowing the 3s -and 3p orbitals to mix with valence NAOs in bond formation. Since -the carbon and oxygen atoms were not included in the modification list, -the nominal set of core orbitals (1s only) is isolated on each -of these atoms. -

-

-[The alternative example - 

-     $CORE   1  0    2  0    3  0   $END
-
-
(no cores) would allow all NAOs to be included in the NBO search; -this would be equivalent to the default treatment in -the earlier version of the program (see Section A.1.5).] -

-B.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH) -

- A $CHOOSE keylist requests that the NBO search be directed -to find a particular Lewis structure ('resonance structure') -chosen by the user. (This -is useful for testing the accuracy of alternative resonance structure -representations of the wavefunction, relative to the optimal -Lewis structure returned in a free NBO search.) In the -$CHOOSE list, a resonance structure is specified by indicating -where lone pairs and bonds (including multiple bonds) are to -be found in the molecule. In some cases, the user may wish to -specify only the location of bonds, letting the NBO algorithm -seek the best location for lone pairs, but it is usually safest to -completely specify the resonance structure, both lone -pairs and bonds. -

- The format of the $CHOOSE list is: -

-first line: The keyword "$CHOOSE" -

-next line: The keyword "ALPHA" (only for open-shell wavefunction) -

-next lines: If one-center ('lone') NBOs are to be searched for, type the -keyword "LONE" followed by a list of pairs of numbers, the -first number of each pair being the atomic center and the -second the number of valence lone pairs on that atom. Terminate the -list with "END". (Note that only the occupied valence lone pairs -should be entered, since the number of core orbitals on each -center is presumed known.) -

-If two-center ('bond') NBOs are to be searched for, type -the keyword "BOND", followed by the list of bond specifiers, -and terminated by "END". Each bond specifier is one of the -letters -

-"S" single bond -
"D" double bond -
"T" triple bond -
"Q" quadruple bond -

-followed by the two atomic centers of the bond (e.g., "D 9 16" for -a double bond between atoms 9 and 16). -

-If three-center NBOs are to be searched for, type -the keyword "3CBOND", followed by the list of 3-c bond -specifiers, and terminated by "END". Each 3-c bond specifier -is again one of the letters "S" (single), "D" (double), "T" -(triple), or "Q" (quadruple), followed by three integers for -the three atomic centers (e.g., "S 4 8 10" for a single -three-center bond 4-8-10). (Note that the 3CBOND keyword -of the $NBO keylist is implicitly activated -if 3-c bonds are included in a $CHOOSE list.) -

-next line: The word "END" to signal the end of the spin list. -

-next line: The keyword "BETA" (for open-shell wavefunctions) -

-next lines: The input for spin, same format as above. The overall $CHOOSE -list should always end with the "$END" keyword. -

-

-Two examples will serve to illustrate the $CHOOSE format (each is -rather artificial, inasmuch as the specified $CHOOSE structure -corresponds to the 'normal' structure that would be found by -the NBO program): -

-The closed-shell H-bonded complex FH...CO, -with atom numbering F(1)-H(2)...C(3)-O(4), might be specified as - 

-     $CHOOSE
-        LONE  1  3
-              3  1
-              4  1     END
-        BOND  S  1  2
-              T  3  4  END
-     $END
-
-
This would direct the NBO program to search for three lone pairs -on atom F(1), one lone pair on atom C(3), one lone pair on atom -O(4), one bond between F(1)-H(2), and three bonds between C(3)-O(4). -

-

-(2) The open-shell FH...O2 complex, with -atom numbering F(1)-H(2)...O(3)-O(4), -and with the unpaired electrons on O2 being of - spin, might be specified as - 

-     $CHOOSE
-       ALPHA
-         LONE  1  3
-               3  3
-               4  3     END
-         BOND  S  1  2
-               S  3  4  END
-       END
-       BETA
-         LONE  1  3
-               3  1
-               4  1     END
-         BOND  S  1  2
-               T  3  4  END
-       END
-     $END
-
-
Note that this example incorporates the idea of "different Lewis -structures for different spins," with a distinct pattern of localized -1-c ('lone') and 2-c ('bond') functions for and spin. -

- As with other keylists, the $CHOOSE keylist can be condensed to -a smaller number of lines, as long as no line is shared with another -keylist. The order of keywords within the $CHOOSE keylist should -be as shown above (i.e., ALPHA before BETA, LONE before BOND, etc.), -but the order of entries within a LONE or BOND list is -immaterial. A $CORE keylist (if present) must precede the $CHOOSE list. -

-B.5 THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS) -

-B.5.1 Introduction to NBO Energetic Analysis -

- The fourth and final type of keylist is a 'deletions' ($DEL) -keylist, to activate NBO energetic analysis. This analysis is -performed by (1) deleting specified elements (or blocks of elements) -from the NBO Fock matrix, (2) diagonalizing this new Fock matrix -to obtain a new density matrix, and (3) passing this density matrix -to the SCF routines for a single pass through the SCF energy -evaluator. The difference between this 'deletion' energy and -the original SCF energy provides a useful measure of the -energy contribution of the deleted terms. Since a Fock matrix -is required, the energetic analysis is performed for RHF and -UHF wavefunctions only. -

- Input for the NBO energetic analysis is through the $DEL keylist, -which specifies the deletions to be performed. Multiple analyses -(deletions) can be performed during a single job, with each deletion -included in the overall $DEL keylist. The nine distinct -types of deletions input are described in Section B.5.2 below. -

- The deletions keylist begins with the "$DEL" keyword. For -the analysis of UHF wavefunctions, the deletions for -the and spin manifolds must be separately -specified (see Section B.5.3). Otherwise, the input for closed -shells RHF and UHF is identical. The input is free format and -the input for a single deletion can be spread over as many lines -as desired. The desired deletions should be listed one after the -other. After the last deletion, the word "$END" signals the -end of the keylist. -

-

-

-WARNING -
-

-If symmetry is used, one must be careful to only do deletions -that will preserve the symmetry of the electronic -wavefunction!! If this is not done, the energy of the -deletion will be incorrect because the assumption is made in -evaluating the energy that the original symmetry still exists, -and the variational principle may be violated. (For example, -if symmetry is used for ethane, is is permissible to do -a "NOSTAR" deletion, but not the deletion of a single C-H -antibond.) The remedy is not to use symmetry in the SCF -calculation. -

- In describing the deletion types, use is made of the terms -"molecular unit" and "chemical fragment." The NBO program -looks at the chemical bonding pattern produced by the bonding NBOs -and identifies the groups of atoms that are linked together -in distinct "molecular units" (usually synonymous with "molecules" -in the chemical sense). The first atom that is not in molecular -unit 1 will be in molecular unit 2, and so forth. For example, if -the list of atoms is C(1), H(2), F(3), O(4), and bonding NBOs are -found between C(1)-O(4) and H(2)-F(3), then molecular unit 1 -will be CO and molecular unit 2 will be HF. A "chemical fragment" -is taken to be any subset of the atoms, usually (but not -necessarily) in the same molecular unit, and usually (but not -necessarily) connected -by bond NBOs. Typically, a chemical fragment might be -specified to be a single atom, the four atoms of a -methyl group, or any other 'radical' of a molecular unit, identified -by giving the atom numbers of which the fragment consists. -

-B.5.2 The Nine Deletion Types -

- The keywords and format to specify each of the nine allowed -deletion types are described below: -

-(1) Deletion of entire orbitals. -

-This is called for by typing "DELETE", then the number of orbitals -to be deleted, then the keyword "ORBITAL" (or "ORBITALS"), then -the list of the orbitals to be deleted. -

- Example: 

DELETE  3  ORBITALS  15  18  29
-
-
[See also deletion types (4) and (7) for deleting sets of orbitals.] -

-

-

-WARNING -
-

-The "single-pass" method of evaluating deletion energies is -appropriate only for deletions of low-occupancy (non-Lewis) -orbitals, for which the loss of self-consistency in the Coulomb -and exchange potentials (due to redistribution of the electron -density of deleted orbitals) is small compared to the net -energy change of deletion. It is fundamentally erroneous -to delete high-occupancy (Lewis) orbitals by this -procedure. -

-(2) Deletion of specific Fock matrix elements. -

-This is called for by typing "DELETE", then the number of elements -to be deleted, then the keyword "ELEMENT" (or "ELEMENTS"), then -the list of the elements to be deleted (each as a pair of integers). -

- Example: 

DELETE  3  ELEMENTS  1 15  3 19  23 2
-
-
This example would result in the zeroing of the following Fock -matrix elements: (1,15), (15,1), (3,19), (19,3), (23,2), (2,23). [See -also deletion types (3), (5), (6), (8), (9) for deleting sets of elements.] -

-(3) Deletion of off-diagonal blocks of the Fock matrix. -

-Each block is specified by two sets of orbitals, and all Fock -matrix elements in common between these two sets are set to -zero. This is called for by typing "ZERO", then the number -of off-diagonal blocks to be zeroed, and then, for each block, -the following: -

-

-(1) the dimensions of the block, separated by the word "BY" (e.g., -"6 BY 3" if the first set has 6 orbitals and the second set -has 3 orbitals); -

-(2) the list of orbitals in the first set; -

-(3) the list of orbitals in the second set. -

-

-An example is shown below: - 

-     ZERO  2  BLOCKS  2  BY  5
-                               3  4
-                               9  10  11  14  19
-                      3  BY  2
-                               1  2  7
-                              20  24
-
-
This will set the following Fock matrix elements to zero: -

-(3,9), (3,10), (3,11), (3,14), (3,19), -(9,3), (10,3), (11,3), (14,3), (19,3), -(4,9), (4,10), (4,11), (4,14), (4,19), -(9,4), (10,4), (11,4), (14,4), (19,4), -(1,20), (1,24), (2,20), (2,24), (7,20), (7,24) -(20,1), (24,1), (20,2), (24,2), (20,7), (24,7) -

-[Usually, in studying the total delocalization from one -molecular unit to another, it is much easier to use deletion -type (8) below. Similarly, in studying the total delocalization -from one chemical fragment to another, it is easier to use -deletion type (9).] -

-(4) Deletion of all Rydberg and antibond orbitals. -

-The Rydberg and antibond orbitals are the non-Lewis NBO orbitals -that have stars in their labels (RY*, BD*) in the NBO analysis -output. To delete all these orbitals, simply enter "NOSTAR". The -result of this deletion is the energy of the idealized NBO natural -Lewis structure, with all Lewis NBOs doubly occupied. (Unlike other -deletions, in which there is a slight loss of variational -self-consistency due to the redistributed occupancy of the deleted -orbitals, the result of a "NOSTAR" deletion corresponds rigorously -to the variational expectation value of the determinant of doubly -occupied Lewis NBOs). -

-

-(5) Deletion of all vicinal delocalizations. -

-To delete all Fock matrix elements between Lewis NBOs and the -vicinal non-Lewis NBOs, simply enter "NOVIC". -

-

-(6) Deletion of all geminal delocalizations. -

-To delete all Fock matrix elements between Lewis NBOs and the -geminal non-Lewis NBOs, simply enter "NOGEM". -

-

-(7) Deletion of all starred (antibond/Rydberg) orbitals on a -particular molecular unit. -

-This is called for by typing "DESTAR", then the number of -molecular units to be destarred, then the keyword "UNIT" -(or "UNITS"), then the list of units. -

- Example: 

DESTAR  2  UNITS  3  4
-
-

-

-(8) Zeroing all delocalization from one molecular unit to another. -

-This is called for by typing "ZERO", then the number of delocalizations -to zero, then the keyword "DELOCALIZATION" (can be abbreviated -to "DELOC"), and then, for each delocalization, the word "FROM", -the number of the donor unit, the word "TO", and -the number of the acceptor unit. -

- Example: 

ZERO  2  DELOC  FROM 1 TO 2   FROM 2 TO 1
-
-
The above example would zero all intermolecular -delocalizations between units 1 and 2 (i.e., both 1 2 and -2 1). The -effect is to remove all Fock matrix elements between high-occupancy -(core/lone pair/bond) NBOs of the donor unit to the low-occupancy -(antibond/Rydberg) NBOs of the acceptor unit. The donor and acceptor -units may be the same. -

-

-(9) Zeroing all delocalization from one chemical fragment to another. -

-This is called for by typing "ZERO", then the number of inter-fragment -delocalizations to be zeroed, then the words "ATOM BLOCKS", -and then, for each delocalization, -the following: -

-(1) the number of atoms in the two fragments, separated by the word "BY" -(e.g., "6 BY 3" if the first fragment has 6 atoms and the second -has 3 atoms); -

-(2) the list of atoms in the first fragment; -

-(3) the list of atoms in the second fragment. -

-For example, to zero all delocalizations between the fragments -defined by atoms (1,2) and by atoms (3,4,5), the $DEL entries would be - 

-     ZERO  2  ATOM BLOCKS
-              2  BY  3
-                       1  2
-                       3  4  5
-              3  BY  2
-                       3  4  5
-                       1  2
-
-
In this example, the first block removes the (1,2) (3,4,5) -delocalizations, while the second removes the (3,4,5) (1,2) -delocalizations. -

- For additional examples of $DEL input, see Section B.6.10. -

-B.5.3 Input for UHF Analysis -

- Deletions of the alpha and beta Fock matrices can be done -independently. The deletions are input as above (Section B.5.2) for -RHF closed shell, but they must be specified separately for alpha -and beta in the UHF case. -

- The deletion to be done on the alpha Fock matrix must be preceded -by the keyword "ALPHA", and the deletion of the beta Fock matrix -must be preceded by the keyword "BETA". (Actually, only the first -letter "A" or "B" is searched for by the program.) The ALPHA -deletion must precede the BETA deletion. The BETA deletion -may be the same as the ALPHA deletion, or different. -

- NOTE: The types of the NBOs often differ from those of -the NBOs, so that distinct , deletions -lists are generally required. For example, O2 (triplet) has one bond in -the system and three in the system, if the unpaired -electrons are in the system. -

- Here are three examples to illustrate UHF open-shell deletions: -

-

-Example 1: - 

-     ALPHA  ZERO  1  DELOC  FROM  1  TO  2
-     BETA   NOSTAR
-
-

-
Example 2: - 
-     ALPHA  ZERO  1  DELOC  FROM  1  TO  2
-     BETA   ZERO  0  DELOC
-
-

-
Example 3: - 
-     ALPHA  DELETE  0  ORBITALS
-     BETA   DELETE  1  ORBITAL  8
-
-
If no deletion is done, this must be specified using zero (0) with -one of the deletion input formats, as shown in Examples 2,3 above. -

-B.6 NBO KEYLIST ILLUSTRATIONS -

-B.6.1 Introduction -

- This section illustrates the output produced by several -important keyword options of the NBO -keylists ($NBO, $CHOOSE, $DEL, $CORE lists), -supplementing the illustrations -of Section A.3. Excerpts are provided -rather than full output, since, e.g., NPA analysis is -unaffected by keywords that modify the NBO search. Keywords -of general applicability are illustrated with the -methylamine example (RHF/3-21G, Pople-Gordon geometry) of -Section A.3, which should be consulted for further -information. More specialized keywords (RESONANCE, 3CBOND, etc.) -are illustrated with prototype molecules (benzene, diborane, etc.) -chosen for the keyword. -

- Sections B.6.2-B.6.8 illustrate representative examples -from the $NBO keyword groups, including NLMO, DIPOLE, BNDIDX, -RESONANCE, NOBOND, 3CBOND, and matrix output -keywords. Section B.6.9 and B.6.10 similarly illustrate -the use of the $CHOOSE and $DEL keylists. Section B.6.11 -illustrates the output for open-shell UHF cases, emphasizing -features associated with the "different Lewis -structures for different spins" representation of and - spin manifolds. Section B.6.12 shows the effect of using -effective core potentials for Cu2, also illustrating -aspects of the inclusion of d functions. -

-B.6.2 NLMO Keyword -

- When the NLMO keyword is activated, the program computes the -NLMOs and prints out three tables summarizing their form. For -the RHF/3-21G methylamine example (cf. Section A.3), the principal -NLMO table is shown below: -

- 

-
-NATURAL LOCALIZED MOLECULAR ORBITAL (NLMO) ANALYSIS:
-
-Maximum off-diagonal element of DM in NLMO basis:   0.00000
-
-Hybridization/Polarization Analysis of NLMOs in NAO Basis:
-NLMO/Occupancy/Percent from Parent NBO/ Atomic Hybrid Contributions
--------------------------------------------------------------------------------
-  1. (2.00000)  99.9290%  BD ( 1) C 1- N 2      
-                          40.039%  C 1 s( 21.54%)p 3.64( 78.46%)
-                          59.891%  N 2 s( 30.98%)p 2.23( 69.02%)
-                           0.015%  H 3 s(100.00%)
-                           0.021%  H 6 s(100.00%)
-                           0.021%  H 7 s(100.00%)
-  2. (2.00000)  99.9301%  BD ( 1) C 1- H 3      
-                          59.675%  C 1 s( 25.44%)p 2.93( 74.56%)
-                           0.040%  N 2 s(  1.99%)p49.22( 98.01%)
-                          40.258%  H 3 s(100.00%)
-  3. (2.00000)  99.6996%  BD ( 1) C 1- H 4      
-                          60.848%  C 1 s( 25.25%)p 2.96( 74.75%)
-                           0.093%  N 2 s( 13.08%)p 6.65( 86.92%)
-                           0.014%  H 3 s(100.00%)
-                          38.861%  H 4 s(100.00%)
-                           0.017%  H 5 s(100.00%)
-                           0.158%  H 6 s(100.00%)
-  4. (2.00000)  99.6996%  BD ( 1) C 1- H 5      
-                          60.848%  C 1 s( 25.25%)p 2.96( 74.75%)
-                           0.093%  N 2 s( 13.08%)p 6.65( 86.92%)
-                           0.014%  H 3 s(100.00%)
-                           0.017%  H 4 s(100.00%)
-                          38.861%  H 5 s(100.00%)
-                           0.158%  H 7 s(100.00%)
-  5. (2.00000)  99.7206%  BD ( 1) N 2- H 6      
-                           0.113%  C 1 s(  5.15%)p18.41( 94.85%)
-                          67.929%  N 2 s( 25.82%)p 2.87( 74.18%)
-                           0.137%  H 4 s(100.00%)
-                           0.014%  H 5 s(100.00%)
-                          31.793%  H 6 s(100.00%)
-  6. (2.00000)  99.7206%  BD ( 1) N 2- H 7      
-                           0.113%  C 1 s(  5.15%)p18.41( 94.85%)
-                          67.929%  N 2 s( 25.82%)p 2.87( 74.18%)
-                           0.014%  H 4 s(100.00%)
-                           0.137%  H 5 s(100.00%)
-                          31.793%  H 7 s(100.00%)
-  7. (2.00000)  99.9499%  CR ( 1) C 1           
-                          99.951%  C 1 s(100.00%)p 0.00(  0.00%)
-                           0.013%  H 3 s(100.00%)
-                           0.013%  H 4 s(100.00%)
-                           0.013%  H 5 s(100.00%)
-  8. (2.00000)  99.9763%  CR ( 1) N 2           
-                           0.010%  C 1 s( 22.30%)p 3.48( 77.70%)
-                          99.980%  N 2 s(100.00%)p 0.00(  0.00%)
-  9. (2.00000)  98.8972%  LP ( 1) N 2           
-                           0.440%  C 1 s(  1.05%)p94.15( 98.95%)
-                          98.897%  N 2 s( 17.85%)p 4.60( 82.15%)
-                           0.489%  H 3 s(100.00%)
-                           0.085%  H 4 s(100.00%)
-                           0.085%  H 5 s(100.00%)
-
-
For each of the nine occuplied NLMOs, the table shows first the -NLMO occupancy (necessarily 2.0000 at SCF level, as in the -present example), the percentage -of the total NLMO composition represented by this parent NBO -(usually > 99%), and the label of the 'parent' -NBO. Below this, there follows an NAO decomposition -of the NLMO, showing the percentage of the NLMO on each atom -and the hybrid composition ratios (effective -sp character and percentage s- and -p-character) of the NAOs. For -example, NLMO 9 is the most delocalized NLMO -of the table, having only about a 98.9% contribution from -the localized N(2) parent lone pair NBO, -with 'delocalization tails' composed -primarily of contributions (~0.4% each) from C(1) and H(3), and -smaller contributions (~0.09%) from H(4) and H(5). This -corresponds to what might have been anticipated from the -NBO summary table (Section A.3.6) or perturbation theory -energy analysis table (Section A.3.5), which showed that -the N(2) lone pair, NBO 9, is principally delocalized -onto NBO 24, the vicinal C(1)-H(3) antibond [with lesser -delocalizations onto NBOs 25, 26, the C(1)-H(4) and C(1)-H(5) -antibonds]. -

-B.6.3 DIPOLE Keyword -

- The DIPOLE keyword activates the NBO/NLMO analysis of the -molecular dipole moment, as shown below for the example -of RHF/3-21G methylamine (cf. Section A.3): -

- 

-
-Dipole moment analysis:
-
-[Print threshold: Net dipole > 0.02 Debye]
-
-                                NLMO bond dipole            NBO bond dipole
-                            -------------------------  ------------------------
-         Orbital              x     y     z   Total      x     y     z   Total
-===============================================================================
-  1. BD ( 1) C 1- N 2       -0.76 -0.08  0.00  0.76    -0.76 -0.09  0.00  0.77
-
-  2. BD ( 1) C 1- H 3        0.49  1.90  0.00  1.96     0.50  1.90  0.00  1.97
-                                            deloc  14:  0.03 -0.01  0.00  0.03
-                                            deloc  25: -0.01  0.00  0.02  0.02
-                                            deloc  26: -0.01  0.00 -0.02  0.02
-
-  3. BD ( 1) C 1- H 4        0.67 -0.77 -1.50  1.81     0.71 -0.79 -1.50  1.84
-                                            deloc  27: -0.05  0.00  0.00  0.05
-                                            deloc  26: -0.02  0.03 -0.03  0.04
-                                            deloc  24: -0.01 -0.02  0.00  0.02
-
-  4. BD ( 1) C 1- H 5        0.67 -0.77  1.50  1.81     0.71 -0.79  1.50  1.84
-                                            deloc  28: -0.05  0.00  0.00  0.05
-                                            deloc  25: -0.02  0.03  0.03  0.04
-                                            deloc  24: -0.01 -0.02  0.00  0.02
-
-  5. BD ( 1) N 2- H 6       -0.45  0.44  0.86  1.06    -0.50  0.44  0.89  1.11
-                                            deloc  25:  0.06 -0.01 -0.02  0.06
-
-  6. BD ( 1) N 2- H 7       -0.45  0.44 -0.86  1.06    -0.50  0.44 -0.89  1.11
-                                            deloc  26:  0.06 -0.01  0.02  0.06
-
-  7. CR ( 1) C 1             0.00  0.00  0.00  0.00     0.00  0.00  0.00  0.00
-
-  8. CR ( 1) N 2             0.00  0.01  0.00  0.01     0.00  0.00  0.00  0.00
-
-  9. LP ( 1) N 2            -0.63 -2.85  0.00  2.91    -0.88 -2.93  0.00  3.06
-                                            deloc  24:  0.16  0.09  0.00  0.18
-                                            deloc  25:  0.03  0.01  0.01  0.03
-                                            deloc  26:  0.03  0.01 -0.01  0.03
-                                            deloc  10:  0.02 -0.02  0.00  0.03
-                           ----------------------------------------------------
-        Net dipole moment   -0.45 -1.67  0.00  1.73    -0.71 -1.82  0.00  1.95
-Delocalization correction                               0.27  0.14  0.00  0.30
-                           ----------------------------------------------------
-      Total dipole moment   -0.45 -1.67  0.00  1.73    -0.45 -1.67  0.00  1.73
- 
-
-

-
The bottom line of the table shows the individual (x,y,z) vector components -(-0.45,-1.67,0.00) -and length (1.73 D) of the total molecular dipole moment, in the coordinate -system of the ESS program. This is decomposed in the main body of -the table into the individual contributions of "NLMO bond dipoles" -(which strictly add to give the net molecule dipole at the SCF level) -and "NBO bond dipoles" (which must be added with their -off-diagonal 'deloc' contributions to give the net molecular -moment). Each NLMO or NBO bond dipole -vector AB is evaluated as -
-

-AB = AB(elec) + AB(nuc) -

-

-where -AB(elec) = 2e<AB | r | AB> -is the electronic dipole expectation value for an electron -pair in the AB NLMO -or NBO, and AB(nuc) is the nuclear contribution of compensating -unit positive charges at the positions of nuclei A and B (or both -on A for a 1-center NBO). The 'deloc' contributions -below each NBO bond dipole -show the off-diagonal corrections -to an additive bond dipole approximation (i.e., -the corrections to localized NBO bond dipoles to get the NLMO bond dipoles) -to account for the delocalization from parent NBO i onto -other (primarily, non-Lewis) NBOs j; in terms of the expansion -of an NLMO in the set {j} of NBOs, -

-

-i(NLMO) = ciii + (j)cjij -
-

-this correction is (for each electron, or spin) -

-cji2[<j |  | j>-<i |  | i>] + 2ciicji<i |  | j> -+ (k)"cjicki<j |  | k> -

-where the primes on the summation denote omission of -terms k equal to i or j. For example, in the above table the -largest individual contribution to is from the -nitrogen lone pair, table entry 9, which has an NLMO dipole -of 2.91 Debye or NBO dipole of 3.06. The latter has also the -largest off-diagonal delocalization correction in the table, -a 0.18 D correction due to the -nN *CH delocalization into the -vicinal C(1)-H(3) antibond, NBO 24. -

- For a post-SCF (correlated) calculation, the dipole table would also -include an additional line for the correction due to non-additivity -of the NLMO bond dipoles. For an ionic species, there -would also be an additional -line for the "residual nuclear charge" contribution; here, one must -be aware that the dipole moment is calculated with respect -to the origin of the cartesian coordinate system chosen by the ESS -program (since the dipole moment is origin-dependent in -this case). -

- Note that the amount of detail in the -dipole table can be altered by using the "DIPOLE=thr" form -of the keyword to alter the threshold dipole ('thr') for printing -[default: 0.02 D]. -

-B.6.4 Matrix Output Keywords -

- Two simple examples will be given to illustrate the -formatting of output for -operators or basis set transformation matrices using the matrix -output keywords of Section B.2.4. For the RHF/3-21G methylamine -example of Section A.3, the keyword "FNHO" would cause the -Fock matrix in the NHO basis to be printed out. Shown below is -a reproduction of the first eight columns (out of 28) of this output: -

- 

-
-NHO Fock matrix:                                                                
-
-         NHO        1       2       3       4       5       6       7       8
-     ---------- ------- ------- ------- ------- ------- ------- ------- -------
-  1.  C1 ( N2 ) -0.0208 -0.7203 -0.0571 -0.0665  0.0438  0.0672  0.0438  0.0672
-  2.  N2 ( C1 ) -0.7203 -0.3083 -0.0773 -0.0627  0.0835  0.0646  0.0835  0.0646
-  3.  C1 ( H3 ) -0.0571 -0.0773 -0.1394 -0.6758  0.0638  0.0746  0.0638  0.0746
-  4.  H3 ( C1 ) -0.0665 -0.0627 -0.6758  0.1349  0.0740  0.0672  0.0740  0.0672
-  5.  C1 ( H4 )  0.0438  0.0835  0.0638  0.0740 -0.1466 -0.6761 -0.0548 -0.0759
-  6.  H4 ( C1 )  0.0672  0.0646  0.0746  0.0672 -0.6761  0.1541 -0.0759 -0.0697
-  7.  C1 ( H5 )  0.0438  0.0835  0.0638  0.0740 -0.0548 -0.0759 -0.1466 -0.6761
-  8.  H5 ( C1 )  0.0672  0.0646  0.0746  0.0672 -0.0759 -0.0697 -0.6761  0.1541
-  9.  N2 ( H6 )  0.0926  0.1499  0.0240 -0.0113  0.0912 -0.0078 -0.0349  0.0134
- 10.  H6 ( N2 )  0.1083  0.0826 -0.0010  0.0232 -0.0118 -0.0242  0.0017 -0.0224
- 11.  N2 ( H7 )  0.0926  0.1499  0.0240 -0.0113 -0.0349  0.0134  0.0912 -0.0078
- 12.  H7 ( N2 )  0.1083  0.0826 -0.0010  0.0232  0.0017 -0.0224 -0.0118 -0.0242
- 13.  C1 (cr)    0.3962  0.4168  0.4400  0.3893 -0.4447 -0.3869 -0.4447 -0.3869
- 14.  N2 (cr)    0.6147  0.7083  0.0039  0.0249 -0.0130 -0.0251 -0.0130 -0.0251
- 15.  N2 (lp)    0.0762  0.0955 -0.1043  0.0254 -0.0386  0.0160 -0.0386  0.0160
- 16.  C1 (ry*)  -0.1320  0.0924  0.0705 -0.0815  0.0022 -0.0037  0.0022 -0.0037
- 17.  C1 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0719 -0.0910 -0.0719  0.0910
- 18.  C1 (ry*)  -0.1023  0.0764 -0.0643  0.0795 -0.0074  0.0105 -0.0074  0.0105
- 19.  C1 (ry*)   0.0266 -0.0213  0.0019 -0.0057  0.0667 -0.0788  0.0667 -0.0788
- 20.  N2 (ry*)   0.0151 -0.0177 -0.0351 -0.0172 -0.0179 -0.0146 -0.0179 -0.0146
- 21.  N2 (ry*)   0.0000  0.0000  0.0000  0.0000 -0.0158 -0.0249  0.0158  0.0249
- 22.  N2 (ry*)   0.1799 -0.1440 -0.0064  0.0295  0.0038 -0.0289  0.0038 -0.0289
- 23.  N2 (ry*)   0.0183 -0.0136 -0.0051  0.0213  0.0032 -0.0095  0.0032 -0.0095
- 24.  H3 (ry*)   0.0253 -0.0038  0.2834 -0.3497 -0.0248  0.0047 -0.0248  0.0047
- 25.  H4 (ry*)   0.0223 -0.0071  0.0211 -0.0068 -0.2789  0.3553 -0.0227  0.0069
- 26.  H5 (ry*)   0.0223 -0.0071  0.0211 -0.0068 -0.0227  0.0069 -0.2789  0.3553
- 27.  H6 (ry*)   0.0124  0.0172 -0.0067  0.0219 -0.0080  0.0097  0.0057 -0.0222
- 28.  H7 (ry*)   0.0124  0.0172 -0.0067  0.0219  0.0057 -0.0222 -0.0080  0.0097
- 
-
-

- The NHO labels on each row identify the atom to which the NHO -belongs, and (in parentheses) the atom toward which the hybrid is -pointed, if a bond hybrid, or a 1-center label (cr, lp, lp*, or ry*), if -a non-bonded hybrid. Thus, "C 1 (N 2)" (NHO 1) -is the bonding hybrid on C(1) directed -toward N(2), "N 2(lp)" (NBO 15) is a non-bonded (lone pair) hybrid -on N(2), etc. This label allows one to find the precise form of -the NHO in the main listing of NBOs. The FNHO matrix shows, for -example, that -the (1,2) Fock matrix element between the directly -interacting NHOs forming the C-N bond NBO is -0.7203 a.u., -whereas the (1,9) matrix element, -between the C(1) hybrid pointing toward N(2) -and the N(2) hybrid pointing toward H(6), is 0.0926 a.u. -

- As a second example, the keyword "NBOMO=PVAL" would print out -the core + valence columns of the NBO MO transformation, -as reproduced below: -

- 

-
-MOs in the NBO basis:                                                           
-
-         NBO        1       2       3       4       5       6       7       8
-     ---------- ------- ------- ------- ------- ------- ------- ------- -------
-  1.  C1 - N2   -0.0661 -0.0574  0.6288 -0.1243  0.0000 -0.3239  0.6816  0.0000
-  2.  C1 - H3   -0.0018 -0.0578  0.2061 -0.4716  0.0000  0.7747  0.1386  0.0000
-  3.  C1 - H4    0.0023  0.0579 -0.1836  0.4908  0.3813  0.2304  0.3921  0.5940
-  4.  C1 - H5    0.0023  0.0579 -0.1836  0.4908 -0.3813  0.2304  0.3921 -0.5940
-  5.  N2 - H6    0.0570  0.0000 -0.4742 -0.3567 -0.5937 -0.1954  0.3035  0.3814
-  6.  N2 - H7    0.0570  0.0000 -0.4742 -0.3567  0.5937 -0.1954  0.3035 -0.3814
-  7.  C1 (cr)   -0.0021  0.9931  0.0692 -0.0920  0.0000  0.0006  0.0019  0.0000
-  8.  N2 (cr)    0.9935 -0.0019  0.1048  0.0348  0.0000 -0.0131  0.0022  0.0000
-  9.  N2 (lp)    0.0432 -0.0037 -0.1676 -0.1219  0.0000  0.3312  0.1525  0.0000
- 10.  C1 (ry*)  -0.0088 -0.0005  0.0114  0.0089  0.0000 -0.0016 -0.0086  0.0000
- 11.  C1 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0109  0.0000  0.0000 -0.0070
- 12.  C1 (ry*)  -0.0063  0.0001 -0.0050 -0.0035  0.0000 -0.0030  0.0026  0.0000
- 13.  C1 (ry*)   0.0020 -0.0002 -0.0003 -0.0003  0.0000 -0.0009  0.0002  0.0000
- 14.  N2 (ry*)  -0.0041 -0.0003 -0.0006  0.0016  0.0000  0.0192  0.0107  0.0000
- 15.  N2 (ry*)   0.0000  0.0000  0.0000  0.0000  0.0080  0.0000  0.0000  0.0124
- 16.  N2 (ry*)   0.0035 -0.0060 -0.0039  0.0102  0.0000 -0.0023  0.0040  0.0000
- 17.  N2 (ry*)  -0.0018  0.0023 -0.0007  0.0013  0.0000 -0.0007  0.0005  0.0000
- 18.  H3 (ry*)  -0.0008 -0.0094 -0.0103  0.0146  0.0000  0.0017 -0.0021  0.0000
- 19.  H4 (ry*)  -0.0008 -0.0100 -0.0061  0.0119  0.0062  0.0004 -0.0054 -0.0098
- 20.  H5 (ry*)  -0.0008 -0.0100 -0.0061  0.0119 -0.0062  0.0004 -0.0054  0.0098
- 21.  H6 (ry*)  -0.0052 -0.0013 -0.0147 -0.0018 -0.0027 -0.0016 -0.0097 -0.0159
- 22.  H7 (ry*)  -0.0052 -0.0013 -0.0147 -0.0018  0.0027 -0.0016 -0.0097  0.0159
- 23.  C1 - N2 * -0.0019 -0.0035 -0.0026  0.0025  0.0000  0.0043  0.0049  0.0000
- 24.  C1 - H3 * -0.0013 -0.0024  0.0059 -0.0018  0.0000 -0.0349 -0.0139  0.0000
- 25.  C1 - H4 *  0.0009  0.0028 -0.0138  0.0033 -0.0408 -0.0188  0.0061  0.0148
- 26.  C1 - H5 *  0.0009  0.0028 -0.0138  0.0033  0.0408 -0.0188  0.0061 -0.0148
- 27.  N2 - H6 * -0.0010  0.0051 -0.0047  0.0182  0.0179  0.0122  0.0154  0.0322
- 28.  N2 - H7 * -0.0010  0.0051 -0.0047  0.0182 -0.0179  0.0122  0.0154 -0.0322
-
-         NBO        9      10      11      12      13      14      15
-     ---------- ------- ------- ------- ------- ------- ------- -------
-  1.  C1 - N2    0.1062 -0.0143  0.0006  0.0000  0.0049  0.0000 -0.0061
-  2.  C1 - H3   -0.3343 -0.0044  0.0015  0.0000  0.0007  0.0000 -0.0080
-  3.  C1 - H4   -0.1186 -0.0186  0.0103  0.0258 -0.0048 -0.0272 -0.0104
-  4.  C1 - H5   -0.1186 -0.0186  0.0103 -0.0258 -0.0048  0.0272 -0.0104
-  5.  N2 - H6   -0.1167 -0.0024 -0.0145 -0.0293 -0.0162 -0.0253  0.0040
-  6.  N2 - H7   -0.1167 -0.0024 -0.0145  0.0293 -0.0162  0.0253  0.0040
-  7.  C1 (cr)    0.0037 -0.0134 -0.0082  0.0000  0.0008  0.0000 -0.0008
-  8.  N2 (cr)   -0.0189 -0.0055  0.0030  0.0000 -0.0026  0.0000  0.0035
-  9.  N2 (lp)    0.9007 -0.0144  0.0055  0.0000  0.0925  0.0000  0.0130
- 10.  C1 (ry*)  -0.0128 -0.0993  0.0553  0.0000  0.0536  0.0000  0.3301
- 11.  C1 (ry*)   0.0000  0.0000  0.0000  0.0836  0.0000  0.1845  0.0000
- 12.  C1 (ry*)  -0.0039 -0.0612  0.0748  0.0000 -0.1160  0.0000  0.1213
- 13.  C1 (ry*)  -0.0018  0.0936  0.0192  0.0000  0.1022  0.0000 -0.1516
- 14.  N2 (ry*)  -0.0086 -0.0232  0.0071  0.0000 -0.0461  0.0000 -0.0178
- 15.  N2 (ry*)   0.0000  0.0000  0.0000  0.0176  0.0000 -0.0856  0.0000
- 16.  N2 (ry*)   0.0006  0.0395 -0.0836  0.0000  0.0221  0.0000 -0.1565
- 17.  N2 (ry*)   0.0003  0.0614 -0.0222  0.0000  0.0114  0.0000  0.0584
- 18.  H3 (ry*)  -0.0218 -0.2483 -0.2232  0.0000  0.4827  0.0000  0.0001
- 19.  H4 (ry*)   0.0060 -0.1973 -0.3224 -0.3372 -0.2069 -0.2151 -0.0483
- 20.  H5 (ry*)   0.0060 -0.1973 -0.3224  0.3372 -0.2069  0.2151 -0.0483
- 21.  H6 (ry*)   0.0027 -0.2869  0.2132  0.2297 -0.0372 -0.3543 -0.1737
- 22.  H7 (ry*)   0.0027 -0.2869  0.2132 -0.2297 -0.0372  0.3543 -0.1737
- 23.  C1 - N2 * -0.0031 -0.2357  0.2598  0.0000 -0.1096  0.0000  0.8051
- 24.  C1 - H3 * -0.0799 -0.3214 -0.2654  0.0000  0.6687  0.0000  0.1133
- 25.  C1 - H4 * -0.0369  0.2559  0.3890  0.4699  0.2968  0.3193 -0.0477
- 26.  C1 - H5 * -0.0369  0.2559  0.3890 -0.4699  0.2968 -0.3193 -0.0477
- 27.  N2 - H6 * -0.0031  0.4339 -0.3112 -0.3280  0.0474  0.4519  0.2168
- 28.  N2 - H7 * -0.0031  0.4339 -0.3112  0.3280  0.0474 -0.4519  0.2168
- 
-
-

- In this transformation matrix, rows correspond to NBOs and -columns to MOs (in the ordering used elesewhere in the program), -and each basis NBO is further identified with -a row label. The print parameter -"PVAL" specified that only 15 MOs (the -number of core + valence orbitals) -should be printed, corresponding to the nine -occupied MOs 1-9 and the lowest six virtual MOs 10-15. The matrix -allows one to see the composition of each canonical MO in terms of -localized bond NBOs. For example, MOs 5 and 8 -can be approximately described as -

-

-5 -0.594(N2H6 - N2H7) + 0.381(C1H4 - C1H5) -

-8 0.381(N2H6 - N2H7) + 0.594(C1H4 - C1H5) -

-

-whereas 6 is primarily the C-H(3) NBO and 9 -the N lone pair NBO. -

-B.6.5 BNDIDX Keyword -

- The BNDIDX keyword activates the printing of several types -of 'bond order' and valency indices, based on different assumptions -and formulas, but all having some connection to the NAO/NBO/NLMO -formalism. We illustrate these bond -order tables for the example of RHF/3-21G methylamine (Section A.3). -

- The first segment of BNDIDX output shows the Wiberg bond index (the sum of -squares of off-diagonal density matrix elements between -atoms), as formulated -in terms of the NAO basis set: -

- 

-
-Wiberg bond index matrix in the NAO basis:                                      
-
-    Atom    1       2       3       4       5       6       7
-    ---- ------  ------  ------  ------  ------  ------  ------
-  1.  C  0.0000  0.9964  0.9472  0.9394  0.9394  0.0020  0.0020
-  2.  N  0.9964  0.0000  0.0208  0.0052  0.0052  0.8611  0.8611
-  3.  H  0.9472  0.0208  0.0000  0.0004  0.0004  0.0002  0.0002
-  4.  H  0.9394  0.0052  0.0004  0.0000  0.0009  0.0079  0.0005
-  5.  H  0.9394  0.0052  0.0004  0.0009  0.0000  0.0005  0.0079
-  6.  H  0.0020  0.8611  0.0002  0.0079  0.0005  0.0000  0.0003
-  7.  H  0.0020  0.8611  0.0002  0.0005  0.0079  0.0003  0.0000
-
-
-Wiberg bond index, Totals by atom:                                              
-
-    Atom    1
-    ---- ------
-  1.  C  3.8265
-  2.  N  2.7499
-  3.  H  0.9691
-  4.  H  0.9544
-  5.  H  0.9544
-  6.  H  0.8720
-  7.  H  0.8720
- 
-
-

- This index is intrinsically a positive quantity, making no -distinction between net bonding -or antibonding character of the density matrix elements. -

-

- The next segment tabulates the "overlap-weighted -NAO bond order," as shown below: -

- 

-
-Atom-atom overlap-weighted NAO bond order:                                      
-
-    Atom    1       2       3       4       5       6       7
-    ---- ------  ------  ------  ------  ------  ------  ------
-  1.  C  0.0000  0.7815  0.7614  0.7633  0.7633 -0.0103 -0.0103
-  2.  N  0.7815  0.0000 -0.0225 -0.0097 -0.0097  0.6688  0.6688
-  3.  H  0.7614 -0.0225  0.0000 -0.0039 -0.0039 -0.0019 -0.0019
-  4.  H  0.7633 -0.0097 -0.0039  0.0000  0.0024  0.0038 -0.0032
-  5.  H  0.7633 -0.0097 -0.0039  0.0024  0.0000 -0.0032  0.0038
-  6.  H -0.0103  0.6688 -0.0019  0.0038 -0.0032  0.0000 -0.0069
-  7.  H -0.0103  0.6688 -0.0019 -0.0032  0.0038 -0.0069  0.0000
-
-
-Atom-atom overlap-weighted NAO bond order, Totals by atom:                      
-
-    Atom    1
-    ---- ------
-  1.  C  3.0488
-  2.  N  2.0772
-  3.  H  0.7273
-  4.  H  0.7527
-  5.  H  0.7527
-  6.  H  0.6503
-  7.  H  0.6503
- 
-
-

- This index corresponds to a sum of off-diagonal -NAO density matrix elements between atoms, -each multiplied by the corresponding PNAO overlap integral. -

- Another type of BNDIDX output appears if the NLMO -keyword is included, summarizing a formal -"NLMO/NPA bond order" that can be associated with each NLMO: -

- 

-
-Individual LMO bond orders greater than 0.002 in magnitude,
- with the overlap between the hybrids in the NLMO given:
-
-Atom I / Atom J / NLMO / Bond Order / Hybrid Overlap /
-   1       2       1     0.8007741       0.7314361
-   1       2       5     0.0022694       0.1796696
-   1       2       6     0.0022694       0.1796696
-   1       2       9     0.0088061       0.3053730
-   1       3       2     0.8051647       0.7862263
-   1       3       9    -0.0088061      -0.5762575
-   1       4       3     0.7772179       0.7874312
-   1       4       5    -0.0022694      -0.5396947
-   1       5       4     0.7772179       0.7874312
-   1       5       6    -0.0022694      -0.5396947
-   1       6       3    -0.0031652      -0.0920524
-   1       6       5     0.0022694       0.0852070
-   1       7       4    -0.0031652      -0.0920524
-   1       7       6     0.0022694       0.0852070
-   2       3       9    -0.0097841      -0.0930204
-   2       4       5    -0.0027437      -0.0701717
-   2       5       6    -0.0027437      -0.0701717
-   2       6       5     0.6358512       0.7286061
-   2       7       6     0.6358512       0.7286061
-   4       6       3     0.0031652       0.0429202
-   4       6       5     0.0027437       0.0399352
-   5       7       4     0.0031652       0.0429202
-   5       7       6     0.0027437       0.0399352
- 
-
-
This NLMO bond order is calculated by the method described by -A. E. Reed and P. v.R. Schleyer [Inorg. Chem. 27, 3969-3987 (1988); -J. Am. Chem. Soc. (to be published)], -based on the shared occupancies and hybrid overlaps (last column) -of NAOs composing the NLMO. In the above table, for example, NLMO 1 -occurs only in the first line, -contributing a bond of formal order 0.801 between C(1) and N(2), whereas -NLMO 9 (the nitrogen lone pair) contributes a slight strengthening -(+0.0088) of the C(1)-N(2) bond, a weakening (-0.0088) of the -vicinal C(1)-H(3) bond, and a slight negative bond order (-0.0098) -between atoms N(2), H(3). -

- The NLMO bond order contributions are then summed for each -atom pair to give the net NLMO/NPA bond orders shown below: -

- 

-
-Atom-Atom Net Linear NLMO/NPA Bond Orders:                                      
-
-    Atom    1       2       3       4       5       6       7
-    ---- ------  ------  ------  ------  ------  ------  ------
-  1.  C  0.0000  0.8174  0.7960  0.7732  0.7732 -0.0013 -0.0013
-  2.  N  0.8174  0.0000 -0.0104 -0.0030 -0.0030  0.6337  0.6337
-  3.  H  0.7960 -0.0104  0.0000 -0.0020 -0.0020  0.0001  0.0001
-  4.  H  0.7732 -0.0030 -0.0020  0.0000  0.0020  0.0062  0.0000
-  5.  H  0.7732 -0.0030 -0.0020  0.0020  0.0000  0.0000  0.0062
-  6.  H -0.0013  0.6337  0.0001  0.0062  0.0000  0.0000 -0.0001
-  7.  H -0.0013  0.6337  0.0001  0.0000  0.0062 -0.0001  0.0000
- 
-
-
For example, the table attributes a formal bond order of 0.8174 to the -C(1)-N(2) bond of methylamine, the highest bond order in this -molecule. (The higher value for C(1)-H(3) than for the other -two CH bonds reflects an unsatisfactory aspect of this -method of assessing bond order.) -

- These bond indices are based on different -assumptions, and each has certain advantages and -disadvantages. Caveat emptor! -

-B.6.6 RESONANCE Keyword: Benzene -

- When NBO analysis is performed on a wavefunction that cannot -be satisfactorily localized [i.e., in which one or more NBOs of -the natural Lewis structure fail to achieve -the threshold occupancy (1.90) for a satisfactory -'pair'], the NBO program aborts with a message indicating that -the wavefunction is unsuitable for localized analysis. For example, -when benzene (RHF/STO-3G level, idealized Pople-Gordon geometry) -is treated by the NBO program in default mode, one obtains the output: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
-  2(2)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
------------------------------------------------------------------------------
-
-Only strongly delocalized resonance structures can be found.
-The default procedure is to abort the NBO search.
- 
-
-
When the RESONANCE keyword is activated for this same example, -one obtains a summary of NBO search cycles as shown below: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
-  2(2)    1.90    38.87476   3.12524      6  12   0   3     3      3    0.44
-  3(1)    1.80    38.87476   3.12524      6  12   0   3     3      3    0.44
-  4(2)    1.80    38.87476   3.12524      6  12   0   3     3      3    0.44
-  5(1)    1.70    38.87476   3.12524      6  12   0   3     3      3    0.44
-  6(2)    1.70    38.87476   3.12524      6  12   0   3     3      3    0.44
-  7(1)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
-  8(2)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
-  9(1)    1.50    40.87476   1.12524      6  15   0   0     0      3    0.44
- 10(2)    1.50    40.87476   1.12524      6  15   0   0     0      3    0.44
- 11(1)    1.60    40.87476   1.12524      6  15   0   0     0      3    0.44
------------------------------------------------------------------------------
-
-Structure accepted: RESONANCE keyword permits strongly delocalized structure
-
-
-

- As this table shows, the occupancy threshold was successively -lowered from 1.90 to 1.50 by 0.1e for each cycle, -and the NBO search repeated. In -this case, the 'best' Lewis structure (lowest overall non-Lewis -occupancy, 1.12524e) was found in cycle 7, with occupancy -threshold 1.60e. The NBO program therefore reset the -threshold to this value and calculated -the set of NBOs corresponding to this -'best' Lewis structure, as shown below: -

- 

-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (1.98940) BD ( 1) C 1- C 2      
-               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.8109  0.0097  0.0000
-               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.8109  0.0097  0.0000
-  2. (1.98940) BD ( 1) C 1- C 6      
-               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.4138 -0.6974  0.0000
-               ( 50.00%)   0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.3971  0.7071  0.0000
-  3. (1.66667) BD ( 2) C 1- C 6      
-               ( 50.00%)   0.7071* C 1 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)   0.7071* C 6 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-  4. (1.98977) BD ( 1) C 1- H 7      
-               ( 51.73%)   0.7193* C 1 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615  0.4137  0.7166  0.0000
-               ( 48.27%)   0.6947* H 7 s(100.00%)
-                                        1.0000
-  5. (1.98940) BD ( 1) C 2- C 3      
-               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.4138 -0.6974  0.0000
-               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.3971  0.7071  0.0000
-  6. (1.66667) BD ( 2) C 2- C 3      
-               ( 50.00%)   0.7071* C 2 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)   0.7071* C 3 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-  7. (1.98977) BD ( 1) C 2- H 8      
-               ( 51.73%)   0.7193* C 2 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615 -0.4137  0.7166  0.0000
-               ( 48.27%)   0.6947* H 8 s(100.00%)
-                                        1.0000
-  8. (1.98940) BD ( 1) C 3- C 4      
-               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.3971 -0.7071  0.0000
-               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.4138  0.6974  0.0000
-  9. (1.98977) BD ( 1) C 3- H 9      
-               ( 51.73%)   0.7193* C 3 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615 -0.8275  0.0000  0.0000
-               ( 48.27%)   0.6947* H 9 s(100.00%)
-                                        1.0000
- 10. (1.66667) BD ( 2) C 4- C 5      
-               ( 50.00%)   0.7071* C 4 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)   0.7071* C 5 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
- 11. (1.98940) BD ( 1) C 4- C 5      
-               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.8109 -0.0097  0.0000
-               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.8109 -0.0097  0.0000
- 12. (1.98977) BD ( 1) C 4- H10      
-               ( 51.73%)   0.7193* C 4 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615 -0.4137 -0.7166  0.0000
-               ( 48.27%)   0.6947* H10 s(100.00%)
-                                        1.0000
- 13. (1.98940) BD ( 1) C 5- C 6      
-               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.4138  0.6974  0.0000
-               ( 50.00%)   0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.3971 -0.7071  0.0000
- 14. (1.98977) BD ( 1) C 5- H11      
-               ( 51.73%)   0.7193* C 5 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615  0.4137 -0.7166  0.0000
-               ( 48.27%)   0.6947* H11 s(100.00%)
-                                        1.0000
- 15. (1.98977) BD ( 1) C 6- H12      
-               ( 51.73%)   0.7193* C 6 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000  0.5615  0.8275  0.0000  0.0000
-               ( 48.27%)   0.6947* H12 s(100.00%)
-                                        1.0000
- 16. (1.99995) CR ( 1) C 1             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
- 17. (1.99995) CR ( 1) C 2             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
- 18. (1.99995) CR ( 1) C 3             s(100.00%)
-                                        1.0000  0.0000 -0.0001  0.0000  0.0000
- 19. (1.99995) CR ( 1) C 4             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
- 20. (1.99995) CR ( 1) C 5             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
- 21. (1.99995) CR ( 1) C 6             s(100.00%)
-                                        1.0000  0.0000  0.0001  0.0000  0.0000
- 22. (0.01077) BD*( 1) C 1- C 2      
-               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.8109  0.0097  0.0000
-               ( 50.00%)  -0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.8109  0.0097  0.0000
- 23. (0.01077) BD*( 1) C 1- C 6      
-               ( 50.00%)   0.7071* C 1 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.4138 -0.6974  0.0000
-               ( 50.00%)  -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.3971  0.7071  0.0000
- 24. (0.33333) BD*( 2) C 1- C 6      
-               ( 50.00%)   0.7071* C 1 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)  -0.7071* C 6 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
- 25. (0.01011) BD*( 1) C 1- H 7      
-               ( 48.27%)   0.6947* C 1 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615 -0.4137 -0.7166  0.0000
-               ( 51.73%)  -0.7193* H 7 s(100.00%)
-                                       -1.0000
- 26. (0.01077) BD*( 1) C 2- C 3      
-               ( 50.00%)   0.7071* C 2 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.4138 -0.6974  0.0000
-               ( 50.00%)  -0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.3971  0.7071  0.0000
- 27. (0.33333) BD*( 2) C 2- C 3      
-               ( 50.00%)   0.7071* C 2 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)  -0.7071* C 3 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
- 28. (0.01011) BD*( 1) C 2- H 8      
-               ( 48.27%)   0.6947* C 2 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615  0.4137 -0.7166  0.0000
-               ( 51.73%)  -0.7193* H 8 s(100.00%)
-                                       -1.0000
- 29. (0.01077) BD*( 1) C 3- C 4      
-               ( 50.00%)   0.7071* C 3 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.3971 -0.7071  0.0000
-               ( 50.00%)  -0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.4138  0.6974  0.0000
- 30. (0.01011) BD*( 1) C 3- H 9      
-               ( 48.27%)   0.6947* C 3 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615  0.8275  0.0000  0.0000
-               ( 51.73%)  -0.7193* H 9 s(100.00%)
-                                       -1.0000
- 31. (0.33333) BD*( 2) C 4- C 5      
-               ( 50.00%)   0.7071* C 4 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
-               ( 50.00%)  -0.7071* C 5 s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  1.0000
- 32. (0.01077) BD*( 1) C 4- C 5      
-               ( 50.00%)   0.7071* C 4 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.8109 -0.0097  0.0000
-               ( 50.00%)  -0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.8109 -0.0097  0.0000
- 33. (0.01011) BD*( 1) C 4- H10      
-               ( 48.27%)   0.6947* C 4 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615  0.4137  0.7166  0.0000
-               ( 51.73%)  -0.7193* H10 s(100.00%)
-                                       -1.0000
- 34. (0.01077) BD*( 1) C 5- C 6      
-               ( 50.00%)   0.7071* C 5 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851  0.4138  0.6974  0.0000
-               ( 50.00%)  -0.7071* C 6 s( 34.23%)p 1.92( 65.77%)
-                                        0.0000  0.5851 -0.3971 -0.7071  0.0000
- 35. (0.01011) BD*( 1) C 5- H11      
-               ( 48.27%)   0.6947* C 5 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615 -0.4137  0.7166  0.0000
-               ( 51.73%)  -0.7193* H11 s(100.00%)
-                                       -1.0000
- 36. (0.01011) BD*( 1) C 6- H12      
-               ( 48.27%)   0.6947* C 6 s( 31.53%)p 2.17( 68.47%)
-                                        0.0000 -0.5615 -0.8275  0.0000  0.0000
-               ( 51.73%)  -0.7193* H12 s(100.00%)
-                                       -1.0000
-
-
-

- As one can see from this table, the set of NBOs -obtained by the program corresponds -to one of the two equivalent Kekulée structures, with -reasonably well -localized CC and CH NBOs (1.98940 and 1.98977 -electrons, respectively), but three severely depleted CC -bonds (1.66667e) and corresponding high occupancy -*CC antibonds (0.33333e). Other sections of the NBO -output (not shown) will similarly exhibit the sharp distinctions -between benzene and more 'typical' non-aromatic compounds. -

-

-WARNING -
-

-If you attempt to analyze an open-shell wavefunction with an -ESS method that produces only the "spinless" (spin-averaged) density -matrix, rather than the separate density matrices for -and spin, the job will likely abort, as in the default -benzene example. However, you should not use the RESONANCE -keyword to bypass this abort! NBO analysis of an open-shell -spinless density matrix is a fundamental misuse -of the program. -

-

-B.6.7 NOBOND Keyword -

- The NOBOND keyword forces the NBO program to analyze the -wavefunction in terms of 1-center functions only, thus forcing -a description of the bonding in terms of atomic or -ionic hybrids. The modifications of NBO output that result -from activating this keyword can be illustrated for the -HF molecule (RHF/3-21G//RHF/3-21G level). This molecule -might be described in terms of a polar covalent H-F -bond or in terms of ionic H+ F- interactions. -

- The default NBO analysis of this example is shown below: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90     9.99942   0.00058      1   1   0   3     0      0    0.00
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
---------------------------------------------------------
-  Core                      1.99994 ( 99.997% of   2)
-  Valence Lewis             7.99948 ( 99.994% of   8)
- ==================       ============================
-  Total Lewis               9.99942 ( 99.994% of  10)
- -----------------------------------------------------
-  Valence non-Lewis         0.00000 (  0.000% of  10)
-  Rydberg non-Lewis         0.00058 (  0.006% of  10)
- ==================       ============================
-  Total non-Lewis           0.00058 (  0.006% of  10)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (2.00000) BD ( 1) F 1- H 2      
-               ( 75.22%)   0.8673* F 1 s( 16.31%)p 5.13( 83.69%)
-                                        0.0000  0.4036  0.0158  0.0000  0.0000
-                                        0.0000  0.0000  0.9148  0.0001
-               ( 24.78%)   0.4978* H 2 s(100.00%)
-                                        1.0000  0.0000
-  2. (1.99994) CR ( 1) F 1             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000
-  3. (2.00000) LP ( 1) F 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  1.0000 -0.0013
-                                        0.0000  0.0000  0.0000  0.0000
-  4. (2.00000) LP ( 2) F 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        1.0000 -0.0013  0.0000  0.0000
-  5. (1.99948) LP ( 3) F 1             s( 83.71%)p 0.19( 16.29%)
-                                        0.0000  0.9149 -0.0052  0.0000  0.0000
-                                        0.0000  0.0000 -0.4036 -0.0062
-  6. (0.00002) RY*( 1) F 1             s(  0.00%)p 1.00(100.00%)
-  7. (0.00000) RY*( 2) F 1             s(  0.00%)p 1.00(100.00%)
-  8. (0.00000) RY*( 3) F 1             s(  0.00%)p 1.00(100.00%)
-  9. (0.00000) RY*( 4) F 1             s( 99.97%)p 0.00(  0.03%)
- 10. (0.00056) RY*( 1) H 2             s(100.00%)
-                                        0.0000  1.0000
- 11. (0.00000) BD*( 1) F 1- H 2      
-               ( 24.78%)   0.4978* F 1 s( 16.31%)p 5.13( 83.69%)
-               ( 75.22%)  -0.8673* H 2 s(100.00%)
- 
-
-

-As the output shows, default NBO analysis -leads to a polar covalent description of HF. The -HF bond, NBO 1, is formed from a p-rich -(sp5.13) hybrid on F and the 1s AO on H, -strongly polarized (about 75.22%) toward F. This provides a -satisfactory Lewis structure, describing 99.994% of -the total electron density. -

- When the NOBOND keyword is activated to bypass -the search for 2-center bonds, the NBO output is -modified as shown below: -

- 

-
-
-       /NOBOND / : No two-center NBO search
-
-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.00     9.50378   0.49622      1   0   0   4     0      1    0.75
------------------------------------------------------------------------------
-
-Structure accepted: Search for bonds prevented by NOBOND keyword
-
---------------------------------------------------------
-  Core                      1.99993 ( 99.997% of   2)
-  Valence Lewis             7.50385 ( 93.798% of   8)
- ==================       ============================
-  Total Lewis               9.50378 ( 95.038% of  10)
- -----------------------------------------------------
-  Valence non-Lewis         0.49564 (  4.956% of  10)
-  Rydberg non-Lewis         0.00058 (  0.006% of  10)
- ==================       ============================
-  Total non-Lewis           0.49622 (  4.962% of  10)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (1.99993) CR ( 1) F 1             s(100.00%)p 0.00(  0.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0001  0.0000
-  2. (2.00000) LP ( 1) F 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  1.0000 -0.0013
-                                        0.0000  0.0000  0.0000  0.0000
-  3. (2.00000) LP ( 2) F 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        1.0000 -0.0013  0.0000  0.0000
-  4. (1.99948) LP ( 3) F 1             s( 83.71%)p 0.19( 16.29%)
-                                        0.0000  0.9149 -0.0052  0.0000  0.0000
-                                        0.0000  0.0000 -0.4036 -0.0062
-  5. (1.50436) LP ( 4) F 1             s( 16.31%)p 5.13( 83.69%)
-                                       -0.0001  0.4036  0.0158  0.0000  0.0000
-                                        0.0000  0.0000  0.9148  0.0001
-  6. (0.49564) LP*( 1) H 2             s(100.00%)
-                                        1.0000  0.0000
-  7. (0.00002) RY*( 1) F 1             s(  0.00%)p 1.00(100.00%)
-  8. (0.00000) RY*( 2) F 1             s(  0.00%)p 1.00(100.00%)
-  9. (0.00000) RY*( 3) F 1             s(  0.00%)p 1.00(100.00%)
- 10. (0.00000) RY*( 4) F 1             s( 99.97%)p 0.00(  0.03%)
- 11. (0.00056) RY*( 1) H 2             s(100.00%)
-                                        0.0000  1.0000
- 
-
-

- In this case, the NBO output indicates a rather poor Lewis -structure (4.962% non-Lewis density), with a severely -depleted F- lone pair (NBO 5, the sp5.13 hybrid) -and significant occupancy (about 0.496e) in the 'empty' H+ -1s orbital (NBO 6) of the cation. The NOBOND comparison -would therefore indicate the superiority of a polar -covalent description in this case. -

-B.6.8 3CBOND Keyword: Diborane -

- When the default NBO analysis is applied to diborane or -related electron-deficient compounds, there is a dramatic -failure to represent the electronic distribution in terms of -1- and 2-center functions only. For example, for -B2H6 at the RHF/3-21G//RHF/3-21G level, -the default NBO search (if the RESONANCE keyword is activated -to allow NBO printout) returns -a fractured set of 4 units (two BH2+ and two H- -fragments), with about 2.13 electrons unaccounted for (~15% -non-Lewis occupancy), symptomatic of general breakdown of the -conventional Lewis structure representation. -

- However, when the NBO search is extended to 3-center bonds -by activating the 3CBOND keyword, one obtains -the NBO output shown below: -

- 

-
-
-       /3CBOND / : Search for 3-center bonds
-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    15.94335   0.05665      2   4   2   0     0      0    0.15
-  2(2)    1.90    15.94335   0.05665      2   4   2   0     0      0    0.15
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
-WARNING:  1 low occupancy (<1.9990e) core orbital  found on  B 1
-          1 low occupancy (<1.9990e) core orbital  found on  B 2
-
---------------------------------------------------------
-  Core                      3.99702 ( 99.925% of   4)
-  Valence Lewis            11.94633 ( 99.553% of  12)
- ==================       ============================
-  Total Lewis              15.94335 ( 99.646% of  16)
- -----------------------------------------------------
-  Valence non-Lewis         0.04565 (  0.285% of  16)
-  Rydberg non-Lewis         0.01100 (  0.069% of  16)
- ==================       ============================
-  Total non-Lewis           0.05665 (  0.354% of  16)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (1.98467) 3C ( 1) B 1- B 2- H 3 
-               ( 26.43%)   0.5141* B 1 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 26.43%)   0.5141* B 2 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000 -0.5657  0.0007
-               ( 47.14%)   0.6866* H 3 s(100.00%)
-                                        1.0000  0.0066
-  2. (1.98467) 3C ( 1) B 1- B 2- H 4 
-               ( 26.43%)   0.5141* B 1 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124  0.7067  0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 26.43%)   0.5141* B 2 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124  0.7067  0.0245
-                                        0.0000  0.0000 -0.5657  0.0007
-               ( 47.14%)   0.6866* H 4 s(100.00%)
-                                        1.0000  0.0066
-  3. (1.99425) BD ( 1) B 1- H 6      
-               ( 48.80%)   0.6985* B 1 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                        0.7067 -0.0243 -0.4239 -0.0222
-               ( 51.20%)   0.7156* H 6 s(100.00%)
-                                        1.0000  0.0004
-  4. (1.99425) BD ( 1) B 1- H 7      
-               ( 48.80%)   0.6985* B 1 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                       -0.7067  0.0243 -0.4239 -0.0222
-               ( 51.20%)   0.7156* H 7 s(100.00%)
-                                        1.0000  0.0004
-  5. (1.99425) BD ( 1) B 2- H 5      
-               ( 48.80%)   0.6985* B 2 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                       -0.7067  0.0243  0.4239  0.0222
-               ( 51.20%)   0.7156* H 5 s(100.00%)
-                                        1.0000  0.0004
-  6. (1.99425) BD ( 1) B 2- H 8      
-               ( 48.80%)   0.6985* B 2 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                        0.7067 -0.0243  0.4239  0.0222
-               ( 51.20%)   0.7156* H 8 s(100.00%)
-                                        1.0000  0.0004
-  7. (1.99851) CR ( 1) B 1             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0002  0.0000  0.0000  0.0000
-                                        0.0000  0.0000 -0.0007  0.0000
-  8. (1.99851) CR ( 1) B 2             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0002  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0007  0.0000
-  9. (0.00147) RY*( 1) B 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0344  0.9994  0.0000  0.0000
- 10. (0.00080) RY*( 2) B 1             s(  4.02%)p23.87( 95.98%)
-                                        0.0000  0.0245  0.1990  0.0000  0.0000
-                                        0.0000  0.0000 -0.0214  0.9795
- 11. (0.00002) RY*( 3) B 1             s( 96.01%)p 0.04(  3.99%)
- 12. (0.00000) RY*( 4) B 1             s(  0.00%)p 1.00(100.00%)
- 13. (0.00147) RY*( 1) B 2             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0344  0.9994  0.0000  0.0000
- 14. (0.00080) RY*( 2) B 2             s(  4.02%)p23.87( 95.98%)
-                                        0.0000  0.0245  0.1990  0.0000  0.0000
-                                        0.0000  0.0000  0.0214 -0.9795
- 15. (0.00002) RY*( 3) B 2             s( 96.01%)p 0.04(  3.99%)
- 16. (0.00000) RY*( 4) B 2             s(  0.00%)p 1.00(100.00%)
- 17. (0.00181) RY*( 1) H 3             s(100.00%)
-                                       -0.0066  1.0000
- 18. (0.00181) RY*( 1) H 4             s(100.00%)
-                                       -0.0066  1.0000
- 19. (0.00070) RY*( 1) H 5             s(100.00%)
-                                       -0.0004  1.0000
- 20. (0.00070) RY*( 1) H 6             s(100.00%)
-                                       -0.0004  1.0000
- 21. (0.00070) RY*( 1) H 7             s(100.00%)
-                                       -0.0004  1.0000
- 22. (0.00070) RY*( 1) H 8             s(100.00%)
-                                       -0.0004  1.0000
- 23. (0.01464) 3C*( 1) B 1- B 2- H 3 
-               ( 23.57%)   0.4855* B 1 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 23.57%)  -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 52.86%)  -0.7271* H 3 s(100.00%)
-                                        1.0000  0.0066
- 24. (0.00026) 3C*( 1) B 1- B 2- H 3 
-               ( 50.00%)   0.7071* B 1 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
-                                        0.0000  0.0000 -0.5657  0.0007
-               ( 50.00%)  -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124  0.7067  0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               (  0.00%)   0.0000* H 3 s(  0.00%)
-                                        0.0000  0.0000
- 25. (0.01464) 3C*( 1) B 1- B 2- H 4 
-               ( 23.57%)   0.4855* B 1 s( 18.00%)p 4.55( 82.00%)
-                                        0.0005  0.4241  0.0124  0.7067  0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 23.57%)  -0.4855* B 2 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               ( 52.86%)  -0.7271* H 4 s(100.00%)
-                                        1.0000  0.0066
- 26. (0.00026) 3C*( 1) B 1- B 2- H 4 
-               ( 50.00%)   0.7071* B 1 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000 -0.5657  0.0007
-               ( 50.00%)  -0.7071* B 2 s( 18.00%)p 4.55( 82.00%)
-                                       -0.0005 -0.4241 -0.0124 -0.7067 -0.0245
-                                        0.0000  0.0000  0.5657 -0.0007
-               (  0.00%)   0.0000* H 4 s(  0.00%)
-                                        0.0000  0.0000
- 27. (0.00396) BD*( 1) B 2- H 5      
-               ( 51.20%)   0.7156* B 2 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                       -0.7067  0.0243  0.4239  0.0222
-               ( 48.80%)  -0.6985* H 5 s(100.00%)
-                                        1.0000  0.0004
- 28. (0.00396) BD*( 1) B 2- H 8      
-               ( 51.20%)   0.7156* B 2 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                        0.7067 -0.0243  0.4239  0.0222
-               ( 48.80%)  -0.6985* H 8 s(100.00%)
-                                        1.0000  0.0004
- 29. (0.00396) BD*( 1) B 1- H 6      
-               ( 51.20%)   0.7156* B 1 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                        0.7067 -0.0243 -0.4239 -0.0222
-               ( 48.80%)  -0.6985* H 6 s(100.00%)
-                                        1.0000  0.0004
- 30. (0.00396) BD*( 1) B 1- H 7      
-               ( 51.20%)   0.7156* B 1 s( 31.98%)p 2.13( 68.02%)
-                                       -0.0002  0.5655 -0.0061  0.0000  0.0000
-                                       -0.7067  0.0243 -0.4239 -0.0222
-               ( 48.80%)  -0.6985* H 7 s(100.00%)
-                                        1.0000  0.0004
- 
-
-

- The resulting NBO Lewis structure has improved significantly -[only 0.057e (0.35%) non-Lewis occupancy]. The structure includes -the expected 3-center B-H-B bonds (NBOs 1, 2), each with reasonably -high occupancy (1.9847e). Each 3-c bond is composed of p-rich -(sp4.55) boron hybrids and the hydrogen 1s NAO, -with about 47.14% of the orbital density on the central hydrogen. Note -that each 3-center bond NBO is associated with two 3-c antibond -NBOs (viz., NBOs 23, 24 for the first 3-c bond, NBO 1), which contribute -in distinct ways to delocalization interactions. Of course, the -accuracy of any molecular Lewis structure might be improved -slightly by extending the NBO search to 3-center bonds (thus -allowing greater variational flexibility to maximize occupancy), -but this example illustrates the kind of qualitative improvement -that indicates when 3-center bonds are needed -in the zeroth-order picture of the bonding. -

- Note that -the NBO 3-c label may frequently have the wrong 'connectivity' (as -in the present case, e.g., where "B 1- B 2- H 3" is written -instead of the more reasonable "B 1- H 3- B 2"). This is a -consequence of the fact that the NBO algorithms have no inkling -of the positions of the atoms in space, and thus of which -label is more 'reasonable.' -

-B.6.9 NBO Directed Search ($CHOOSE Keylist) -

- To illustrate the $CHOOSE keylist for a directed NBO search, we -again make use of the methylamine example (Section A.3). The vicinal -nN *CH delocalization, to which attention -has been repeatedly called in the examples, -may be associated, in resonance theory terms, -with the "double-bond, no-bond" resonance structure shown below: -

- -
-

-To investigate the suitability of this resonance structure -for describing the methylamine wavefunction, we would -specify the $CHOOSE keylist (Section B.4) as follows: - 

-     $CHOOSE            !double-bond, no-bond resonance
-        LONE  3  1  END
-        BOND  S 1 4  S 1 5  D 1 2  S 2 6  S 2 7  END
-     $END
-
-
When this is included in the input file, the NBO program produces -the output shown below: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    16.66741   1.33259      2   6   0   1     1      2    0.95
------------------------------------------------------------------------------
-
-Structure accepted: NBOs selected via the $CHOOSE keylist
-
-WARNING:  1 low occupancy (<1.9990e) core orbital  found on  C 1
-
---------------------------------------------------------
-  Core                      3.99853 ( 99.963% of   4)
-  Valence Lewis            12.66888 ( 90.492% of  14)
- ==================       ============================
-  Total Lewis              16.66741 ( 92.597% of  18)
- -----------------------------------------------------
-  Valence non-Lewis         1.30491 (  7.249% of  18)
-  Rydberg non-Lewis         0.02768 (  0.154% of  18)
- ==================       ============================
-  Total non-Lewis           1.33259 (  7.403% of  18)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (1.95945) BD ( 1) C 1- N 2      
-               (  7.66%)   0.2768* C 1 s(  0.63%)p99.99( 99.37%)
-                                       -0.0001 -0.0770 -0.0186  0.5107 -0.0551
-                                        0.8520 -0.0632  0.0000  0.0000
-               ( 92.34%)   0.9609* N 2 s( 19.31%)p 4.18( 80.69%)
-                                        0.0000  0.4395 -0.0001 -0.1175 -0.0067
-                                        0.8905 -0.0110  0.0000  0.0000
-  2. (1.93778) BD ( 2) C 1- N 2      
-               ( 39.14%)   0.6256* C 1 s( 36.80%)p 1.72( 63.20%)
-                                       -0.0004 -0.6055 -0.0371 -0.7047 -0.0632
-                                        0.3594 -0.0471  0.0000  0.0000
-               ( 60.86%)   0.7801* N 2 s( 19.33%)p 4.17( 80.67%)
-                                       -0.0001 -0.4396  0.0011  0.8364 -0.0016
-                                        0.3271 -0.0137  0.0000  0.0000
-  3. (1.98365) BD ( 1) C 1- H 4      
-               ( 61.02%)   0.7811* C 1 s( 31.10%)p 2.22( 68.90%)
-                                        0.0001  0.5577  0.0006 -0.3480  0.0095
-                                        0.2603  0.0094  0.7070 -0.0103
-               ( 38.98%)   0.6244* H 4 s(100.00%)
-                                        1.0000  0.0008
-  4. (1.98365) BD ( 1) C 1- H 5      
-               ( 61.02%)   0.7811* C 1 s( 31.10%)p 2.22( 68.90%)
-                                        0.0001  0.5577  0.0006 -0.3480  0.0095
-                                        0.2603  0.0094 -0.7070  0.0103
-               ( 38.98%)   0.6244* H 5 s(100.00%)
-                                        1.0000  0.0008
-  5. (1.99491) BD ( 1) N 2- H 6      
-               ( 68.46%)   0.8274* N 2 s( 30.67%)p 2.26( 69.33%)
-                                        0.0000  0.5538  0.0005  0.3785  0.0165
-                                       -0.2232  0.0044 -0.7070 -0.0093
-               ( 31.54%)   0.5616* H 6 s(100.00%)
-                                        1.0000  0.0031
-  6. (1.99491) BD ( 1) N 2- H 7      
-               ( 68.46%)   0.8274* N 2 s( 30.67%)p 2.26( 69.33%)
-                                        0.0000  0.5538  0.0005  0.3785  0.0165
-                                       -0.2232  0.0044  0.7070  0.0093
-               ( 31.54%)   0.5616* H 7 s(100.00%)
-                                        1.0000  0.0031
-  7. (1.99900) CR ( 1) C 1             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0003  0.0000 -0.0001  0.0000
-                                        0.0002  0.0000  0.0000  0.0000
-  8. (1.99953) CR ( 1) N 2             s(100.00%)p 0.00(  0.00%)
-                                        1.0000 -0.0001  0.0000  0.0001  0.0000
-                                        0.0000  0.0000  0.0000  0.0000
-  9. (0.81453) LP ( 1) H 3             s(100.00%)
-                                        1.0000  0.0000
- 10. (0.01893) RY*( 1) C 1             s( 10.61%)p 8.42( 89.39%)
-                                        0.0000 -0.0737  0.3173 -0.0090  0.7223
-                                        0.0971  0.6021  0.0000  0.0000
- 11. (0.00034) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0146  0.9999
- 12. (0.00025) RY*( 3) C 1             s( 57.37%)p 0.74( 42.63%)
-                                        0.0000 -0.0012  0.7575 -0.0176  0.1886
-                                       -0.0071 -0.6248  0.0000  0.0000
- 13. (0.00002) RY*( 4) C 1             s( 32.38%)p 2.09( 67.62%)
- 14. (0.00117) RY*( 1) N 2             s(  1.48%)p66.74( 98.52%)
-                                        0.0000 -0.0067  0.1213  0.0062  0.0380
-                                        0.0166  0.9917  0.0000  0.0000
- 15. (0.00044) RY*( 2) N 2             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000 -0.0132  0.9999
- 16. (0.00038) RY*( 3) N 2             s( 33.41%)p 1.99( 66.59%)
-                                        0.0000  0.0133  0.5779  0.0087 -0.8150
-                                       -0.0120 -0.0392  0.0000  0.0000
- 17. (0.00002) RY*( 4) N 2             s( 65.14%)p 0.54( 34.86%)
- 18. (0.00177) RY*( 1) H 3             s(100.00%)
-                                        0.0000  1.0000
- 19. (0.00096) RY*( 1) H 4             s(100.00%)
-                                       -0.0008  1.0000
- 20. (0.00096) RY*( 1) H 5             s(100.00%)
-                                       -0.0008  1.0000
- 21. (0.00122) RY*( 1) H 6             s(100.00%)
-                                       -0.0031  1.0000
- 22. (0.00122) RY*( 1) H 7             s(100.00%)
-                                       -0.0031  1.0000
- 23. (1.02290) BD*( 1) C 1- N 2      
-               ( 92.34%)   0.9609* C 1 s(  0.63%)p99.99( 99.37%)
-                                       -0.0001 -0.0770 -0.0186  0.5107 -0.0551
-                                        0.8520 -0.0632  0.0000  0.0000
-               (  7.66%)  -0.2768* N 2 s( 19.31%)p 4.18( 80.69%)
-                                        0.0000  0.4395 -0.0001 -0.1175 -0.0067
-                                        0.8905 -0.0110  0.0000  0.0000
- 24. (0.22583) BD*( 2) C 1- N 2      
-               ( 60.86%)   0.7801* C 1 s( 36.80%)p 1.72( 63.20%)
-                                       -0.0004 -0.6055 -0.0371 -0.7047 -0.0632
-                                        0.3594 -0.0471  0.0000  0.0000
-               ( 39.14%)  -0.6256* N 2 s( 19.33%)p 4.17( 80.67%)
-                                       -0.0001 -0.4396  0.0011  0.8364 -0.0016
-                                        0.3271 -0.0137  0.0000  0.0000
- 25. (0.01415) BD*( 1) C 1- H 4      
-               ( 38.98%)   0.6244* C 1 s( 31.10%)p 2.22( 68.90%)
-                                       -0.0001 -0.5577 -0.0006  0.3480 -0.0095
-                                       -0.2603 -0.0094 -0.7070  0.0103
-               ( 61.02%)  -0.7811* H 4 s(100.00%)
-                                       -1.0000 -0.0008
- 26. (0.01415) BD*( 1) C 1- H 5      
-               ( 38.98%)   0.6244* C 1 s( 31.10%)p 2.22( 68.90%)
-                                       -0.0001 -0.5577 -0.0006  0.3480 -0.0095
-                                       -0.2603 -0.0094  0.7070 -0.0103
-               ( 61.02%)  -0.7811* H 5 s(100.00%)
-                                       -1.0000 -0.0008
- 27. (0.01394) BD*( 1) N 2- H 6      
-               ( 31.54%)   0.5616* N 2 s( 30.67%)p 2.26( 69.33%)
-                                        0.0000 -0.5538 -0.0005 -0.3785 -0.0165
-                                        0.2232 -0.0044  0.7070  0.0093
-               ( 68.46%)  -0.8274* H 6 s(100.00%)
-                                       -1.0000 -0.0031
- 28. (0.01394) BD*( 1) N 2- H 7      
-               ( 31.54%)   0.5616* N 2 s( 30.67%)p 2.26( 69.33%)
-                                        0.0000 -0.5538 -0.0005 -0.3785 -0.0165
-                                        0.2232 -0.0044 -0.7070 -0.0093
-               ( 68.46%)  -0.8274* H 7 s(100.00%)
-                                       -1.0000 -0.0031
- 
-
-

- One can see that the $CHOOSE resonance structure is significantly -inferior to the principal resonance structure -found by the default NBO search in -Section A.3. About 1.333e, or 7.4% of the electron density, -is found in non-Lewis NBOs of -the $CHOOSE structure (compared to 0.05e, or 0.3%, for -the principal structure). Particularly defective is the hydride -'lone pair' (NBO 9), which has less than half the -expected occupancy (0.81453e). The C-N bond (NBO 1) is seen -to be more than 92% polarized toward N, indicative of essential -lone pair character. -

- Note that structural elements shared by the two resonance -structures (e.g., the two N-H bonds, which are common to -both structures) need not have identical -forms, since each detail of the NBOs -is optimized with respect to the overall structure. -

-B.6.10 NBO Energetic Analysis ($DEL Keylist) -

- The NBO energetic analysis with deletions ($DEL keylist) will be -illustrated with two simple examples for RHF/3-21G methylamine -(Section A.3). -

- The first example is the "NOSTAR" option (type 4, -Section B.5), requesting deletion -of all non-Lewis orbitals, and hence leading to the energy of the -idealized natural Lewis structure. The $DEL keylist in this case is - 

-     $DEL  NOSTAR  $END
-
-
This leads to the output shown below: -

- 

-
-NOSTAR: Delete all Rydberg/antibond NBOs
-Deletion of the following orbitals from the NBO Fock matrix:
-  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28
-
-Occupations of bond orbitals:
-
-      Orbital                   No deletions   This deletion   Change
-------------------------------------------------------------------------------
-  1. BD ( 1) C 1- N 2               1.99858        2.00000    0.00142
-  2. BD ( 1) C 1- H 3               1.99860        2.00000    0.00140
-  3. BD ( 1) C 1- H 4               1.99399        2.00000    0.00601
-  4. BD ( 1) C 1- H 5               1.99399        2.00000    0.00601
-  5. BD ( 1) N 2- H 6               1.99442        2.00000    0.00558
-  6. BD ( 1) N 2- H 7               1.99442        2.00000    0.00558
-  7. CR ( 1) C 1                    1.99900        2.00000    0.00100
-  8. CR ( 1) N 2                    1.99953        2.00000    0.00047
-  9. LP ( 1) N 2                    1.97795        2.00000    0.02205
- 10. RY*( 1) C 1                    0.00105        0.00000   -0.00105
- 11. RY*( 2) C 1                    0.00034        0.00000   -0.00034
- 12. RY*( 3) C 1                    0.00022        0.00000   -0.00022
- 13. RY*( 4) C 1                    0.00002        0.00000   -0.00002
- 14. RY*( 1) N 2                    0.00116        0.00000   -0.00116
- 15. RY*( 2) N 2                    0.00044        0.00000   -0.00044
- 16. RY*( 3) N 2                    0.00038        0.00000   -0.00038
- 17. RY*( 4) N 2                    0.00002        0.00000   -0.00002
- 18. RY*( 1) H 3                    0.00178        0.00000   -0.00178
- 19. RY*( 1) H 4                    0.00096        0.00000   -0.00096
- 20. RY*( 1) H 5                    0.00096        0.00000   -0.00096
- 21. RY*( 1) H 6                    0.00122        0.00000   -0.00122
- 22. RY*( 1) H 7                    0.00122        0.00000   -0.00122
- 23. BD*( 1) C 1- N 2               0.00016        0.00000   -0.00016
- 24. BD*( 1) C 1- H 3               0.01569        0.00000   -0.01569
- 25. BD*( 1) C 1- H 4               0.00769        0.00000   -0.00769
- 26. BD*( 1) C 1- H 5               0.00769        0.00000   -0.00769
- 27. BD*( 1) N 2- H 6               0.00426        0.00000   -0.00426
- 28. BD*( 1) N 2- H 7               0.00426        0.00000   -0.00426
-
-NEXT STEP:  Evaluate the energy of the new density matrix
-            that has been constructed from the deleted NBO
-            Fock matrix by doing one SCF cycle.
-
-------------------------------------------------------------------------------
-  Energy of deletion :        -94.618081014
-    Total SCF energy :        -94.679444944
-                         -------------------
-       Energy change :          0.061364 a.u.,          38.506 kcal/mol
-
-
-

- In the output above, the NBO program first enumerates the 19 NBOs -to be deleted by the "NOSTAR" request, then gives the complete list -of NBOs with their occupancies before ("no deletions") and after -("this deletion") deletions, with the -net change for each. For this NOSTAR deletion, each of the -nine Lewis NBOs (1-9) necessarily gets 2.0000 electrons, and each -of the non-Lewis NBOs (10-28) gets occupancy 0.0000. The program -than reports the energy (-94.618081 a.u.) obtained from a single -pass through the SCF evaluator with the modified density matrix. In -this case, deletion of the 19 non-Lewis orbitals led to an energy -change of only 0.061364 a.u. (38.5 kcal/mol), less than 0.07% of the -total energy. -

- The next example is a more selective set of deletions between -'chemical fragments' (type 9), selected by the $DEL keylist input -shown below: - 

-     $DEL 
-        ZERO  2  ATOM BLOCKS
-                 4  BY  3
-                    1  3  4  5
-                    2  6  7
-                 3  BY  4
-                    2  6  7
-                    1  3  4  5
-     $END
-
-
This specifies removal of all delocalizing interactions from -Lewis NBOs of the methyl fragment (atoms 1,3,4,5) into non-Lewis -NBOs of the amine fragment (atoms 2,6,7), or vice versa. The -NBO output for this example is shown below: -

- 

-
-Zero delocalization from NBOs localized on atoms:
-   1   3   4   5
-to NBOs localized on atoms:
-   2   6   7
-    (NBOs in common to the two groups of atoms left out)
-Zero delocalization from NBOs localized on atoms:
-   2   6   7
-to NBOs localized on atoms:
-   1   3   4   5
-    (NBOs in common to the two groups of atoms left out)
-Deletion of the NBO Fock matrix elements between orbitals:
-   2   3   4   7
-and orbitals:
-  14  15  16  17  21  22  27  28
-Deletion of the NBO Fock matrix elements between orbitals:
-   5   6   8   9
-and orbitals:
-  10  11  12  13  18  19  20  24  25  26
-
-Occupations of bond orbitals:
-
-      Orbital                   No deletions   This deletion   Change
-------------------------------------------------------------------------------
-  1. BD ( 1) C 1- N 2               1.99858        1.99860    0.00002
-  2. BD ( 1) C 1- H 3               1.99860        1.99937    0.00077
-  3. BD ( 1) C 1- H 4               1.99399        1.99911    0.00512
-  4. BD ( 1) C 1- H 5               1.99399        1.99911    0.00512
-  5. BD ( 1) N 2- H 6               1.99442        1.99979    0.00537
-  6. BD ( 1) N 2- H 7               1.99442        1.99979    0.00537
-  7. CR ( 1) C 1                    1.99900        1.99919    0.00019
-  8. CR ( 1) N 2                    1.99953        1.99974    0.00021
-  9. LP ( 1) N 2                    1.97795        1.99996    0.02201
- 10. RY*( 1) C 1                    0.00105        0.00016   -0.00090
- 11. RY*( 2) C 1                    0.00034        0.00000   -0.00033
- 12. RY*( 3) C 1                    0.00022        0.00002   -0.00020
- 13. RY*( 4) C 1                    0.00002        0.00002    0.00000
- 14. RY*( 1) N 2                    0.00116        0.00004   -0.00112
- 15. RY*( 2) N 2                    0.00044        0.00000   -0.00044
- 16. RY*( 3) N 2                    0.00038        0.00003   -0.00035
- 17. RY*( 4) N 2                    0.00002        0.00001   -0.00001
- 18. RY*( 1) H 3                    0.00178        0.00088   -0.00090
- 19. RY*( 1) H 4                    0.00096        0.00057   -0.00038
- 20. RY*( 1) H 5                    0.00096        0.00057   -0.00038
- 21. RY*( 1) H 6                    0.00122        0.00057   -0.00065
- 22. RY*( 1) H 7                    0.00122        0.00057   -0.00065
- 23. BD*( 1) C 1- N 2               0.00016        0.00034    0.00018
- 24. BD*( 1) C 1- H 3               0.01569        0.00027   -0.01542
- 25. BD*( 1) C 1- H 4               0.00769        0.00055   -0.00714
- 26. BD*( 1) C 1- H 5               0.00769        0.00055   -0.00714
- 27. BD*( 1) N 2- H 6               0.00426        0.00009   -0.00417
- 28. BD*( 1) N 2- H 7               0.00426        0.00009   -0.00417
-
-NEXT STEP:  Evaluate the energy of the new density matrix
-            that has been constructed from the deleted NBO
-            Fock matrix by doing one SCF cycle.
-
-------------------------------------------------------------------------------
-  Energy of deletion :        -94.635029232
-    Total SCF energy :        -94.679444944
-                         -------------------
-       Energy change :          0.044416 a.u.,          27.871 kcal/mol
-
-
-

- The output first lists the various orbitals and Fock matrix -elements affected by this deletion, then the 'before' and 'after' -occupancies and net changes for each NBO. In this case, one can -see that the principal effect of the deletion was increased occupancy -(+0.022) of the nitrogen lone pair, NBO 9, and depleted occupancy -(-0.015) of the antiperiplanar *C1H3 -antibond, NBO 24, with somewhat lesser depletion (-0.007) -of the other two C-H antibonds. The total energy change (loss of -delocalization energy) associated with this deletion -was 27.9 kcal/mol. -

- To further pinpoint the source of this delocalization, one could -do more selective deletions of individual orbitals or Fock -matrix elements. For example, if one uses -deletion type 2 (deletion of a single -Fock matrix element, Section B.5.2) to delete the -(9,24) element associated with the -nN *C1H3 interaction, one finds -a deletion energy of 7.06 kcal/mol associated with this -interaction alone. [This value may be compared with the simple second-order -perturbative estimate (8.13 kcal/mol) of the -nN *C1H3 (924) interaction -that was noted in Section A.3.5.] -

-B.6.11 Open-Shell UHF Output: Methyl Radical -

- Open-shell NBO output will be illustrated with the simple -example of the planar methyl radical (CH3), treated at the UHF/6-31G* -level (RCH = 1.0736 Å). In -the open-shell case, one obtains -two separate NPA and NBO listings, one for the and one for -the spin set, corresponding to the "different Lewis structures -for different spins" description. A portion of the NBO output for -the spin manifold is reproduced below: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS, alpha spin orbitals:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    0.90     4.99903   0.00097      1   3   0   1     0      0    0.00
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
---------------------------------------------------------
-  Core                      0.99984 ( 99.984% of   1)
-  Valence Lewis             3.99919 ( 99.980% of   4)
- ==================       ============================
-  Total Lewis               4.99903 ( 99.981% of   5)
- -----------------------------------------------------
-  Valence non-Lewis         0.00081 (  0.016% of   5)
-  Rydberg non-Lewis         0.00016 (  0.003% of   5)
- ==================       ============================
-  Total non-Lewis           0.00097 (  0.019% of   5)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (0.99973) BD ( 1) C 1- H 2      
-               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000  0.5772 -0.0070  0.0000 -0.4076
-                                       -0.0110  0.7060  0.0191  0.0000  0.0000
-                                       -0.0338  0.0000  0.0000 -0.0195 -0.0090
-               ( 38.86%)   0.6233* H 2 s(100.00%)
-                                        1.0000  0.0080
-  2. (0.99973) BD ( 1) C 1- H 3      
-               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000  0.5772 -0.0070  0.0000 -0.4076
-                                       -0.0110 -0.7060 -0.0191  0.0000  0.0000
-                                        0.0338  0.0000  0.0000 -0.0195 -0.0090
-               ( 38.86%)   0.6233* H 3 s(100.00%)
-                                        1.0000  0.0080
-  3. (0.99973) BD ( 1) C 1- H 4      
-               ( 61.14%)   0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000  0.5772 -0.0070  0.0000  0.8153
-                                        0.0221  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0391 -0.0090
-               ( 38.86%)   0.6233* H 4 s(100.00%)
-                                        1.0000  0.0080
-  4. (0.99984) CR ( 1) C 1             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-  5. (1.00000) LP ( 1) C 1             s(  0.00%)p 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.9978 -0.0668
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-  6. (0.00000) RY*( 1) C 1             s(100.00%)p 0.00(  0.00%)d 0.00(  0.00%)
-  7. (0.00000) RY*( 2) C 1             s(100.00%)
-  8. (0.00000) RY*( 3) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
-  9. (0.00000) RY*( 4) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
- 10. (0.00000) RY*( 5) C 1             s(  0.00%)p 1.00(100.00%)
- 11. (0.00000) RY*( 6) C 1             s(  0.00%)p 1.00(  0.23%)d99.99( 99.77%)
- 12. (0.00000) RY*( 7) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 13. (0.00000) RY*( 8) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 14. (0.00000) RY*( 9) C 1             s(  0.00%)p 1.00(  0.23%)d99.99( 99.77%)
- 15. (0.00000) RY*(10) C 1             s(  0.02%)p 0.00(  0.00%)d99.99( 99.98%)
- 16. (0.00005) RY*( 1) H 2             s(100.00%)
- 17. (0.00005) RY*( 1) H 3             s(100.00%)
- 18. (0.00005) RY*( 1) H 4             s(100.00%)
- 19. (0.00027) BD*( 1) C 1- H 2      
-               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000 -0.5772  0.0070  0.0000  0.4076
-                                        0.0110 -0.7060 -0.0191  0.0000  0.0000
-                                        0.0338  0.0000  0.0000  0.0195  0.0090
-               ( 61.14%)  -0.7819* H 2 s(100.00%)
-                                       -1.0000 -0.0080
- 20. (0.00027) BD*( 1) C 1- H 3      
-               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000 -0.5772  0.0070  0.0000  0.4076
-                                        0.0110  0.7060  0.0191  0.0000  0.0000
-                                       -0.0338  0.0000  0.0000  0.0195  0.0090
-               ( 61.14%)  -0.7819* H 3 s(100.00%)
-                                       -1.0000 -0.0080
- 21. (0.00027) BD*( 1) C 1- H 4      
-               ( 38.86%)   0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00(  0.16%)
-                                        0.0000 -0.5772  0.0070  0.0000 -0.8153
-                                       -0.0221  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000 -0.0391  0.0090
-               ( 61.14%)  -0.7819* H 4 s(100.00%)
-                                       -1.0000 -0.0080
-
-
-

- As can be seen in the output, the NBO spin-orbital -occupancy threshold was set at 0.90 (rather than 1.90), and the -occupancies of Lewis spin-NBOs (1-5) are about 1.0000, but -other aspects of the output are familiar. Note the slight admixture -of d-character (0.16%) in the CH bond hybrids -(NBOs 1-3), whereas the out-of-plane radical non-bonded orbital (NBO 5) has -pure p-character. -

- The NBO output for the ('ionized') spin set then follows: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS, beta spin orbitals:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    0.90     3.99981   0.00019      1   3   0   0     0      0    0.00
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
---------------------------------------------------------
-  Core                      0.99985 ( 99.985% of   1)
-  Valence Lewis             2.99996 ( 99.999% of   3)
- ==================       ============================
-  Total Lewis               3.99981 ( 99.995% of   4)
- -----------------------------------------------------
-  Valence non-Lewis         0.00002 (  0.000% of   4)
-  Rydberg non-Lewis         0.00017 (  0.004% of   4)
- ==================       ============================
-  Total non-Lewis           0.00019 (  0.005% of   4)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (0.99999) BD ( 1) C 1- H 2      
-               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-                                        0.0000  0.5762  0.0080  0.0000 -0.4076
-                                       -0.0125  0.7059  0.0217  0.0000  0.0000
-                                       -0.0345  0.0000  0.0000 -0.0199 -0.0350
-               ( 44.20%)   0.6649* H 2 s(100.00%)
-                                        1.0000 -0.0069
-  2. (0.99999) BD ( 1) C 1- H 3      
-               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-                                        0.0000  0.5762  0.0080  0.0000 -0.4076
-                                       -0.0125 -0.7059 -0.0217  0.0000  0.0000
-                                        0.0345  0.0000  0.0000 -0.0199 -0.0350
-               ( 44.20%)   0.6649* H 3 s(100.00%)
-                                        1.0000 -0.0069
-  3. (0.99999) BD ( 1) C 1- H 4      
-               ( 55.80%)   0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-                                        0.0000  0.5762  0.0080  0.0000  0.8151
-                                        0.0251  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0399 -0.0350
-               ( 44.20%)   0.6649* H 4 s(100.00%)
-                                        1.0000 -0.0069
-  4. (0.99985) CR ( 1) C 1             s(100.00%)
-                                        1.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-  5. (0.00002) LP*( 1) C 1             s( 10.35%)p 0.00(  0.00%)d 8.66( 89.65%)
-  6. (0.00000) RY*( 1) C 1             s( 98.99%)p 0.00(  0.00%)d 0.01(  1.01%)
-  7. (0.00000) RY*( 2) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
-  8. (0.00000) RY*( 3) C 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
-  9. (0.00000) RY*( 4) C 1             s(  0.00%)p 1.00(100.00%)
- 10. (0.00000) RY*( 5) C 1             s(  0.00%)p 1.00(100.00%)
- 11. (0.00000) RY*( 6) C 1             s(  0.00%)p 1.00(  0.24%)d99.99( 99.76%)
- 12. (0.00000) RY*( 7) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 13. (0.00000) RY*( 8) C 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 14. (0.00000) RY*( 9) C 1             s(  0.00%)p 1.00(  0.24%)d99.99( 99.76%)
- 15. (0.00000) RY*(10) C 1             s( 91.02%)p 0.00(  0.00%)d 0.10(  8.98%)
- 16. (0.00006) RY*( 1) H 2             s(100.00%)
- 17. (0.00006) RY*( 1) H 3             s(100.00%)
- 18. (0.00006) RY*( 1) H 4             s(100.00%)
- 19. (0.00000) BD*( 1) C 1- H 2      
-               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-               ( 55.80%)  -0.7470* H 2 s(100.00%)
- 20. (0.00000) BD*( 1) C 1- H 3      
-               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-               ( 55.80%)  -0.7470* H 3 s(100.00%)
- 21. (0.00000) BD*( 1) C 1- H 4      
-               ( 44.20%)   0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01(  0.28%)
-               ( 55.80%)  -0.7470* H 4 s(100.00%)
-
-
-

- The principal difference to be seen is that the radical -orbital (NBO 5) is essentially empty in this spin set, and -the polarization of the CH bonds is somewhat altered -(about 55.8% on the C atom in the set set, -vs. 61.1% in the set). [In other cases, the - and NBO Lewis structures might differ even -in the number and location of 1-c (non-bonding) and 2-c (bond) -structural elements.] Note that the overall quality of the open-shell -natural Lewis structure description (> 99.9%) is -comparable to that of ordinary closed-shell molecules, and the -interpretation of the NBO output follows -familiar lines. -

-

-WARNING -
-

-You should not attempt to analyze an open-shell wavefunction with an -ESS method that produces only the "spinless" (spin-averaged) density -matrix, rather than the separate density matrices for -and spin. Although NAOs and their total populations are -calculated correctly from the spinless density matrix, NBOs -and NLMOs are not. NBO analysis of an open-shell -spinless density matrix is a fundamental misuse -of the program. -

-B.6.12 Effective Core Potential: Cu2 Dimer -

- To illustrate some of the variations of NBO output associated -with use of effective core potentials (ECP) and inclusion of -d orbitals, we use the example of the copper dimer Cu2 -(R = 2.2195 Å), -treated at the RHF level with a Hay-Wadt ECP and valence DZ -basis (RHF/LANL1DZ), carried out with -the GAUSSIAN-88 system. (The wavefunction returned by GAUSSIAN-88 -in this case corresponds -to an excited state configuration of Cu2.) Since the -NBO program communicates directly with -the ESS program for details -about the ECP, no special keywords are necessary. -

- Use of an ECP shows up most directly in the NPA portion -of the output, shown below: -

- 

-
-NATURAL POPULATIONS:  Natural atomic orbital occupancies 
-                                                         
- NAO Atom #  lang   Type(AO)    Occupancy      Energy    
----------------------------------------------------------
-  1   Cu  1  s      Val( 4s)     0.94240      -0.26321
-  2   Cu  1  s      Ryd( 5s)     0.00019       0.92165
-  3   Cu  1  px     Ryd( 4p)     0.99604      -0.06989
-  4   Cu  1  px     Ryd( 5p)     0.00001       0.09916
-  5   Cu  1  py     Ryd( 4p)     0.99604      -0.06989
-  6   Cu  1  py     Ryd( 5p)     0.00001       0.09916
-  7   Cu  1  pz     Ryd( 5p)     0.05481       1.09062
-  8   Cu  1  pz     Ryd( 4p)     0.00062       0.52821
-  9   Cu  1  dxy    Val( 3d)     0.00000      -0.36077
- 10   Cu  1  dxy    Ryd( 4d)     0.00000       0.72280
- 11   Cu  1  dxz    Val( 3d)     1.99997      -1.29316
- 12   Cu  1  dxz    Ryd( 4d)     0.00398       0.75681
- 13   Cu  1  dyz    Val( 3d)     1.99997      -1.29316
- 14   Cu  1  dyz    Ryd( 4d)     0.00398       0.75681
- 15   Cu  1  dx2y2  Val( 3d)     1.99939      -1.38791
- 16   Cu  1  dx2y2  Ryd( 4d)     0.00061       0.67825
- 17   Cu  1  dz2    Val( 3d)     1.99890      -1.26114
- 18   Cu  1  dz2    Ryd( 4d)     0.00308       1.16392
-
- 19   Cu  2  s      Val( 4s)     0.94240      -0.26321
- 20   Cu  2  s      Ryd( 5s)     0.00019       0.92165
- 21   Cu  2  px     Ryd( 4p)     0.99604      -0.06989
- 22   Cu  2  px     Ryd( 5p)     0.00001       0.09916
- 23   Cu  2  py     Ryd( 4p)     0.99604      -0.06989
- 24   Cu  2  py     Ryd( 5p)     0.00001       0.09916
- 25   Cu  2  pz     Ryd( 5p)     0.05481       1.09062
- 26   Cu  2  pz     Ryd( 4p)     0.00062       0.52821
- 27   Cu  2  dxy    Val( 3d)     0.00000      -0.36077
- 28   Cu  2  dxy    Ryd( 4d)     0.00000       0.72280
- 29   Cu  2  dxz    Val( 3d)     1.99997      -1.29316
- 30   Cu  2  dxz    Ryd( 4d)     0.00398       0.75681
- 31   Cu  2  dyz    Val( 3d)     1.99997      -1.29316
- 32   Cu  2  dyz    Ryd( 4d)     0.00398       0.75681
- 33   Cu  2  dx2y2  Val( 3d)     1.99939      -1.38791
- 34   Cu  2  dx2y2  Ryd( 4d)     0.00061       0.67825
- 35   Cu  2  dz2    Val( 3d)     1.99890      -1.26114
- 36   Cu  2  dz2    Ryd( 4d)     0.00308       1.16392
-
-[ 36 electrons found in the effective core potential]
-
-WARNING:  Population inversion found on atom Cu 1
-          Population inversion found on atom Cu 2
-
-
-Summary of Natural Population Analysis:                  
-                                                         
-                                      Natural Population 
-              Natural   -----------------------------------------------
-   Atom #     Charge        Core      Valence    Rydberg      Total
------------------------------------------------------------------------
-    Cu  1    0.00000     18.00000     8.94064    2.05936    29.00000
-    Cu  2    0.00000     18.00000     8.94064    2.05936    29.00000
-=======================================================================
-  * Total *  0.00000     36.00000    17.88127    4.11873    58.00000
-
-                                Natural Population      
---------------------------------------------------------
-  Effective Core            36.00000
-  Valence                   17.88127 ( 81.2785% of  22)
-  Natural Minimal Basis     53.88127 ( 92.8987% of  58)
-  Natural Rydberg Basis      4.11873 (  7.1013% of  58)
---------------------------------------------------------
-
-   Atom #          Natural Electron Configuration
-----------------------------------------------------------------------------
-    Cu  1      [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)
-    Cu  2      [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05)
- 
-
-

- As noted below the first NPA table, 36 electrons were found -in the ECP, so the labels for NAOs in the table begin with the -designations 4s, 5s, etc. of the presumed extra-core -electrons. The ECP electrons are duly entered in the NPA tables -(labelled as "effective core" in the NPA summary table) -as part of the total Lewis occupancy, -and are taken into proper account in assigning atomic charges. The -NPA output in this case includes a "population inversion" message to -warn that one or more NAO occupancies are not ordered in accordance -with the energy order [e.g., the 3dxy orbital (NAO 9) -is unoccupied in this excited configuration, although -its energy lies below the occupied 4s, 4py, 4pz -levels.] -

-

- The main ECP effect in the NBO portion of the output is the -omission of core NBOs, as illustrated below: -

- 

-
-NATURAL BOND ORBITAL ANALYSIS:
-
-                      Occupancies       Lewis Structure    Low   High
-          Occ.    -------------------  -----------------   occ   occ
- Cycle   Thresh.   Lewis   Non-Lewis     CR  BD  3C  LP    (L)   (NL)   Dev
-=============================================================================
-  1(1)    1.90    57.99970   0.00030      0   3   0   8     0      0    0.00
------------------------------------------------------------------------------
-
-Structure accepted: No low occupancy Lewis orbitals
-
---------------------------------------------------------
-  Effective Core           36.00000
-  Valence Lewis            21.99970 ( 99.999% of  22)
- ==================       ============================
-  Total Lewis              57.99970 ( 99.999% of  58)
- -----------------------------------------------------
-  Valence non-Lewis         0.00000 (  0.000% of  58)
-  Rydberg non-Lewis         0.00030 (  0.001% of  58)
- ==================       ============================
-  Total non-Lewis           0.00030 (  0.001% of  58)
---------------------------------------------------------
-
-
-    (Occupancy)   Bond orbital/ Coefficients/ Hybrids
--------------------------------------------------------------------------------
-  1. (2.00000) BD ( 1)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
-                                        0.9702 -0.0003  0.0000  0.0000  0.0000
-                                        0.0000 -0.2340  0.0245  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0225  0.0530
-               ( 50.00%)   0.7071*Cu 2 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
-                                        0.9702 -0.0003  0.0000  0.0000  0.0000
-                                        0.0000  0.2340 -0.0245  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0225  0.0530
-  2. (2.00000) BD ( 2)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-                                        0.0000  0.0000  0.9980  0.0029  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                       -0.0035 -0.0630  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000
-               ( 50.00%)   0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-                                        0.0000  0.0000  0.9980  0.0029  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0035  0.0630  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000
-  3. (2.00000) BD ( 3)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-                                        0.0000  0.0000  0.0000  0.0000  0.9980
-                                        0.0029  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000 -0.0035 -0.0630  0.0000
-                                        0.0000  0.0000  0.0000
-               ( 50.00%)   0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-                                        0.0000  0.0000  0.0000  0.0000  0.9980
-                                        0.0029  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0035  0.0630  0.0000
-                                        0.0000  0.0000  0.0000
-  4. (2.00000) LP ( 1)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.9998
-                                       -0.0175  0.0000  0.0000
-  5. (2.00000) LP ( 2)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0037
-                                       -0.0010  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  1.0000  0.0026  0.0000
-                                        0.0000  0.0000  0.0000
-  6. (2.00000) LP ( 3)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000  0.0037 -0.0010  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        1.0000  0.0026  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000
-  7. (1.99985) LP ( 4)Cu 1             s(  0.06%)p 0.02(  0.00%)d99.99( 99.94%)
-                                        0.0231  0.0070  0.0000  0.0000  0.0000
-                                        0.0000 -0.0030 -0.0008  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000 -0.9996 -0.0115
-  8. (2.00000) LP ( 1)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.9998
-                                       -0.0175  0.0000  0.0000
-  9. (2.00000) LP ( 2)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000  0.0000  0.0000 -0.0037
-                                        0.0010  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  1.0000  0.0026  0.0000
-                                        0.0000  0.0000  0.0000
- 10. (2.00000) LP ( 3)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
-                                        0.0000  0.0000 -0.0037  0.0010  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        1.0000  0.0026  0.0000  0.0000  0.0000
-                                        0.0000  0.0000  0.0000
- 11. (1.99985) LP ( 4)Cu 2             s(  0.06%)p 0.02(  0.00%)d99.99( 99.94%)
-                                        0.0231  0.0070  0.0000  0.0000  0.0000
-                                        0.0000  0.0030  0.0008  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000 -0.9996 -0.0115
- 12. (0.00015) RY*( 1)Cu 1             s( 63.84%)p 0.51( 32.31%)d 0.06(  3.85%)
-                                       -0.1106  0.7913  0.0000  0.0000  0.0000
-                                        0.0000 -0.4699  0.3199  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0064 -0.1962
- 13. (0.00000) RY*( 2)Cu 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
- 14. (0.00000) RY*( 3)Cu 1             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
- 15. (0.00000) RY*( 4)Cu 1             s( 31.12%)p 2.21( 68.87%)d 0.00(  0.00%)
- 16. (0.00000) RY*( 5)Cu 1             s(  7.79%)p11.84( 92.21%)d 0.00(  0.00%)
- 17. (0.00000) RY*( 6)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 18. (0.00000) RY*( 7)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 19. (0.00000) RY*( 8)Cu 1             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
- 20. (0.00000) RY*( 9)Cu 1             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
- 21. (0.00000) RY*(10)Cu 1             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 22. (0.00000) RY*(11)Cu 1             s(  3.06%)p 0.35(  1.07%)d31.35( 95.87%)
- 23. (0.00015) RY*( 1)Cu 2             s( 63.84%)p 0.51( 32.31%)d 0.06(  3.85%)
-                                       -0.1106  0.7913  0.0000  0.0000  0.0000
-                                        0.0000  0.4699 -0.3199  0.0000  0.0000
-                                        0.0000  0.0000  0.0000  0.0000  0.0000
-                                        0.0000  0.0064 -0.1962
- 24. (0.00000) RY*( 2)Cu 2             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
- 25. (0.00000) RY*( 3)Cu 2             s(  0.00%)p 1.00(100.00%)d 0.00(  0.00%)
- 26. (0.00000) RY*( 4)Cu 2             s( 31.12%)p 2.21( 68.87%)d 0.00(  0.00%)
- 27. (0.00000) RY*( 5)Cu 2             s(  7.79%)p11.84( 92.21%)d 0.00(  0.00%)
- 28. (0.00000) RY*( 6)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 29. (0.00000) RY*( 7)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 30. (0.00000) RY*( 8)Cu 2             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
- 31. (0.00000) RY*( 9)Cu 2             s(  0.00%)p 1.00(  0.40%)d99.99( 99.60%)
- 32. (0.00000) RY*(10)Cu 2             s(  0.00%)p 0.00(  0.00%)d 1.00(100.00%)
- 33. (0.00000) RY*(11)Cu 2             s(  3.06%)p 0.35(  1.07%)d31.35( 95.87%)
- 34. (0.00000) BD*( 1)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
-               ( 50.00%)  -0.7071*Cu 2 s( 94.13%)p 0.06(  5.54%)d 0.00(  0.33%)
- 35. (0.00000) BD*( 2)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-               ( 50.00%)  -0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
- 36. (0.00000) BD*( 3)Cu 1-Cu 2      
-               ( 50.00%)   0.7071*Cu 1 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-               ( 50.00%)  -0.7071*Cu 2 s(  0.00%)p 1.00( 99.60%)d 0.00(  0.40%)
-
-
-
-
-Natural Bond Orbitals (Summary):
-
-                                                    Principal Delocalizations
-          NBO              Occupancy    Energy      (geminal,vicinal,remote)
-===============================================================================
-Molecular unit  1  (Cu2)
-  1. BD ( 1)Cu 1-Cu 2       2.00000    -0.53276
-  2. BD ( 2)Cu 1-Cu 2       2.00000    -0.21503
-  3. BD ( 3)Cu 1-Cu 2       2.00000    -0.21503
-  4. LP ( 1)Cu 1            2.00000    -1.38854
-  5. LP ( 2)Cu 1            2.00000    -1.29317
-  6. LP ( 3)Cu 1            2.00000    -1.29317
-  7. LP ( 4)Cu 1            1.99985    -1.26133
-  8. LP ( 1)Cu 2            2.00000    -1.38854
-  9. LP ( 2)Cu 2            2.00000    -1.29317
- 10. LP ( 3)Cu 2            2.00000    -1.29317
- 11. LP ( 4)Cu 2            1.99985    -1.26133
- 12. RY*( 1)Cu 1            0.00015     0.70166
- 13. RY*( 2)Cu 1            0.00000     0.09932
- 14. RY*( 3)Cu 1            0.00000     0.09932
- 15. RY*( 4)Cu 1            0.00000     1.09217
- 16. RY*( 5)Cu 1            0.00000     0.44430
- 17. RY*( 6)Cu 1            0.00000    -0.36077
- 18. RY*( 7)Cu 1            0.00000     0.72280
- 19. RY*( 8)Cu 1            0.00000     0.75266
- 20. RY*( 9)Cu 1            0.00000     0.75266
- 21. RY*(10)Cu 1            0.00000     0.67888
- 22. RY*(11)Cu 1            0.00000     1.26372
- 23. RY*( 1)Cu 2            0.00015     0.70166
- 24. RY*( 2)Cu 2            0.00000     0.09932
- 25. RY*( 3)Cu 2            0.00000     0.09932
- 26. RY*( 4)Cu 2            0.00000     1.09217
- 27. RY*( 5)Cu 2            0.00000     0.44430
- 28. RY*( 6)Cu 2            0.00000    -0.36077
- 29. RY*( 7)Cu 2            0.00000     0.72280
- 30. RY*( 8)Cu 2            0.00000     0.75266
- 31. RY*( 9)Cu 2            0.00000     0.75266
- 32. RY*(10)Cu 2            0.00000     0.67888
- 33. RY*(11)Cu 2            0.00000     1.26372
- 34. BD*( 1)Cu 1-Cu 2       0.00000     0.41179
- 35. BD*( 2)Cu 1-Cu 2       0.00000     0.08327
- 36. BD*( 3)Cu 1-Cu 2       0.00000     0.08327
-      -------------------------------
-             Total Lewis   57.99970  ( 99.9995%)
-       Valence non-Lewis    0.00000  (  0.0000%)
-       Rydberg non-Lewis    0.00030  (  0.0005%)
-      -------------------------------
-           Total unit  1   58.00000  (100.0000%)
-          Charge unit  1    0.00000
- 
-
-

- As the output shows, the NBO tables include reference -to only 11 occupied NBOs, rather than -the 29 that would appear in a full calculation. Semi-empirical -methods that neglect core electrons (AMPAC, etc.) are -handled similarly. -

- The output for the Cu2 -example also illustrates some aspects of the inclusion of d orbitals -in the basis set. NBOs 4-7 and 8-11 represent the 3d8 -subshells on each atom, essentially of pure atomic d -character (except for a small admixture -of p character in NBOs 7, 11). Both -the CuCu bond (NBO 1) and the two CuCu bonds -(NBOs 2, 3) have very slight admixtures (< 0.4%) of d -character. The remaining orbitals of predominant d -character (NBOs 17-22 and 28-33) are of negligible occupancy. Note -that the abbreviated "spd" designations -can lead to strange variations among hybrids -of essentially similar character; thus, NBO 20 (p1.0d99.9), -NBO 21 (d1.0), and NBO 22 (s3.1p0.4d31.4) -are all of nearly pure (> 95%) d character, the difference in -labelling stemming from -whether there is sufficient -s or p character (in numerical terms) to express the -hybrid ratios in spd form. Consult -the percentages of s-. -p-, and d-character whenever there is doubt about how to -interpret a particular spd designation. -

-B.7 FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM -

-B.7.1 Introduction -

- The general NBO program, GENNBO, is a stand-alone program which is not -directly attached to an ESS program. Rather, information about the -wavefunction is provided to the core NBO routines by a sequential input -file, FILE47, described in this section. -

- Some knowledge of FILE47 is useful even if your NBO program is attached -to an ESS package. If requested (see the ARCHIVE option, Section B.2.5), -the NBO program writes out FILE47 which summarizes all information pertaining -to the computed electronic wavefunction. This file can be subsequently -used as input to the GENNBO program (reassigned as LFN 5) -to repeat the analysis of this -wavefunction; simply include the $NBO, $CORE, and $CHOOSE keylists in -FILE47 and execute GENNBO. You need never recompute the wavefunction to -vary its NBO analysis! In fact, generating the FILE47 input file is a -useful way to archive a wavefunction for future use or reference. [Note: -the GENNBO program can not perform the NBO energetic analysis ($DEL keylist) -since this would require access to the formatted one- and two-electron -integrals of the parent ESS package.] -

- If you intend to use the NBO program in conjunction with an ESS package -not supported in this distribution (i.e. for which no custom drivers are -provided), you might consider attaching a routine to your ESS program which -would write the proper form of FILE47 for input into the GENNBO program. -Thus, a two-step process would be required to obtain the NBO analysis of -a wavefunction: (i) the initial calculation of the wavefunction with the -ESS package, writing FILE47; (ii) the NBO analysis using the GENNBO program -with FILE47 as input. Alternatively, you may decide to attach the NBO program -directly to your ESS package by writing your own driver routines. See -the Programmer's Guide, Section C.13, for direction. -

- Section B.7.2 describes and illustrates the overall -format of FILE47. Sections B.7.3-B.7.7 detail the entries of the -keylists and datalists that compose this file. -

-B.7.2 Format of the FILE47 Input File -

- The FILE47 input file is composed of a set of keylists and datalists, each -list beginning with a "$" identifier (e.g. "$BASIS") and ending with -"$END", -

-

     $BASIS   entries  $END
-

-Individual lists are used to specify basis set information ($BASIS), -density matrix elements ($DENSITY), and so forth. The order of the -lists within FILE47 is immaterial. Entries within each datalist are generally -free format, and may be continued on as many lines as desired. An -exclamation point (!) on any line terminates input from the line, and may -be followed by arbitrary comments. The $GENNBO keylist and -the $COORD, $BASIS, $DENSITY, and $OVERLAP datalists -are required, but the other -datalists ($FOCK, $LCAOMO, $CONTRACT, $DIPOLE) or the standard -NBO keylists ($NBO, $CORE, $CHOOSE) are optional, depending on the requested -application. If the $NBO keylist is not present in FILE47, the default -NBO analysis is performed. -

- The entries of each keylist or datalist may be keywords, numerical matrix -elements, or other parameters of prescribed form. A sample FILE47 input -file (for the RHF/3-21G methylamine example of Section A.3) is shown below: - 

-
- $GENNBO  NATOMS=7  NBAS=28  UPPER  BODM $END
- $NBO  NAOMO=PVAL  $END
- $COORD
- Methylamine...Pople-Gordon standard geometry...RHF/3-21G                
-  6   6   -0.74464  -0.03926   0.00000    ! Carbon
-  7   7    0.71885   0.09893   0.00000    ! Nitrogen
-  1   1   -1.00976  -1.09653   0.00000    ! Hydrogen
-  1   1   -1.15467   0.43814   0.88998    ! Hydrogen
-  1   1   -1.15467   0.43814  -0.88998    ! Hydrogen
-  1   1    1.09878  -0.34343  -0.82466    ! Hydrogen
-  1   1    1.09878  -0.34343   0.82466    ! Hydrogen
- $END
- $BASIS
-   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
-    LABEL = 1,1,101,102,103,1,101,102,103,1,1,101,102,103,1,101,102,103,
-            1,1,1,1,1,1,1,1,1,1
- $END
- $CONTRACT
-  NSHELL =  16
-    NEXP =  21
-   NCOMP =   1,  4,  4,  1,  4,  4,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1 
-   NPRIM =   3,  2,  1,  3,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1 
-    NPTR =   1,  4,  6,  7, 10, 12, 13, 15, 16, 18, 16, 18, 19, 21, 19, 21 
-     EXP =   0.1722560E+03,  0.2591090E+02,  0.5533350E+01,  0.3664980E+01,
-             0.7705450E+00,  0.1958570E+00,  0.2427660E+03,  0.3648510E+02,
-             0.7814490E+01,  0.5425220E+01,  0.1149150E+01,  0.2832050E+00,
-             0.5447178E+01,  0.8245472E+00,  0.1831916E+00,  0.5447178E+01,
-             0.8245472E+00,  0.1831916E+00,  0.5447178E+01,  0.8245472E+00,
-             0.1831916E+00 
-      CS =   0.2093132E+01,  0.2936751E+01,  0.1801737E+01, -0.7473843E+00,
-             0.7126610E+00,  0.2098285E+00,  0.2624092E+01,  0.3734359E+01,
-             0.2353454E+01, -0.1047101E+01,  0.9685501E+00,  0.2766851E+00,
-             0.3971513E+00,  0.5579200E+00,  0.1995672E+00,  0.3971513E+00,
-             0.5579200E+00,  0.1995672E+00,  0.3971513E+00,  0.5579200E+00,
-             0.1995672E+00 
-      CP =   0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.1709178E+01,
-             0.8856221E+00,  0.1857223E+00,  0.0000000E+00,  0.0000000E+00,
-             0.0000000E+00,  0.2808586E+01,  0.1456735E+01,  0.2944871E+00,
-             0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.0000000E+00,
-             0.0000000E+00,  0.0000000E+00,  0.0000000E+00,  0.0000000E+00,
-             0.0000000E+00 
- $END
- $OVERLAP   ! Overlap matrix elements in the AO basis
-  0.10000000E+01  0.19144744E+00  0.10000000E+01  . . .
- $END
- $DENSITY   ! Bond-order matrix elements in the AO basis
-  0.20363224E+01  0.11085239E+00  0.10393086E+00  . . .
- $END
- $FOCK      ! Fock matrix elements in the AO basis
- -0.11127777E+02 -0.28589754E+01 -0.89570272E+00  . . .
- $END
- $LCAOMO    ! AO to MO transformation matrix
- -0.57428375E-03 -0.23835711E-02  0.17741799E-02  . . .
- $END
- $DIPOLE    ! dipole matrix elements in the AO basis
- -0.14071733E+01 -0.26939974E+00 -0.14071733E+01  . . .
- $END
-
-
-

-The nine lists of FILE47 are described in turn in -the following sections, making use of this -example for illustration. -

-B.7.3 $GENNBO Keylist -

- The $GENNBO keylist (required) contains keywords -essential to the proper execution -of the NBO program. The following is the list of keywords recognized -by this keylist: -

-KEYWORD OPTION DESCRIPTION -

-REUSE Instructs GENNBO to reuse an old NBO direct-access file, FILE48, -rather than create a new FILE48 from the wavefunction information -contained in the FILE47 datalists. Therefore, if the REUSE keyword -is specified, all datalists in FILE47 will be ignored, but the -$NBO, $CORE, and $CHOOSE keylists will still be recognized. This keyword -preempts all other keywords of the $GENNBO keylist. -

-NATOMS Number of atoms in the molecule (required). -

-NBAS Number of basis functions (required). -

-OPEN Designates an open shell wavefunction. GENNBO will subsequently -read in alpha and beta density, Fock, and MO coefficient matrices. -

-ORTHO Indicates that the AO basis set is orthogonal (basis -functions are always assumed normalized). If this keyword is -specified, GENNBO will not read the $OVERLAP datalist. This keyword -is incompatible with $NBO keywords for 'pre-orthogonal' -basis sets (SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, AOPNHO, AOPNBO, -AOPNLMO). -

-UPPER Indicates that only the upper triangular portions of the overlap, -density, Fock, and dipole matrices are listed in the their respective -datalists. By default, GENNBO assumes that the full matrices are -given. -

-BODM Indicates that the $DENSITY datalist contains the -bond-order matrix ("Fock-Dirac density matrix") rather -than the density matrix (i.e., matrix elements of the -density operator). (In orthogonal AO basis sets, the bond-order matrix -and density matrix are identical, but in nonorthogonal basis sets they -must be distinguished.) By default, GENNBO assumes this datalist contains -the density matrix elements. If "BODM" is included, the datalist -elements are transformed with the AO overlap matrix to produce the -true density matrix. -

-BOHR Indicates that the atomic coordinates ($COORD) and the dipole -integrals ($DIPOLE) are in atomic units, rather than the default -angstroms. -

-EV Indicates that the Fock matrix elements ($FOCK) have units of -electron volts (eV), rather than the default atomic units (Hartrees). -

-CUBICF Instructs GENNBO to use the set of seven cubic f-type functions -rather than the ten Cartesian or seven pure f functions -(cf. Section B.7.5). -

-The methylamine sample $GENNBO keylist -specifies 7 atoms, 28 basis -functions, upper triangular matrix input, and $DENSITY datalist containing -the bond-order matrix. -

-B.7.4 $COORD Datalist -

- The $COORD datalist (required, unless REUSE is -specified in $GENNBO) contains the job title and information indicating -the identity and coordinates of each atom, including missing core electrons -or effective core potentials. -

- The first line following the $COORD identifier is an arbitrary -job title, up to 80 characters. -

- Subsequent lines are used to specify the -atomic number, the nuclear charge, and the (x,y,z) coordinates of each -atom. -[For example, atom 1 in the methylamine sample input is a carbon -atom (atomic number 6) with nuclear charge 6 and coordinates -x = -0.74464, -y = -0.03926, z = 0.00000, in angstroms.] -Coordinates are assumed to be in angstroms unless the BOHR keyword -appears in the $GENNBO keylist, specifying atomic units. The -atomic number and nuclear charge -are generally identical, but if core electrons are neglected (as in most -semi-empirical treatments) or if effective core potentials (ECP) are employed, -the nuclear charge will be less than the atomic number by the number of -electrons neglected on that particular atom. Thus, for an AMPAC calculation, -in which the two 1s core electron of a carbon atom are neglected, the line -following the job title in the methylamine example would read -

-

   6    4    -0.74464   -0.03926    0.00000   ! Carbon
-

-where "4" is the effective (valence) nuclear charge of the atom. -

-B.7.5 $BASIS Datalist -

- The $BASIS datalist (required, unless REUSE is specified -in $GENNBO) provides essential information about the AO basis -functions, -specifying the atomic center and the angular symmetry (s, px, -py, pz, -etc.) of each AO. This information is contained -in two arrays in this datalist called CENTER and LABEL. -

- The atomic center for each AO is -specified by entering "CENTER=" followed -by the serial number of the atom for each AO, separated by commas or spaces. -[For example, the entry -

-

   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
-

-of the methylamine sample file indicates that the first 9 AOs (1-9) are -centered on atom 1 (the carbon atom), the next nine AOs (10-18) on center 2, -and so forth.] -

- The angular symmetry for each AO is specified by entering "LABEL=" -followed by a symmetry label for each AO, separated by commas or -spaces. The NBO program handles s, p, d, -or f (l = 0-3) basis AOs, of either cartesian or pure angular -symmetry types. The label for each AO is a 3-digit integer of the -form l*100 + k + m, where k is 0 (cartesian) or 50 (pure), -and m is a particular component of the l-type symmetry (see -table below). For -s or p AOs, -the cartesian and pure l-symmetry sets are identical, so each AO can be -labelled in two distinct ways, but -the six cartesian d functions can be transformed to the five pure d -functions plus an additional s function, and the ten cartesian f -functions can be transformed to the seven -pure f functions plus three additional p -functions. Two distinct sets of pure f -functions are recognized, the "standard" [default] set and -the "cubic" set, the latter being used whenever the "CUBICF" -keyword is included in the $GENNBO keylist. - - The labels associated -with each allowed AO function type are tabulated below, -where x, y, z refer to the -specified cartesian axis system: -

-

- - - - - - - - - - - - - - - - - - - - - - - - - -
labelAO typelabelAO typelabelAO type
Pure s, p sets: Cartesian f set: Pure f "cubic" set:
1 (51)s301fxxx351f(D1): x(5x2-3r2)
101 (151)px302fxxy352f(D2): y(5y2-3r2)
102 (152)py303fxxz353f(D3): z(5z2-3r2)
103 (153)pz304fxyy354f(B): xyz
305fxyz355f(E1): x(z2-y2)
Cartesian d set: 306fxzz356f(E2): y(z2-x2)
201dxx307fyyy357f(E3): z(x2-y2)
202dxy308fyyz
203dxz309fyzz
204dyy310fzzz
205dyz
206dzzPure f "standard" set:
351f(0): z(5z2-3r2)
Pure d set: 352f(c1): x(5z2-r2)
251dxy353f(s1): y(5z2-r2)
252dxz354f(c2): z(x2-y2)
253dyz355f(s2): xyz
254dx2-y2356f(c3): x(x2-3y2)
255dz2 = d3z2-r2357f(s3): y(3x2-y2)
- -[For example, in the methylamine sample input, -the first nine entries of the LABEL array, -

-

    LABEL = 1,1,101,102,103,1,101,102,103,. . .
-

-identify the first 9 AOs (of carbon) as being of s, s, px, py, pz, -s, px, py, pz type, respectively.] -

-B.7.6 $CONTRACT Datalist -

- The $CONTRACT datalist (optional) -contains additional information about the contraction coefficients -and orbital exponents of AO basis functions. This information is -not used in the NBO analysis of a wavefunction. However, if the -AOINFO or PLOT keyword is specified in the $NBO keylist (See Section B.2.5), -the GENNBO driver routines write out this information to -an external file (LFN 31) in the proper format for orbital plotting with -the ORBPLOT program. Omit the $CONTRACT datalist if you do not -intend to make orbital plots. -

- Two integers must be initially given: NSHELL (the number of shells of -basis functions) and NEXP (the number of orbital exponents). -[In the methylamine example, there are 16 shells of basis functions and 27 -orbital exponents.] These integers should precede -the remainder of the basis set information -of this datalist. -

- The number of components (basis functions) in each shell is specified in -the NCOMP array. The sum of the components for each shell should equal -the total number of basis functions. This list of components is a -partitioning of the basis function centers and labels (in the $BASIS -datalist) into shells. [For example, in the methylamine sample, the NCOMP array -

-

    NCOMP = 1,4,4,. . .
-

-indicates that the first three shells have a total of 9 (i.e. 1+4+4) basis -functions. These are the 9 AOs (1-9) discussed previously in the $BASIS -datalist.] -

- The NPRIM array gives the number of primitive gaussian functions of each -shell. [For the methylamine example, the first three shells of the AO -basis are contractions of -

-

    NPRIM = 3,2,1,. . .
-

-three, two, and one primitives, respectively, corresponding to -the conventional "3-21G" basis set designation.] -

- Pointers for each shell are listed in the NPTR array. These pointers -specify the location of the orbital exponents (EXP) and contraction -coefficients (CS, CP, CD, CF) for each shell. [In the sample input file, -

-

     NPTR = 1,4,6,. . .
-

-the orbital exponents and contraction coefficients for the first three -shells begin at elements 1, 4, and 6, respectively.] -

- EXP, CS, CP, CD, and CF are free format, real arrays containing the orbital -exponents, and the s, p, d, and f contraction coefficients of the AO basis set. -NEXP elements should appear in each array, and the arrays of contraction -coefficients need only appear if there are basis functions of that particular -symmetry in the basis set. [For example, the 3-21G basis of the sample -methylamine input only has s and p basis functions. Therefore, the -CD and CF arrays are not necessary.] -

- The information in the $CONTRACT datalist along with that in the $BASIS -datalist is enough to completely determine the AO basis set. [For example, -the second shell on the methylamine sample contains 4 basis functions -(NCOMP). These are s, px, py, and pz -orbitals (LABEL), all centered on atom 1 (CENTER), and each basis function -is a contraction of two primitive gaussians (NPRIM). From NPTR, EXP, CS, -and CP, we find the explicit form of these functions: -

-

-s(r)  = -0.747 e-3.66 r2  + 0.713 e-0.77 r2 -

-px(r) = 1.709 x e-3.66 r2 + 0.886 x e-0.77 r2 -

-py(r) = 1.709 y e-3.66 r2 + 0.886 y e-0.77 r2 -

-pz(r) = 1.709 z e-3.66 r2 + 0.886 z e-0.77 r2 -

-

-where r=(x,y,z) is measured in bohr units relative to the cartesian -coordinates of atom 1.] -

-B.7.7 Matrix Datalists -

- The remaining datalists ($OVERLAP, $DENSITY, $FOCK, $LCAOMO, $DIPOLE) -specify various matrix elements possibly used by the NBO analysis. All -entries in these datalists are free format, with entries separated -by commas or spaces. Only the upper triangular portions of each symmetric -matrix (overlap, density, Fock, dipole) should be provided if the -UPPER keyword is specified in the $GENNBO keylist. The numbering of the -matrix rows and columns must correspond to the ordering of the AOs in -the $BASIS datalist. All three matrices of dipole integrals should appear -in the $DIPOLE datalist, all x integrals before y before z. -

- Of the matrix datalists, the $DENSITY datalist is -always required, and -the $OVERLAP datalist is required for all non-orthogonal -AO basis sets, but other datalists are optional (unless implicitly -required by specified keyword options). Nevertheless, it is good practice -to include as many of these datalists -in FILE47 as possible for later use with keyword options which require -them. The following table lists the $NBO keywords that require -each datalist to be included in FILE47: -

-Datalist $NBO Keywords Requiring the Datalist -

-$OVERLAP SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, -AOPNHO, AOPNBO, AOPNLMO -

-$FOCK E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO -

-$LCAOMO AOMO, NAOMO, NHOMO, NBOMO, NLMOMO -

-$DIPOLE DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE -

-$CONTRACT AOINFO, PLOT -

- For example, in the methylamine sample input, the keyword "NAOMO=PVAL" -of the $NBO keylist requires that the $LCAOMO datalist be present (in -addition to the $OVERLAP, $DENSITY, and $FOCK datalists used for default -PRINT=2 analysis), but the $DIPOLE datalist might have been omitted in -this case. Inclusion of the $LCAOMO datalist (in addition to the $FOCK -datalist) insures that degenerate MOs will be chosen in a prescribed way -for decomposition in terms of other functions. -

-

-

Section C: NBO PROGRAMMER'S GUIDE

-
-

-C.1 INTRODUCTION -

- Section C constitutes the -programmer's guide to the NBO.SRC program. It -assumes that the user has a thorough familiarity with Fortran -programming and the operations of the NBO program (Sections -A and B) as well as some familiarity with -published algorithms for NAO/NBO/NLMO -determination. This section is intended for the accomplished -programmer who wishes to inquire into the details of the -NBO numerical methods and find the specific source -code associated with individual steps of the published -NAO/NBO/NLMO algorithms or segments of NBO output. -

- The NBO.SRC program consists of about 20000 lines, of which -more than 6000 are comment lines (approximately the length of -this manual!). These comment statements provide the principal -documentation of the steps within each subroutine -or function, and should be consulted on questions pertaining -to individual subprograms. -

- In this Programmer's Guide, -we focus on global aspects of program organization -and data structure. Individual subprograms -(about 180 in number) are described in capsule form, in the -order in which they appear in the source listing, to -indicate the relationship to -program tasks and the association with specific segments -of NBO output. The capsule descriptions include mention [in -brackets] of numerical thresholds -or possible dependencies on machine precision that are of particular -concern to the programmer. Throughout the Programmer's Guide, -in referring to individual subprograms, we -use the abbreviation "SR" for "subroutine" and "FN" for -"function". -

- Sections C.2-C.4 describe the overall NBO.SRC source layout, -labelled COMMON blocks, and I/O structures (including the -FILE48 direct access file). Sections C.5-C.11 then -follow the layout of the source code in describing the principal -groupings of subprograms, with a brief description of each -subprogram. Section C.12 similarly describes subprograms of -the GENNBO stand-alone program. The final section C.13 provides -guidance on attaching the NBO program to a new ESS package not -supported by this distribution. -

-

-C.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS -

- The NBO.SRC program is organized into seven principal groups -of routines (I-VII), described in Sections C.5-C.11, respectively, -as shown below: -

- - - - - - - - - - - - -
Groupdescriptionno.Section
I.NAO/NBO/NLMO routines61C.5
II.Energy analysis routines6C.6
III.Direct access file (DAF) routines41C.7
IV.Free format input routines7C.8
V.Other I/O routines27C.9
VI.General utility routines31C.10
VII.System-dependent routines(3)C.11
-The routines of Groups I, II are associated with the two -main tasks of the NBO program: (1) NAO/NBO/NLMO formation, -and (2) NBO energetic analysis. Group II routines generally -require Fock matrix information, and thus are restricted to -RHF and UHF wavefunctions, whereas Group I are -applicable to general wavefunctions. Each of these -groups is controlled by a master subroutine -(NBO and NBOEAN, respectively) of highest precedence, which in turn -calls routines of secondary precedence (such -as NAODRV, NBODRV, etc.) to control the -task. Routines are generally clustered together under the -subroutine of next higher precedence, and within each cluster, the order -of routines generally corresponds to the chronological -sequence in which the routines are called in execution. -

- The remaining Groups III-VI 'serve' various routines of Groups -I-II, and are ordered more loosely by function, -or alphabetically. Groups I-VI -are system-independent, whereas Group VII contains the special -drivers (RUNNBO, FEAOIN, DELSCF) for individual ESS programs, whose -generic function is described in Section C.11. Further information -on the ESS-specific forms of the Group VII driver routines is given -in the Appendix. -

- A general overview of the subprograms of Groups I and II -is shown in the accompanying flow chart, -indicating the logical relationship of the routines to -be discussed in Sections C.5, C.6. The sequence of execution -is generally from top to bottom and from left to right, -with subprograms of equal precedence shown at an equal vertical level. -

-

- - - -

-

NBO Flow Chart for Group I, II Subprograms

-

- -

-

-C.3 LABELLED COMMON BLOCKS -

- The NBO programs contain eighteen -labelled COMMON blocks -to control information flow between subprograms -(other than through explicit argument -lists). Each COMMON -block name begins with "NB" to minimize -possible conflicts with a linked ESS program. -

-The eighteen COMMON blocks can be divided into six 'primary' -and twelve 'secondary' blocks, with regard to claim on the -programmer's attention. The 'primary' -COMMON blocks 1-6 (/NBINFO/, /NBFLAG/, /NBOPT/, -/NBAO/, /NBATOM/, and /NBIO/) -contain variables that must be set by the -ESS-specific driver routine FEAOIN, or by an equivalent interface -provided by the programmer. The remaining 'secondary' -blocks 7-18 are for internal communication -only, and are ordinarily of lesser concern. -

-The dimensions of COMMON block arrays are -fixed by PARAMETER declarations of the form - 

-     PARAMETER(MAXATM = 99,MAXBAS = 500)
-
-
where MAXATM and MAXBAS are, respectively, -the maximum allowed numbers of atoms and basis -functions. These program limits can therefore be simply -altered. There is no difficulty in decreasing either of these values, -or in increasing MAXBAS (up to 999). However, the program cannot -readily adapt to MAXATM > 99, since this -would result in format overflows in orbital labels throughout the output. -

-All entries of a given COMMON block are generally of the same -numeric type (INTEGER, LOGICAL, etc.), as specified below. The names (dummy), -and meaning of variables in each primary COMMON block 1-6 are -described briefly, with an asterisk (*) marking the items -that must be passed from the external ESS program via driver routines: -

-1. COMMON/NBINFO/

-The INTEGER variables of this block store general information -related to basis set dimensionality, spin manifold, number of atoms, -and energy units: -

-

- - - - - - - - - - - - - -
variablemeaning
ISPIN+2 for spin, -2 for spin
*NATOMSnumber of atoms ( MAXATM)
*NDIMdeclared dimensionality of matrices (overlap, density, etc.)
*NBASnumber of basis AOs ( NDIM MAXBAS)
MXBOmaximum number of AOs per 2-c or 3-c NBO
MXAOmaximum AOs per atom
MXAOLMmaximum AOs of the same symmetry per atom
*MUNIT0 for Hartree energy units, 1 for eV units, 2 for kcal/mol.
-

-2. COMMON/NBFLAG/

-The LOGICAL variables of this block are set .TRUE. or .FALSE. -depending on whether the "condition" (type of wavefunction, spin -set, etc.) is satisfied: -

- - - - - - - - - - - - - - - -
variable (FLAG)condition that FLAG=.TRUE.
*ROHFRestricted open-shell Hartree-Fock wavefunction
*UHFUnrestricted Hartree-Fock wavefunction
*CIConfiguration Interaction wavefunction
*OPENopen-shell calculation
*COMPLXcomplex-valued wavefunction (not currently implemented)
ALPHA spin set
BETA spin set
*MCSCFMulti-Configuration Self-Consistent-Field wavefunction
*AUHFSpin-Annihilated UHF wavefunction
*ORTHObasis set is orthonormal
-Note (Section B.6.11) that both and spin density matrices -should be available if OPEN is set '.TRUE.' for the open-shell case. -

-

-3. COMMON/NBOPT/

-The INTEGER variables (flags) of this block are used for storing the keyword -options selected by the user in the $NBO keylist. In many cases, a variable -of the form IWOPT ("IW" stands for "I Want") is set to one or zero -(or to some Hollerith content; see below) depending on whether -the "requested option" has been specified or not. The table also -lists the keyword (if any) that requests the option: -

-

- - - - - - - - - - - - - - - - - - - - - - - -
variablekeywordrequested option
*IWDMBODM1 to transform input bond-order matrix, 0 otherwise
IW3C3CBOND3-center bonds
IWAPOL 'apolar' bonds, cA = cB (not used)
IWHYBS$NBOset equal to JPRINT(5)
IWPNAO(PAOPNAO)PAOPNAO transformation
IWTNAOAONAOAONAO transformation
IWTNABNAONBONAONBO transformation
IWTNBOAONBOAONBO transformation
IWFOCK +1 if Fock matrix available on DAF, 0 otherwise
*IWCUBFCUBICFcubic f functions
*IPSEUD effective core potential
KOPT (not used)
IPRINTPRINT=nprint level
IWDETLDETAILdetailed output
IWMULPMULATMulliken population analysis
ICHOOS$CHOOSEdirected NBO ($CHOOSE) search
JCORE$COREuser-specified core list
JPRINT(60)variousprinting option flags
-

-The keyword associated with each element I=1-54 -of the JPRINT array is shown below (55-60 are not currently used): -

- - -
JPRINT(I) associated keywords:
- - - - - - - - - - - - - - - - - - -
IkeywordIkeywordIkeywordIkeyword
1SKIPBO15FNLMO29FNHO43PLOT
2version16DMNBO30AOPNHO44AOPNAO
3E2PERT17DMNLMO31FNAO45NBOMO
4NPA18NAONLMO32(reserved)46DIPOLE
5NBO19SPNAO33NAONHO47NBONLMO
6NBOSUM20SPNHO34DMNHO48SPNLMO
7ARCHIVE21SPNBO35DMNAO49AOPNLMO
8NLMO22AOINFO36BEND50DIAO
9NAOMO23AONLMO37FNBO51DINAO
10NOBOND24NHONLMO38NHOMO52DINHO
11RPNAO25AOPNBO39SAO53DINBO
12BNDIDX26AOMO40FAO54DINLMO
13NLMOMO27DMAO41NHONBO55-60(not used)
14RESONANCE28AONHO42BOAO
-
-In general, if the flag is -set to zero, its associated keyword option has not been specified. However, -if an option is requested, its flag can be set to a variety of -positive, negative, or Hollerith values, depending on the parameters -specified with the keyword option. In particular, the option flags associated -with the matrix output keywords, described in Section B.2.4, are set -according to the following scheme: -

-

- - - - - - - - - - - - -
valueeffect
0Do nothing
0 < nPrint n columns of the matrix
-1000 < n < 0Write matrix to external file |n|
n < -999Read matrix from external file |n/1000|
'FULL'Print the full matrix to the output file
'VAL'Print only core plus valence orbitals
'LEW'Print only the occupied (Lewis) orbitals
-

-4. COMMON/NBAO/

-The INTEGER arrays of this block store information on the -atomic centers and angular symmetry of each AO: -

- - - - - - - - -
variablemeaning
*LCTR(MAXBAS)list of atomic centers of the basis AOs
(LCTR(3)=2 if AO 3 is on atom 2)
*LANG(MAXBAS)angular symmetry labels (Sec. B.7.5) of the basis AOs
-

-5. COMMON/NBATOM/

-The INTEGER arrays of this block store information about the -orbitals on each atomic center: -

- - - - - - - - - - - - -
variablemeaning
*IATNO(MAXATM)atomic number for each atom
INO(MAXATM)number of atomic hybrids on each atom
NORBS(MAXATM)number of AOs on each atom
LL(MAXATM)number of the first NAO on each atom
LU(MAXATM)number of the last NAO on each atom
*IZNUC(MAXATM)nuclear charge on each atom ( IATNO)
IATCR(MAXATM)atomic core list for modified $CORE table
-

-6. COMMON/NBIO/

-The INTEGER variables of this block are the -stored default logical file -numbers for I/O operations. The table below identifies -the value (default file assignment) and the -contents of the file associated with each LFN (cf. Section B.2.4): -

- - - - - - - - - - - - - - - - - - - - - - - -
LFNvaluefile contents
*LFNIN standard ESS input file
*LFNPR standard ESS output (print) file
LFNAO31AO info file
LFNPNA32AOPNAO transformation
LFNNAO33AONAO transformation
LFNPNH34AOPNHO transformation
LFNNHO35AONHO transformation
LFNPNB36AOPNBO transformation
LFNNBO37AONBO transformation
LFNPNL38AOPNLMO transformation
LFNNLM39AONLMO transformation
LFNMO40AOMO transformation (LCAO-MO coeffs.)
LFNDM41density matrix in AO basis
LFNNAB42NAONBO transformation
LFNPPA43PAOPNAO transformation
LFNGEN47'archive' file
LFNDAF48direct access file (DAF)
LFNDEF49'default' for other file output
-

-The remaining 'secondary' COMMON blocks 7-18 contain variables that -remain wholly within the system-independent code, and thus can be -ignored with respect to interfacing to a new ESS. Blocks 7-13 -involve communication with the Group I, II subprograms, whereas -blocks 14-18 are wholly within the 'support' routines of -Groups III-VII. -

-

-7. COMMON/NBBAS/

-The INTEGER arrays of this block generally store information about -the atomic, bond, and molecular units with which the NBOs or NAOs are -associated. The meaning of all entries in COMMON/NBBAS/ changes -between the NAO and NBO segments of the program, so this block -functions virtually as 'scratch storage,' and its entries must be -approached with extreme caution! The following table indicates the meaning -of COMMON/NBBAS/ entries during NBO segments (only!): -

- - - - - - - - - - - - - - -
variablemeaning
LABEL(MAXBAS,6)NBO label information (lbl; *; bond no.; at1; at2; at3)
NBOUNI(MAXBAS)molecular unit of each NBO
NBOTYP(MAXBAS)no. centers + 10 (if low-occ LP) + 20 (if BD* or RY*)
LSTOCC(MAXBAS)1 (NMB) or 0 (NRB) NAO labels
IBXM(MAXBAS)NBO label permutation list
LARC(MAXBAS)re-ordering list
LBL(MAXBAS)atomic center of AO
LORBC(MAXBAS)angular momentum label of AO
LORB(MAXBAS)(variable)
-

-8. COMMON/NBTHR/

-The DOUBLE PRECISION variables of this block store the -default values of various -numerical thresholds that can be set by the user: -

- - - - - - - - - - - - - - -
variablemeaning
THRSETNBO occupancy threshold
PRJSETprojection threshold
ACCTHRthreshold [0.1] for assigning acceptor orbital NBOTYP
CRTSETthreshold for core-occupancy warning
E2THRminimum E for 2nd-order energy analysis printing
ATHRminimum bend angle for BEND printing
PTHRminimum % p-character for BEND printing
ETHRminimum NBO occupancy for BEND printing
DTHRminimum dipole moment for DIPOLE printing
-

-9. COMMON/NBLBL/

-The INTEGER variables of this block store the number of -orbitals associated with the "LEW" and "VAL" print parameters -(Section B.2.4) and the 10 Hollerith fragments required to compose each of -the 4 possible types of localized orbital labels (AO, NAO, NHO, NBO): -

- - - - - - - - -
variablemeaning
NLEWnumber of Lewis NBOs (= number of occupied MOs)
NVALnumber of minimal basis (NMB) NAOs
LBL(10,MAXBAS,4)label fragments (AO; NAO; NHO; NBO)
-

-10. COMMON/NBNAO/

-The INTEGER arrays of this block store information pertaining -to the labelling of NAOs in the NPA output: -

- - - - - - - - - -
variablemeaning
NAOC(MAXBAS)atomic center of each NAO
NAOA(MAXBAS)angular symmetry label (Sec. B.7.5) of each NAO
LTYP(MAXBAS)'Cor', 'Val', or 'Ryd' label for each NAO
IPRIN(MAXBAS)principal quantum number (n) of each NAO
-

-11. COMMON/NBMOL/

-The INTEGER scalars, vectors, and arrays of this block -store information pertaining to "molecular units": -

- - - - - - - - - - - -
variablemeaning
NMOLECnumber of molecular units
MOLAT(MAXATM)molecular unit of each atom
MOLEC(MAXATM,MAXATM)list of atoms (J) in each molecular unit (I)
NMOLAscratch storage for open-shell case
MOLATA(MAXATM)scratch storage for open-shell case
MOLECA(MAXATM,MAXATM)scratch storage for open-shell case
-

-12. COMMON/NBTOPO/

-The INTEGER variables of this block contain atom search lists to direct -the search for NBOs and information pertaining -to the 'topology' (bond connectivity) of the molecule: -

- - - - - - - - - - - -
variablemeaning
IORDER(MAXATM)permuted atom order for NBO search
JORDER(MAXATM)atom ordering for 'best' resonance structure
NTOPO(MAXATM,MAXATM)number of bonds between atoms I,J
(or number of lone pairs on I, if I = J)
N3CTRnumber of 3-center bonds ( 10)
IC3TR(10,3)the 3 atoms of each 3-c bond
-

-13. COMMON/NBDXYZ/

-The DOUBLE PRECISION variables of this block store -information pertaining to the molecular dipole moment and charge -distribution: -

- - - - - - - - - -
variablemeaning
XDIPx-component of molecular dipole moment ( spin)
YDIPy-component of molecular dipole moment ( spin)
ZDIPz-component of molecular dipole moment ( spin)
CHARGE(MAXATM)list of 'uncompensated' nuclear charges (dipole loops)
-

-14. COMMON/NBCRD1/

-The INTEGER variables of this block store general information -related to the 'card image' (line) being processed -by the free-format input routines: -

- - - - - - - - - - - -
variablemeaning
ICD(80)array of Hollerith characters ( 80) of the input line
LOOK(80)scratch buffer for card image
LENGTHlength of the non-blank string in LOOK
IPTpointer to current location in ICD
LFNinput file assignment
NEXPexponent of a number in exponential format
-

-15. COMMON/NBCRD2/

-The LOGICAL variables of this block store information -related to the current line being read -by the free-format input routines. In each case, the -variable is set .TRUE. if the specified condition is met: -

- - - - - - - - - -
variablecondition that variable is .TRUE.
POINTa number containing a decimal point is present
ENDword 'END' or EOF has been encountered
NEXTready for reading next word in line (ICD)
EXPa number in exponential notation is present
-

-16. COMMON/NBODAF/

-The INTEGER variables of this block store information -related to the NBO direct access file (FILE48). The PARAMETER statement - 

-     PARAMETER (NBDAR = 100)
-
-
sets the maximum number of logical records accessible in FILE48: -

- - - - - - - - -
variablemeaning
INBOlogical file number [48] for DAF
NAVlast-accessed physical record of DAF
IONBO(NBDAR)mapping of physical and logical record numbers
-

-17. COMMON/NBONAV/

-The INTEGER variables of this block provide scratch storage -for writing to the NBO direct access file (FILE48). The PARAMETER statement - 

-     PARAMETER (ISINGL = 2, LENGTH = 256)
-
-
sets the FILE48 physical record LENGTH to 256 longwords -(1024 bytes): -

- - - - - - - -
variablemeaning
IXDNBO(LENGTH)scratch array for DAF writes
NBNAVnumber of physical records in IXDNBO
-

-18. COMMON/NBGEN/

-The LOGICAL variables of this block store information related -to running the GENNBO program in stand-alone mode. In each case, the -variable is set .TRUE. if the specified condition is met: -

- - - - - - - - - -
variablecondition that variable is .TRUE.
REUSE"REUSE" keyword requests use of an existing DAF
UPPER"UPPER" keyword specifies upper-triangular matrices
BOHR"BOHR" keyword specifies atomic units of length
DENOPdensity matrix is provided (i.e., "BODM" not set)
-

-C.4 DIRECT ACCESS FILE AND OTHER I/O -

- The principal I/O routines of Groups III-V are described in -Sections C.7-C.9. The input to the NBO programs is primarily -from the standard ESS input file (LFN 5), -and the output is primarily to the -standard ESS output file (LFN 6). Other "matrix output" -(read/write) I/O is by default assigned to LFNs 31-49 (see -Table of Section B.2.4), or to a user-selectable LFN, based -on keyword entries in the $NBO keylist. -

- The remaining two files that are routinely created or modified -by the NBO programs are the FILE48 direct access file (LFN 48) -and the FILE47 'archive' file -(LFN 47, described in Section B.7). The latter file can also serve -as the main input file (reassigned as LFN 5) when the NBO program is run in -stand-alone GENNBO mode. -

- From the programmer's viewpoint, the most important information -concerns the organization of the FILE48 direct access file. The -records of this file are assigned as shown in the following -table. The items marked with an asterisk (*) must be provided -from the ESS program (e.g., through the FEAOIN driver), and hence -are of particular importance to the programmer: -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
record content
1 NBODAF common block
2 *Job title
3 *NATOMS,NDIM,NBAS,MUNIT,wavefunction flags
4 *IATNO,IZNUC,LCTR,LANG
5 *AO basis set info
8 *Deletion energy, total energy
9 *Atomic coordinates
10 *AO overlap matrix
11 PNAO overlap matrix
20 *AO density matrix (alpha)
21 *AO density matrix (beta)
22 Pure AO density matrix
23 NAO density matrix (alpha)
24 NAO density matrix (beta)
25 AO density matrix with NBO deletions (alpha)
26 AO density matrix with NBO deletions (beta)
27 NBO occupancies (alpha)
28 NBO occupancies (beta)
30 *AO Fock matrix (alpha)
31 *AO Fock matrix (beta)
32 NAO Fock matrix (alpha)
33 NAO Fock matrix (beta)
34 NBO Fock matrix (alpha)
35 NBO Fock matrix (beta)
40 *AO to MO transformation matrix (alpha)
41 *AO to MO transformation matrix (beta)
42 AO to PNAO transformation matrix
43 AO to NAO transformation matrix
44 AO to NBO transformation matrix (alpha)
45 AO to NBO transformation matrix (beta)
46 AO to NLMO transformation matrix
47 NAO to NHO transformation matrix
48 NAO to NBO transformation matrix
49 NBO to NLMO transformation matrix
50 *X dipole integrals
51 *Y dipole integrals
52 *Z dipole integrals
60 NBO labels (alpha)
61 NBO labels (beta)
-[Cartesian coordinates (record 9) and dipole integrals -(records 50-52) should be in angstrom units.] -

- The direct access file serves as -a principal medium of communication between -all segments of the NBO program. Input received from the ESS -program (Section C.11) is immediately saved in the direct access file -and subsequently fetched by other subprograms, using -the fetch/save I/O routines of Section C.7. Further information on -the structure of the direct access file is specified in COMMON -blocks 16, 17 of Section C.3. -

-

-C.5 NAO/NBO/NLMO ROUTINES (GROUP I) -

-C.5.1 SR NBO Master Subroutine -

- The subroutine of highest precedence in the core NBO program is -SR NBO. This routine initially requests that the input file be searched for -the $NBO keylist (See NBOINP, Section C.9). If found, SR NBO continues by -calling three main clusters of programs, as shown below: -

-

                    SR NBO(CORE,MEMORY,NBOOPT)
-

- - - - -
Job InitializationNAO FormationNBO/NLMO Formation
RoutinesRoutinesRoutines
(Sec. C.5.2)(Sec. C.5.3)(Sec. C.5.4)
-In addition, SR NBO creates a new NBO direct access file (DAF) each time -it is called, and closes this file upon completion (See NBOPEN and NBCLOS, -Section C.9). -

- SR NBO is provided a memory vector, CORE, which is -'MEMORY' double precision words in length. For modest-sized calculations -(e.g. 10 heavy atoms with a double-zeta basis set), a vector -of 50,000 words should be adequate. Although SR NBO performs an initial -partitioning of this memory vector, the majority of the dynamic memory -allocation occurs in the NAO and NBO/NLMO formation routines, described -in Sections C.5.3 and C.5.4. -

- An array of job options, NBOOPT(10), is also passed to SR NBO. -These job options identify the current version of the NBO program -(i.e., the identity of the ESS calling program), -control program input and execution, -and determine several of the default options of the NBO analysis, as -summarized in the following table. [Entries marked with an asterisk (*) -contain information pertaining to the identity or job options of the -calling ESS program, and thus are of special concern to the -programmer.] -

-

-OPTION
ENTRY DESCRIPTION -

-*
NBOOPT(1)
-2 Do nothing (return control to calling program) -
-1 Perform Natural Population Analysis (NPA) only -
0 Perform NPA/NBO/NLMO analyses, normal program run -
1 Perform NPA/NBO/NLMO analyses, don't read $NBO keylist -
2 Initiate energetic analysis, read one deletion from $DEL -
3 Complete energetic analysis, print the energy change -

-*
NBOOPT(2)
0 SCF density -
1 MP first order density -
3 MP2 density -
4 MP3 density -
5 MP4 density -
6 CI one-particle density -
7 CI density -
8 QCI/CC density -
9 Density correct to second order -

-NBOOPT(3)
1 Perform the NBO/NLMO dipole analysis -(force the DIPOLE keyword) -

-NBOOPT(4)
1 Allow strongly delocalized Lewis structures -(force the RESONANCE keyword) -

-NBOOPT(5)
1 Spin-annihilated UHF (AUHF) wavefunction (unused) -

-NBOOPT(6-9) (unused) -

-*
NBOOPT(10)
0 General version of the NBO program (GENNBO) -
1 AMPAC version -
6 GAMESS version -
7 HONDO version -
8x GAUSSIAN-8x version -

-These options are read by job -initialization routines (Section C.5.2) and stored in COMMON/NBOPT/, -where they control events throughout the program. [Note that NBOOPT(2) -is only used by the Gaussian versions.] -

-

-C.5.2 Job Initialization Routines -

- The routines of this section initialize the default options -and parameters, read and store the user's $NBO keyword options: -

-

-This routine sets default option flags -(COMMON/NBOPT/), default logical file numbers (COMMON/NBIO/), and -default thresholds (COMMON/NBTHR/) for the NBO program. In addition, -SR NBOSET interprets the NBOOPT array, setting -option flags appropriately. -

-

-This routine is primarily responsible for reading and setting -option flags (COMMON/NBOPT/) -according to the keywords specified in the $NBO keylist. It reads -the $NBO keywords using the free format routines described in Section C.8, -continuing until the word "$END" terminates the keylist. Options which -are incompatible with the chosen wavefunction or program version are 'shut -off', and other options are 'turned on' in accord with the requested print -level ($NBO keyword PRINT). All keywords which are selected in the $NBO -keylist are echoed in the output file. -

-

- -Determines the scratch memory -requirements of the NBO program, as determined by the options selected -in the $NBO keylist. Program execution halts if the memory requirements -exceed the available memory. -

-

-C.5.3 NAO Formation Routines -

- The principal task of this cluster of routines is to control the formation -of the NAOs from the input AO basis. In addition, these routines -are responsible for the writing (to an external file) or printing (to the -output file) of a variety of matrices in the AO, PNAO, and NAO basis sets, -according to job options requested in the $NBO keylist. The first set of -routines are called by SR NBO: -

-

-

SR NAODRV(DM,T,A)
-This is the principal controller routine for non-orthogonal basis sets. -The scratch vector A is partitioned within this routine according to the -memory requirements of the NAO subprograms. -

-

-

SR NAOSIM(DM,T,A)
-This routine 'simulates' SR NAODRV in the case of a semi-empirical -calculation, where the (orthonormal) basis AOs are the presumed -effective valence shell atomic orbitals, and no NAO transformation is -needed. -

-

-

SR DMNAO(DM,T,A)
-Performs the transformation and analysis of the open-shell AO density -matrix (alpha or beta spin) to the NAO basis. This routine employs the -AO to NAO transformation, T, determined by SR NAODRV: -

-

-

SR DMSIM(DM,T,A)
-Simulates SR DMNAO for the open-shell semi-empirical case, when no -transformation is required. -

-

-

SR NBODRV(DM,T,A)

-Principal driver program for NBO formation; Section C.5.4. -

-The next set of routines are called by the main NAO driver, -SR NAODRV. They include the principal subroutine, SR NAO, -which generates the NAOs: -

-

-

SR SIMTRM(A,S,V,NDIM,N,IWMULP,IWCUBF)
>> -Performs the similarity transformation St*A*S leading to -Mulliken populations, with S = overlap matrix, A = bond-order matrix. -

-

-

SR MULANA(BS,VMAYER,BMAYER,IWMULP,IWCUBF)
-Evaluates Mulliken gross populations and performs Mayer-Mulliken -bond-order analysis (requires bond order matrix). -

-

-

SR DFGORB(RENORM,DM,T,ITRAN,IWCUBF,ITOPT,LFNPR)
-Performs the decomposition of 'raw' cartesian d, f, or g -AO sets to pure angular symmetry AOs (e.g., 6 cartesian d -5 pure d + 1 s); cf. Section B.7.5. -

-

-

SR NAO(T,S,OCC,BLK,SBLK,EVAL,C,EVECT,EVAL2,LISTAO,NBLOCK)
-This is the principal routine for formation of NAOs, following -closely the algorithm described by A. E. Reed, R. B. Weinstock, and -F. Weinhold, J. Chem. Phys. 83, 735-746 (1985). -

-

-

SR NAOANL(DM,SPNAO,BINDEX,BINDT,OVPOP,F,ENAO)
-This is the principal routine for performing and printing out natural -population analysis (NPA). The routine assigns orbital labels -and energies and writes out the NPA, natural electron configuration (NEC), -NAO-Wiberg bond index and overlap-weighted bond population tables. -[Thresholds TEST, TEST2, ALLOW, ALLOW2 test for numerical conservation of -an integer number of electrons.] -

-

-

SR FRMTMO(T,TMO,C,SCR,INDEX,NCOL)

-Forms and outputs NCOL columns of the transformation matrix to MOs -from a chosen localized set, specified by INDEX = 2 (NAO), 3 (NHO), -4 (NBO), or 5 (NLMO). Input matrix T is the transformation from AOs -to the basis set specified by INDEX, and matrices TMO, C, and SCR are -scratch arrays employed by this routine. -

-The remaining routines of this section are auxiliary subroutines -called by SR NAO to perform individual steps of the NAO algorithm: -

-

-

SR LOADAV(LISTAO,NL,M,S,NDIM,A,B,MXAOLM)
-Averages the AO density matrix elements over the 2l + 1 components -of l for a particular atom, and loads the density matrix and -overlap integrals for the orbitals of LISTAO into -matrices A, B, respectively. -

-

-

SR ATDIAG(N,A,B,EVAL,C)
-Solves the generalized eigenvalue problem (A - EVAL*B)*C = 0 -to diagonalize an atomic block. -

-

-

SR SETBAS(LSTOCC,LSTEMT,NOCC,NEMT,IAT,L,NL,NF,NDIM)
-Selects the 'occupied' NAOs to be included in the natural minimal basis -set for a particular atom (up to Z = 105) and angular -momentum symmetry type (L), and stores them in LSTOCC. -

-

-

SR NEWWTS(S,T,WT)

-Recomputes symmetry-averaged occupancy weights for PNAOs. This routine is -only used in conjunction with the 'PAOPNAO=R' keyword. -

-

-

SR WORTH(S,T,BLK,LIST,NDIM,NBAS,N,OCC,EVAL,BIGBLK)
-This subroutine implements the occupancy-weighted symmetric -orthogonalization (OWSO), a key feature of the NAO algorithm. [Note -that BLK and BIGBLK share the same storage area, though they -are dimensioned differently. The routine includes three -numerical thresholds, WTTHR (10-3) for occupancy weight, -DIAGTH (10-12) for Jacobi diagonalization, and DANGER (103) -for linear dependence difficulties.] -

-

-

SR SHMDT(T,S,NDIM,NBAS,NOCC,LSTOCC,NEMT,LSTEMT,SBLK)
-Schmidt orthogonalization of column vectors of T. -

-

-

SR NEWRYD(T,S,TPNAO,DMBLK,SBLK,EVECT,OCC,EVAL,EVAL2,LIST,IRPNAO)

-Computes new Rydberg NAOs after Schmidt orthogonalization of -the Rydberg space to the NMB set. -

-

-

SR RYDIAG(T,S,TPNAO,DMBLK,SBLK,OCC,EVAL,EVECT,EVAL2,

-IORB,NC,NM,NSTART,NRYDC,LARC,LIST,IRPNAO) -Diagonalizes an atomic Rydberg block and updates the PNAO -transformation matrix. -

-

-

SR RYDSEL(LSTEMT,NEMT,NSEL1,LIST1,NSEL2,LIST2,WT)
-Partitions Rydbergs into 'significantly occupied' (> WTTHR) -and 'negligibly occupied' ( WTTHR) sets, assigning the -latter to have equal (non-zero) occupancy weighting. This -avoids numerical singularities associated with the OWSO occupancy -weighting for orbitals of negligible occupancy, effectively -replacing OWSO by ordinary Löwdin-orthogonalization -of these 'residual' Rydbergs among themselves. [Threshold -WTTHR (10-4) controls singularities of the inverse -square-root weighting matrix.] -

-

-

SR REDIAG(DM,T,TPNAO,EVAL,BLK,C,IRANK,IRPNAO)
-Rediagonalizes the atomic density matrix blocks after symmetry -averaging. -

-

-

SR REDBLK(T,TPNAO,IL,DM,BLK,EVAL,C,NF,IORB,NC,IRANK,IRPNAO)
-Finds the rediagonalization transformation for a specific -l-symmetry atomic subblock of the density matrix. -

-

-C.5.4 NBO/NLMO Formation Routines -

- The master routine of this cluster is -SR  NBODRV(DM,T,A), which partitions the scratch storage -vector (A) according to the memory requirements of the NBO formation -and analysis subprograms and controls the calculation of the -transformation (T) from NAOs to NBOs using the NAO density matrix (DM). -SR NBODRV calls either SR NATHYB (for the default NBO search) or SR CHSDRV -(for the $CHOOSE directed NBO search) to form the NBOs. It -also calls the NLMO -formation routine (SR NLMO) and dipole analysis routine (SR DIPANL). -According to job options selected in the $NBO keylist, SR NBODRV also -transforms and outputs a variety of matrices in the PNHO, NHO, PNBO, NBO, -PNLMO, and NLMO basis sets. [Note that the first NATOMS*NATOMS -elements of the A vector store the Wiberg bond index elements -determined in the NAO routines; these should not be destroyed until -calculation of NBOs is complete.] -

-

- The following routines are called by SR NBODRV: -

-

SR NATHYB(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,

-P,TA,HYB,VA,VB,TOPO) -This routine performs the basic NBO search, the central task of -NBO analysis, closely following the description given by -J. P. Foster and F. Weinhold, J. Am. Chem. Soc. 102, -7211-7218 (1980). The routine constructs the -orthogonal matrix (T) for the NAO to NBO -transformation from the input NAO density matrix (DM). The efficiency -of the search procedure is enhanced by using the -NAO-Wiberg bond index as a 'GUIDE' to order the NBO search. -

-[Beware the IBXM bond orbital permutation list (!), which reorders the -LABEL array of COMMON/NBBAS/. The occupancy threshold, THRESH, determines -whether an NBO is accepted during the search for bond orbitals (cf. SR CYCLES). -Two numerical thresholds -(PRJTHR, PRJINC) control possible linear dependencies: In -the main loops over 1-c, 2-c (and 3-c) functions, each prospective -NBO is checked for possible redundancy with previous NHOs by -the PRJEXP (projection operator expectation value) test. The -threshold PRJTHR for a 'new' hybrid is initially set -conservatively low (0.20), -but will be auto-incremented by PRJINC (0.05) as needed to prevent -linear dependency; any numerical singularity triggers IALARM and -causes PRJTHR to be incremented and the entire NBO search repeated.] -

-

-

SR CHSDRV(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,

-P,TA,HYB,VA,VB,TOPO) -This routine, the "$CHOOSE driver," reads the $CHOOSE keylist, -setting up the arrays NTOPO and I3CTR of COMMON/NBTOPO/ which will -control the directed NBO search of SR CHOOSE. -

-

-

SR CHOOSE(DM,T,GUIDE,BNDOCC,POL,Q,V,BLK,C,EVAL,BORB,

-P,TA,HYB,VA,VB,TOPO,IFLG) -This routine is essentially similar to SR NATHYB, but the search -loops are directed by the $CHOOSE specification. -

-

-

SR SRTNBO(T,BNDOCC)
-Reorders (dangerous!) the NBOs according to bond type and constituent atomic -centers. NBOs are ordered BD (and 3C), CR, LP, LP*, RY*, BD* (and 3C*). -Note that this step is not required for the proper execution of any of the -NBO analysis or NLMO formation routines, but it leads to more readable -output. -

-

-

SR XCITED(DM,T,HYB,THYB,S,OCC,SCR,ISCR)
-Examines PNHO overlaps to determine whether NBOs were properly labelled -as 'bonds' (unstarred, Lewis) or 'antibonds' (starred, non-Lewis) -in the NBO formation routines (SR NATHYB and SR CHOOSE). If incorrect -nodal character is recognized in a bond or antibond (generally indicative -of an excited state), a warning is printed -and the orbital is relabelled. Note that this will probably mix the -NBO ordering set by SR SRTNBO. -

-

-

SR ANLYZE(T,BNDOCC,HYB,HYCOEF,THYB)
-Prints out the principal table (Section A.3.3) -of NBO analysis [using the IBXM ordering!], -expressing each NHO in sp form. - -

-

SR HTYPE(HYB,LTYP,MXAO,NH,COEF,PCT,NL,ISGN)

-Analyzes input hybrid for polarization coefficient and percentages -of each angular momentum component (accepts up to g orbitals). -

-

-

SR FRMHYB(HYB,THYB,COEFF,HYCLEF,KL,KU,NHYB)

-Forms the NAO to NHO transformation (THYB) and saves it on the DAF. -

-

-

SR HYBDIR(BNDOCC,ATCOOR,THYB,TBND,SCR)
-Computes hybrid directionality and bond bending angles as determined from -percentage p-character for selected -NBOs, and prints the BEND table -(Section A.3.4). [Keyword-selectable thresholds -ATHR (angular deviation), PTHR (% p-character), and ETHR (occupancy) -control printing.] -

-

-

SR HYBCMP(XYZ,PCENT,IHYB,JCTR,HYB)
-Finds direction and percentage p-character of a given hybrid. -

-

-

SR FNDMOL(IATOMS)
-Finds 'molecular units' from NBO connectivity. -

-

-

SR NBOCLA(BNDOCC,ACCTHR)
-Classifies NBOs according to donor/acceptor type, number of atomic centers, -and parent molecular unit. -

-

-

SR FNBOAN(BNDOCC,F,MOLNBO)
-Performs the 2nd-order perturbation theory energy analysis of -the NBO Fock matrix and prints the table (Section A.3.5). [Thresholds ETHR1 -(intramolecular) and ETHR2 (intermolecular) control printing.] -

-

-

SR NBOSUM(F,BNDOCC,LIST,LISTA,SCR)
-Prepares and prints the NBO summary table (Section A.3.6). -

-

-

SR GETDEL(IBO,OCC,THR1,THR2,NL,LIST,DEL,DELOC,IFLG)

-Assembles the delocalization list, LIST(NL), for the IBOth -NBO. Only intramolecular and intermolecular delocalizations which are -stronger than THR1 and THR2 (in kcal mol-1), respectively, -are included in the list. -

-

-

SR BLDSTR(IBO,IL,NL,LIST,ML,ISTR)
-Builds a character string containing delocalization information for the -NBO summary table. -

-

-

SR NLMO(N,A,EVAL,EVEC,TSYM,RESON,NOCC,IALARM)

-This is the main routine for determination of the NLMOs, following -closely the description given by A. E. Reed and F. Weinhold, -J. Chem. Phys. 83, 1736-1740 (1985). [Numerical thresholds -DIFFER (10-5), DONE (10-10), and EPS (10-11) -control the modified Jacobi diagonalizations.] -

-

-

SR LMOANL(T,S,RESON,OCC,TS,BORDER,OWBORD,ATLMO,SIAB,NOCC,NAB)

-Prints out details of the NAONLMO transformation and -the NAO/NLMO bond order table (Section B.6.2). -

-

-

SR DIPANL(DM,T,C,TNBO,DX,DY,DZ,SCR,INDEX)
-Calculates and prints out the DIPOLE analysis table (Section B.6.3). -

-

-

SR DIPELE(DXYZ,C,T,SCR,ETA,TOANG,NOCC,INDEX)
-Evaluates the x,y,z (INDEX = 1,2,3) electronic dipole moment -contributions, including delocalization contributions, for each -occupied NBO. -

-

-

SR DIPNUC(DX,DY,DZ,ATCOOR,ETA,NOCC)

-Evaluates the nuclear contributions (DX, DY, DZ) to the molecular -dipole moment. -

-

-The following routines are called by SR NATHYB and SR CHOOSE -in calculating the NBOs. Overall supervision -of this set of routines is exercised by SR CYCLES. Other routines -are associated with specific steps of the NBO algorithm: -

-

-

SR CORE(DM,T,BORB,POL,Q,HYB,BNDOCC,IBD,DETAIL,LFNPR)

-Performs the first step in the search for NBOs. This routine identifies -core orbitals and depletes the NAO density matrix of their contributions. -

-

-

FN IWPRJ(NCTR)
-This function returns zero (no projection wanted) -if still on the same atomic center, or one (projection operator should -be formed) if this is a new center. -

-

-

SR DEPLET(DM,T,Q,POL,BORB,BNDOCC,NBD)
-'Depletes' density matrix of contribution from bond orbital (BORB), by -subtracting its diagonal contribution from the spectral expansion of -the density operator. This insures that the same electron pair will -not be found twice in the NBO loops. -

-

-

SR LOAD(DM,IAT1,IAT2,IAT3,BLK,NB)
-Loads the appropriate atomic blocks of the density matrix -into the local (2-c, 3-c) density matrix subblock (BLK), in -preparation for diagonalization. -

-

-

SR PRJEXP(BORB,IAT1,IAT2,IAT3,Q,P,PK,HYB,VA,VB,HYBEXP)

-Determines how much of a prospective bond orbital (BORB) is composed -of hybrids already used. The projection operator onto the space of -previously accepted hybrids is used to evaluate the expectation -value of each hybrid component of BORB. -

-

-

SR STASH(BORB,IBD,IAT1,IAT2,IAT3,POL,Q,HYB)

-Decomposes bond orbital (BORB) into constituent normalized hybrids -and stores them in the hybrid array (Q). -

-

-

SR ORTHYB(Q,S,TA,EVAL,C,IALARM,IFLG)

-Performs symmetric (Löwdin) orthogonalization on occupied -atomic hybrids (PNHOs) to give final NHOs. [Threshold TOOSML -(10-4) turns on the alarm (IALARM) to warn of numerical -instabilities due to linear dependence.] -

-

-

SR FRMPRJ(P,IA,Q,NK,PK,VK,PI)

-Forms projection matrix to annihilate components of the occupied -atomic hybrids on a given center. -

-

-

SR AUGMNT(P,BLK,C,EVAL,DM,TA,BORB,V,LARC,IA,NOCC,NORB)

-This routine augments the set of occupied atomic hybrids on a center -with a sufficient number of Rydberg AOs (in order of occupancy) to -complete the span of the basis set on that atom. -

-

-

SR REPOL(DM,Q,POL,BLK,EVAL,C,NBD)

-Diagonalizes each 2x2 block of the density matrix in the basis of -final NHOs to get the optimal polarization coefficients for each NBO. -

-

-

SR FORMT(T,Q,POL)
-Constructs the final NAO to NBO transformation matrix (T) from -the final array of NHOs (Q) and polarization coefficients (POL). -

-

-

SR CYCLES(ITER,THRESH,GUIDE,BNDOCC,TOPO,ICONT)

-Controls the overall search for an acceptable resonance structure, -including the lowering of the occupancy threshold (THRESH) for the -RESONANCE keyword. Decides whether a structure is acceptable, -initiates reordered searches over atoms for alternative resonance structures, -and returns with the best overall structure. Prints the -initial table (Section A.3.3) of the NBO output. -

-The final routines of this group are auxiliary to the formation -of NLMOs, called by SR NLMO: -

-

-

SR SYMUNI(TSYM,A,COS,SIN,OVLP,BLK,EVAL,NROT,NIUNIQ,NJUNIQ,ILIST,

-JLIST,NOFF,IOFF,JOFF,NDIM)

-Symmetrizes the unitary transformation matrix (TSYM) to preserve -symmetries inherent in the density matrix, using symmetric -orthogonalization of columns (if necessary) to preserve unitarity. -

-

-

SR SYMORT(S,T,BLK,NDIM,N,EVAL)
-Symmetric orthogonalization of a set of column vectors (T). [Thresholds -DIAGTH (10-12) for off-diagonal Jacobi diagonalization -and DANGER (103) to detect singularities of the overlap matrix; -all eigenvalues of S must be less than DIAGTH*DANGER.] -

-C.6 ENERGY ANALYSIS ROUTINES (GROUP II) -

-The small set of routines in this group carry out the second main -task of NBO analysis, the NBO Energetic Analysis ("deletions," -associated with inclusion of a $DEL keylist; Section B.5). These routines -depend on the presence of a Fock matrix, and are bypassed in -any non-SCF calculation. -

-Overall control of Group II routines is with SR NBOEAN, which in turn -calls the remaining programs of this group: -

-

SR NBOEAN(A,MEMORY,NBOOPT,IDONE)

-The task performed by this subroutine is dependent of the value of -NBOOPT(1). If set to 2, this routine initiates (by calling SR NBODEL) -the calculation of the next NBO deletion of the $DEL keylist. If set -to 3, this routine completes the NBO deletion by computing the energy -for the deletion. INTEGER variable IDONE is set to 1 if no additional -deletions are found in the $DEL keylist. -

-

-

SR NBODEL(A,MEMORY,IDONE)
-Controls the calculation of the new AO density matrix from the requested -deletion in the $DEL keylist. A modified NBO Fock matrix is created -(SR DELETE) and diagonalized (SR JACOBI), leading to a new AO density -matrix (SR NEWDM). This routine also prints the NBO deletions table -(Section B.6.10). -

-

-

SR DELETE(F,TRF,NDIM,IDEL,LEN,ITYPE,NDEL,NTRUNC,DONE,ISPIN)

-Reads the $DEL list for the next deletion, deletes (sets -to zero) the appropriate -elements from the Fock matrix, and prints out the deletion specification -Section B.6.10). -

-

-

SR NEWDM(DM,U,EIG,NDIM,IDEL,LEN,NDEL,ITYPE,NMOOCC,ISPIN)
-Constructs a new density matrix corresponding to the deleted Fock matrix. -

-

-

SR RNKEIG(RANK,EIG,N,NDIM,ARCRNK)

-Ranks the eigenvalues found in vector EIG (lowest eigenvalue having -first rank). I = ARCRNK(N) is the entry whose rank is N. -

-

-

SR SIMLTR(N,NDIM,F,U,R,S,KNTROL)

-Performs the similarity transform Ut*F*U on a packed -upper-triangular matrix F. -

-C.7 DIRECT ACCESS FILE ROUTINES (GROUP III) -

- The routines of Group III are involved in communication between -the NBO programs and the FILE48 -direct access file (DAF), whose contents -are described in Section C.4. Two levels of I/O routines are employed. -

- The higher-level 'fetch/save' routines are called directly by the NBO -subroutines. -In most cases, the -function of the fetch/save routines can be recognized by its name or argument -list; e.g., "FETITL(TITLE)" fetches -the job title line, "FEFAO(F,IWFOCK)" fetches -the AO Fock matrix (FAO), -and so forth. Each routine can also be associated with a -logical record number (IDAR) of the direct access file (Section C.4), -where the I/O item is stored. We list these -routines in order of appearance, together with the associated -direct access file record number(s) IDAR, without further description: -

- - - - - - - - - - - - - - - - - - - - - - - -
routineIDARroutineIDAR
SR FETITL(TITLE)2SR SVTLMO(T)49
SR FEE0(EDEL,ETOT)8SR FETLMO49
SR SVE0(EDEL)8SR SVTNHO47
SR FECOOR(ATCOOR)9SR FETNHO47
SR FESRAW(S)10SR SVPPAO(DM)22
SR FEDRAW(DM,SCR)20,21SR FEPPAO(DM)22
SR FEFAO(F,IWFOCK)30,31SR SVTNAO(T)43
SR FEAOMO(T,IT)40,41SR FETNAO(T)43
SR FEDXYZ(DXYZ,I)50-52SR SVNLMO(T)46
SR SVNBO(T,OCC,ISCR)44,45SR FENLMO(T)46
SR FENBO(T,OCC,ISCR,NELEC)44,45SR SVDNAO(DM)23,24
SR FETNBO(T)44,45SR FEDNAO(DM)23,24
SR SVPNAO(T)42SR SVFNBO(F)34,35
SR FEPNAO(T)42SR FEFNBO(F)34,35
SR SVSNAO(S)11SR SVNEWD(DM)25,26
SR FESNAO(S)11SR FENEWD(DM)25,26
SR SVTNAB(T)48SR FEINFO(ICORE,ISWEAN)3
SR FETNAB(T)48SR FEBAS(NSHELL,NEXP,ISCR)5
- In turn, the fetch/save routines call the following lower-level, -primitive subprograms, -which open, close, read, write, and test the contents of the DAF -(these are heavily modified versions of the direct -access file subroutines of HONDO): -

-

-

SR NBOPEN(NEW,ERROR)

-Opens a new or existing unformatted DAF depending in the value of logical -variable NEW. Record lengths are currently set at 256 (LENGTH) single -precision words (1024 bytes), and -up to 100 (NBDAR) logical records can be written. Note that logical records -and physical records of the DAF are not equivalent; single logical records -can span several physical records and need not be ordered sequentially. -The array IONBO (in COMMON/NBODAF/) maps each logical record with its -associated physical records. The first physical record of the DAF is -reserved for COMMON/NBODAF/. [Note: Some machines may require -that you alter the parameters LENGTH (the chosen -record length) and ISINGL (a record length scaling factor).] -

-

-

SR NBWRIT(IX,NX,IDAR)

-Writes NX double precision words of array IX to logical record number IDAR -of the NBO DAF. -

-

-

SR NBREAD(IX,NX,IDAR)
-Reads NX double precision words of the logical record number IDAR of the -NBO DAF. -

-

-

SR NBCLOS
-Rewrites common block /NBODAF/ on the first physical record of the DAF, and -closes the file. -

-

-

SR NBINQR(IDAR)

-Inquires whether information has been stored in logical record IDAR of -the direct access file, and sets IDAR=0 if the record is empty. -

-C.8 FREE FORMAT INPUT ROUTINES (GROUP IV) -

- The routines of Group IV are the small set of system-independent -free-format input routines that are used in reading the various -keylists and datalists of the input -file. The routines of this group are the -'primitives' that read and interpret individual keywords or -entries of a keylist. They are called by higher-level -I/O routines (such as SR JOBOPT of Group I) throughout the NBO program. -

-The free-format input primitive routines are: -

-

SR STRTIN(LFNIN)

-Initializes input from the LFNIN input file. -

-

-

SR RDCARD

-Reads the next 'card' (line) of the input file, and stores this line in -the integer array ICD in COMMON/NBCRD1/ with all lower case characters -converted -to upper case. Logical variable END in COMMON/NBCRD2/ is set to .TRUE. if -the end-of-file is encountered. -

-

-

SR IFLD(INT,ERROR)

-Searches input file LFNIN for the next string of non-blank characters, -and checks to see if they form an integer. If so, the numerical value -of the integer is placed in INT. If not, the logical variable ERROR is -set to .TRUE. and INT is set positive (indicating an "END" terminating -mark or end-of-file was encountered) or negative (indicating that the -character string is not an integer). -

-

-

SR RFLD(REAL,ERROR)

-Similar to SR IFLD, but for a real number REAL. This routine will accept -real numbers in a variety of different formats. For example, 1000 can be -represented by 1000, 1000.0, 1.0E3, D3, 1+3, etc. -

-

-

SR HFLD(KEYWD,LENG,ENDD)

-Similar to SR IFLD and RFLD, but for a Hollerith array KEYWD(LENG). -The logical variable ENDD is set to .TRUE. if the "END" terminating -mark or the -end-of-file is encountered. On return to the calling subroutine, LENG -is set to the length of the string in KEYWD or to zero if the end-of-file -is encountered. -

-

-

SR FNDFLD

-Searches for the next non-blank field on the input file, reading -additional lines if necessary. Commas and equal signs are treated as -blanks, and any character string which follows an exclamation point -is treated as an arbitrary comment, and is ignored. -The contents of this field are stored -in the integer array LOOK of length LENGTH in COMMON/NBCRD1/. - -

FN EQUAL(IA,IB,L)

-This logical function tests the equivalence of the first 'L' elements of -the Hollerith strings IA and IB. -

-C.9 OTHER SYSTEM-INDEPENDENT I/O ROUTINES (GROUP V) -

- This section summarizes the I/O routines of Group V. These routines -perform a variety of auxiliary I/O tasks, such as the reading -or writing of matrices, or perform functions closely related to I/O. -

- The first set of programs in this group are responsible for -searching for the $GENNBO, $NBO, $CORE, $CHOOSE, and $DEL identifiers -of the job input file LFNIN: -

-

-

SR GENINP(NEWDAF)

-Searches for the $GENNBO identifier. In addition, this routine -reads in the keywords of the $GENNBO keylist (see Section B.7), -setting the option flags of COMMON/NBOPT/ and COMMON/NBGEN/ appropriately. -

-

-

SR NBOINP(NBOOPT,IDONE)

-Searches for the $NBO identifier according to the program version number, -NBOOPT(10). The integer variable IDONE is -set to 0 if this identifier is located, or 1 otherwise. -

-

-

SR CORINP(IESS,ICOR)

-Searches for the $CORE identifier according to the program version number, -IESS. The integer variable ICOR is -set to 1 if this identifier is located, or 0 otherwise. -

-

-

SR CHSINP(IESS,ICHS)

-Searches for the $CHOOSE identifier according to the program version number, -IESS. The integer variable ICHS is -set to 1 if this identifier is located, or 0 otherwise. -

-

-

SR DELINP(NBOOPT,IDONE)

-Searches for the $DEL identifier according to the program version number, -NBOOPT(10). The integer variable IDONE is -set to 0 if this identifier is located, or 1 otherwise. -

- The remaining routines of this group perform miscellaneous I/O functions: -

-

-

SR RDCORE(JCORE)

-Initializes the atomic core array (IATCR on COMMON/NBATOM/), and reads -the entries of the $CORE keylist. -

-

-

SR WRPPNA(T,OCC,IFLG)

-Writes the transformation from 'pure' -AOs to PNAOs, the NAO labels (NAOCTR, NAOL, and LSTOCC from COMMON/NBBAS/), -and PNAO occupancies (diagonal PNAO density matrix elements) to an external -file (LFN = -IFLG). Pure AOs (PAOs) are obtained -from 'raw' cartesian AOs by the transformations of SR DFGORB. -

-

-

SR RDPPNA(T,OCC,IFLG)

-Reads the transformation from 'pure' AOs (PAOs) to PNAOs, NAO labels, and -PNAO occupancies from an external file (LFN = -IFLG/1000) (cf. -SR WRPPNA). -

-

-

SR WRTNAO(T,IFLG)

-Writes the AO to NAO transformation (fetched from the DAF), NAO labels, and -the PNAO overlap matrix (also fetched from the DAF) to an external file -(LFN = -IFLG). Note that T is the PNAO overlap matrix when control is -returned to the calling routine. -

-

-

SR RDTNAO(DM,T,SCR,IFLG)

-Reads the AO to NAO transformation, NAO labels, and PNAO overlap matrix from an -external file (LFN = -IFLG/1000). The transformation and overlap -matrices are saved on the -DAF, and the input AO density matrix is transformed to the NAO basis. Note -that T is the PNAO overlap matrix on return to the calling routine -(cf. SR WRTNAO). -

-

-

SR WRTNAB(T,IFLG)
-Writes the NAO to NBO transformation and NBO info (LABELS and IBXM arrays of -COMMON/NBBAS/) to an external file (LFN = -IFLG). -

-

-

SR RDTNAB(T,DM,BNDOCC,SCR,IFLG)

-Reads the NAO to NBO transformation and NBO info from an external -disk file (LFN = -IFLG/1000). The input NAO density matrix is also -transformed to the NBO basis, and the NBO occupancies are stored in -BNDOCC (cf. WRTNAB). -

-

-

SR WRTNBO(T,BNDOCC,ISCR,IFLG)

-Writes the AO to NBO transformation, the NBO occupancies, and additional -NBO info (NBOUNI, NBOTYP, LABEL, IBXM, and IATNO arrays) to an external -disk file (LFN = -IFLG). -

-

-

SR WRNLMO(T,DM,ISCR,IFLG)

-Similar to SR WRTNBO but for NLMOs. Note that the NLMO labels are -identical to the NBO labels. -

-

-

SR WRBAS(SCR,ISCR,LFN)

-Writes the atomic coordinates and AO basis set information to the 'AOINFO' -file LFN. The information contained in this file is identical to that of the -$COORD, $BASIS, and $CONTRACT datalists of the GENNBO input file (see Section -B.7). For more information on the file format, see the subroutine source code. -

-

-

SR WRARC(SCR,ISCR,LFN)

-Writes the 'ARCHIVE' file LFN (see Section B.7). -

-

-

SR AOUT(A,MR,NR,NC,TITLE,INDEX,IFLG)

-General utility to write matrix A(MR,1) to an external file (LFN = -IFLG) -or print it to the output file (IFLG = number of columns to print, 'FULL', -'VAL', or 'LEW'). TITLE is a CHARACTER*80 matrix label, and the -rows of A are labelled according to the value of INDEX = 0 (atoms), 1 (AOs), -2 (NAOs), 3 (NHOs), 4 (NBOs), or 5 (NLMOs). This routine calls SR APRINT or -SR AWRITE. -

-

-

SR APRINT(A,MR,NR,NC,TITLE,INDEX,MCOL)

-Prints MCOL columns of matrix A to the output file. The format of the -matrix is chosen according to the magnitude of the largest matrix element -in A (cf. SR AOUT). -

-

-

SR AWRITE(A,MR,NR,NC,TITLE,LFN)

-Writes matrix A to external disk file LFN (cf. SR AOUT). -

-

-

SR AREAD(A,MR,NR,NC,JOB,LFN,ERROR)

-Reads NC columns of the matrix A(MR,1) from the external file LFN. -The job title in the external file is returned to the calling subroutine -in the Hollerith array, JOB(20), and the LOGICAL -variable ERROR is set to .TRUE. if an error occurred while reading. -

-

-

SR OUTPUT(A,MR,MC,NR,NC)
-Prints the matrix A(MR,MC) to the standard output file. This routine is -called only when the print formats of SR APRINT are unsuitable for matrix A. -

-

-

SR INTERP(STRING,LEN,IFLG,LFN,READ,ERROR)

-Interprets the Hollerith array STRING(LEN), storing the result in IFLG. The -contents of STRING can be any of the read/write/print parameters -such as 'W38', 'PVAL', 'R43', etc., described in Section B.2.4, -and the resulting value of IFLG is determined according to the -discussion of COMMON/NBOPT/ in -Section C.3. When this routine is called, IFLG should be set to its -default value, -LFN should be the default file for writing or reading, and LOGICAL variable -READ should be set to .TRUE. if reading from an external file is allowed. -The LOGICAL variable ERROR is set to .TRUE. if STRING is uninterpretable. -

-

-

FN IOINQR(IFLG)

-Interprets IFLG as to whether the I/O item should be printed (IOINQR = 'PRNT'), -read (IOINQR = 'READ'), or written out (IOINQR = 'WRIT') to an external file. -

-

-

SR LBLAO

-Forms labels for AOs and stores them in COMMON/NBLBL/. -

-

-

SR LBLNAO

-Forms labels for NAOs and stores them in COMMON/NBLBL/. -

-

-

SR LBLNBO

-Forms labels for NBOs and stores them in COMMON/NBLBL/. -

-

-

SR LBLNHO(INHO,INBO,ICTR,NCTR)

-Forms labels for NHOs and stores them in COMMON/NBLBL/. -

-

-C.10 GENERAL UTILITY ROUTINES (GROUP VI) -

-The utility routines of Group VI perform a variety of mathematical -and other general tasks (such as solving sets of linear -equations), and are called from routines -throughout the NBO program. They are grouped in alphabetical -order (except for the final group of routines controlled by -the SR LINEQ driver): -

-

-

SR ANGLES(X,Y,Z,THETA,PHI)

-Converts cartesian coordinates (X,Y,Z) to corresponding polar -angle THETA and azimuthal angle PHI in spherical polar coordinates. -

-

-

FN BDFIND(IAT,JAT)

-LOGICAL function BDFIND is set to .TRUE. if there is at least one bond -between atoms IAT, JAT. -

-

-

SR CHEM(NAT,NATOMS,LISTA,NL,ISTR)

-Builds a 'chemical formula' for the list of atoms in LISTA having -been identified as belonging to a particular 'molecular unit'. The -chemical formula is stored in the Hollerith array ISTR(NL). -

-

-

SR CONSOL(AUT,ALT,NDIM,N)

-Consolidates an upper-triangular (AUT) and lower-triangular (ALT) -matrix in a single matrix, stored in AUT. -

-

-Converts the Hollerith array IJ(LEN) into an integer IK. This is the -inverse of SR IDIGIT. -

-

-

SR CONVRT(N,NC1,NC2)
-Converts a 2-digit integer N to two Hollerith characters NC1, NC2. -

-

-

SR COPY(A,B,NDIM,NR,NC)
-Copies matrix A to matrix B. -

-

-

SR CORTBL(IAT,ICORE,IECP)
-Stores the nominal "core table," giving the number of core -s, p, d, f orbitals for elements 1-105 (H to Lw, -and elements 104, 105). This table controls the number of -high-occupancy unhybridized NAOs that will be isolated and -removed as core NBOs (taking account also of any effective -core potential). -

-

-

SR DEBYTE(I,IBYTE)

-Decomposes a Hollerith variable I into its four individual -Hollerith 'bytes' IBYTE(4). -

-

-

SR HALT(WORD)

-Halts the execution of the NBO program if an unrecognizable keyword -is found in the $NBO keylist. -

-

-

SR IDIGIT(KINT,IK,ND,MAXD)

-Converts the INTEGER variable KINT in the first ND elements of the -Hollerith array IK(MAXD). This is the inverse of SR CONVIN. -

-

-

FN IHTYP(IBO,JBO)
-This Hollerith function determines whether the IBOJBO delocalization -is vicinal ('v'), geminal ('g'), or remote ('r'), based on the derived NBO -connectivity. -

-

-

SR JACOBI(N,A,EIVU,EIVR,NDIM,NVDIM,ICONTR)

-Diagonalizes a real symmetric matrix by the Jacobi rotations -method. If ICONTR=0, a standard Jacobi diagonalization (unconstrained -2x2 rotations) is carried out. If ICONTR=1, the algorithm is -prevented from mixing orbitals that are degenerate within 'DIFFER' -if the off-diagonal element connecting them is less -than 'DIFFER'. [Threshold DIFFER (10-5) controls -degenerate mixing, DONE (10-13) is the maximum allowed -off-diagonal element, and EPS (0.5x10-13) is a number -between DONE and the machine precision.] -

-

-

SR LIMTRN(T,M,A,B,NDIM,NBAS,NCDIM,NC,IOPT)

-This routine carries out a 'limited' transformation of a matrix (T), -using only the rows and columns specified by vector M. The -operations performed are T*A, At*T*A, or At*T -according to the value of IOPT. -

-

-

SR MATMLT(A,B,V,NDIM,N)
-Multiplies square matrices A*B (using scratch vector V) and -stores result in A. -

-

-

SR MATML2(A,B,V,NDIM,N)

-Multiplies At*B (using scratch vector V) and stores the -result in B. The algorithm assumes that A*B is a symmetric, -so about half the work is saved. [SR MATML2 is typically the second step -in a similarity transform of B by A, where B (and thus -At*B*A) is symmetric.] -

-

-

FN NAMEAT(IZ)

-Returns the (Hollerith) atomic symbol for -atomic number IZ 103. -

-

-

SR NORMLZ(A,S,M,N)
-Normalizes the columns of A using the overlap matrix S. -

-

-

SR ORDER(RANK,LIST,N,NDIM,ARCRNK)

-Ranks the positive elements of integer LIST(N), lowest values first. [RANK -and ARCRNK are integer vectors, with I = ARCRNK(N) if LIST(I) is the -element of rank N.] -

-

-

SR PACK(T,NDIM,NBAS,L2)
-Packs the upper-triangular portion of the symmetric matrix T(NBAS,NBAS) -the first L2 elements of T. -

-

-

SR RANK(EIG,N,NDIM,ARCRNK)

-Orders the entries of vector EIG, highest values first. ARCRNK(I) -is the old location of the Ith highest value in EIG. On return, -EIG(I) is the Ith highest value. [Entries are not switched -unless they differ by more than a DIFFER (5x10-8) -threshold.] -

-

-

SR SIMTRN(A,T,V,NDIM,N)

-Performs the general similarity transform Tt*A*T of A by T, using -scratch vector V. -

-

-

SR SIMTRS(A,S,V,NDIM,N)

-Performs the 'fast' similarity transform St*A*S, assuming the -result is symmetric. -

-

-

SR TRANSP(A,NDIM,N)
-Transposes the matrix A: AAt. -

-

-

SR UNPACK(T,NDIM,NBAS,L2)
-Unpacks an upper triangular matrix (vector of length L2) into a -symmetric matrix T(NBAS,NBAS). -

-

-

SR VALTBL(IAT,IVAL)

-Specifies the nominal "valence table," giving the number of valence -AOs of each symmetry type for elements 1-105. -

-

-

FN VECLEN(X,N,NDIM)

-Evaluates Euclidean length of vector X. -

-

-

SR LINEQ(A,X,B,SCR,N,M,NDIM,MDIM,ZERTOL,EPS,MAXIT,LFNPR,IERR)

-This and the three following routines constitute -the linear equations package for solving the system -A*X = B for matrix X by the method of Gaussian elimination. -

-

-

SR FACTOR(A,W,D,IPIVOT,N,NDIM,ZERTOL,IFLAG)

-Supports SR LINEQ. -

-

-

SR FNDSOL(A,X,B,W,R,E,IPIVOT,N,NDIM,EPS,MAXIT,LFNPR,IERR)

-Supports SR LINEQ. -

-

-

SR SUBST(X,W,B,IPIVOT,N,NDIM)

-Supports SR LINEQ. -

-C.11 SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII) -

- The routines of Group VII comprise the set of ESS-dependent -driver routines which initiate the NBO and NBO energetic analyses and -provide the NBO program with a variety of information about the -electronic wavefunction. This section provides a brief, generic description of -each of the driver routines. If you intend to write a set of routines -for an ESS program not supported by this distribution, refer to the -driver source code -for additional guidance. Also, see Section C.13 for helpful -hints for attaching the NBO program to an ESS package. -

- The driver routines are grouped together at the end of the NBO source -code. Since multiple versions of each driver are provided (one for each -supported ESS package and GENNBO), all of the executable lines in these -routines are 'commented out' with an asterisk in the first column. In -addition, every line of the drivers has an identifier 'XXXDRV' in -columns 73-78, where 'XXX' is a 3-letter identifier for the associated -ESS package. It is the responsibility of the program ENABLE to 'uncomment' -the appropriate lines of the code for the requested program version -(see Section A.2). -

- The system-dependent driver routines are: -

-

-

SR RUNNBO

-Determines the -logical file numbers for the input and output files (LFNIN and LFNPR) -of the parent program, initializes the NBOOPT job option array -Section C.5.1), -and initiates the NBO analysis (SR NBO) and energetic analysis -(SR NBOEAN). This routine is the only routine -of the NBO program called directly -by the parent ESS package. -

-

-

SR FEAOIN(CORE,ICORE,NBOOPT)

-Interrogates the scratch files and COMMON blocks of the parent program, -providing the NBO program with required information of the electronic -wavefunction via the NBO COMMON blocks and FILE48 direct access file. -(Note that for GENNBO, this routine directs the input of information -from the GENNBO input file, FILE47.) The NBO COMMON blocks and FILE48 -records which must be initialized by SR FEAOIN are discussed in Sections -C.3, C.4. Additional information on the COMMON blocks and scratch files -of the parent ESS package is provided in the Appendices. -

-

-

SR DELSCF(CORE,ICORE,NBOOPT)

-Performs one of two tasks, depending of the value of NBOOPT(1). If -NBOOPT(1) is set to 2, SR DELSCF provides the parent ESS program with -the modified density matrix generated by the NBO energetic analysis -routines. The parent program will then compute the "deletion energy" -for this modified wavefunction. If NBOOPT(1) is set to 3, SR DELSCF -fetches the deletion energy from the parent program and writes it to -the FILE48 direct access file. (The NBOOPT array is discussed in -Section C.5.1). -

-

-C.12 GENNBO AUXILIARY ROUTINES -

- An additional set of routines is provided for the GENNBO stand-alone -program. These routines are called by the GENNBO driver routine FEAOIN -and are responsible for reading the datalists of the GENNBO input file. -Each of these routines rewinds the input file before searching sequentially -for its associated datalist. Thus, the order of datalists (as well as -keylists) in the input file is immaterial. Each routine also checks -that all required information in the datalist is given and stores -this information on the FILE48 direct access file or in the NBO COMMON blocks. -

- Below we list each GENNBO auxiliary routine, indicating its associated -datalist, but without furthur explanation: -

- - - - - - - - - - - - - -
DatalistAuxiliary routine to read datalist
$COORDSR CRDINP(TITLE,ATCOOR,BOHR)
$BASISSR BASINP
$CONTRACTSR CONINP(CORE,ICORE)
$OVERLAPSR SINP(CORE,UPPER)
$DENSITYSR DMINP(CORE,UPPER)
$FOCKSR FINP(CORE,UPPER,END)
$LCAOMOSR TINP(CORE)
$DIPOLESR DIPINP(CORE,UPPER,BOHR)
-

-C.13 ATTACHING NBO TO A NEW ESS PROGRAM -

-This section briefly outlines the steps to be considered -when attaching the NBO program to a new ESS package that is not supported -by this distribution. -

-In general, you should try to identify the supported -ESS package that is most similar to the ESS package you wish to use, -and try to create driver routines modelled as closely as -possible on those provided for the ESS. [In fact, examining the source code -for driver routines of all supported ESS packages is -good preparation for writing your own drivers.] -

-1. Decide where in the parent ESS package you wish to perform the NBO -analysis. This will necessarily be placed after the calculation of the -wavefunction (and the associated density matrix), usually near -the wavefunction analysis routines (e.g., the perennial -"Mulliken population -analysis" section) or wavefunction properties -section of the code. If possible, -restrict the modification of your ESS source code to insertion of -a single "CALL RUNNBO" statement at some point where -the information required for NBO analysis is known to be available. -

-2. Check carefully for possible conflicts between the parent ESS program and -the NBO program in (1) function or subroutine names, (2) COMMON -block names, and (3) logical file assignments (LFNs) for I/O. NBO -common block names all begin with /NB.../, and default -LFN assignments are in the range 31-49. (Duplicate FN or SR names -are detected by a linker.) -

-3. Create new driver (interfacing) subroutines RUNNBO, FEAOIN, -and DELSCF to perform the functions briefly described in Section -C.11, using the drivers provided with this -distribution as templates insofar as possible. The following -are a few helpful hints for each driver: -

-a. The RUNNBO routine should be relatively straightforward to write, following -an analogous example provided in this distribution. Note that you -can simply omit the calls to SR NBOEAN and SR DELSCF from RUNNBO if -you do not plan to use the NBO energetic analysis (for example, because -the DELSCF driver is unmanageable). -

-If your parent program is quite different from any of those supported by this -distribution, choose an alternate version number [NBOOPT(10)], and carefully -consider step 4 below. -

-b. Routine FEAOIN should fetch information about the electronic wavefunction -from your ESS package and load it into the NBO COMMON blocks and FILE48 -direct access file. This requires intimate knowledge of where these items -are stored in the ESS program, so the FEAOIN examples of the -distribution may provide little direct guidance. See Sections -C.3, C.4 for description of the NBO -COMMON blocks and file records which must be initialized by this routine. -

-Note that the NBO analysis will perform properly without the information -stored on logical records 2, 5, 9, 30, 31, 40, 41, and 50-52 of the -direct access file. If information is not provided on these records, the -NBO program will simply shut off (with warnings) any requested keyword -options which are thereby incompatible. In addition, the overlap matrix -of record 10 need not be provided if the input basis set is orthogonal, -and the energies of record 8 are not required if the NBO energetic analysis -is not implemented for your ESS package. -

-c. Creating routine DELSCF will require intimate knowledge of the SCF routines -in the parent ESS program; again, versions of DELSCF -provided with this distribution may only be of minimal -assistance. As described in Section C.11, SR DELSCF is -responsible for providing a modified AO density matrix to an SCF energy -evaluator (one pass throught the SCF routines) and returning this -new energy to the NBO deletion routines via the FILE48 direct access -file. If you do not intend to employ the NBO -energetic analysis, you need not provide this routine to the -NBO program. [Note that the 2nd-order perturbation theory energy analysis -will be carried out (provided the Fock matrix is available) -even if you do not include the NBOEAN and DELSCF -energy analysis routines.] -

-4. In addition to the explicitly system-dependent subroutines -RUNNBO, FEAOIN, and DELSCF, there are -a few routines within the NBO program which can be considered -quasi-system dependent, and might, therefore, require modification. -These are SR NBOSET (Section C.5.2) and the 'INP' routines NBOINP, CORINP, -CHSINP, and DELINP (Section C.9): -

-a. SR NBOSET assigns the logical file -numbers (LFNs) 31-49 to be used by the NBO program. As mentioned -above, if these are in conflict -with the files employed by the parent ESS program, the conflicting -LFNs will have to be reassigned in this subroutine. -

-b. The 'INP' routines may have to be modified according to -the manner in which the input file of the parent program should be processed by -the NBO program. More specifically, these routines either -rewind the input file before searching -for their associated keylist identifier, or they simply begin searching -the input file sequentially at the point where the parent program left off, -depending on the version number specified in NBOOPT(10). Be sure this -parameter is consistent with the way you wish to modify the -ESS input file for NBO input. -

-

-

Section D: APPENDIX

-
-

-D.1 INTRODUCTION -

- This Appendix contains system-dependent information about NBO input -and source code for the ESS (electronic structure system) packages supported -by this distribution. We assume that the user has basic familiarity with -the ESS program of interest. -

- The Appendix is organized according to the ESS packages supported, -which are described in Sections D.2-D.7, as shown below: -

- - - - - - - - - - - -
ESS packageSection
GAUSSIAN 88D.2
GAUSSIAN 86D.3
GAUSSIAN 82D.4
GAMESSD.5
HONDOD.6
AMPACD.7
- Each ESS section contains information on: -

-1. Sample input file for RHF/3-21G methylamine -

-2. NBO program installation -

-3. Communication between the NBO drivers and the ESS program -

- For most users, only the first section(s) on sample input file will -be required reading. For the programmer responsible for attaching the NBO -program to an ESS package, the final section on NBO drivers will be -important only if the available ESS version differs significantly from -that assumed in the installation instructions. -

- In the Appendix we use "SR" and "FN" to denote subroutines -and functions, respectively. -

-

-D.2 GAUSSIAN 88 VERSION -

-D.2.1 GAUSSIAN 88 sample input -

- A sample GAUSSIAN 88 input file to -recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry) -output displayed in Section A.3 is shown below: -

-

- 

-
-# RHF/3-21G
-
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-
- 0   1
- C
- N   1   CN
- H   1   CH   2   tet
- H   1   CH   2   tet   3   120.  0
- H   1   CH   2   tet   3   240.  0
- H   2   NH   1   tet   3    60.  0
- H   2   NH   1   tet   3   300.  0
-
- CN        1.47
- CH        1.09
- NH        1.01
- tet     109.4712
-
-$NBO  $END
-
-
The keylists of the NBO program should always appear at the bottom of the -GAUSSIAN 88 input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL. -NBO job options are selected by inserting their -associated keywords (Section B.2) into the $NBO keylist. All NBO keywords -are applicable to the electronic wavefunctions computed by the GAUSSIAN 88 -programs. -

- If the NBO program -encounters the end-of-file while searching for a keylist, the input file -is rewound and the search for the keylist is continued. This is particularly -useful for jobs which call the NBO analysis several times. For example, an -MP2 calculation with the GAUSSIAN 88 option DENSITY=ALL causes Link 601 to -loop over three densities (SCF, Rho2, and MP2), and hence, the NBO analysis -is called three times, once for each density. A single $NBO keylist -(and $CORE and $CHOOSE keylists) will suffice as input for all three analyses. -Alternatively, separate $NBO keylists, one for each density, could be inserted -at the bottom of the GAUSSIAN 88 input file. -

- The IOp parameters 40-43 of Link 601 exert additional control over the -NBO program, as listed below: -

-

- - - - - - - - - - - - - - - - - - - - - - - - - - -
parametervalueeffect
IOp(40)-2skip the NBO analysis
-1perform the NPA only
0perform the NBO analysis
(read keywords in $NBO)
1perform the default NBO analysis
(do not read keywords in $NBO)
2initiate NBO energetic analysis
3complete NBO energetic analysis
IOp(41)0SCF density
1MP first order density
2MP2 density
3MP3 density
4MP4 density
5CI one-particle density
6CI density
7QCI/CC density
8density correct to second order
IOp(42)1perform the dipole analysis
(force the DIPOLE keyword)
IOp(43)1allow strongly delocalized structures
(force the RESONANCE keyword)
-For example, to restrict the NBO output to the Natural Population -analysis (NPA) only, set IOp(40) to -1 in all -Link 601 entries of a GAUSSIAN 88 non-standard route, as shown below: -

-

     6/40=-1/1;
-
-
By default, the NBO analysis will be performed, reading keywords from -the $NBO keylist [IOp(40)=0], on the density matrix for the current -wavefunction. The DIPOLE and RESONANCE keywords are generally activated -through the $NBO keylist rather than via the IOp parameters. -

-D.2.2 NBO energetic analysis -

- Due to the overlay structure of the GAUSSIAN 88 programs, a non-standard -route must be employed to perform the NBO energetic analysis. The following -table lists and describes the tasks of the GAUSSIAN 88 links in the order that -they appear in the non-standard route: -

-

-LINK DESCRIPTION -

-6/7=2,8=2,9=2,10=2,19=1/1; Perform the normal NBO analysis, storing information about the NBOs for -the NBO energetic analysis on the FILE48 direct access file. -

-6/40=2/1(1); Read the next deletion listed in the $DEL keylist. If there are no more -deletions, move to the next link. Otherwise, compute the modified density -matrix, store it on the read-write files, and skip the next link in the -non-standard route. -

-99/5=1,9=1/99; Finish GAUSSIAN 88 execution. -

-5/7=1,13=1/1,2; Using the modified density matrix, compute the deletion energy by -a single pass through the SCF energy evaluator. Store the deletion energy -on the read-write files. -

-6/40=3/1(-3); Read the deletion energy from the read-write files and complete the energetic -analysis. Step backwards, in the non-standard route, three links. -

- The following is a GAUSSIAN 88 input file -that will generate, in addition to the default NBO output, the NLMO -(Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic -(Section B.6.10) analyses of methylamine: -

- 

-
-# NONSTD
-1//1;
-2//2;
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;
-4/7=1/1;
-5//1;
-6/7=2,8=2,9=2,10=2,19=1/1;
-6/40=2/1(1);
-99/5=1,9=1/99;
-5/7=1,13=1/1;
-6/40=3/1(-3);
-
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-
- 0   1
- C
- N   1   CN
- H   1   CH   2   tet
- H   1   CH   2   tet   3   120.  0
- H   1   CH   2   tet   3   240.  0
- H   2   NH   1   tet   3    60.  0
- H   2   NH   1   tet   3   300.  0
-
- CN        1.47
- CH        1.09
- NH        1.01
- tet     109.4712
-
-$NBO  NLMO  DIPOLE  $END
-$DEL  NOSTAR
-      ZERO 2 ATOM BLOCKS   4  BY  3
-                           1  3  4  5
-                           2  6  7
-                           3  BY  4
-                           2  6  7
-                           1  3  4  5
-$END
-
-
Note that for the GAUSSIAN 88 version of the NBO program, each deletion -in the $DEL keylist must begin on a new line of the input file (the first -deletion can follow the "$DEL" keylist identifier, as shown above). The -"$END" keylist terminator must also appear on its own line. -

-D.2.3 Geometry reoptimization with NBO deletions -

- The structural effects of electron delocalization can be examined -by coupling the NBO energetic analysis to the Fletcher-Powell (numerical) -geometry optimization routines of the GAUSSIAN 88 package. The -following GAUSSIAN 88 input file will reoptimize selected internal -coordinates of RHF/3-21G methylamine in the absence of its strong -nN*CH hyperconjugative interaction: -

- 

-
-#NONSTD
-1//1,2;
-2//2;
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;
-4/7=1/1;
-5//1;
-6/7=2,8=2,9=2,10=2,19=1/1;
-6/40=2/1(2);
-1//2(3);
-99/9=1/99;
-5/7=1,13=1/1;
-6/40=3/1(-4);
-2//2;
-3/5=5,11=1,25=14,30=1/1,2,3,11,14;
-4/5=5,7=1,16=2/1;
-5//1;
-6/7=2,8=2,9=2,10=2,19=1/1;
-6/40=2/1(3);
-1//2(-6);
-2//2;
-99/9=1/99;
-5/7=1,13=1/1;
-6/40=3/1(-5);
-
-Methylamine...RHF/3-21G optimization with deletions
-
- 0    1
- C
- N    1    CN
- H    1    CHa    2   alfa
- H    1    CHb    2   beta    3   dlta  0
- H    1    CHb    2   beta    3  -dlta  0
- H    2    NH     1   gama    3   epsn  0
- H    2    NH     1   gama    3  -epsn  0
-
- CN           1.4713
- CHa          1.0901
- alfa       114.7843
-
- CHb          1.0825
- NH           1.0035
- beta       108.9484
- gama       113.6544
- dlta       121.4265
- epsn        64.2369
-
-$NBO  PRINT=0  NBO  $END   ! Request reduced NBO output
-$DEL
-      DELETE 1 ELEMENT  9  24
-$END
-
-
Reoptimization of the internal coordinates specified in this example -leads to lengthening of the C-N bond (1.513 Å) and closing of -the H-C-N bond angle (108.3 °), as expected from -lone pair/antibond overlap arguments. The C-H bond length contracts -(1.075 Å) due to the removal of electron density from its antibond. -

- Note that the numerical optimization routines of the GAUSSIAN 88 program -must be employed since analytic gradients are not available for the modified -wavefunction of the NBO energetic analysis. Hence, these optimizations are -time-consuming, generally requiring 8n-12n single point -calculations (n = number of symmetry unique internal coordinates) before -convergence of the gradients is obtained (the example requires 28 single -point calculations before convergence). Careful selection of the coordinates -to be optimized is recommended. -

-D.2.4 NBO program installation -

- The NBO interfacing (driver) routines provided -in this distribution were written for the Revision C version of -GAUSSIAN 88, dated 19-AUG-1988. -Section D.2.5 lists the GAUSSIAN 88 -dependent elements of the NBO driver routines that may need slight -modification for other versions of the GAUSSIAN 88 programs. -

- Three modifications to SR MulDrv of Link 601 are required to run the -NBO analysis: -

- 

-
-*Deck MulDrv
-      Subroutine MulDrv(Core)
-
-      .
-      .
-      .
-
-      IEnd1  = IScr2  + NBasis - 1
-      Call GetSCM(-1,Core,NGot,6hMulDrv,0)
-C
-C     <<< Beginning of first NBO insert >>
-C
-C     Run the NBO energetic analysis.
-C
-      If(IOp(40).ge.2) then
-        IDens = 0                  ! SCF density for deletion runs
-        IOp(41) = IDens
-        Call RunNBO(Core,NGot,IOp,IContr)
-        go to 999
-      endIf
-C
-C     <<< End of first NBO insert >>
-C
-C     Put density matrices first.
-C
-      IPA = IEnd1 + 1
-
-      .
-      .
-      .
-
-          Call ElEner(IOut,ISelfE,SCFDen,ISCF,IROHF,NAE,NBE,NBasis,
-     $      Core(IPA),Core(IV),MDV)
-C
-C     <<< Beginning of second NBO insert >>>
-C
-C     Run the NBO analysis.
-C
-          If(IOp(40).ne.-2) then
-            IOp(41) = IDens
-            Call RunNBO(Core,NGot,IOp,IContr)
-          endIf
-C
-C     <<< End of second NBO insert >>>
-C
-        else if(IDens1.eq.IDSt.and.IDens1.eq.IDEnd) then
-
-      .
-      .
-      .
-
-      Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
-     $    Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))
-C
-C     <<< Beginning of third NBO insert >>>
-C
-C     The following line has been changed from "Call ChainX(0)" in
-C     order to exit the NBO deletion loop after the deletions are done:
-C
-  999 Call ChainX(IContr)
-C
-C     <<< End of third NBO insert >>>
-C
-      Return
-      End
-
-
The first NBO insert initiates the NBO energetic analysis of -SCF wavefunctions. The second insert lies within a loop over densities, -and thus, the NBO program is called once for each density matrix analyzed -by this link. The third insert allows the NBO energetic analysis to exit -from the loop in the non-standard route. -

-The NBO program installation should continue as discussed in Section A.2. -

-D.2.5 NBO communication with GAUSSIAN 88 -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -GAUSSIAN 88 routines, read-write files, and COMMON blocks: -

-GAUSSIAN 88 routines:

-
-    SR CharPn(IString)
-    SR DENGET(IOut,IODens,IMeth,LenDen,GotIt,P)
-    FN ILSW(IOPER,WHERE,WHAT)
-    FN InToWP(Nints)
-    FN ITqry(Ifile)
-    SR TRead(IARN,X,M,N,MM,NN,K)
-    SR TWrite(IARN,X,M,N,MM,NN,K)
-
-
GAUSSIAN 88 read-write files: -

- - - - - - - - - - - - - - - - - - -
filecontents
501Total energy
502Job title
506Basis set information
512Effective core potential information
514AO overlap matrix
518AO dipole integrals
524MO coefficients (alpha)
526MO coefficients (beta)
528SCF density matrix (alpha)
530SCF density matrix (beta)
536AO Fock matrix (alpha)
538AO Fock matrix (beta)
603AO density matrix
-GAUSSIAN 88 COMMON blocks:

-
-    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
-   +           ATMCHG(400),C(1200)
-    COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
-   +  KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
-    COMMON/B/EXX(6000),C1(6000),C2(6000),C3(6000),X(2000),Y(2000),
-   +     Z(2000),JAN(2000),SHELLA(2000),SHELLN(2000),SHELLT(2000),
-   +     SHELLC(2000),AOS(2000),AON(2000),NSHELL,MAXTYP
-    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
-    DIMENSION C4(2000),SHLADF(2000)
-    EQUIVALENCE(C4(1),C3(2001)),(SHLADF(1),C3(4001))
-
-

-D.3 GAUSSIAN 86 VERSION -

-D.3.1 GAUSSIAN 86 sample input -

- See Section D.2.1. Note that the NBO IOp parameters of Link 601 -are set to 40-43 (changed from 20-23 in previous distributions of the NBO -program). -

-D.3.2 NBO energetic analysis -

- See Section D.2.2. -

-D.3.3 Geometry reoptimization with NBO deletions -

- See Section D.2.3. -

-D.3.4 NBO program installation -

- The NBO interfacing (driver) routines provided -in this distribution were written for the Revision C version of -GAUSSIAN 86, dated 30-APR-1986. -Section D.3.5 lists the GAUSSIAN 86 -dependent elements of the NBO driver routines that may need slight -modification for other versions of the GAUSSIAN 86 programs. -

- Two modifications to SR MulDrv of Link 601 are required to run the -NBO analysis: -

- 

-
-*Deck MulDrv
-      Subroutine MulDrv(Core)
-      .
-      .
-      .
-
-      If(NGot.lt.IEnd1) Write(IOut,2002) IEnd1, NGot
-      Len2 = (NGot-I2A+1)/NTT
-C
-C     <<< Beginning of first NBO insert >>>
-C
-      IF(IOp(40).GE.2.OR.IOp(41).NE.0) GO TO 999
-C
-C     <<< End of first NBO insert >>>
-C
-C     Do population analysis.
-C
-      CALL MULPOP(MaxAtm,IOP,IROHF,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,
-
-      .
-      .
-      .
-
-      Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
-     $    Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip))
-C
-C     <<< Beginning of second NBO insert >>>
-C
-  999 Call GetSCM(-1,Core(1),NGot,3HNBO,0)
-      Call RunNBO(Core,NGot,IOp,IContr)
-C
-C     The following line has been changed from "999 Call ChainX(0)" in
-C     order to exit the NBO deletion loop after deletions are complete.
-C
-      Call ChainX(IContr)
-C
-C     <<< End of second NBO insert >>>
-C
-      Return
-      End
-
-
The first NBO insert allows Link 601 to by-pass the Mulliken -Population and electric moment analysis routines if the NBO energetic -analysis is to be performed or if a correlated wavefunction is being -analyzed. The second insert requests all available memory be allocated -for the NBO program and initiates the NBO analysis. Note that the call -to SR ChainX has been altered from the original code. -

-The NBO program installation should continue as discussed in Section A.2. -

-D.3.5 NBO communication with GAUSSIAN 86 -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -GAUSSIAN 86 routines, read-write files, and COMMON blocks: -

-GAUSSIAN 86 routines:

-
-    SR CharPn(IString)
-    FN ILSW(IOPER,WHERE,WHAT)
-    FN InToWP(Nints)
-    FN ITqry(Ifile)
-    SR TRead(IARN,X,M,N,MM,NN,K)
-    SR TWrite(IARN,X,M,N,MM,NN,K)
-
-
GAUSSIAN 86 read-write files: -

- - - - - - - - - - - - - - - - - - - -
filecontents
203CI density matrix (alpha)
204CI density matrix (beta)
501Total energy
502Job title
506Basis set information
512Effective core potential information
514AO overlap matrix
518AO dipole integrals
524MO coefficients (alpha)
526MO coefficients (beta)
528SCF density matrix (alpha)
530SCF density matrix (beta)
536AO Fock matrix (alpha)
538AO Fock matrix (beta)
-GAUSSIAN 86 COMMON blocks:

-
-    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
-   +           ATMCHG(400),C(1200)
-    COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
-   +  KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
-    COMMON/B/EXX(1200),C1(1200),C2(1200),C3(1200),X(400),Y(400),
-   +     Z(400),JAN(400),SHELLA(400),SHELLN(400),SHELLT(400),
-   +     SHELLC(400),AOS(400),AON(400),NSHELL,MAXTYP
-    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
-    DIMENSION C4(400),SHLADF(400)
-    EQUIVALENCE(C4(1),C3(401)),(SHLADF(1),C3(801))
-
-

-D.4 GAUSSIAN 82 VERSION -

-D.4.1 GAUSSIAN 82 sample input -

- See Section D.2.1. Note that the NBO IOp parameters of Link 601 -are set to 40-43 (changed from 20-23 in previous distributions of the NBO -program). -

-D.4.2 NBO energetic analysis -

- See Section D.2.2. -

-D.4.3 Geometry reoptimization with NBO deletions -

- See Section D.2.3. -

-D.4.4 NBO program installation -

- The NBO interfacing (driver) routines provided -in this distribution were written for the Revision H version of -GAUSSIAN 82, dated 28-NOV-1983. -Section D.4.5 lists the GAUSSIAN 82 -dependent elements of the NBO driver routines that may need slight -modification for other versions of the GAUSSIAN 82 programs. -

- Two modifications to SR MulDrv of Link 601 are required to run the -NBO analysis: -

- 

-
-*Deck MulDrv
-      Subroutine MulDrv(Core)
-
-      .
-      .
-      .
-
-      IF(IPRINT.NE.0)
-     $WRITE(IOUT,2001)I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,IEND
-C
-C     <<< Beginning of first NBO insert >>>
-C
-C     The following line has been changed from "CALL GETSCM(IEND,...)",
-C     in order to ask for all available memory.
-C
-      CALL GETSCM(-1,CORE(1),JJJMEM,6HMULDRV,0)
-C
-      IF(IOP(40).GE.2.OR.IOP(41).NE.0) GO TO 100
-C
-C     <<< End of first NBO insert >>>
-C
-C     DO THE POPULATION ANALYSIS.
-      CALL MULPOP(IOP,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,IAN,AtmChg,
-     $  C,Core(I1),CORE(I2),CORE(I3),CORE(I4),CORE(I5),
-     $  CORE(I6),CORE(I7),CORE(I8),CORE(I9),CORE(I10))
-C
-C     <<< Beginning of second NBO insert >>>
-C
-  100 CALL RUNNBO(CORE,JJJMEM,IOP,ICONTR)
-C
-C     The following line has been changed from "CALL CHAINX(0)" in
-C     order to exit the NBO deletion loop after deletions are complete.
-C
-      CALL CHAINX(ICONTR)
-C
-C     <<< End of second NBO insert >>>
-C
-      RETURN
-      END
-
-
The first NBO insert allows Link 601 to by-pass the Mulliken -Population analysis routines if the NBO energetic -analysis is to be performed or if a correlated wavefunction is being -analyzed. The second insert initiates the NBO analysis. Note that the calls -to routines GETSCM and CHAINX have been altered from the original code. -

-The NBO program installation should continue as discussed in Section A.2. -

-D.4.5 NBO communication with GAUSSIAN 82 -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -GAUSSIAN 82 routines, read-write files, and COMMON blocks: -

-GAUSSIAN 82 routines:

-
-    SR CharPn(IString)
-    FN ILSW(IOPER,WHERE,WHAT)
-    FN InToWP(Nints)
-    FN ITqry(Ifile)
-    SR TRead(IARN,X,M,N,MM,NN,K)
-    SR TWrite(IARN,X,M,N,MM,NN,K)
-
-
GAUSSIAN 82 read-write files: -

- - - - - - - - - - - - - - - - - - - - - -
filecontents
203CI density matrix (alpha)
204CI density matrix (beta)
501Total energy
502Job title
506Basis set information
512Effective core potential information
514AO overlap matrix
518x dipole integrals
519y dipole integrals
520z dipole integrals
524MO coefficients (alpha)
526MO coefficients (beta)
528SCF density matrix (alpha)
530SCF density matrix (beta)
536AO Fock matrix (alpha)
538AO Fock matrix (beta)
-GAUSSIAN 82 COMMON blocks:

-
-    COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(101),
-   +           ATMCHG(100),C(300)
-    COMMON/LP2/NLP(400),CLP(400),ZLP(400),KFIRST(100,5),
-   +  KLAST(100,5),LMAX(100),LPSKIP(100),NFroz(100)
-    COMMON/B/EXX(240),C1(240),C2(240),C3(240),X(80),Y(80),
-   +     Z(80),JAN(80),SHELLA(80),SHELLN(80),SHELLT(80),
-   +     SHELLC(80),AOS(80),AON(80),NSHELL,MAXTYP
-    INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
-    DIMENSION C4(80),SHLADF(80)
-    EQUIVALENCE(C4(1),C3(81)),(SHLADF(1),C3(161))
-
-

-D.5 GAMESS VERSION -

-D.5.1 GAMESS sample input -

- A sample GAMESS input file to -recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry) -output displayed in Section A.3 is shown below: -

- 

-
- $CONTRL  SCFTYP=RHF  RUNTYP=ENERGY  $END
- $DATA
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-CS       0
-
-Carbon       6.       -0.713673           -0.014253            0.000000
-    1   SV    3  N21
-
-Nitrogen     7.        0.749817            0.123940            0.000000
-    1   SV    3  N21
-
-Hydrogen     1.       -0.978788           -1.071520            0.000000
-    1   SV    3  N21
-
-Hydrogen     1.       -1.123702            0.463146           -0.889982
-    1   SV    3  N21
-
-Hydrogen     1.        1.129752           -0.318420            0.824662
-    1   SV    3  N21
-
- $END
- $GUESS  GUESS=EXTGUESS  $END
- $NBO  $END
-
-
NBO job options are selected by inserting their associated keywords -(Section B.2) into the $NBO keylist. All NBO keywords are applicable to the -electronic wavefunctions computed by GAMESS. -

- The following is a modified GAMESS input file that will generate, in -addition to the default NBO output, the NLMO (Section B.6.2), the dipole -moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of -methylamine: -

- 

-
- $CONTRL  SCFTYP=RHF  RUNTYP=ENERGY  $END
- $DATA
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-CS       0
-
-Carbon       6.       -0.713673           -0.014253            0.000000
-    1   SV    3  N21
-
-Nitrogen     7.        0.749817            0.123940            0.000000
-    1   SV    3  N21
-
-Hydrogen     1.       -0.978788           -1.071520            0.000000
-    1   SV    3  N21
-
-Hydrogen     1.       -1.123702            0.463146           -0.889982
-    1   SV    3  N21
-
-Hydrogen     1.        1.129752           -0.318420            0.824662
-    1   SV    3  N21
-
- $END
- $GUESS  GUESS=EXTGUESS  $END
- $NBO  NLMO  DIPOLE  $END
- $DEL  NOSTAR
-       ZERO 2 ATOM BLOCKS     4  BY  3
-                              1  3  4  5
-                              2  6  7
-                              3  BY  4
-                              2  6  7
-                              1  3  4  5
- $END
-
-
In general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted -in any order within the GAMESS input file; the NBO program rewinds the -input file each time it searches for a keylist. -

-D.5.2 NBO program installation -

- The NBO interfacing (driver) routines provided in this -distribution were written for the GAMESS program dated 6-DEC-1989. -Section D.5.3 lists the GAMESS -dependent elements of the NBO driver routines that may need slight -modification for other versions of the GAMESS program. -

- Only one command line is added to the GAMESS source code to run the -NBO analysis. A call ("IF(RHO) CALL RUNNBO") should be inserted at the -end of the GAMESS properties package (SR HFPROP in module PRPLIB), -as shown below: -

- 

-
-C*MODULE PRPLIB  *DECK HFPROP
-      SUBROUTINE HFPROP(SCFTYP)
-
-                 .
-                 .
-                 .
-
-C
-C     ----- SELECT DESIRED ELECTROSTATIC PROPERTIES -----
-C
-      CALL PRSELC(SCFTYP)
-C
-      WRITE(IW,FMT='(" ...... END OF PROPERTY EVALUATION ......")')
-      CALL TIMIT(1)
-C
-C     <<< BEGINNING OF NBO INSERT >>>
-C
-      IF(RHO) CALL RUNNBO
-C
-C     <<< END OF NBO INSERT >>>
-C
-      RETURN
-      END
-
-
If the density matrix is available (RHO = .TRUE.), the NBO analysis -is performed each time the properties package is called within GAMESS. -For example, the NBO analysis of the computed wavefunction will be performed -for every single point calculation and for both the -initial and final points of a geometry optimization. The NBO output will -appear immediately after the Mulliken Population Analysis and the electric -properties in the GAMESS output file. -

- The NBO program installation should continue as discussed in Section A.2. -D.5.3 NBO communication with GAMESS -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -GAMESS routines, records of the dictionary file, and COMMON blocks: -

-GAMESS routines:

-
-    SR DAREAD(IDAF,IODA,V,LEN,NREC,NAV)
-    FN ENUC(N,Z,C)
-    ENTRY GOTFM(IPAR)
-    SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
-    SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
-    SR SYMH(F,H,IA)
-    FN TRACEP(A,B,N)
-    SR VADD(A,I,B,J,C,K,N)
-    ENTRY VALFM(IPAR)
- 
-
GAMESS dictionary file: -

- - - - - - - - - - - - - - - - -
recordcontents
2total energy
12AO overlap matrix
14AO Fock matrix (alpha)
15AO to MO transformation matrix (alpha)
16AO density matrix (alpha bond-order matrix)
18AO Fock matrix (beta)
19AO to MO transformation matrix (beta)
20AO density matrix (beta bond-order matrix)
23x dipole integrals
24y dipole integrals
25z dipole integrals
-GAMESS COMMON blocks:

-
-    PARAMETER (MXGTOT=5000, MXSH=1000, MXATM=50)                      
-    COMMON /ECP2  / CLP(400),ZLP(400),NLP(400),KFIRST(MXATM,6),       
-   +                KLAST(MXATM,6),LMAX(MXATM),LPSKIP(MXATM),         
-   +                IZCORE(MXATM)                                     
-    COMMON /FMCOM / CORE(1)
-    COMMON /INFOA / NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(MXATM),C(3,MXATM) 
-    COMMON /INTFIL/ NINTMX,NHEX,NTUPL,PACK2E,INTG76
-    COMMON /IOFILE/ IR,IW,IP,IS,IPK,IDAF,NAV,IODA(99)
-    COMMON /NSHEL / EX(MXGTOT),CS(MXGTOT),CP(MXGTOT),CD(MXGTOT),      
-   +                KSTART(MXSH),KATOM(MXSH),KTYPE(MXSH),KNG(MXSH),   
-   +                KLOC(MXSH),KMIN(MXSH),KMAX(MXSH),NSHELL           
-    COMMON /OUTPUT/ NPRINT,ITOL,ICUT,NORMF,NORMP,NOPK
-    COMMON /RUNLAB/ TITLE(10),A(MXATM),B(MXATM),BFLAB(2047)
-    COMMON /SCFOPT/ SCFTYP,BLKTYP,MAXIT,MCONV,NCONV,NPUNCH
-    COMMON /XYZPRP/ X(3)
-
D.6 HONDO VERSION -

-D.6.1 HONDO sample input -

- A sample HONDO input file to -recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry) -output displayed in Section A.3 is shown below: -

- 

-
- $CNTRL  RUNFLG=0  $END
- $BASIS
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-    0    0   15    1  N21
-CS       0
-
-Carbon       6.       -0.713673           -0.014253            0.000000
-Nitrogen     7.        0.749817            0.123940            0.000000
-Hydrogen     1.       -0.978788           -1.071520            0.000000
-Hydrogen     1.       -1.123702            0.463146           -0.889982
-Hydrogen     1.        1.129752           -0.318420            0.824662
- $END
- $GUESS  NGUESS=4  $END
- $INTGRL  $END
- $WFN  WFNFLG=0  $END
- $SCF  NCO=9  $END
- $NBO  $END
-
-
NBO job options are selected by inserting their associated keywords -(Section B.2) into the $NBO keylist. All NBO keywords are applicable to the -electronic wavefunctions computed by HONDO. -

- The following is a modified HONDO input file that will generate, in -addition to the default NBO output, the NLMO (Section B.6.2), the dipole -moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of -methylamine: -

- 

-
- $CNTRL  RUNFLG=0  $END
- $BASIS
-Methylamine...RHF/3-21G//Pople-Gordon standard geometry
-    0    0   15    1  N21
-CS       0
-
-Carbon       6.       -0.713673           -0.014253            0.000000
-Nitrogen     7.        0.749817            0.123940            0.000000
-Hydrogen     1.       -0.978788           -1.071520            0.000000
-Hydrogen     1.       -1.123702            0.463146           -0.889982
-Hydrogen     1.        1.129752           -0.318420            0.824662
- $END
- $GUESS  NGUESS=4  $END
- $INTGRL  $END
- $WFN  WFNFLG=0  $END
- $SCF  NCO=9  $END
- $NBO  NLMO  DIPOLE  $END
- $DEL  NOSTAR
-       ZERO 2 ATOM BLOCKS     4  BY  3
-                              1  3  4  5
-                              2  6  7
-                              3  BY  4
-                              2  6  7
-                              1  3  4  5
- $END
-
-
In general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted -in any order within the HONDO input file; the NBO program rewinds the -input file each time it searches for a keylist. -

-D.6.2 NBO program installation -

- The NBO interfacing (driver) routines provided in this -distribution were written for HONDO 7.0, dated 18-JAN-1988. -Section D.6.3 lists the HONDO -dependent elements of the NBO driver routines that may need slight -modification for other versions of the HONDO program. -

- Only one command line is added to the HONDO source code to run the -NBO analysis. A call ("CALL RUNNBO") should be inserted at the -end of the HONDO properties package (SR PROPTY in module PRP), -as shown below: -

- 

-
-      SUBROUTINE PROPTY
-
-      .
-      .
-      .
-
-C
-C     ----- ELECTRON AND SPIN DENSITIES -----
-C
-      IF(NODEN.EQ.0) CALL ELDENS
-C
-C     <<< BEGINNING OF NBO INSERT >>>
-C
-      CALL RUNNBO
-C
-C     <<< END OF NBO INSERT >>>
-C
-      NCALL=0
-      IF(SOME) NCALL=1
-      CALL TIMIT(NCALL)
-      RETURN
-
-      .
-      .
-      .
-
-      END
-
-
The NBO analysis -is performed each time the properties package is called within HONDO. -For example, the NBO analysis of the computed wavefunction will be performed -(unless NOPROP=1 in the $CONTRL namelist) for every single point calculation, -for each point on a scan of a potential energy surface, and for both the -initial and final points of a geometry optimization. The NBO output will -appear immediately after the Mulliken Population Analysis and the electric -properties in the HONDO output file. -

- The NBO program installation should continue as discussed in Section A.2. -D.6.3 NBO communication with HONDO -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -HONDO routines, records of the dictionary file, and COMMON blocks: -

-HONDO routines:

-
-    SR DAREAD(IDAF,IODA,IX,NX,IDAR)
-    SR DIPAMS(BMASS,NCALL,NCODE,SOME)
-    FN DOTTRI(A,B,N)
-    FN ENUC(N,Z,C)
-    SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
-    SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
-    SR SYMFCK(F,H,IA)
- 
-
HONDO dictionary file: -

- - - - - - - - - - - - - - - - -
recordcontents
2total energy
12AO overlap matrix
14AO Fock matrix (alpha)
15AO to MO transformation matrix (alpha)
16AO density matrix (alpha bond-order matrix)
18AO Fock matrix (beta)
19AO to MO transformation matrix (beta)
20AO density matrix (beta bond-order matrix)
33x dipole integrals
34y dipole integrals
35z dipole integrals
-HONDO COMMON blocks:

-
-    COMMON/IJPAIR/IA(1)
-    COMMON/INFOA/NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(50),C(3,50)
-    COMMON/INTFIL/NOPK,NOK,NOSQUR,NINTMX,NHEX,NTUPL,PACK2E
-    COMMON/IOFILE/IR,IW,IP,IJK,IPK,IDAF,NAV,IODA(99)
-    COMMON/MEMORY/MAXCOR,MAXLCM
-    COMMON/MOLNUC/NUC(50)
-    COMMON/NSHEL/EX(440),CS(440),CP(440),CD(440),CF(440),CG(440),
-   +             KSTART(120),KATOM(120),KTYPE(120),KNG(120),
-   +             KLOC(120),KMIN(120),KMAX(120),NSHELL
-    COMMON/RUNLAB/TITLE(10),ANAM(50),BNAM(50),BFLAB(512)
-    COMMON/SCFOPT/SCFTYP
-    COMMON/SCM/CORE(1)
-    COMMON/WFNOPT/WFNTYP
-
-

-D.7 AMPAC VERSION -

-D.7.1 AMPAC sample input -

- A sample AMPAC input file that will create default methylamine -(AM1 at Pople-Gordon idealized geometry) output similar to the -ab initio output displayed in Section A.3 is shown below: -

- 

-
-AM1
-
-CH3NH2...AM1//Pople-Gordon standard geometry
-   C      0.000000  0    0.000000  0    0.000000  0   0  0  0
-   N      1.470000  0    0.000000  0    0.000000  0   1  0  0
-   H      1.090000  0  109.471230  0    0.000000  0   1  2  0
-   H      1.090000  0  109.471230  0  120.000000  0   1  2  3
-   H      1.090000  0  109.471230  0  240.000000  0   1  2  3
-   H      1.010000  0  109.471230  0   60.000000  0   2  1  3
-   H      1.010000  0  109.471230  0  300.000000  0   2  1  3
-
-$NBO  $END
-
-
-
The keylists of the NBO program should always appear at the bottom of the -AMPAC input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL. -NBO job options are selected by inserting their associated keywords -(Section B.2) into the $NBO keylist. -

- Due to the implicit orthogonality of the basis functions, the -following NBO keywords are not applicable to the wavefunctions -computed by AMPAC (or other semi-empirical packages): - 

-       AOPNAO        AOPNLMO       NAONHO        SPNAO
-       AONAO         DINAO         NAONLMO       SPNHO
-       AOPNHO        DMNAO         NAOMO         SPNBO
-       AOPNBO        FNAO          SAO           SPNLMO
-
-
In addition, the NBO keywords that require access to the AO dipole -integrals (DIPOLE, DIAO, DINAO, DINHO, DINBO, DINLMO) are not applicable -with AMPAC, since these integrals are unavailable to the NBO program. -

- The following is a modified AMPAC input file that will generate, in -addition to the default NBO output, the NLMO and the -NBO energetic analyses of methylamine: -

- 

-
-AM1
-
-CH3NH2...AM1//Pople-Gordon standard geometry
-   C      0.000000  0    0.000000  0    0.000000  0   0  0  0
-   N      1.470000  0    0.000000  0    0.000000  0   1  0  0
-   H      1.090000  0  109.471230  0    0.000000  0   1  2  0
-   H      1.090000  0  109.471230  0  120.000000  0   1  2  3
-   H      1.090000  0  109.471230  0  240.000000  0   1  2  3
-   H      1.010000  0  109.471230  0   60.000000  0   2  1  3
-   H      1.010000  0  109.471230  0  300.000000  0   2  1  3
-
-$NBO  NLMO  $END
-$DEL  NOSTAR
-      ZERO 2 ATOM BLOCKS  3 BY 4
-                          1 3 4 5
-                          2 6 7
-                          4 BY 3
-                          2 6 7
-                          1 3 4 5
-$END
-
-D.7.2 Sample NBO output for AMPAC wavefunctions
-

- Since the AMPAC output differs in significant respects from the -ab initio examples presented in Sections A,B, we present -some excerpts from the NBO output and a -brief discussion of the NBO analysis of the AM1 wavefunction for -methylamine (Pople-Gordon idealized geometry). The numerical values -in these exerpts (summary tables) should be adequate for checking -purposes. -

- The summary of the Natural Population Analysis (NPA) -for methylamine is shown below: - 

-
-Summary of Natural Population Analysis:                  
-                                                         
-                                      Natural Population 
-              Natural   -----------------------------------------------
-   Atom #     Charge        Core      Valence    Rydberg      Total
------------------------------------------------------------------------
-     C  1   -0.13281      2.00000     4.13281    0.00000     6.13281
-     N  2   -0.34739      2.00000     5.34739    0.00000     7.34739
-     H  3    0.03346      0.00000     0.96654    0.00000     0.96654
-     H  4    0.08488      0.00000     0.91512    0.00000     0.91512
-     H  5    0.08488      0.00000     0.91512    0.00000     0.91512
-     H  6    0.13849      0.00000     0.86151    0.00000     0.86151
-     H  7    0.13849      0.00000     0.86151    0.00000     0.86151
-=======================================================================
-  * Total *  0.00000      4.00000    14.00000    0.00000    18.00000
-
-
Note that the core electrons of all heavy atoms (neglected in the -semi-empirical AMPAC procedure) are incorporated into the NPA, along the -lines of the treatment of effective core potentials (Section B.6.12). -Note also that the numerical values of AM1 natural charges (and other -quantities) differ significantly from those presented in Section A.3.2, -reflecting a tendency toward somewhat reduced bond polarities in AM1 -wavefunctions. -

-The NBO summary table is shown below: - 

-
-Natural Bond Orbitals (Summary):
-
-                                                    Principal Delocalizations
-          NBO              Occupancy    Energy      (geminal,vicinal,remote)
-===============================================================================
-Molecular unit  1  (CH5N)
-  1. BD ( 1) C 1- N 2       1.99095   -20.60408    9(g),10(g),11(g),12(g),13(g)
-  2. BD ( 1) C 1- H 3       1.99184   -17.81012    8(g),10(g),11(g),9(g)
-  3. BD ( 1) C 1- H 4       1.98864   -17.75195    12(v),9(g),11(g),8(g)
-  4. BD ( 1) C 1- H 5       1.98864   -17.75195    13(v),9(g),10(g),8(g)
-  5. BD ( 1) N 2- H 6       1.98916   -19.74256    13(g),8(g),10(v)
-  6. BD ( 1) N 2- H 7       1.98916   -19.74256    12(g),8(g),11(v)
-  7. LP ( 1) N 2            1.98489   -15.52775    9(v)
-  8. BD*( 1) C 1- N 2       0.01048     4.75597
-  9. BD*( 1) C 1- H 3       0.02306     4.29359
- 10. BD*( 1) C 1- H 4       0.01070     4.57248
- 11. BD*( 1) C 1- H 5       0.01070     4.57248
- 12. BD*( 1) N 2- H 6       0.01090     5.27834
- 13. BD*( 1) N 2- H 7       0.01090     5.27834
-      -------------------------------
-             Total Lewis   17.92328  ( 99.5738%)
-       Valence non-Lewis    0.07672  (  0.4262%)
-       Rydberg non-Lewis    0.00000  (  0.0000%)
-      -------------------------------
-           Total unit  1   18.00000  (100.0000%)
-          Charge unit  1    0.00000
-
-
Note that in this case the orbital energies and other matrix elements -of the Fock operator are printed in electron volts, the energy units of the -AMPAC package. Note also that the physical pattern of delocalization effects -differs significantly from that shown in Section A.3.6, the AM1 results -portraying numerous strong geminal interactions that are not present -in the ab initio output. Other differences between the AM1 and -ab initio wavefunctions will be evident throughout the NBO output. -

- Finally, we include the output segment showing the NBO energetic analysis -of methylamine: - 

-
-NOSTAR: Delete all Rydberg/antibond NBOs
-Deletion of the following orbitals from the NBO Fock matrix:
-   8   9  10  11  12  13
-
-Occupations of bond orbitals:
-
-      Orbital                   No deletions   This deletion   Change
-------------------------------------------------------------------------------
-  1. BD ( 1) C 1- N 2               1.99095        2.00000    0.00905
-  2. BD ( 1) C 1- H 3               1.99184        2.00000    0.00816
-  3. BD ( 1) C 1- H 4               1.98864        2.00000    0.01136
-  4. BD ( 1) C 1- H 5               1.98864        2.00000    0.01136
-  5. BD ( 1) N 2- H 6               1.98916        2.00000    0.01084
-  6. BD ( 1) N 2- H 7               1.98916        2.00000    0.01084
-  7. LP ( 1) N 2                    1.98489        2.00000    0.01511
-  8. BD*( 1) C 1- N 2               0.01048        0.00000   -0.01048
-  9. BD*( 1) C 1- H 3               0.02306        0.00000   -0.02306
- 10. BD*( 1) C 1- H 4               0.01070        0.00000   -0.01070
- 11. BD*( 1) C 1- H 5               0.01070        0.00000   -0.01070
- 12. BD*( 1) N 2- H 6               0.01090        0.00000   -0.01090
- 13. BD*( 1) N 2- H 7               0.01090        0.00000   -0.01090
-
-NEXT STEP:  Evaluate the energy of the new density matrix
-            that has been constructed from the deleted NBO
-            Fock matrix by doing one SCF cycle.
-
-------------------------------------------------------------------------------
-  Energy of deletion :        22.024
-    Total SCF energy :        -5.051
-                         -------------------
-       Energy change :        27.075 kcal/mol,          27.075 kcal/mol
-------------------------------------------------------------------------------
-
-
Note that the "energy of deletion" (22.0 kcal/mol), "total SCF -energy" (-5.1 kcal/mol) and "energy change" (27.1 kcal/mol) are all -given in terms of heats of formation, the standard AM1 form of expressing -molecular energies. -

-D.7.3 NBO program installation -

- The NBO interfacing (driver) routines provided in this -distribution were written for AMPAC, version 1.00. -Section D.7.4 lists the AMPAC -dependent elements of the NBO driver routines that may need slight -modification for other versions of the AMPAC program. -

- Only one command line is added to the AMPAC source code to run the -NBO analysis. A command "CALL RUNNBO" should be inserted in the -AMPAC properties package (SR WRITE in module WRITE), as shown below: -

- 

-
-      SUBROUTINE WRITE(TIME0,FUNCT)
-
-      .
-      .
-      .
-
-         X=MECI(EIGS,C,CBETA,EIGB, NORBS,NMOS,NCIS, .TRUE.)
-      ENDIF
-C
-C     <<< BEGINNING OF NBO INSERT >>>
-C
-      CALL RUNNBO
-C
-C     <<< END OF NBO INSERT >>>
-C
-      IF (INDEX(KEYWRD,'MULLIK') +INDEX(KEYWRD,'GRAPH') .NE. 0) THEN
-         IF (INDEX(KEYWRD,'MULLIK') .NE. 0) THEN
-
-      .
-      .
-      .
-
-
The NBO analysis is performed each time SR WRITE is called. -For example, the NBO analysis of the computed wavefunction will be performed -for every single point calculation and at the end of geometry optimizations. -The NBO output will appear immediately after the Mulliken Population Analysis -in the AMPAC output file. -

- The NBO program installation should continue as discussed in Section A.2. -D.7.4 NBO communication with AMPAC -

- The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following -AMPAC routines and COMMON blocks: -

-AMPAC routines:

-
-    SR GMETRY(GEO,COORD)
-    SR HCORE(COORD,H,W,WJ,WK,ENUCLR)
-    SR FOCK2(F,PTOT,P,W,WJ,WK,NUMAT,NFIRST,NMIDLE,NLAST)
-    SR FOCK1(F,PTOT,PA,PB)
-    FN HELECT(N,P,H,F)
- 
-
AMPAC COMMON blocks:
-
-    INCLUDE 'SIZES'
-    COMMON /ATHEAT/ ATHEAT
-    COMMON /DENSTY/ P(MPACK),PA(MPACK),PB(MPACK)
-    COMMON /ENUCLR/ ENUCLR
-    COMMON /FOKMAT/ F(MPACK),FB(MPACK)
-    COMMON /GEOKST/ NATOM,LABELS(NUMATM),NA(NUMATM),NB(NUMATM),
-   +                NC(NUMATM)
-    COMMON /GEOM  / GEO(3,NUMATM)
-    COMMON /HMATRX/ H(MPACK)
-    COMMON /KEYWRD/ KEYWRD
-    COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
-   +                NLAST(NUMATM),NORBS,NELECS,NALPHA,NBETA,NCLOSE,
-   +                NOPEN,NDUMY,FRACT
-    COMMON /NATORB/ NATORB(107)
-    COMMON /TITLES/ COMENT(10),TITLE(10)
-    COMMON /VECTOR/ C(MORB2),EIGS(MAXORB),CBETA(MORB2),EIGB(MAXORB)
-    COMMON /WMATRX/ WJ(N2ELEC),WK(N2ELEC)
-
-

-

-

INDEX

-
-

-

- Acceptor orbital,A21
- ACS Software,A11
- AMPAC version,A2,A7,A8,B66,C17
- Angular symmetry labels,A5,B68,C7
- Antiperiplanar interaction,A19,A23,B50
- Archive file (FILE47),A5,
-        B62-71,C8,C14,C31,C36
- Arrays
-      IBXM,C9,C22,C23
-      JPRINT,C6
-      NBOOPT,C16,C17,C18,
-            C26,C30,C36,C39
- Atom-centered basis functions,A1
- Atomic charge,A14
- Atomic orbitals,A1,A5,A6,B67-68
-      Contracted gaussian,A6,B69-70
-      Pure (PAO),B11,B67-68,C19,C30
-      Slater-type,A6
-      see Atomic shell
-      see Core orbitals
-      see Pre-orthogonal orbitals
- Atomic shell
-      Core,A7,A8,A13,A14,A16,C24
-      Rydberg,A2,A8,A13,A14,A16,C25
-      Valence,A8,A13,A14,A16
- Atomic units,A13,B65,C4,C13
- Attaching NBO to ESS program,
-        A10-11,C36,C38-39
- AUHF method
-      see Wavefunction type
- Azimuthal angle (),A20,C33
- 
- Basis set
-      see Atomic orbitals
- Benzene (C6H6),B3,B32-36
- Bond bending,A8,A20
-      see Hybrid direction
- BONDO program,A7
- Bond order,B29-31
-      Matrix,B11,B65,C19
- Boys LMOs,B3
- Brunck, T. K.,A7
- 
- Canonical MOs,B6,B27-28,B71,C20
- Carpenter, J. E.,A7
- Chemical fragment,B16,B19
-

- $CHOOSE list
-      see Keylists
- Comments (!),B1,B63,C29
- Comment statements,C1
- COMMON blocks
-      /NBAO/,C7
-      /NBATOM/,C7
-      /NBBAS/,C9,C22,C31,C30
-      /NBCRD1/,C11,C29
-      /NBCRD2/,C12,C29
-      /NBDAF/,C12,C27,C28
-      /NBDXYZ/,C11
-      /NBFLAG/,C5
-      /NBGEN/,C13,C30
-      /NBINFO/,C4
-      /NBIO/,C8,C18
-      /NBLBL/,C10,C32
-      /NBMOL/,C10
-      /NBNAO/,C10
-      /NBONAV/,C12
-      /NBOPT/,C6-7,C18,C30
-      /NBTHR/,C9,C18
-      /NBTOPO/,C11,C22
- Contour plotting program,A8,B9,B69
- Contracted gaussian orbitals
-      see Atomic orbitals
- Copper dimer (Cu2),B56-61
- $CORE list
-      see Keylists
- Core orbitals,A6,A7,A8,A16,
-        B12-13,B56-61,B66,C24,C30,C33
- Core polarization,A8,B12
- Core table,B12,C33
-

- DAF
-      see Direct access file
- Datalists,B63-64
-      $BASIS,B67-68,B71,C31,C37
-      $CONTRACT,B69-70,C31,C37
-      $COORD,B63,B65,B66,C31,C37
-      $DENSITY,B71
-      $DIPOLE,B65,B71,C37
-      $FOCK,B65,B71,C37
-      $LCAOMO,B71,C37
-      Matrix,B71
-      $OVERLAP,B65,B71,C37
- d-orbitals,B53,B56,B61
- Default output,A12,B10
- Deletion types,B17-19
-

- $DEL (deletions) list
-      see Keylists
- Delocalization,A1,A2,A21,B3,B32,B51
- Delocalization tail,A22,B23
-

- Density matrix,A1,A5,A6,B6-7,C13
-      see Bond-order matrix
-      see Spin density matrices
- Depletion of density matrix,C24
- Diborane (B2H6),B40-43
- Dictionary file,A4
- Different Lewis structures for
-   different spin
-      see Open-shell calculation
- Dimension specification,C4
- Dipole moment,A5,A6,A8,B5,B6-7,
-        B24-25,B65,B71,C11,C15,C24
-

- Direct access file (FILE48),A3,A4,A5,
-        B9,B65,C12,C14-15,C16,C27,
-        C28,C36-39
- Directed NBO search
-      see Keylists, $CHOOSE
- Directional analysis
-      see Hybrid direction
- Distribution tape,A10
- Donor orbital,A21,A22
- Double-bond, no-bond resonance,B44-47
- Driver routines,A3
-      see Subroutines RUNNBO, etc.
- 
- Edmiston-Ruedenberg LMOs,B3
- Effective core potential (ECP),
-        A8,B56-61,B66
- Electronic structure system (ESS),A3
-      Common blocks,A4
-      Connection to NBO program,A3,A4,A7,
-         A10-11,B56,B62,C36,C38-39
-      Input file,A5,A11,A12
-      Output file,A5,A12
-      Scratch files,A4
-      see AMPAC, GAUSSIAN-8X, etc.
- ENABLE program,A10,C36
- Energetic analysis,A3,A5,B16-19,
-        C2,C26,C38,C39
-      see Perturbation theory...
- Excited state,A6,A8,A15,B56,C23
- 
-

- f-orbitals
-      see Angular symmetry labels
-      see Keyword CUBICF
-

- Fenske-Hall method
-      see MEDVL 
- Fetch/Save routines,C15,C27
-

- FILE48
-      see Direct access file
-

- FILE47 
-      see Archive file
- Flow chart,A4,C3,C16
- Fock matrix,A2,A5,A6,A8,A14,A21,
-        B6,B16-20,B26,B48-51,B65,B71,
-        C2,C23,C26,C39
- Fortran 77,A6,A10
- Foster, J.P.,C22
- Free format,B1,C29
- Freezing a transformation,B8
- Functions
-      EQUAL,C29
-      IHTYP,C34
-      IOINQR,C32
-      IWPRJ,C24
-      NAMEAT,C34
-      VECLEN,C35
- 
- GAMESS version,A1,A2,A7,A10,A12,C17
- Gaussian elimination,C35
- GAUSSIAN-8X version,A2,A7,
-        A10,B56,C17
- Geminal interaction,A22,B18,C33
- Generalized eigenvalue problem,C20
-

- GENNBO input file 
-      see Archive file
-

- GENNBO stand-alone program
-        A10,B9,B62-71,C13,C36,C37,C38
- Geometry,B66
- Glendening, E. D.,A7
- Groups of routines
-      I   (NAO/NBO/NLMO),C2,C16-25
-      II  (energy analysis),C2,C26
-      III (direct access file),C2,C27-28
-      IV  (free format input),C2,C29
-      V   (other I/O),C2,C30-32
-      VI  (general utility),C2,C33-35
-      VII (system-dependent),C2,C36
- GUGA formalism,A1
- GVB method
-      see Wavefunction type
- 
- Hay-Wadt ECP,B56
- HONDO version,A2,A10,C17,C27
- Hybrid composition,A19,B23
- Hybrid direction,A8,A20,B4,C23
- Hydrogen fluoride (HF),B37-39
- 
- I/O routines
-      see Groups of routines
- INP routines,C30,C39
- Input file,A5,B62,C14
- Installation procedure,A10-11
- Ionic hybrids,B37-39
- 
- Job control keywords,B2,B3
- Job initialization routines,C16,C18
- Job threshold keywords,B2,B4-5
- 
- Kekulée structure,B36
- Keylist,A5,A11,A12,B1
-

- Keylists
-      $CHOOSE,B1,B2,B12,B14-15,B44-47,
-           B62,B63,B65,C6,C22,C30
-      $CORE,B1,B2,B12-B13,
-           B62,B63,B65,C3,C6-7,C30
-      $DEL,B1,B2,B12,B16-20,
-           B48-51,B62,C17,C26,C30
-      $GENNBO,B65,B66,C30
-      $NBO,B1,B2-11,B21-43,B62,B63,
-           B65,B69,C6,C17,C18,C22,C30
- Keyword names (matrix output),B6-7
- Keyword parameters (matrix output),B7-8
- Keywords
-      AOINFO,B2,B9,B69,B71,C6,C31
-      AOMO,B2,B6,B71,C6
-      AONAO,B2,B6,C6,C30-31
-      AONBO,B2,B6,C6,C31
-      AONHO,B2,B6,C6
-      AONLMO,B2,B3,B6,C6,C31
-      AOPNAO,B2,B6,B71,C6
-      AOPNBO,B2,B6,B71,C6
-      AOPNHO,B2,B6,B71,C6
-      AOPNLMO,B2,B6,B71,C6
-      ARCHIVE,B2,B9,B62-71,C6,C31
-      BEND,A8,A20,B2,B4,B5,B10,C6,C23
-      BNDIDX,B2,B9,B10,B21,
-         B29-B31,C6
-      BOAO,B11,C6
-      BODM,B65,C6,C13
-      BOHR,B65,B66,,C13
-      CUBICF,B65,B68,C6
-      DESTAR,B18
-      DETAIL,B2,B9,C6
-      DIAO,B2,B7,B71,C6
-      DINAO,B2,B7,B71,C6
-      DINBO,B2,B7,B71,C6
-      DINHO,B2,B7,B71,C6
-      DINLMO,B2,B6,B7,B71,C6
-      DIPOLE,A8,B2,B3,B5,B10,B21,
-         B24-25,B71,C6,C17,C24
-      DMAO,B2,B7,C6
-      DMNAO,B2,B7,C6
-      DMNBO,B2,B7,C6
-      DMNHO,B2,B7,C6
-      DMNLMO,B2,B7,C6
-      E2PERT,A21,B2,B4,B5,B10,B71,C6
-      EV,B65
-      FAO,B2,B7,B71,C6
-      FNAO,B2,B7,B71,C6
-      FNBO,B2,B6-8,B7,B71,C6
-      FNHO,B2,B7,B26,B71,C6
-      FNLMO,B2,B7,B71,C6
-      LFNPR,B2,B9,C8
-      Matrix output,B6-8,B26-28
-      MULAT,B11,C6
-      MULORB,B11
-      NAOMO,B2,B6-8,B71,C6
-      NAONBO,B6-8,C6
-      NAONHO,B6-8,C6
-      NAONLMO,B6-8,C6
-      NATOMS,B65
-      NBAS,B65
-      NBODAF,B2,B9
-      NBO,A16-19,B2,B3,B10,C6
-      NBOMO,B2,B6-8,B27-28,B71,C6
-      NBONLMO,B2,B6-8,C6
-      NBOSUM,A22-23,B2,B3,B10,C6,C23
-      NHOMO,B2,B6-8,B71,C6
-      NHONBO,B2,B6-8,C6
-      NHONLMO,B2,B6-8,C6
-      NLMO,B2,B3,B5,B10,B22-23,C6
-      NLMOMO,B2,B6-8,B71,C6
-      NOBOND,B2,B3,B21,B37-39,C6
-      NOGEM,B18
-      NOSTAR,B18,B48-49
-      NOVIC,B18
-      NPA,A13-15,B2,B3,B10,C6,C20
-      OPEN,B65
-      ORTHO,B65
-      PAOPNAO,B11,C6
-      PLOT,A8,B2,B9,B69,B71,C6
-      PRINT,B2,B5,B10,B71,C18,C6
-      PRJTHR,B11
-      RESONANCE,A16,B2,B3,B21,
-         B32-36,C6,C17,C25
-      REUSE,B65,B66,B67,C13
-      RPNAO,B11,C6
-      SAO,B2,B7,B71,C6
-      SKIPBO,B2,B3,B10,C6
-      SPNAO,B2,B6-8,B7,B71,C6
-      SPNBO,B2,B7,B71,C6
-      SPNHO,B2,B7,B71,C6
-      SPNLMO,B2,B3,B7,B71,C6
-      3CBOND,B2,B3,B14,B21,B40-43,C6
-      THRESH,B11
-      UPPER,B65,B71,C13
-      ZERO,B19,B49-51
-

- Kinks
-      see Hybrid direction, Bond bending
- 
-

- Labelled COMMON blocks,A3,A6,C4-13
-      see COMMON blocks
-

- Lewis orbitals
-      see Natural bond orbitals
- Linear equations package,C35
- Linear independence,A1,C22,C24
- Logical file number (LFN),C8,C38,C39
- Löwdin, P.-O.,A1
- Löwdin orthogonalization,C21
- 
- Matrix multiplication,C34
-

- Matrix output keywords,
-        B2,B6-8,B9,B26-28,C7
- Mayer-Mulliken bond-order,C19
- MCSCF method
-      see Wavefunction type
- MEDVL version,A10
- Memory allocation,
-        A6,A12,C16,C18,C19,C22
- Methylamine (CH3NH2),
-        A12-23,B21-31,B44-51,B63-71
- Methyl radical (CH3),B52-55
- Molecular units,B16,B18,B19,C10,C23
- Møller-Plesset method
-      see Wavefunction type
- MOPAC version,A10
-

- Mulliken population analysis,
-         A10,B11,C19,C38
- Multiple bonds,A19,B14,B44-47,B56-61
- 
- Naaman, R.,A7
- NAO formation routines,C16,C19-21
-

- Natural atomic orbital (NAO)
-      Formation,A1,A7,C16,C19-21
-      Labels,A13-14,C10
-      Listing,A13,C10
-      Summary table,A7
-      see Natural population analysis
-

- Natural bond orbital (NBO)
-      Analysis,A1-2,A16-19
-      Formalism,A1-A2,A7
-      Labels,A8,A19,B27-28,B43,C9,C10,C32
-      Lewis,A2,A16,A19,A21,A23,B48-51,B17
-      Listing,A17-19,B2
-      Non-Lewis,A2,A16,A19,
-         A21,A23,B17,B18,B48-51
-      Summary table,A22-23,C23
-      3-center,A16,B40-43
-      see Perturbation theory...
-      see NBO/NLMO formation routines
-

- Natural electron configuration (NEC),
-        A7,A15,C20
-

- Natural hybrid orbital (NHO)
-      Directional analysis,A20
-      Formation,A1-2
-      Labels,B26,C10
-      Listing,A-19
-      see Natural bond orbitals
-      see Hybrid direction
-

- Natural Lewis structure,A1-2,A16,
-        A19,B3,B18,B48,B49
-      Energy,B18,B48
-

- Natural localized molecular orbital (NLMO)
-      Formation,A7,B3,C25
-      Listing,B3,B22-23
- Natural minimal basis (NMB) set,A2,A14
- Natural population analysis (NPA),
-         A3,A6,A7,A13-14,B3,
-         B10,B21,B56-57,C20
- Natural Rydberg basis (NRB) set,A2,A18
- NBO direct access file
-      see Direct access file
- $NBO keylist
-      see Keylists
- NBO energetic analysis
-      see Energetic analysis
-      see Perturbation theory...
- NBO.MAN file,A10,A11
- NBO/NLMO formation routines,
-        C16,C22-25
- NBO program,Section C
-      I/O,A5,A12,C27-32
-      Installation,A10-11
-      Organization,A3-4,C2-4
-      Restrictions,A6
-      see Electronic structure system
- NBO.SRC file,A10,C1,C2
- NBO summary table,A22-23,C23
- NLMO/NPA bond order,B30-31
- Non-Lewis orbitals
-      see Natural Bond Orbital
- 
- Open-shell calculation,
-        A1,A5,B14,B25,B52-55,B65,C5
-      see Wavefunction type
- Orbital contour plotting program,
-        A8,B9,B69
- Orthogonalization,C20
-      Löwdin (symmetric),C24
-      Occupancy-weighted (OWSO),C20,C21
-      Schmidt,C20
- Output control keywords,B2,B9-10
- Output file,A8,A12,C1
-

- Overlap matrix,A5,A6,A8,B6,B71,C38
-      singularities,C25
- Overlap-weighted NAO bond order,B30
- 
-

- Perturbation theory energy analysis,
-        A8,A21,B3,B4,C23,C39
- Phi,A20,C33
-

- PNAO, PNBO, PNHO, PNLMO
-      see Pre-orthogonal orbitals
- Polar angle (),A20,C33
- Polarization coefficients,A2,A19,C25
- Pople-Gordon geometry,A12,A20,B21,B32
-

- Population analysis
-      see Mulliken population analysis
-      see Natural population analysis
- Population inversion,A14,B57
-

- Pre-orthogonal orbitals,
-         A1-2,A6,A8,B6,B65,B71
-

- Print parameters,B2,B7-8,
-         B11,B27-28,C7,C10
-

- Program groups,C2
-      see Groups of routines
-

- Program limits
-      Atoms,A6,C4
-      Basis functions,A6,C4
- Program precedence,C2,C3
- Pseudopotential
-      see Effective core potential
- Pure AOs,B11
-      see Atomic orbital
- 
- QCPE,A7,A8
- 
- Read (R) parameter
-      see Print parameters
- Read-write file,A4
- Reed, A. E.,A7,B11,B31,C19
- References,A7
- Remote interaction,A22,C33
- Resonance structures,A9,B14-15,B32-33,
-        B38,B39,B44-47,C11,C25
- Rewind input file,C39
- RHF method
-      see Wavefunction type
- Rives, A. B.,A7
- ROHF method
-      see Wavefunction type
- 
- Schleyer, P. v.R.,B31
- 2nd-order perturbation theory analysis
-      see Perturbation theory energy...
- Semi-documented keywords,B2,B11
- Similarity transformation,C19,C26,C34
-

- Slater-type orbitals
-      see AO basis functions
-

- Spin
-      see Open-shell calculations
-

- Spin-annihilated UHF (AUHF) method
-      see Wavefunction type
- Spin density matrices,A1,B52-55,C5
-

- Storage
-      see Memory allocation
-

- Subroutines,C2,C3
-      ANGLES,C33
-      ANLYZE,C23
-      AOUT,C31
-      APRINT,C31,C32
-      AREAD,C31
-      ATDIAG,C20
-      AUGMNT,C25
-      AWRITE,C31
-      BDFIND,C33
-      BLDSTR,C23
-      CHEM,C33
-      CHOOSE,C22,C23,C24
-      CHSDRV,C22
-      CHSINP,C30
-      CONSOL,C33
-      CONVIN,C33
-      CONVRT,C33
-      COPY,C33
-      CORE,C24
-      CORINP,C30
-      CORTBL,C33
-      CYCLES,C22,C25
-      DEBYTE,C33
-      DELETE,C26
-      DELINP,C30
-      DELSCF,A3,A4,A5,C2,C36,C38,C39
-      DEPLET,C24
-      DFGORB,C19,C30
-      DIPANL,A6,C22,C24
-      DIPELE,C24
-      DIPNUC,C24
-      DMNAO,C19
-      DMSIM,C19
-      FACTOR,C35
-      FEAOIN,A3,A4,A5,C2,C6,
-         C14,C36,C38,C39
-      FEAOMO,C27
-      FEAOM,C27
-      FEBAS,C27
-      FECOOR,C27
-      FEDNAO,C27
-      FEDRAW,C27
-      FEDXYZ,C27
-      FEE0,C27
-      FEFAO,C27
-      FEFNBO,C27
-      FEINFO,C27
-      FENBO,C27
- Subroutines (continued)
-      FENEWD,C27
-      FENLMO,C27
-      FEPNAO,C27
-      FEPPAO,C27
-      FESNAO,C27
-      FESRAW,C27
-      FETITL,C27
-      FETLMO,C27
-      FETNAB,C27
-      FETNAO,C27
-      FETNBO,C27
-      FETNHO,C27
-      FNBOAN,C23
-      FNDFLD,C29
-      FNDMOL,C23
-      FNDSOL,C35
-      FORMT,C25
-      FRMHYB,C23
-      FRMPRJ,C25
-      FRMTMO,C20
-      GENINP,C30
-      GETDEL,C23
-      HALT,C33
-      HFLD,C29
-      HTYPE,C23
-      HYBCMP,C23
-      HYBDIR,C23
-      IDIGIT,C33
-      IFLD,C29
-      INTERP,C32
-      JACOBI,C25,C34
-      JOBOPT,C18,C29
-      LBLAO,C32
-      LBLNAO,C32
-      LBLNBO,C32
-      LBLNHO,C32
-      LIMTRN,C34
-      LINEQ,C33,C35
-      LMOANL,C24
-      LOADAV,C20
-      LOAD,C24
-      MATML2,C34
-      MATMLT,C34
-      MULANA,C19
-      NAOANL,C21
-      NAODRV,C2,C19
-      NAOSIM,C19
-      NAO,C19
-      NATHYB,C22,C23,C24
-      NBCLOS,C16,C28
-      NBINQR,C28
-      NBOCLA,C23
-      NBODEL,C26
-      NBODIM,C18
-      NBODRV,C2,C19,C22
-      NBOEAN,A3,A4,A6,C3,C26,C36,C39
-      NBOINP,C30
-      NBOPEN,C16,C27
-      NBOSET,C18,C39
-      NBO,A3,A4,C2,C16,C36
-      NBOSUM,C23
-      NBREAD,C28
-      NBWRIT,C28
-      NEWDM,C26
-      NEWRYD,C20
-      NEWWTS,C20
-      NLMO,C22,C24
-      NORMLZ,C34
-      ORDER,C34
-      ORTHYB,C24
-      OUTPUT,C32
-      PACK,C34
-      PRJEXP,C24
-      RANK,C34
-      RDCARD,C29
-      RDCORE,C30
-      RDPPNA,C30
-      RDTNAB,C31
-      RDTNAO,C31
-      REDBLK,C21
-      REDIAG,C21
-      REPOL,C25
-      RFLD,C29
-      RNKEIG,C26
-      RUNNBO,A3,A4,C36,C38,C39
-      RYDIAG,C20
-      RYDSEL,C21
-      SETBAS,C20
-      SHMDT,C20
-      SIMLTR,C26
-      SIMTRM,C19
-      SIMTRN,C34
-      SIMTRS,C34
-      SRTNBO,C22
-      STASH,C24
-      STRTIN,C29
-      SUBST,C35
-      SVDNAO,C27
-      SVE0,C27
-      SVFNBO,C27
-      SVNBO,C27
-      SVNEWD,C27
-      SVNLMO,C27
-      SVPNAO,C27
-      SVPPAO,C27
-      SVSNAO,C27
-      SVTLMO,C27
- Subroutines (continued)
-      SVTNAB,C27
-      SVTNAO,C27
-      SVTNHO,C27
-      SYMORT,C25
-      SYMUNI,C25
-      TRANSP,C34
-      UNPACK,C35
-      VALTBL,C35
-      WRARC,C31
-      WRBAS,C31
-      WRMLMO,C31
-      WRPPNA,C30
-      WRTNAB,C31
-      WRTNAO,C30,C31
-      WRTNBO,C312
-      XCITED,C23
- Symmetric orthogonalization,C24,C25
- Symmetry,B16
- System-dependent driver routines,C36
- 
- TechSet,A11,A20
- Theta,A20,C33
- 3-center bonds
-      see Natural bond orbitals
- Thresholds,C9
-      ALLOW2,C20
-      ALLOW,C20
-      ANG,B4
-      ATHR,C23
-      DANGER,C20,C25
-      DIAGTH,C20,C25
-      DIFFER,C24,C34,C34
-      DONE,C34
-      DVAL,B5,B25
-      EPS,C24,C34
-      ETHR1,C23
-      ETHR2,C23
-      ETHR,C23
-      EVAL,B4
-      OCC,B4
-      PCT,B4
-      PRJINC,C22
-      PRJTHR,B11,C22
-      PTHR,C23
-      TEST2,C20
-      TEST,C20
-      THRESH,C22
-      THR1,C23
-      THR2,C23
-      THRESH,B11,C25
-      TOOSML,C24
-      WORTH,C20
-      WTTHR,C20,C21
- 2e-stabilization,A21
- 
-

- UHF method
-      see Wavefunction type
-

- Upper triangular matrix,
-        B65,B71,C13,C33,C34
- 
- Vager, Z.,A7
-

- Valency index
-      see Bond order
- Versions, previous,A7,A9,B13
-

- Vicinal interaction,A22-23,B18,
-        B23,B25,B51,C33
- 
- Warnings,B16,B17,B36,B55
-

- Wavefunction type
-      AUHF,C5,C17
-      CI,A6,C5,C17
-      Complex,A6,C5
-      Correlated,B25
-      GVB,A6
-      MCSCF,A1,A6,C5
-      Møller-Plesset,A6,C17
-      RHF,A6,A12,B16,B56,C2
-      ROHF,A6,C5
-      SCF,A6,B16,B25,C17
-      Semi-empirical,A7,A8,B66
-      UHF,A6,B16,B20,B52-55,C2,C5
- Weinhold, F.,A7,B11,C19,C22
- Weinstock, R. B.,A7,B11,C19
- Wiberg bond index,A16,B9,B29,C20,C22
- Write (W) parameter
-      see Print parameters
-
-
diff --git a/Documents/etc/nbo/lambda.gif b/Documents/etc/nbo/lambda.gif
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zqnxzbi?iOm`wxcVNLs*IGAEF>?hD8AOxJeC-e0cw{tpZahb11-V?3skN+GiejlyzI
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-参考のため、GNU 一般公衆利用許諾契約書の非公式日本語訳を添付します。ただし、正式な文書は英語版の方です。
+参考のため、GNU 一般公衆利用許諾契約書の非公式日本語訳を添付します。ただし、正式な文書は英語版の方です。
 

 
 
-- 
2.11.0

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