.TP2
.CM-----------------------------------------------------------------------
.CJ
#HNBO 3.0 Program Manual#N
.HR<<5//+1//32//58>>
#N(#INatural Bond Orbital / Natural Population Analysis /
Natural Localized Molecular Orbital Programs#N)
E. D. Glendening, A. E. Reed,\dagger J. E. Carpenter,\ddagger and F. Weinhold
#ITheoretical Chemistry Institute and Department of Chemistry,
University of Wisconsin, Madison, Wisconsin 53706#N
.LN50
.LM10
.RM80
.FJ
\dagger #RPresent address: Bayer AG, Abteilung AV-IM-AM,
5090 Leverkusen, Bayerwerk, Federal Republic of Germany.
\ddagger #RPresent address: Department of Chemistry, University of
California-Irvine, Irvine, California 92717.#N
.PN1r
.DF\np =\thsp \nthsp
.LM10
.RM80
.HF<
>
.CJ
#HTable of Contents#N
.FJ
.TB
.FM<<6L4//0L55//0R5>>
.RW<< //#BTable of Contents//#Ii>>
.RW<< //#BPreface: HOW TO USE THIS MANUAL//#Iiii>>
.RW
.RW
.RW
.FM<<1L4//0L60//0R5>>
.RW<<#HA.//GENERAL INTRODUCTION AND INSTALLATION// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BA.1//INTRODUCTION TO THE NBO PROGRAM//#IA-1>>
.FM<<10L5//0L50//0R5>>
.RW<<#IA.1.1//What does the NBO Program Do?//#IA-1>>
.RW<<#IA.1.2//Structure of the NBO Program//#IA-3>>
.RW<<#IA.1.3//Input and Output//#IA-5>>
.RW<<#IA.1.4//General Capabilities and Restrictions//#IA-6>>
.RW<<#IA.1.5//References and Relationship to Previous Versions//#IA-7>>
.FM<<6L4//0L55//0R5>>
.RW<<#BA.2//INSTALLING THE NBO PROGRAM//#IA-10>>
.RW<<#BA.3//TUTORIAL EXAMPLE FOR METHYLAMINE//#IA-12>>
.FM<<10L5//0L50//0R5>>
.RW<<#IA.3.1//Running the Example//#IA-12>>
.RW<<#IA.3.2//Natural Population Analysis//#IA-13>>
.RW<<#IA.3.3//Natural Bond Orbital Analysis//#IA-16>>
.RW<<#IA.3.4//NHO Directional Analysis//#IA-20>>
.RW<<#IA.3.5//Perturbation Theory Energy Analysis//#IA-21>>
.RW<<#IA.3.6//NBO Summary//#IA-22>>
.ET
.TB
.FM<<1L4//0L60//0R5>>
.RW<<#HB.//NBO USER'S GUIDE// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BB.1//INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS//#IB-1>>
.RW<<#BB.2//THE $NBO KEYLIST//#IB-2>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.2.1//Overview of $NBO Keywords//#IB-2>>
.RW<<#IB.2.2//Job Control Keywords//#IB-3>>
.RW<<#IB.2.3//Job Threshold Keywords//#IB-4>>
.RW<<#IB.2.4//Matrix Output Keywords//#IB-6>>
.RW<<#IB.2.5//Other Output Control Keywords//#IB-9>>
.RW<<#IB.2.6//Print Level Keywords//#IB-10>>
.RW<<#IB.2.7//Semi-Documented Additional Keywords//#IB-11>>
.FM<<6L4//0L55//0R5>>
.RW<<#BB.3//THE $CORE LIST//#IB-12>>
.RW<<#BB.4//THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)//#IB-14>>
.RW<<#BB.5//THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)//#IB-16>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.5.1//Introduction to NBO Energetic Analysis//#IB-16>>
.RW<<#IB.5.2//The Nine Deletion Types//#IB-17>>
.RW<<#IB.5.3//Input for UHF Analysis//#IB-20>>
.RW
.RW
.RW
.FM<<6L4//0L55//0R5>>
.RW<<#BB.6//NBO KEYLIST ILLUSTRATIONS//#IB-21>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.6.1//Introduction//#IB-21>>
.RW<<#IB.6.2//NLMO Keyword//#IB-22>>
.RW<<#IB.6.3//DIPOLE Keyword//#IB-24>>
.RW<<#IB.6.4//Matrix Output Keywords//#IB-26>>
.RW<<#IB.6.5//BNDIDX Keyword//#IB-29>>
.RW<<#IB.6.6//RESONANCE Keyword: Benzene//#IB-32>>
.RW<<#IB.6.7//NOBOND Keyword: Hydrogen Fluoride//#IB-37>>
.RW<<#IB.6.8//3CBOND Keyword: Diborane//#IB-40>>
.RW<<#IB.6.9//NBO Directed Search ($CHOOSE Keylist)//#IB-44>>
.RW<<#IB.6.10//NBO Energetic Analysis ($DEL Keylist)//#IB-48>>
.RW<<#IB.6.11//Open-Shell UHF Output: Methyl Radical//#IB-52>>
.RW<<#IB.6.12//Effective Core Potential: Cu#d2#u Dimer//#IB-56>>
.FM<<6L4//0L55//0R5>>
.RW<<#BB.7//FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM//#IB-62>>
.FM<<10L5//0L50//0R5>>
.RW<<#IB.7.1//Introduction//#IB-62>>
.RW<<#IB.7.2//Format of the FILE47 Input File//#IB-63>>
.RW<<#IB.7.3//$GENNBO Keylist//#IB-65>>
.RW<<#IB.7.4//$COORD Keylist//#IB-66>>
.RW<<#IB.7.5//$BASIS Datalist//#IB-67>>
.RW<<#IB.7.6//$CONTRACT Datalist//#IB-69>>
.RW<<#IB.7.7//Matrix Datalists//#IB-71>>
.ET
.TB
.FM<<1L4//0L60//0R5>>
.RW<<#HC.//NBO PROGRAMMER'S GUIDE// >>
.RW=
.FM<<6L4//0L55//0R5>>
.RW<<#BC.1//INTRODUCTION//#IC-1>>
.RW<<#BC.2//OVERVIEW OF NBO.SRC SOURCE PROGRAM GROUPS//#IC-2>>
.RW<<#BC.3//LABELLED COMMON BLOCKS//#IC-4>>
.RW<<#BC.4//DIRECT ACCESS FILE AND OTHER I/O//#IC-14>>
.RW<<#BC.5//NAO/NBO/NLMO ROUTINES (GROUP I)//#IC-16>>
.FM<<10L5//0L50//0R5>>
.RW<<#IC.5.1//SR NBO Master Routine//#IC-16>>
.RW<<#IC.5.2//Job Initialization Routines//#IC-18>>
.RW<<#IC.5.3//NAO Formation Routines//#IC-19>>
.RW<<#IC.5.4//NBO/NLMO Formation Routines//#IC-22>>
.FM<<6L4//0L55//0R5>>
.RW<<#BC.6//ENERGY ANALYSIS ROUTINES (GROUP II)//#IC-26>>
.RW<<#BC.7//DIRECT ACCESS FILE (DAF) ROUTINES (GROUP III)//#IC-27>>
.RW<<#BC.8//FREE FORMAT INPUT ROUTINES (GROUP IV)//#IC-29>>
.RW<<#BC.9//OTHER SYSTEM INDEPENDENT I/O ROUTINES (GROUP V)//#IC-30>>
.RW<<#BC.10//GENERAL UTILITY ROUTINES (GROUP VI)//#IC-33>>
.RW<<#BC.11//SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)//#IC-36>>
.RW<<#BC.12//GENNBO AUXILLIARY ROUTINES//#IC-37>>
.RW<<#BC.13//ATTACHING NBO TO A NEW ESS PROGRAM//#IC-38>>
.RW
.RW
.RW
.FM<<6L4//0L55//0R5>>
.RW<< //#BAPPENDIX: Specific ESS Versions#N// >>
.RW<< //#BINDEX#N// >>
.ET
.HF<>
.RL55
.LJ
#HPREFACE: HOW TO USE THIS MANUAL#N
.FJ
\np The NBO manual is divided into three major sections:
\np 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.
\np 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 #Ikeywords#N 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.
\np 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.
.PR10
.CM----------------------------------NBOA.MAN----------------------
.TP2
.HF<>
.NF<>
.PN1
.DF\degree =\*degree
.DF\np =\thsp \nthsp
.CM----------------------------------------------------------------
.CJ
#HSection A: GENERAL INTRODUCTION AND INSTALLATION#N
.FJ
.RL15
#BA.1 INTRODUCTION TO THE NBO PROGRAM#N
#IA.1.1 #IWhat Does the NBO Program Do?#N
\np 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 \alpha
and \beta spin.\dagger This
section provides a brief introduction to NBO algorithms and
nomenclature.
\np 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 L\umlaut owdin, 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.
.DF\ha =#C#Ih#O#dA#u
.DF\hb =#C#Ih#O#dB#u
.DF\ca =#C#Ic#O#dA#u
.DF\cb =#C#Ic#O#dB#u
.DF\sab =\sigma #dAB#u
.DF\ssab =\sigma *#d#>
.CM--------------------------------------------------------------------
.CJ
input basis \rarr NAOs \rarr NHOs \rarr NBOs \rarr NLMOs
.FJ
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.
\np 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 (\sab ) and antibond (\ssab )
in the NBO basis,
.CJ
\sab = \ca \ha + \cb \hb
\ssab = \cb \ha \minus \ca \hb
.FJ
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.
\np 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.
\np 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 #Iab initio#N and
semi-empirical packages (GAUSSIAN-8X, GAMESS, HONDO, AMPAC,
etc.). These versions are described in
individual Appendices.
.RL55
#IA.1.2 #IStructure of the NBO Program#N
\np 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).
\np 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.
\np 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.
.CM-------------------------Figure 1-------------------------------------
.RL55
.DF\@line1 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0>>
.ED
.DF\@line2 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0//
'\line2 ' 2//+0 +\!lf 0>>
.ED
.DF\@line3 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0>>
.ED
.DF\@line4 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0//'\line4 ' 2//
+0 +\!lf 0>>
.ED
.DF\@line5 =
.GR<<\!dhl \!dvl 0//'\line1 ' 2//+0 +\!lf 0//
'\line2 ' 2//+0 +\!lf 0//'\line3 ' 2//+0 +\!lf 0//'\line4 ' 2//
+0 +\!lf 0//'\line5 ' 2//+0 +\!lf 0>>
.ED
.DF\!dpx =68
.DF\!dpy =120
.DF\!lf =\!dpy
.DF\!ipen =1
.BX<<3//15//75//8//35>>
.CM----draw box at 10,55 and save coords of bottom
.DF\!hl =45
.DF\!vl =8
.DF\!nl =3
.DF\line1 =ab initio or
.DF\line2 =semi-empirical
.DF\line3 =program (ESS)
.DF\!wess =12
.DF\!wid =\!wess
.GS$box
.DF\!hess =\!dhl
.DF\!vess =\!dbot
.CM----draw scratch disk
.DF\!hs =-15
.DF\!hl =\!hl +\!hs
.DF\!hscr =\!hl
.DF\!vscr =\!vl
.DF\!a =4
.DF\!b =0.5
.DF\!ht =3.5
.DF\text =SCRATCH
.GS$cyl
.DF\!hl =\!hl -\!hs
.CM----draw line from ESs to scratch
.DF\!h1 =\!hess -\!wess *\!dpx /2
.DF\!v1 =(\!vscr +1)*\!dpy
.DF\!h2 =(\!hscr +\!a )*\!dpx
.DF\!v2 =\!v1
.GS$gline
.CM----move to bottom of ESS box
.DF\!vl =\!vl +3
.CM----draw runnbo box & save coords
.DF\!vl =\!vl +3
.DF\!nl =1
.DF\line1 =RUNNBO
.DF\!wid =8
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hrun =\!dhl
.DF\!trun =\!dtop
.DF\!brun =\!dbot
.CM----move to bottom of box
.DF\!vl =\!vl +1
.CM----draw line from bottom of ess to top of runnbo
.DF\!h1 =\!hess
.DF\!v1 =\!vess
.DF\!h2 =\!hrun
.DF\!v2 =\!trun
.GS$gline
.CM----draw FEAOIN box & save coords
.DF\!hl =45-15
.DF\!vl =\!vl +5
.DF\!hfetch =\!hl
.DF\!vfetch =\!vl
.DF\!nl =1
.DF\line1 =FEAOIN
.DF\!wid =8
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hfet =\!dhl
.DF\!tfet =\!dtop
.DF\!bfet =\!dbot
.CM----draw dashed line from scratch to feaoin
.DF\!h1 =\!hscr *\!dpx
.DF\!v1 =(\!vscr +3.5+\!b )*\!dpy
.DF\!h2 =\!h1
.DF\!v2 =\!tfet
.DF\!ipen =7
.GS$gline
.DF\!ipen =1
.CM----draw NBO box & save coords
.DF\!hl =45-5
.DF\!hnbo =\!hl
.DF\!vnbo =\!vl
.DF\!wid =5
.DF\!nl =1
.DF\line1 =NBO
.GS$box
.DF\!hnbo =\!dhl
.DF\!tnbo =\!dtop
.DF\!bnbo =\!dbot
.CM----draw horizontal line from FEAOIN to to NBO
.DF\!h1 =\!hfet +4*\!dpx
.DF\!v1 =\!tnbo +0.5*(\!bnbo -\!tnbo )
.DF\!h2 =\!hnbo -2.5*\!dpx
.DF\!v2 =\!v1
.GS$gline
.CM----draw line from bottom of runnbo to to top of nbo
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hnbo
.DF\!v2 =\!tnbo
.GS$gline
.CM----draw NBOEAN box & store coords
.DF\!hl =45+5
.DF\!hean =\!hl
.DF\!wid =8
.DF\!nl =1
.DF\line1 =NBOEAN
.GS$box
.DF\!hean =\!dhl
.DF\!tean =\!dtop
.DF\!bean =\!dbot
.CM---draw line from bottom of runnbo to top of nboean
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hean
.DF\!v2 =\!tean
.GS$gline
.CM---draw DELSCF box & save coords
.DF\!hl =45+15
.DF\!hdel =\!hl
.DF\!wid =8
.DF\!nl =1
.DF\line1 =DELSCF
.DF\!ipen =5
.GS$box
.DF\!ipen =1
.DF\!hdel =\!dhl
.DF\!tdel =\!dtop
.DF\!bdel =\!dbot
.CM-----draw line from bottom of runnbo to top of delscf
.DF\!h1 =\!hrun
.DF\!v1 =\!brun
.DF\!h2 =\!hdel
.DF\!v2 =\!tnbo
.GS$gline
.CM-----draw NBODAF cylinder
.DF\!hl =45
.DF\!vl =\!vl +5
.DF\!a = 4
.DF\!b =0.5
.DF\text =NBODAF
.GS$cyl
.DF\!hdaf =\!dhl
.DF\!tdaf =\!dvl
.CM-----draw line from bottom of delscf to top of daf
.DF\!h1 =\!hdel
.DF\!v1 =\!bdel
.DF\!h2 =\!hdaf
.DF\!v2 =\!tdaf
.DF\!ipen =1
.GS$gline
.CM-----draw line from bottom of nboean to top of daf
.DF\!h1 =\!hean
.DF\!v1 =\!bean
.GS$gline
.CM-----draw line from bottom of nbo to top of daf
.DF\!h1 =\!hnbo
.DF\!v1 =\!bnbo
.GS$gline
.CM-----draw line from bottom of feaoin to top of daf
.DF\!h1 =\!hfet
.DF\!v1 =\!bfet
.GS$gline
.DF\!ipen =1
.CM-----draw dashed line from ESS to DELSCF
.DF\!h1 =\!hess +6*\!dpx
.DF\!v1 =\!vess -\!dpy
.DF\!h2 =\!hdel
.DF\!v2 =\!v1
.DF\!ipen =7
.GS$gline
.DF\!h1 =\!h2
.DF\!v1 =\!v2
.DF\!v2 =\!tdel
.GS$gline
.DF\!ipen =1
.GT$onward
.CM$gline ---------------------------------------------------------
.GR<<\!h1 \!v1 0//\!h2 \!v2 \!ipen >>
.RT
.CM$box ----------------------------------------------------------
.CM draw box centered below pointer, and return to pointer origin
.CM---------set \!nl = no. lines, \!wid = width (characters),
.CM---------and \line1 , \line2 , ...
.DF\!lfh =\!dpy /2
.DF\!dhl =\!hl *\!dpx
.DF\!dvl =\!vl *\!dpy
.DF\!dwid =\!wid *\!dpx
.DF\!dht =(\!nl +0.5)*\!dpy
.DF\!dhlfwid =\!dwid /2
.DF\!test1 =0.5-ABS((\!nl -1))
.DF\!test2 =0.5-ABS((\!nl -2))
.DF\!test3 =0.5-ABS((\!nl -3))
.DF\!test4 =0.5-ABS((\!nl -4))
.DF\!test5 =0.5-ABS((\!nl -5))
.IF<<\!test1 >>THEN<<\@line1 >>
.IF<<\!test2 >>THEN<<\@line2 >>
.IF<<\!test3 >>THEN<<\@line3 >>
.IF<<\!test4 >>THEN<<\@line4 >>
.IF<<\!test5 >>THEN<<\@line5 >>
.GR<<\!dhl +0 0//+0 -\!lfh 0//+\!dhlfwid +0 \!ipen //+0 -\!dht \!ipen //
-\!dwid +0 \!ipen //+0 +\!dht \!ipen //+\!dhlfwid +0 \!ipen >>
.DF\!dbot =\!dvl +(\!nl -1.25)*\!dpy +\!lfh
.DF\!dtop =\!dbot -\!dht
.RT
.CM$cyl -----------------------------------------------------
.CM set \!a =hor. radius, \!b = vert. radius, \!ht =height
.CM.DF\!a =4
.CM.DF\!b =0.5
.CM.DF
.DF\!dhl =\!hl *\!dpx
.DF\!dvl =\!vl *\!dpy
.DF\!t =0
.DF\!twopi =2*3.1415926
.DF\!dht =\!ht *\!dpy
.DF\!dhlfht =\!dht /2 -\!dpy /2
.DF\!radius =\!a *\!dpx
.DF\!diam =2*\!radius
.DF\!a2 =\!a *\!a
.DF\!b2 =\!b *\!b
.DF\!x =\!a *COS(\!t *\!twopi )
.DF\!y =-SQR(\!b2 *(1-\!x *\!x /\!a2 ))
.DF\!ym =-\!y
.GR<<\!dhl \!dvl 0//
F \!x \!y \!t 0.0001 0.5 .05 \!dpx \!dpy 0 1 \!ipen //+\!radius +0 0//
F \!x \!ym \!t 0.0001 0.5 .05 \!dpx \!dpy 0 1 \!ipen //
+0 +\!dht \!ipen //+\!diam -\!dht 0//+0 +\!dht \!ipen //-\!radius +0 0//
F \!x \!ym \!t 0.0001 -0.5 -0.05 \!dpx \!dpy 0 1 \!ipen //
+\!radius -\!dhlfht 0//'\text ' 2//+0 +\!lf 0//'file' 2>>
.RT
.CM----------------------------------------------------------------
.CM$onward
.LM15
.RM75
.FJ
.LN37
#BFigure 1:#N Schematic diagram depicting flow of information
between the electronic
structure system (ESS) and the NBO program,
and the commun#|ication 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.
.LM10
.RM80
.FJ
.CM------------------end of Figure 1----------------------------------
.RL55
#IA.1.3 #IInput and Output#N
\np 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 #Ikeylist#N) 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.
\np The following information is passed from
the ESS to the NBO program (transparent to the user):
.LM+5
.RM-5
.OS<<3//1.>>
The one-electron density matrix #BD#N (or density matrices in the
open-shell case) in the chosen atomic orbital (AO) basis set;
.OS<<3//2.>>
The AO overlap matrix #BS#N, and label information identifying the
symmetry (angular momentum type) and location (number of the atom
to which affixed) for each AO;
.OS<<3//3.>>
Atomic number (nuclear charge) of each atom.
.LM-5
.RM+5
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 #BF#N, if energy analysis is requested; the
AO dipole matrix #BM#N, 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.
\np 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.
.RL55
#IA.1.4 #IGeneral Capabilities and Restrictions#N
\np Principal capabilities of the NBO program are:
.LM+5
.RM-5
.OS<<3//1.>>
Natural population, natural bond orbital, and natural localized
molecular orbital analysis of SCF, MCSCF, CI, and M\not oller-Plesset
wavefunctions (main subroutine: NBO);
.OS<<3//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);
.OS<<3//3.>>
Localized analysis of molecular dipole moment in terms of NLMO
and NBO bond moments and their interactions (main subroutine: DIPANL).
.LM-5
.RM+5
\np 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:
.LM+10
.OS<<6//S>>
= overlap matrix
.OS<<6//DM>>
= density matrix (or D)
.OS<<6//F>>
= Fock matrix
.OS<<6//DI>>
= dipole matrix (or DXYZ, or DX, DY, DZ)
.OS<<6//NPA>>
= Natural Population Analysis
.OS<<6//NAO>>
= Natural Atomic Orbital
.OS<<6//NBO>>
= Natural Bond Orbital
.OS<<6//NLMO>>
= Natural Localized Molecular Orbital
.OS<<6//PNAO>>
= pre-orthogonal NAO (i.e., omit interatomic orthogonalization)
.OS<<6//PNHO, PNBO, PNLMO = pre-orthogonal NHO, etc. (formed from PNAOs)>>
\thsp
.LM-10
\np 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 M\not oller-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
(``pseudo#|potentials'') can be handled, including complete neglect
of core electrons as assumed in semi-empirical treatments. The
atomic orbital basis functions (up to #If#N orbitals in angular
symmetry) may be of general Slater-type, contracted Gaussian-type,
or other general composition,
including the ``effective'' ortho#|normal valence-shell AOs of
semi-empirical treatments. AO basis functions are
assumed to be normalized, but in general non-orthogonal.
.RL55
#IA.1.5 #IReferences and Relationship to Previous Versions#N
\np This program (``version 3.0'') is an extension of previous versions of the
NBO method incorporated in the semi-empirical program #IBONDO#N
[F. Weinhold, #IQuantum Chemistry Program Exchange No. 408#N
(1980); ``version 1.0'']
and in a GAUSSIAN-82 implementation [A. E. Reed and F. Weinhold, #IQCPE
Bull. #B5#N, 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
.TB
.FM<<10L20//5L25>>
.RW<>
.RW<>
.RW<>
.RW<>
.ET
Principal references to the development and applications of NAO/NBO/NLMO
methods are:
.LM+3
.OS<<3//#_Natural Bond Orbitals:#/>>
J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc. #B102#N, 7211-7218
(1980).
.OS<<3//#_Natural Atomic Orbitals and Natural Population Analysis:#/>>
A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B78#N, 4066-4073 (1983);
A. E. Reed, R. B. Weinstock, and F. Weinhold, #IJ. Chem. Phys. #B83#N,
735-746 (1985).
.OS<<3//#_Natural Localized Molecular Orbitals:#/>>
A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B83#N, 1736-1740 (1985).
.OS<<3//#_Open-Shell NBO:#/>>
J. E. Carpenter and F. Weinhold, #IJ. Molec. Struct. (Theochem) #B169#N,
41-62 (1988); J. E. Carpenter, #IPh. D. Thesis#N, University of Wisconsin,
Madison, 1987.
.OS<<3//#_Review Articles:#/>>
A. E. Reed, L. A. Curtiss, and F. Weinhold, #IChem. Rev. #B88#N,
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.
.LM10
\np The principal enhancements of version 3.0 include:
.LM+5
.RM-5
.OS<<3//1.>>
#IGeneralized Program Interface.#N
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.
.OS<<3//2.>>
#INAO/NPA Summary Table.#N
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 (1#Is#N,
2#Is#N, 2#Ip#N, 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.
.OS<<3//3.>>
#INBO Summary Table.#N
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.
.OS<<3//4.>>
#IBond Bending Analysis.#N
The program includes a new analysis of hydrid directionality
and bond ``bending'' (keyword BEND, Section A.3.4).
.OS<<3//5.>>
#IDipole Moment Analysis.#N
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.
.OS<<3//6.>>
#IPrint options.#N
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.
.OS<<3//7.>>
#IOrbital Contour Info.#N
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.
.OS<<3//8.>>
#IEffective Core Potentials.#N
The program now handles effective core potentials (pseudo#|potentials),
or the complete neglect of core levels characteristic of semi-empirical
wavefunctions (Section B.6.12).
.LM-5
.RM+5
The program also includes three changes to
correct problems of the previous version (which may have
affected a small number of users):
.LM+5
.RM-5
.OS<<3//9.>>
#IUnpolarized Cores.#N
NAOs identified as ``core'' orbitals are now auto#|matically 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.
.OS<<3//10.>>
#IExcited State Antibond Labels.#N
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.]
.OS<<3//11.>>
#IAlternative Resonance Structures.#N 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.
.LM-5
.RM+5
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.
.HF<>
.RL55
#BA.2 INSTALLING THE NBO PROGRAM#N
\np 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).
\np In overview, the installation procedure involves the following steps
(the details of each step being dependent on your operating system):
.LM+5
.OS<<3//1.>>
#IEnabling the NBO routines.#N 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
#T
FOR ENABLE
LINK ENABLE
#NNow, run the ENABLE program (e.g., type ``RUN ENABLE'' in
a VMS system), and
answer the prompt
#T
NBO program version to enable?
#Nby 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 #IXXX#NNBO.FOR (where `#IXXX#N' is the identifier)
that incorporates the appropriate drivers for
your ESS.
.OS<<3//2.>>
#ICompiling the NBO routines.#N Using your system Fortran 77 compiler,
compile the #IXXX#NNBO.FOR file to an object code file (say,
#IXXX#NNBO.OBJ). [Compiler
errors (if any) should be fixed before proceeding. Please notify the
authors if you encounter undue difficulties in this step.]
.OS<<3//3.>>
#IModifying the ESS routines.#N 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.
.OS<<3//4.>>
#IRebuilding the integrated ESS/NBO program.#N Re-compile your modified
ESS programs and link the resulting object file (say, ESS.OBJ) with
the #IXXX#NNBO.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 #IXXX#NNBO.OBJ file must be included
in the link statement (or deposited in one of the libraries accessed
by the linker, etc.).
.LM10
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.
\np 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.
\np 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].
.HF<>
.RL55
#BA.3 TUTORIAL EXAMPLE FOR METHYLAMINE#N
#IA.3.1 Running the Example#N
\np 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 (CH#d3#uNH#d2#u) in
Pople-Gordon idealized geometry, treated at the #Iab initio#N
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.
\np 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
#T
$NBO $END
#Nat the end of the file. This is an `empty' NBO keylist, specifying
that NBO analysis should be carried out at the #Idefault#N level.
\np 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:
.HR<<5//+0//5//85>>
.CM----------------------output file----------------------------------------
.DF\@seg =
.RL9
*******************************************************************************
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)
.ED
.DF\!lm =5
.DF\!rm =88
.LM\!lm
.RM\!rm
#T
\@seg
.LM10
.RM80
.HR<<5//+0//5//85>>
#NNote 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.
.RL55
.FJ
#IA.3.2 Natural Population Analysis#N
#N\np 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:
.HR<<5//+0//5//85>>
.DF\@seg =
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
.ED
.LM\!lm
.RM\!rm
#T
.RS#~
\@seg
.RS~#
.LM10
.RM80
.HR<<5//+0//5//85>>
#NFor 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' (#Is#N, #Ip#dx#u#N, 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 2#Ip#N#dx#u orbital on carbon, occupied
by 0.8909 electrons, whereas NAO 5 is a Rydberg
3#Ip#N#dx#u 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.
\np The principal quantum numbers for the
NAO labels (1#Is#N, 2#Is#N, 3#Is#N, 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.
.CM------------------------------------------------------------------------
.DF\@seg =
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
.ED
.RL19
#NThe 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:
.HR<<5//+0//5//85>>
.LM\!lm
.RM\!rm
#T
.RS#~
\@seg
.RS~#
.LM10
.RM80
.HR<<5//+0//5//85>>
#NThis 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 \minus 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.]
.DF\@seg =
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)
--------------------------------------------------------
.ED
.RL15
#NNext follows a summary of the NMB and NRB populations
for the composite
system, summed over atoms:
.HR<<5//+0//5//85>>
#T
.LM\!lm
.RM\!rm
\@seg
.LM10
.RM80
.HR<<5//+0//5//85>>
#NThis 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.]
.RL16
#NFinally, the natural populations are summarized as an effective
valence electron configuration (``natural electron configuration'')
for each atom:
.DF\@seg =
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)
.ED
.HR<<5//+0//5//85>>
#T
.LM\!lm
.RM\!rm
.RS#~
\@seg
.RS~#
.LM10
.RM80
.HR<<5//+0//5//85>>
#NAlthough 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
1s#u2#d2s#u1#d2p#u3#d electron configuration.]
.RL55
#IA.3.3 Natural Bond Orbital Analysis#N
#N\np 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:
.DF\@seg =
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
.ED
.HR<<5//+0//5//85>>
#T
.LM\!lm
.RM\!rm
\@seg
.LM10
.RM80
.HR<<5//+0//5//85>>
#NNormally, 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 thresh#|old 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 thresh#|old (default, 1.90 electrons).
.RL22
\np #NNext follows a more detailed breakdown of the Lewis and non-Lewis
occupancies into core, valence, and Rydberg shell contributions:
.DF\@seg =
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)
--------------------------------------------------------
.ED
.HR<<5//+0//5//85>>
#T
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.LM10
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.HR<<5//+0//5//85>>
#NThis 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.)
.DF\@seg =
(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
.ED
.RL20
#NNext follows the main listing of NBOs, displaying the form and occupancy
of the complete set of NBOs that span the input AO space:
#T
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\@seg
.LM10
.RM80
.HR<<5//+0//5//85>>
#NFor 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 \sigma #dCN#u
bond.] The next lines summarize
the natural atomic hybrids #Ih#N#dA#u
of which the NBO is composed, giving the
percentage (100|#Ic#N#dA#u|#u2#d) of the NBO on each hybrid (in parentheses),
the polarization coefficient #Ic#N#dA#u, the atom label, and a hybrid
label showing the #Isp#N#u\lambda #d composition
(percentage #Is#N-character, #Ip#N-character, etc.) of
each #Ih#N#dA#u. [For example, the \sigma #dCN#u NBO
is formed from an #Isp#N#u3.61#d hybrid (78.3%
#Ip#N-character) on carbon interacting with an #Isp#N#u2.24#d hybrid
(69.1% #Ip#N-character) on nitrogen,
.CJ
\sigma #dCN#u = 0.633(#Isp#N#u3.61#d)#dC#u + 0.774(#Isp#N#u2.24#d)#dN#u
.FJ
corresponding roughly to the qualitative concept
of interacting #Isp#N#u3#d hybrids (75% #Ip#N-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 #Ih#N#dC#u
of the \sigma #dCN#u bond has largest coefficients for the 2#und#d
and 4#uth#d NAOs, corresponding to the approximate description
.CJ
#Ih#N#dC#u \~= \minus 0.4653(2#Is#N)#dC#u \minus 0.8808(2#Ip#N#dx#u)#dC#u
.FJ
in terms of the valence NAOs of the carbon atom.] In
the CH#d3#uNH#d2#u 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
\sigma #dCH#u NBOs, and the slightly higher occupancy
(0.01569 #Ivs.#N 0.0077
electrons) in the \sigma *#<#dC#d1#uH#d3#u#u antibond
(NBO 24) lying #Itrans#N to the
nitrogen lone pair.
.RL55
#IA.3.4 NHO Directional Analysis#N
\np The next segment of output
summarizes the angular properties of
the natural hybrid orbitals:
.DF\@seg =
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 -- -- -- --
.ED
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#T
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\@seg
.LM10
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#NThe `direction' of a hybrid is specified
in terms of the polar (\theta ) and
azimuthal (\phi ) angles (in the ESS coordinate system) of the vector
describing its #Ip#N-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 CH#d3#uNH#d2#u case shown above, the nitrogen NHO
of the \sigma #dCN#u bond (NBO 1) is bent away
from the line of C-N
centers by 3.0\degree , whereas the carbon NHO is approximately
aligned with the C-N axis (within the 1.0\degree threshold for
printing). The N-H bonds (NBOs 5, 6) are
bent even further (4.4\degree ). 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 -NH#d2#u group to relieve the nitrogen bond `kinks' found
in the tetrahedral Pople-Gordon geometry).
.RL55
#IA.3.5 Perturbation Theory Energy Analysis#N
\np The next segment summarizes the second-order perturbative estimates
of `donor-acceptor' (bond-antibond) interactions in the NBO basis:
.DF\@seg =
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
.ED
.HR<<5//+0//5//85>>
#T
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\@seg
.LM10
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#NThis 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 (#Ii#N) and acceptor NBO (#Ij#N),
the stabilization energy E(2) associated with delocalization
(``2e-stabilization'') #Ii \rarr j#N is estimated as
.CJ
.DF\denom =\epsilon #dj#u \minus \epsilon #di#u
E(2) = \Delta E#dij#u = q#di#u \quo <>
.FJ
where #Iq#N#di#u is the donor orbital occupancy,
\epsilon #di#u, \epsilon #dj#u are diagonal elements (orbital energies)
and F(i,j) is the off-diagonal NBO Fock matrix element. [In the example
above, the #In#N#dN#u \rarr \sigma *#<#dCH#u interaction between the
nitrogen lone pair (NBO 8) and the antiperiplanar C#d1#u-H#d3#u 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.
.RL55
#IA.3.6 NBO Summary#N
\np Next appears a condensed summary of the principal NBOs, showing the
occupancy, orbital energy, and the qualitative pattern of delocalization
interactions associated with each:
.DF\@seg =
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
.ED
.HR<<5//+0//5//85>>
#T
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\@seg
.LM10
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.HR<<5//+0//5//85>>
#NThis 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
(\minus 0.44592 a.u.) Lewis NBO, and to
be primarily
delocalized into antibonds 24, 25, 26 (the vicinal \sigma *#<#dCH#u
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).]
.CM-----------------------------NBOB.MAN---------------------------
.TP2
.DF\np =\thsp \nthsp
.DF\degree =\*degree
.HF<>
.NF<>
.PN1
.CM----------------------------------------------------------------
.CJ
#HSection B: NBO USER'S GUIDE#N
.FJ
#BB.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS#N
\np 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.
\np 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 #Ikeywords#N in a prescribed #Ikeylist#N format. Four distinct
keylist ($KEY) types are recognized ($NBO, $CORE, $CHOOSE, and $DEL), and
these will be described in turn in Sections B.2-B.5. Some of the details
of inserting NBO keylists into the input file depend on the details
of your ESS method, and are described in the appropriate Appendix for
the ESS. However, the general form of NBO keylists and the meaning and
function of each keyword are identical for all versions (insofar as the
option is meaningful for the ESS), and are described herein.
\np The four keylist types have common rules of syntax: Keylist
delimiters are identified by a ``$'' 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,
#T
$NBO keyword1 keyword2 . . . $END !comment
#N(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.
.HF<>
.RL55
#BB.2 THE $NBO KEYLIST#N
#IB.2.1 Overview of $NBO keywords#N
\np 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:
.RL5
.LM+5
#IJob Control Keywords:#N
.LM+0
.TB
.FM<<5L15//0L15//0L15//0L15>>
.RW<>
.RW<>
.ET
.LM+0
#IJob Threshold Keywords:#N
.LM+0
.TB
.FM<<5L40>>
.RW<>
.RW<>
.RW<>
.ET
.LM+0
.RL13
#IMatrix Output Keywords:#N
.LM+0
.TB
.FM<<5L10//0L10//0L10//0L10//0L10>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.FM<<5L10//0L10//0L10//0L10>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.ET
.LM+0
.RL3
#IOther Output Control Keywords:#N
.LM+0
.TB
.FM<<5L10//0L10//0L10//0L10>>
.RW<>
.RW<>
.ET
.LM+0
.RL2
#IPrint Level Control:#N
.LM+5
PRINT=n
.LM-5
.LM-5
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.
\np 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:
#T
E2PERT=2.5 LFNPR 16 NBOMO=W25
#N(The equal sign is recommended, and will be used in the remaining
examples.)
[\np 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.]
.RL55
#IB.2.2 Job Control Keywords#N
\np 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):
.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>
.OS<<12//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.
.OS<<12//NBO>>
Request calculation of NBOs and printing of the main NBO table
(Section A.3.3).
.OS<<12//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.
.OS<<12//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.)
.OS<<12//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.)
.OS<<12//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.)
.OS<<12//SKIPBO>>
Skip the computation of NBOs, i.e., only determine NAOs and
perform natural population analysis. (Useful when only NPA is
desired.)
.OS<<12//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).
.HR<<1//+1//10//80>>
.LM10
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.
.RL55
#IB.2.3 Job Threshold Keywords#N
.BM61
\np 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].)
.LM30
.OS<<20//#IKEYWORD parameter(s)#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//18>>
.HR<<1//+1//19//29>>
.HR<<1//+1//30//80>>
.OS<<20//BEND ang, pct, occ>>
Request the NHO Directional Analysis table (Section A.3.4). The
three parameters [and default values] have the following
significance:
.LM+10
.OS<<8//ang [1.0]>>
= threshold angular deviation for printing
.OS<<8//pct [25]>>
= threshold percentage #Ip#N-character for printing
.OS<<8//occ [0.1]>>
= threshold NBO occupancy for printing
.LM-10
#NParameter values may be separated by a space or a comma.
Example:#T BEND=2,10,1.9
#NThis example specifies that the bond-bending table should
only include entries for angular deviations of at least 2\degree (ang),
hybrids of at least 10% #Ip#N-character (pct), and NBOs of occupancy
at least 1.9 electrons (occ).
.RL13
.OS<<20//E2PERT eval>>
Request the Perturbation Theory Energy Analysis
table (Section A.3.5), where
.LM+10
.OS<<8//eval [0.5]>>
= threshold energy (in kcal/mol) for printing
.LM-10
Entries will be printed for NBO donor-acceptor interaction energies
that exceed the `eval' threshold.
Example:#T E2PERT=5.0
#NThis example would print only interactions of at least 5 kcal/mol
(i.e., only the single entry for the 8.13 kcal/mol
#In#N#dN#u \rarr \sigma *#<#dCH#u interaction in the output
of Section A.3.5).
.RL16
.OS<<20//DIPOLE dval>>
Request the Molecular Dipole Moment Analysis table (Section B.6.3), where
.LM+10
.OS<<9//dval [0.02]>>
= threshold dipole moment (Debye) for printing
.LM-10
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:#T DIPOLE=0.1
#NThis example would print out dipole contributions of all NBOs (and
their delocalization interactions) of magnitude \ge 0.1\thsp D.
.LM10
.HR<<1//+1//10//80>>
.BM60
#NBoth 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
#T
$NBO DIPOLE $END
#Nin 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.
.RL55
.LM10
#IB.2.4 Matrix Output Keywords#N
\np 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,
.DF\steps1 =input AOs \rarr (PNAOs) \rarr NAOs \rarr NHOs \rarr
.DF\steps2 =NBOs \rarr NLMOs \rarr canonical MOs
.CJ
\steps1 \steps2
.FJ
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#/
\np The keyword for printing the matrix for a particular basis
transformation, IN \rarr OUT, is constructed from the
corresponding acronymns
for the two sets in the generic form ``INOUT''. For example,
the transformation AO \rarr 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 #Iall possible#N 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.,
.LM+15
.OS<<12//#IAO basis:#N>>
AONAO AONHO AONBO AONLMO AOMO
.LM+0
AOPNAO AOPNHO AOPNBO AOPNLMO
.LM10
and from each of the orthonormal natural localized sets to sets
lying to the right in the sequence, i.e.,
.RL8
.LM+15
.OS<<12//#INAO basis:#N>>
NAONHO NAONBO NAONLMO NAOMO
.OS<<12//#INHO basis:#N>>
NHONBO NHONLMO NHOMO
.OS<<12//#INBO basis:#N>>
NBONLMO NBOMO
.OS<<12//#INLMO basis:#N>>
NLMOMO
.LM10
The matrix T#dIN,OUT#u for a specified IN \rarr OUT transform has
rows labelled by the IN set and columns labelled by the OUT set.
\np 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:
.RL7
.LM+20
.OS<<15//#IFock matrix:#N>>
FAO FNAO FNHO FNBO FNLMO
.OS<<15//#Idensity matrix:#N>>
DMAO DMNAO DMNHO DMNBO DMNLMO
.OS<<15//#Idipole matrix:#N>>
DIAO DINAO DINHO DINBO DINLMO
.OS<<15//#Ioverlap matrix:#N>>
SAO SPNAO SPNHO SPNBO SPNLMO
.LM10
Other desired transformations
can be readily obtained from the keyword transformations
by matrix multiplication.
.RL10
#_Keyword Parameters#/
\np 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):
.LM+20
.OS<<15//MATKEY=P[c]>>
(print out the matrix in the standard output file, 'c' columns)
.OS<<15//MATKEY=W[n]>>
(write out the matrix to disk file #In#N)
.LM10
#NThe 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
#T
MATKEY=P16 (print 16 columns)
#NFor 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
#T
MATKEY=PVAL (print core + valence MO columns only)
#Nwhere ``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 pre#|dominant valence character. Similarly,
for the transformations to NBOs or NLMOs, use the form
#T
MATKEY=PLEW (print Lewis orbital columns only)
#Nwhere ``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.
#NThe 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:
.TB
.FM<<5C10//2C6//5C10//2C6//5C10//2C6>>
.RW<<#I //default// //default// //default>>
.RW<>
.FM<<5L18//5L18//5L18>>
.RW<<_//_//_>>
.FM<<5L10//2C6//5L10//2C6//5L10//2C6>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.ET
#NWhen 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
#T
AONBO=W22
#Nwould write out the AO \rarr NBO transformation to LFN = 22 (rather
than the default LFN = 37).
\np 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.
\np For the AONAO, NAONBO matrices (only), one can also include a
read parameter (R),
#T
AONAO=Rn
NAONBO=Rn
#Nwhich causes the matrix to be input to the
program from LFN #In#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 \rarr 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).
.RL55
#IB.2.5 Other Output Control Keywords#N
\np 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:
.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>
.OS<<12//LFNPR=n>>
Set the logical file number (LFN) for NBO program output. The default
LFN is #In#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:#T LFNPR=25 (re-direct NBO output to LFN 25)
#N
.OS<<12//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.
.OS<<12//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 #B24#N,
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.)
.OS<<12//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 ORB#|PLOT orbital contour plotting programs (cf. ``PLOT''
keyword below.)
.RL4
.NH
.OS<<12//PLOT>>
Request writing of #Iall#N files required by orbital contour plotting
programs ORB#|PLOT. This activates the AOINFO keyword, as well
as all the necessary matrix output keywords (AONBO=W37, etc.)
that could be required for ORBPLOT.
.HY
.OS<<12//ARCHIVE=n>>
Request writing the FILE47 `archive' file to external disk
file LFN = #In#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).
.OS<<12//NBODAF=n>>
Request writing the NBO direct access file (DAF) to external
disk file LFN = #In#N (or, if ``=n'' is not present, to the
default LFN =48).
.LM10
.HR<<1//+1//10//80>>
.RL55
#IB.2.6 Print Level Keywords#N
\np The keyword ``PRINT=n'' (#In#N = 0-4) can be used to give
convenient, flexible control of all NBO output in terms of
a specified print level #In#N. This keyword
activates groups of keywords in a heirarchical manner, and
thus incrementally increases the volume of output, ranging
from #Ino#N 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]:
.LM+5
.TB
.FM<<0C8//2L45>>
.RW<<#Iprint level#N//#Iadditional output or activated keywords#N>>
.RW<<_//_>>
.FM<<0C8//2L55>>
.RW<<0//suppress #Iall#N output from the NBO program>>
.RW<<1//activate NPA and NBO keywords>>
.RW<<[2]//activate BEND, NBOSUM, and E2PERT keywords>>
.RW<<3//activate NLMO, DIPOLE, and BNDIDX keywords>>
.RW<<4//activate all(!) keywords>>
.ET
.LM10
For each print level #In#N, the NBO output will include items activated
by the listed keywords, as well as all items from lower
print levels.
\np 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
#T
$NBO PRINT=2 NLMO FNBO=P NAOMO=P11 $END
#Nwould 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
#T
$NBO PRINT=1 SKIPBO $END
#Nor
#T
$NBO PRINT=0 NPA $END
#N[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.']
.RL55
#IB.2.7 Semi-Documented Additional Keywords#N
\np Some additional keywords are listed below that may of use
to specialists or program developers:
.LM+15
.OS<<15//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//25//80>>
.OS<<15//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).
.OS<<15//PRJTHR=val>>
Set the projection threshold [default 0.20] to determine if
a `new' hybrid orbital has too high overlap with hybrids
previously found.
.OS<<15//MULAT>>
Print total gross Mulliken populations by atom.
.OS<<15//MULORB>>
Print gross Mulliken populations, by orbital and atom.
.OS<<15//RPNAO>>
Revises PAO to PNAO transformation matrix by post-multiplying
by #BT#N#dRyd#u and #BT#N#dred#u [see the NPA paper:
A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. #B83#N,
735-746 (1985)].
.OS<<15//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.
.OS<<15//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.
.HR<<1//+1//10//80>>
.LM10
.HF<>
.RL55
#BB.3 THE $CORE LIST#N
\np 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.
\np [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.]
\np The NBO program contains a table giving the nominal number of
core orbitals to be isolated on each type of atom (e.g., 1#Is#N for
first-row atoms Li-Ne, 1#Is#N, 2#Is#N, 2#Ip#N 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.
.RL10
\np The format of the $CORE modification list is:
.LM+15
.OS<<10//first line:>>
The keyword ``$CORE''
.OS<<10//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.
.OS<<10//last line:>>
The keyword ``$END'', to indicate the end of core input.
.LM-15
The entire list may also be condensed to a single line,
but the word ``$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.
\np 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
#In#N = 1 and #In#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 1#Is#N, 2#Is#N, and
all three 2#Ip#N orbitals. The $CORE modification list
is read only once, and applies to both
\alpha and \beta spin manifolds in an open-shell calculation.
.RL6
An example, appropriate for Ni(1)-C(2)-O(3) with the indicated numbering
of atoms, is shown below:
#T
$CORE
1 5
$END
#NThis 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 1#Is#N, 2#Is#N, and 2#Ip#N orbitals will be considered
as core orbitals in the search for NBOs of NiCO, allowing the 3#Is#N
and 3#Ip#N 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 (1#Is#N only) is isolated on each
of these atoms.
.RL8
[The alternative example
#T
$CORE 1 0 2 0 3 0 $END
#N(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).]
.HF<>
.RL55
#BB.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)#N
\np 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.
\np The format of the $CHOOSE list is:
.LM+15
.OS<<10//first line:>>
The keyword ``$CHOOSE''
.OS<<10//next line:>>
The keyword ``ALPHA'' (only for open-shell wavefunction)
.OS<<10//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 #Ivalence#N 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
.LM+10
.OS<<5//``S''>>
single bond
.OS<<5//``D''>>
double bond
.OS<<5//``T''>>
triple bond
.OS<<5//``Q''>>
quadruple bond
.LM-10
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.)
.OS<<10//next line:>>
The word ``END'' to signal the end of the \alpha spin list.
.OS<<10//next line:>>
The keyword ``BETA'' (for open-shell wavefunctions)
.OS<<10//next lines:>>
The input for \beta spin, same format as above. The overall $CHOOSE
list should always end with the ``$END'' keyword.
.RL16
.LM10
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):
.LM+5
.DF\dots =#+.\thsp .\thsp .#-
.OS<<4//(1)>>
The closed-shell H-bonded complex FH\dots CO,
with atom numbering F(1)-H(2)\dots C(3)-O(4), might be specified as
#T
$CHOOSE
LONE 1 3
3 1
4 1 END
BOND S 1 2
T 3 4 END
$END
#NThis 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).
.RL18
.OS<<4//(2)>>
The open-shell FH\dots O#d2#u complex, with
atom numbering F(1)-H(2)#+...#-O(3)-O(4),
and with the unpaired electrons on O#d2#u being of
\alpha spin, might be specified as
#T
$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
.LM10
#NNote 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 \alpha and \beta spin.
\np 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.
.HF<>
.RL55
#BB.5 THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)#N
#IB.5.1 Introduction to NBO Energetic Analysis#N
\np The fourth and final type of keylist is a `deletions' ($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.
\np 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 $DEL keylist. The nine distinct
types of deletions input are described in Section B.5.2 below.
\np The deletions keylist begins with the ``$DEL'' keyword. For
the analysis of UHF wavefunctions, the deletions for
the \alpha and \beta 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.
.RL15
.LM+10
.RM-10
.BX<<3//18//72//+0//+13>>
.CJ
#BWARNING#N
.FJ
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.
.LM10
.RM80
\np 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.
.RL55
#IB.5.2 The Nine Deletion Types#N
\np 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: #TDELETE 3 ORBITALS 15 18 29
#N[See also deletion types (4) and (7) for deleting sets of orbitals.]
.RL15
.LM+10
.RM-10
.BX<<3//18//72//+0//+11>>
.CJ
#BWARNING#N
.FJ
The ``single-pass'' method of evaluating deletion energies is
appropriate only for deletions of #Ilow#N-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 #Ihigh#N-occupancy (Lewis) orbitals by this
procedure.
.LM10
.RM80
#_(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: #TDELETE 3 ELEMENTS 1 15 3 19 23 2
#NThis 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:
.RL6
.LM+5
(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.
.LM-5
.RL8
An example is shown below:
#T
ZERO 2 BLOCKS 2 BY 5
3 4
9 10 11 14 19
3 BY 2
1 2 7
20 24
#NThis will set the following Fock matrix elements to zero:
.LM+5
(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)
.LM-5
[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).
.RL4
#_(5) Deletion of all vicinal delocalizations.#/
To delete all Fock matrix elements between Lewis NBOs and the
vicinal non-Lewis NBOs, simply enter ``NOVIC''.
.RL4
#_(6) Deletion of all geminal delocalizations.#/
To delete all Fock matrix elements between Lewis NBOs and the
geminal non-Lewis NBOs, simply enter ``NOGEM''.
.RL6
#_(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 de#|starred, then the keyword ``UNIT''
(or ``UNITS''), then the list of units.
Example: #TDESTAR 2 UNITS 3 4
#N
.RL13
#_(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: #TZERO 2 DELOC FROM 1 TO 2 FROM 2 TO 1
#NThe above example would zero #Iall#N intermolecular
delocalizations between units 1 and 2 (i.e., both 1 \rarr 2 and
2 \rarr 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.
.RL4
#_(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:
.LM+5
(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.
.LM-5
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
#T
ZERO 2 ATOM BLOCKS
2 BY 3
1 2
3 4 5
3 BY 2
3 4 5
1 2
#NIn this example, the first block removes the (1,2) \rarr (3,4,5)
delocalizations, while the second removes the (3,4,5) \rarr (1,2)
delocalizations.
\np For additional examples of $DEL input, see Section B.6.10.
.RL55
#IB.5.3 Input for UHF Analysis#N
\np Deletions of the alpha and beta Fock matrices can be done
independently. The deletions are input as above (Section B.5.2) for
RHF closed shell, but they must be specified separately for alpha
and beta in the UHF case.
\np The deletion to be done on the alpha Fock matrix must be preceded
by the keyword ``ALPHA'', and the deletion of the beta Fock matrix
must be preceded by the keyword ``BETA''. (Actually, only the first
letter ``A'' or ``B'' is searched for by the program.) The ALPHA
deletion must precede the BETA deletion. The BETA deletion
may be the same as the ALPHA deletion, or different.
\np NOTE: The types of the \alpha NBOs often differ from those of
the \beta NBOs, so that distinct \alpha , \beta deletions
lists are generally required. For example, O#d2#u (triplet) has one bond in
the \alpha system and three in the \beta system, if the unpaired
electrons are in the \alpha system.
\np Here are three examples to illustrate UHF open-shell deletions:
.RL4
Example 1:
#T
ALPHA ZERO 1 DELOC FROM 1 TO 2
BETA NOSTAR
.RL4
#NExample 2:
#T
ALPHA ZERO 1 DELOC FROM 1 TO 2
BETA ZERO 0 DELOC
.RL4
#NExample 3:
#T
ALPHA DELETE 0 ORBITALS
BETA DELETE 1 ORBITAL 8
#NIf no deletion is done, this must be specified using zero (0) with
one of the deletion input formats, as shown in Examples 2,3 above.
.CM-----------------------------------------------------------------
.HF<>
.RL55
#BB.6 NBO KEYLIST ILLUSTRATIONS#N
#IB.6.1 Introduction#N
\np This section illustrates the output produced by several
important keyword options of the NBO
keylists ($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.
\np 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 \alpha and
\beta spin manifolds. Section B.6.12 shows the effect of using
effective core potentials for Cu#d2#u, also illustrating
aspects of the inclusion of #Id#N functions.
.CM-----------------------------------------------------------------
.HF<>
.RL55
#IB.6.2 NLMO Keyword#N
\np 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:
.DF\@seg =
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%)
.ED
.HR<<3//+1//5//85>>
.LM5
.RM85
#T
.LJ
\@seg
.FJ
.HR<<3//+1//5//85>>
.LM10
.RM80
#NFor 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
#Isp#N#u\lambda #d character and percentage #Is-#N and
#Ip#N-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].
.CM-----------------------------------------------------------------
.HF<>
.RL55
.BM62
#IB.6.3 DIPOLE Keyword#N
\np 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):
.DF\@seg =
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
.ED
.HR<<3//+1//5//85>>
#T
.LM5
.RM85
.LJ
\@seg
.FJ
.LM10
.RM80
.HR<<3//+1//5//85>>
.RL5
#NThe bottom line of the table shows the individual (x,y,z) vector components
(\minus 0.45,\minus 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 \vect \mu #dAB #u is evaluated as
.DF\mab =\vect \mu #dAB#u
.DF\mabe =\mab #<#<#<#u#u(elec)#d#d
.DF\mabn =\mab #<#<#<#u#u(nuc)#d#d
.DF\sab =\sigma #dAB#u
.DF\si =\sigma #di#u
.DF\sj =\sigma #dj#u
.DF\dk =\sigma #dk#u
.DF\sinlmo =\si #<#u#u(NLMO)#d#d
.DF\cii =#Ic#N#dii#u
.DF\cji =#Ic#N#dji#u
.DF\cki =#Ic#N#dki#u
.CJ
\mab = \mabe + \mabn
.FJ
.DF\sbar =\thsp |\thsp
where
\mabe = 2#Ie#N\bra \sab \sbar \vect r#N\sbar \sab \ket
is the electronic dipole expectation value for an electron
pair in the \sab NLMO
or NBO, and \mabn 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 #Ii#N onto
other (primarily, non-Lewis) NBOs #Ij#N; in terms of the expansion
of an NLMO in the set {\sj } of NBOs,
.CJ
\sinlmo = \cii \si + \sum <<#Rj#N>>\cji \sj
.FJ
this correction is (for each electron, \alpha or \beta spin)
.LM+10
.DF\&m =\bra \sigma #d&1#u\sbar \vect \mu \sbar \sigma #d&2#u\ket
.DF\mideloc =\vect \mu #di#u#<#u#u(deloc)#d#d
.DF\&s =\sum <<#R&1#N>>#+\dprime #-
.DF\term =2\cii \&m <> + \&sall <> \cki \&m <>
.DF\term2 =\&sall <>\cji \[2 \term \]2
\cji #u2#d[\&m <>\minus \&m <>] + 2\cii \cji \&m <>
+ \&s <>\cji \cki \&m <>
.LM-10
where the primes on the summation denote omission of
terms #Ik#N equal to #Ii#N or #Ij#N. For example, in the above table the
largest individual contribution to \vect \mu 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
#In#N#dN#u \rarr \sigma *#<#dCH#u delocalization into the
vicinal C(1)-H(3) antibond, NBO 24.
\np 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).
\np 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].
.BM60
.CM-----------------------------------------------------------------
.HF<>
.RL55
#IB.6.4 Matrix Output Keywords#N
\np 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:
.DF\@seg =
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
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#N
\np 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.
\np As a second example, the keyword ``NBOMO=PVAL'' would print out
the core + valence columns of the NBO \rarr MO transformation,
as reproduced below:
.DF\@seg =
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
.ED
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#N
\np 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
.CJ
.DF\sch14 =\sigma #dC#d1#uH#d4#u#u
.DF\sch15 =\sigma #dC#d1#uH#d5#u#u
.DF\snh16 =\sigma #dN#d2#uH#d6#u#u
.DF\snh17 =\sigma #dN#d2#uH#d7#u#u
.DF\tc =(\sch14 \minus \sch15 )
.DF\tn =(\snh16 \minus \snh17 )
\phi #d5#u \~= \minus 0.594\tn + 0.381\tc
\phi #d8#u \~= 0.381\tn + 0.594\tc
.FJ
whereas \phi #d6#u is primarily the C-H(3) NBO and \phi #d9#u
the N lone pair NBO.
.CM-----------------------------------------------------------------
.HF<>
.RL55
#IB.6.5 BNDIDX Keyword#N
\np 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).
\np 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:
.DF\@seg =
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
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#N
\np This index is intrinsically a positive quantity, making no
distinction between net bonding
or antibonding character of the density matrix elements.
.RL15
\np The next segment tabulates the ``overlap-weighted
NAO bond order,'' as shown below:
.DF\@seg =
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
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#N
\np This index corresponds to a sum of off-diagonal
NAO density matrix elements between atoms,
each multiplied by the corresponding PNAO overlap integral.
\np 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:
.DF\@seg =
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
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#NThis NLMO bond order is calculated by the method described by
A. E. Reed and P. v.R. Schleyer [#IInorg. Chem. #B27#N, 3969-3987 (1988);
#IJ. Am. Chem. Soc.#N (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).
\np The NLMO bond order contributions are then summed for each
atom pair to give the net NLMO/NPA bond orders shown below:
.DF\@seg =
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
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#NFor 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.)
\np These bond indices are based on different
assumptions, and each has certain advantages and
disadvantages. #ICaveat emptor!#N
.CM-----------------------------------------------------------------
.HF<>
.RL55
#IB.6.6 RESONANCE Keyword: Benzene#N
\np 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:
.DF\@seg =
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.
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\np #NWhen the RESONANCE keyword is activated for this same example,
one obtains a summary of NBO search cycles as shown below:
.DF\@seg =
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
.ED
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\np 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
thresh#|old 1.60e. The NBO program therefore reset the
thresh#|old to this value and calculated
the set of NBOs corresponding to this
`best' Lewis structure, as shown below:
.DF\@seg =
(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
.ED
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#N
\np As one can see from this table, the set of NBOs
obtained by the program corresponds
to one of the two equivalent Kekul\acute e structures, with
reasonably well
localized \sigma #dCC#u and \sigma #dCH#u NBOs (1.98940 and 1.98977
electrons, respectively), but three severely depleted \pi #dCC#u
bonds (1.66667e) and corresponding high occupancy
\pi *#<#dCC#u 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.
.LM+10
.RM-10
.BX<<3//18//72//+1//+11>>
.CJ
#-#BWARNING#N#+
.FJ
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 \alpha
and \beta spin, the job will likely abort, as in the default
benzene example. However, you should #Inot#N use the RESONANCE
keyword to bypass this abort! NBO analysis of an open-shell
spinless density matrix is a fundamental misuse
of the program.
.LM10
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.HF<>
.RL55
#IB.6.7 NOBOND Keyword#N
\np 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#u+#d\thsp F#u\minus #d interactions.
\np The default NBO analysis of this example is shown below:
.DF\@seg =
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%)
.ED
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#N
As the output shows, default NBO analysis
leads to a polar covalent description of HF. The
\sigma #dHF#u bond, NBO 1, is formed from a #Ip#N-rich
(#Isp#N#u5.13#d) hybrid on F and the 1#Is#N AO on H,
strongly polarized (about 75.22%) toward F. This provides a
satisfactory Lewis structure, describing 99.994% of
the total electron density.
\np When the NOBOND keyword is activated to bypass
the search for 2-center bonds, the NBO output is
modified as shown below:
.DF\@seg =
/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
.ED
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#N
\np In this case, the NBO output indicates a rather poor Lewis
structure (4.962% non-Lewis density), with a severely
depleted F#u\minus #d lone pair (NBO 5, the #Isp#N#u5.13#d hybrid)
and significant occupancy (about 0.496e) in the `empty' H#u+#d
1#Is#N orbital (NBO 6) of the cation. The NOBOND comparison
would therefore indicate the superiority of a polar
covalent description in this case.
.CM-----------------------------------------------------------------
.HF<>
.RL55
#IB.6.8 3CBOND Keyword: Diborane#N
\np 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
B#d2#uH#d6#u 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 BH#d2#u#u+#d and two H#u\minus #d
fragments), with about 2.13 electrons unaccounted for (~15%
non-Lewis occupancy), symptomatic of general breakdown of the
conventional Lewis structure representation.
\np However, when the NBO search is extended to 3-center bonds
by activating the 3CBOND keyword, one obtains
the NBO output shown below:
.DF\@seg =
/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
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\np 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 #Ip#N-rich
(#Isp#N#u4.55#d) boron hybrids and the hydrogen 1#Is#N NAO,
with about 47.14% of the orbital density on the central hydrogen. Note
that each 3-center bond NBO is associated with #Itwo#N 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 #Iany#N 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 #Iqualitative#N improvement
that indicates when 3-center bonds are needed
in the zeroth-order picture of the bonding.
\np 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.'
.CM-----------------------------------------------------------------
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#IB.6.9 NBO Directed Search ($CHOOSE Keylist)#N
\np To illustrate the $CHOOSE keylist for a directed NBO search, we
again make use of the methylamine example (Section A.3). The vicinal
#In#N#dN#u \rarr \sigma *#<#dCH#u 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:
.DF\:nobond =<<0B3'C#d1#u'//0B7R'\umlaut H#d3#u#+\minus #-'//
W10R'#-\nthsp H#d4#u#+\thsp '//
D11R'H#d5#u'//BD3'N#d2#u#<#+#++#-#-'//W5R'H#d6#u'//D4R'H#d7#u'>>
.CJ
\:nobond
.FJ
To investigate the suitability of this resonance structure
for describing the methylamine wavefunction, we would
specify the $CHOOSE keylist (Section B.4) as follows:
#T
$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
#NWhen this is included in the input file, the NBO program produces
the output shown below:
.DF\@seg =
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
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#N
\np 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 $CHOOSE structure (compared to 0.05e, or 0.3%, for
the principal structure). Particularly defective is the hydride
`lone pair' (NBO 9), which has less than half the
expected occupancy (0.81453e). The C-N \pi bond (NBO 1) is seen
to be more than 92% polarized toward N, indicative of essential
lone pair character.
\np Note that structural elements shared by the two resonance
structures (e.g., the two N-H bonds, which are common to
both structures) need not have identical
forms, since each detail of the NBOs
is optimized with respect to the overall structure.
.CM-----------------------------------------------------------------
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#IB.6.10 NBO Energetic Analysis ($DEL Keylist)#N
\np The NBO energetic analysis with deletions ($DEL keylist) will be
illustrated with two simple examples for RHF/3-21G methylamine
(Section A.3).
\np 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
#T
$DEL NOSTAR $END
#NThis leads to the output shown below:
.DF\@seg =
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
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#N
\np 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 (\minus 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.
\np The next example is a more selective set of deletions between
`chemical fragments' (type 9), selected by the $DEL keylist input
shown below:
#T
$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
#NThis 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:
.DF\@seg =
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
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.RM80
#N
\np 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
(\minus 0.015) of the antiperiplanar \sigma *#<#dC#d1#uH#d3#u#u
antibond, NBO 24, with somewhat lesser depletion (\minus 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.
\np 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
#In#N#dN#u \rarr \sigma *#<#dC#d1#uH#d3#u#u 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
#In#N#dN#u \rarr \sigma *#<#dC#d1#uH#d3#u#u (9\rarr 24) interaction
that was noted in Section A.3.5.]
.CM------------------------------------------------------------------
.HF<>
.RL55
#IB.6.11 Open-Shell UHF Output: Methyl Radical#N
\np Open-shell NBO output will be illustrated with the simple
example of the planar methyl radical (CH#d3#u), treated at the UHF/6-31G*
level (#IR#N#dCH#u = 1.0736\thsp \angstrom ). In
the open-shell case, one obtains
two separate NPA and NBO listings, one for the \alpha and one for
the \beta spin set, corresponding to the ``different Lewis structures
for different spins'' description. A portion of the NBO output for
the \alpha spin manifold is reproduced below:
.DF\@seg =
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
.ED
.HR<<3//+1//5//85>>
.LM5
.RM85
#T
.LJ
\@seg
.FJ
.HR<<3//+1//5//85>>
.LM10
.RM80
#N
\np 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 \alpha Lewis spin-NBOs (1-5) are about 1.0000, but
other aspects of the output are familiar. Note the slight admixture
of #Id#N-character (0.16%) in the \sigma #dCH#u bond hybrids
(NBOs 1-3), whereas the out-of-plane radical non-bonded orbital (NBO 5) has
pure #Ip#N-character.
\np The NBO output for the \beta (`ionized') spin set then follows:
.DF\@seg =
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%)
.ED
.HR<<3//+1//5//85>>
.LM5
.RM85
#T
.LJ
\@seg
.FJ
.HR<<3//+1//5//85>>
.LM10
.RM80
#N
\np 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 \sigma #dCH#u bonds is somewhat altered
(about 55.8% on the C atom in the \beta set set,
#Ivs.#N 61.1% in the \alpha set). [In other cases, the
\alpha and \beta 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.
.LM+10
.RM-10
.BX<<3//18//72//+1//+11>>
.CJ
#-#BWARNING#N#+
.FJ
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 \alpha
and \beta 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.
.LM10
.RM80
.CM------------------------------------------------------------------
.HF<>
.RL55
#IB.6.12 Effective Core Potential: Cu#d2#u Dimer#N
\np To illustrate some of the variations of NBO output associated
with use of effective core potentials (ECP) and inclusion of
#Id#N orbitals, we use the example of the copper dimer Cu#d2#u
(#IR#N = 2.2195\thsp \angstrom ),
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 Cu#d2#u.) Since the
NBO program communicates directly with
the ESS program for details
about the ECP, no special keywords are necessary.
\np Use of an ECP shows up most directly in the NPA portion
of the output, shown below:
.DF\@seg =
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)
.ED
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#T
.LM5
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.RS#~
.LJ
\@seg
.FJ
.RS~#
.LM10
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.HR<<3//+1//5//85>>
#N
\np 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 4#Is#N, 5#Is#N, 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 3#Id#N#dxy#u orbital (NAO 9)
is unoccupied in this excited configuration, although
its energy lies below the occupied 4#Is#N, 4#Ip#N#dy#u, 4#Ip#N#dz#u
levels.]
.RL20
\np The main ECP effect in the NBO portion of the output is the
omission of core NBOs, as illustrated below:
.DF\@seg =
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
.ED
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#N
\np 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.
\np The output for the Cu#d2#u
example also illustrates some aspects of the inclusion of #Id#N orbitals
in the basis set. NBOs 4-7 and 8-11 represent the 3#Id#N#u8#d
subshells on each atom, essentially of pure atomic #Id#N
character (except for a small admixture
of #Ip#N character in NBOs 7, 11). Both
the \sigma #dCuCu#u bond (NBO 1) and the two \pi #dCuCu#u bonds
(NBOs 2, 3) have very slight admixtures (< 0.4%) of #Id#N
character. The remaining orbitals of predominant #Id#N
character (NBOs 17-22 and 28-33) are of negligible occupancy. Note
that the abbreviated ``#Isp#u\lambda #dd#u\mu #d#N'' designations
can lead to strange variations among hybrids
of essentially similar character; thus, NBO 20 (#Ip#u1.0#dd#u99.9#d#N),
NBO 21 (#Id#N#u1.0#d), and NBO 22 (#Is#u3.1#dp#u0.4#dd#u31.4#d#N)
are all of nearly pure (> 95%) #Id#N character, the difference in
labelling stemming from
whether there is sufficient
#Is#N or #Ip#N character (in numerical terms) to express the
hybrid ratios in #Isp#u\lambda #dd#u\mu #d#N form. Consult
the percentages of #Is#N-.
#Ip#N-, and #Id#N-character whenever there is doubt about how to
interpret a particular #Isp#u\lambda #dd#u\mu #d#N designation.
.CM------------------------------------------------------------------
.DF\ss =#Is#N
.DF\px =#Ip#N#dx#u
.DF\py =#Ip#N#dy#u
.DF\pz =#Ip#N#dz#u
.HF<>
.RL55
#BB.7 FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM#N
#IB.7.1 Introduction#N
\np 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.
\np 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.]
\np 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.
\np 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.
.RL55
#IB.7.2 Format of the FILE47 Input File#N
\np 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'',
#T $BASIS entries $END#N
Individual lists are used to specify basis set information ($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.
\np 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 methyl#|amine example of Section A.3) is shown below:
.DF\@seg =
$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
.ED
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#N
The nine lists of FILE47 are described in turn in
the following sections, making use of this
example for illustration.
.RL55
#IB.7.3 $GENNBO Keylist#N
\np 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:
.LM+12
.OS<<12//#IKEYWORD#N>>
#IOPTION DESCRIPTION#N
.HR<<1//+1//10//20>>
.HR<<1//+1//22//80>>
.OS<<12//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 data#|lists. Therefore, if the REUSE keyword
is specified, all data#|lists 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.
.OS<<12//NATOMS>>
Number of atoms in the molecule (required).
.OS<<12//NBAS>>
Number of basis functions (required).
.OS<<12//OPEN>>
Designates an open shell wavefunction. GENNBO will subsequently
read in alpha and beta density, Fock, and MO coefficient matrices.
.OS<<12//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).
.OS<<12//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.
.OS<<12//BODM>>
Indicates that the $DENSITY datalist contains the
bond-order matrix (``Fock-Dirac density matrix'') rather
than the density matrix (i.e., matrix elements of the
density operator). (In orthogonal AO basis sets, the bond-order matrix
and density matrix are identical, but in nonorthogonal basis sets they
must be distinguished.) By default, GENNBO assumes this data#|list contains
the density matrix elements. If ``BODM'' is included, the datalist
elements are transformed with the AO overlap matrix to produce the
true density matrix.
.OS<<12//BOHR>>
Indicates that the atomic coordinates ($COORD) and the dipole
integrals ($DIPOLE) are in atomic units, rather than the default
angstroms.
.OS<<12//EV>>
Indicates that the Fock matrix elements ($FOCK) have units of
electron volts (eV), rather than the default atomic units (Hartrees).
.OS<<12//CUBICF>>
Instructs GENNBO to use the set of seven cubic #If#N-type functions
rather than the ten Cartesian or seven pure #If#N functions
(cf. Section B.7.5).
.HR<<1//+1//10//80>>
.LM10
The methylamine sample $GENNBO keylist
specifies 7 atoms, 28 basis
functions, upper triangular matrix input, and $DENSITY datalist containing
the bond-order matrix.
.RL55
#IB.7.4 $COORD Datalist#N
\np 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.
\np The first line following the $COORD identifier is an arbitrary
job title, up to 80 characters.
\np 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 = \minus 0.74464,
y = \minus 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 1#Is#N core electron of a carbon atom are neglected, the line
following the job title in the methylamine example would read
#T 6 4 -0.74464 -0.03926 0.00000 ! Carbon#N
where ``4'' is the effective (valence) nuclear charge of the atom.
.RL55
#IB.7.5 $BASIS Datalist#N
\np 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 (\ss , \px ,
\py , \pz ,
etc.) of each AO. This information is contained
in two arrays in this datalist called CENTER and LABEL.
\np 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
#T 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#N
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.]
\np 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 #Is#N, #Ip#N, #Id#N,
or #If#N (\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 + #Ik#N + #Im#N, where #Ik#N is 0 (cartesian) or 50 (pure),
and #Im#N is a particular component of the \l -type symmetry (see
table below). For
#Is#N or #Ip#N AOs,
the cartesian and pure \l -symmetry sets are identical, so each AO can be
labelled in two distinct ways, but
the six cartesian #Id#N functions can be transformed to the five pure #Id#N
functions plus an additional #Is#N function, and the ten cartesian #If#N
functions can be transformed to the seven
pure #If#N functions plus three additional #Ip#N
functions. Two distinct sets of pure #If#N
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.
\np The labels associated
with each allowed AO function type are tabulated below,
where #Ix, y, z#N refer to the
specified cartesian axis system:
.RL32
.VS160
.TB
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW-
.RW<<#Ilabel#N//#IAO type#N//#Ilabel#N//#IAO type#N//#Ilabel#N//#IAO type#N>>
.RW=
.FM<<0L23//0L23//0L23>>
.RW<<#_Pure #Is, p#N sets:#/ //#_Cartesian #If#N set:#/ //
#_Pure #If#N ``cubic'' set:#/>>
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW<<1 (51)//#Is#N//301//#If#N#dxxx#u//
351//#If#N(D1): x(5x#u2#d\minus 3r#u2#d)>>
.RW<<101 (151)//#Ip#N#dx#u//302//#If#N#dxxy#u//
352//#If#N(D2): y(5y#u2#d\minus 3r#u2#d)>>
.RW<<102 (152)//#Ip#N#dy#u//303//#If#N#dxxz#u//
353//#If#N(D3): z(5z#u2#d\minus 3r#u2#d)>>
.RW<<103 (153)//#Ip#dz#u#N//304//#If#N#dxyy#u//
354//#If#N(B): xyz>>
.RW<< // //305//#If#N#dxyz#u//
355//#If#N(E1): x(z#u2#d\minus y#u2#d)>>
.FM<<0L23//1C6//2L14//1C6//2L14>>
.RW<<#_Cartesian #Id#N set:#/ //306//#If#N#dxzz#u//
356//#If#N(E2): y(z#u2#d\minus x#u2#d)>>
.FM<<1C6//2L14//1C6//2L14//1C6//2L14>>
.RW<<201//#Id#N#dxx#u//307//#If#N#dyyy#u//
357//#If#N(E3): z(x#u2#d\minus y#u2#d)>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<<202//#Id#N#dxy#u//308//#If#N#dyyz#u>>
.RW<<203//#Id#N#dxz#u//309//#If#N#dyzz#u>>
.RW<<204//#Id#N#dyy#u//310//#If#N#dzzz#u>>
.RW<<205//#Id#N#dyz#u// // >>
.FM<<1C6//2L14//0L23>>
.RW<<206//#Id#N#dzz#u//#_Pure #If#N ``standard'' set:#/>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<< // //351//#If#N(0): z(5z#u2#d\minus 3r#u2#d)>>
.FM<<0L23//1C6//2L14>>
.RW<<#_Pure #Id#N set:#/ //352//#If#N(c1): x(5z#u2#d\minus r#u2#d)>>
.FM<<1C6//2L14//1C6//2L14>>
.RW<<251//#Id#N#dxy#u//353//#If#N(s1): y(5z#u2#d\minus r#u2#d)>>
.RW<<252//#Id#N#dxz#u//354//#If#N(c2): z(x#u2#d\minus y#u2#d)>>
.RW<<253//#Id#N#dyz#u//355//#If#N(s2): xyz>>
.RW<<254//#Id#R#dx#u2#d\minus y#u2#N//
356//#If#N(c3): x(x#u2#d\minus 3y#u2#d)>>
.RW<<255//#Id#R#dz#u2#N = #Id#R#d3z#u2#d\minus r#u2#N//
357//#If#N(s3): y(3x#u2#d\minus y#u2#d)>>
.FM<<0L69>>
.RW-
.ET
.VS120
[For example, in the methylamine sample input,
the first nine entries of the LABEL array,
#T LABEL = 1,1,101,102,103,1,101,102,103,. . .#N
identify the first 9 AOs (of carbon) as being of \ss , \ss , \px , \py , \pz ,
\ss , \px , \py , \pz type, respectively.]
.RL55
#IB.7.6 $CONTRACT Datalist#N
\np 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.
\np 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.
\np 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
#T NCOMP = 1,4,4,. . .#N
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.]
\np 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
#T NPRIM = 3,2,1,. . .#N
three, two, and one primitives, respectively, corresponding to
the conventional ``3-21G'' basis set designation.]
\np 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,
#T NPTR = 1,4,6,. . .#N
the orbital exponents and contraction coefficients for the first three
shells begin at elements 1, 4, and 6, respectively.]
\np 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 #Is#N and #Ip#N basis functions. Therefore, the
CD and CF arrays are not necessary.]
\np The information in the $CONTRACT datalist along with that in the $BASIS
datalist is enough to completely determine the AO basis set. [For example,
the second shell on the methylamine sample contains 4 basis functions
(NCOMP). These are #Is#N, #Ip#N#dx#u, #Ip#N#dy#u, and #Ip#N#dz#u
orbitals (LABEL), all centered on atom 1 (CENTER), and each basis function
is a contraction of two primitive gaussians (NPRIM). From NPTR, EXP, CS,
and CP, we find the explicit form of these functions:
.CJ
.DF\s1 =\minus 0.747\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\s2 =0.713\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p1 =1.709\thsp x\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p2 =0.886\thsp x\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p3 =1.709\thsp y\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p4 =0.886\thsp y\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
.DF\p5 =1.709\thsp z\thsp e#u#u\minus 3.66\thsp r#u2#d#d#d
.DF\p6 =0.886\thsp z\thsp e#u#u\minus 0.77\thsp r#u2#d#d#d
\phi #ds#u(#Br#N) \thsp = \s1 \thsp + \s2
\phi #dp#dx#u#u(#Br#N) = \p1 + \p2
\phi #dp#dy#u#u(#Br#N) = \p3 + \p4
\phi #dp#dz#u#u(#Br#N) = \p5 + \p6
.FJ
where #Br#N=(x,y,z) is measured in bohr units relative to the cartesian
coordinates of atom 1.]
.RL55
#IB.7.7 Matrix Datalists#N
\np The remaining datalists ($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 #Ix#N integrals before #Iy#N before #Iz#N.
\np Of the matrix datalists, the $DENSITY datalist is
always required, and
the $OVERLAP data#|list is required for all non-orthogonal
AO basis sets, but other data#|lists 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 $NBO keywords that require
each datalist to be included in FILE47:
.LM+5
.LM+12
.OS<<12//#IDatalist#N>>
#I$NBO Keywords Requiring the Datalist#N
.HR<<1//+1//15//25>>
.HR<<1//+1//27//75>>
.OS<<12//$OVERLAP>>
SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO,
.LM+0
AOPNHO, AOPNBO, AOPNLMO
.OS<<12//$FOCK>>
E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO
.OS<<12//$LCAOMO>>
AOMO, NAOMO, NHOMO, NBOMO, NLMOMO
.OS<<12//$DIPOLE>>
DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE
.OS<<12//$CONTRACT>>
AOINFO, PLOT
.HR<<1//+1//15//75>>
.LM10
\np For example, in the methylamine sample input, the keyword ``NAOMO=PVAL''
of the $NBO keylist requires that the $LCAOMO data#|list be present (in
addition to the $OVERLAP, $DENSITY, and $FOCK data#|lists used for default
PRINT=2 analysis), but the $DIPOLE data#|list might have been omitted in
this case. Inclusion of the $LCAOMO data#|list (in addition to the $FOCK
datalist) insures that degenerate MOs will be chosen in a prescribed way
for decomposition in terms of other functions.
.CM-------------------------END OF NBOB.MAN------------------------------
.CM-----------------------------NBOC.MAN---------------------------
.TP2
.DF\np =\thsp \nthsp
.HF<>
.NF<>
.PN1
.CM----------------------------------------------------------------
.CJ
#HSection C: NBO PROGRAMMER'S GUIDE#N
.FJ
#BC.1 INTRODUCTION#N
\np 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.
\np 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.
\np 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''.
\np 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.
.CM------------------------------------------------------------------
.HF<>
.RL55
#BC.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS#N
\np 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:
.LM+5
.TB
.FM<<0R5//3L27//0C6//0C6>>
.RW-
.RW<>
.RW=
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.LM10
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.
\np 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.
\np 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.
.RL55
.CM------------------------------------------------------------------
.LM10
.RM80
.CJ
#HNBO Flow Chart for Group I, II Subprograms#N
.LJ
.LM15
.DF\!hs =4
.DF\!w =3
.DF\!wl =1
.BX<<3//10//80//+2//+42>>
#T
.BX<<\!w //\!hs +38//\!hs +47//+1//+3>>
.CM-------runnbo to nbo-------------------
.VR<<\!wl //\!hs +41//+3//+5>>
.HR<<\!wl //+5//\!hs +20//\!hs +41>>
.VR<<\!wl //\!hs +20//+5//+6>>
.CM-------runnbo to nboean----------------
.VR<<\!wl //\!hs +44//+3//+5>>
.HR<<\!wl //+5//\!hs +44//\!hs +65>>
.VR<<\!wl //\!hs +65//+5//+6>>
RUNNBO
I II
.BX<<\!w //\!hs +17//\!hs +23//+1//+3>>
.BX<<\!w //\!hs +61//\!hs +70//+1//+3>>
.VR<<\!wl //\!hs +65//+3//+6>>
.CM------nbo to startup-----------------
.VR<<\!wl //\!hs +19//+3//+5>>
.HR<<\!wl //+5//\!hs +15//\!hs +19>>
.VR<<\!wl //\!hs +15//+5//+6>>
.CM------nbo to naodrv------------------
.VR<<\!wl //\!hs +20//+3//+5>>
.HR<<\!wl //+5//\!hs +20//\!hs +30>>
.VR<<\!wl //\!hs +30//+5//+6>>
.CM------nbo to nbodrv------------------
.VR<<\!wl //\!hs +21//+3//+4>>
.HR<<\!wl //+4//\!hs +21//\!hs +47>>
.VR<<\!wl //\!hs +47//+4//+6>>
NBO NBOEAN
.BX<<\!w //\!hs +11//\!hs +20//+1//+6>>
.BX<<\!w //\!hs +22//\!hs +38//+1//+4>>
.BX<<\!w //\!hs +43//\!hs +51//+1//+3>>
.BX<<\!w //\!hs +57//\!hs +73//+1//+5>>
.CM------naodrv to prepare---------------
.VR<<\!wl //\!hs +28//+4//+7>>
.HR<<\!wl //+7//\!hs +15//\!hs +28>>
.VR<<\!wl //\!hs +15//+7//+9>>
.CM------naodrv to nao-------------------
.VR<<\!wl //\!hs +30//+4//+8>>
.HR<<\!wl //+8//\!hs +27//\!hs +30>>
.VR<<\!wl //\!hs +27//+8//+9>>
.CM------naodrv to naoanl----------------
.VR<<\!wl //\!hs +32//+4//+8>>
.HR<<\!wl //+8//\!hs +32//\!hs +36>>
.VR<<\!wl //\!hs +36//+8//+9>>
.CM------nbodrv to nathyb----------------
.VR<<\!wl //\!hs +47//+3//+9>>
.CM------nbodrv to nlmo------------------
.VR<<\!wl //\!hs +48//+3//+8>>
.HR<<\!wl //+8//\!hs +48//\!hs +59>>
.VR<<\!wl //\!hs +59//+8//+9>>
.CM------nbodrv to dipanl----------------
.VR<<\!wl //\!hs +49//+3//+7>>
.HR<<\!wl //+7//\!hs +49//\!hs +69>>
.VR<<\!wl //\!hs +69//+7//+9>>
(init.) NAODRV NBODRV NBODEL,DELETE,
NBOSET (& simulation) NEWDM,RNKEIG,
JOBOPT SIMTRN
NBODIM
.BX<<\!w //\!hs +10//\!hs +21//+1//+6>>
.BX<<\!w //\!hs +24//\!hs +30//+1//+3>>
.BX<<\!w //\!hs +32//\!hs +40//+1//+3>>
.BX<<\!w //\!hs +42//\!hs +52//+1//+5>>
.BX<<\!w //\!hs +55//\!hs +62//+1//+3>>
.BX<<\!w //\!hs +65//\!hs +73//+1//+3>>
.CM---nao to nao formation----------------
.VR<<\!wl //\!hs +27//+3//+7>>
.HR<<\!wl //+7//\!hs +18//\!hs +27>>
.VR<<\!wl //\!hs +18//+7//+8>>
.CM---nathyb to nbo formation-------------
.VR<<\!wl //\!hs +47//+5//+7>>
.HR<<\!wl //+7//\!hs +42//\!hs +47>>
.VR<<\!wl //\!hs +42//+7//+8>>
.CM----nlmo to lmoanl---------------------
.VR<<\!wl //\!hs +59//+3//+8>>
.CM----dipanl to dipele-------------------
.VR<<\!wl //\!hs +69//+3//+8>>
(prepare) NAO NAOANL NATHYB NLMO DIPANL
SIMTRM (CHSDRV,
MULANA CHOOSE)
DFGORB
.BX<<\!w //\!hs +10//\!hs +27//+1//+9>>
.BX<<\!w //\!hs +29//\!hs +53//+1//+12>>
.BX<<\!w //\!hs +55//\!hs +63//+1//+5>>
.BX<<\!w //\!hs +65//\!hs +73//+1//+4>>
(NAO formation) (NBO formation) LMOANL DIPELE
LOADAV,ATDIAG, SRTNBO,XCITED,ANLYZE, SYMUNI DIPNUC
SETBAS,NEWWTS, HTYPE,FRMHYB,HYBDIR, SYMORT
WORTH,SCHMDT, HYBCMP,FNDMOL,NBOCLA,
NEWRYD,RYDIAG, FNBOAN,NBOSUM,GETDEL,
RYDSEL,REDIAG, BLDSTR,CORE,IWPRJ,
REDBLK DEPLET,LOAD,PRJEXP,
STASH,ORTHYB,FRMPRJ,
ANGMNT,REPOL,FORMT,
CYCLES
.LM10
.RM80
.FJ
.CM----------------------------------------------------------------------
.HF<>
.RL55
#BC.3 LABELLED COMMON BLOCKS#N
\np 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
#T
PARAMETER(MAXATM = 99,MAXBAS = 500)
#Nwhere 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 #Idecreasing#N 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:
.LM+3
.OS<<3//#_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:
.RL12
.TB
.FM<<0L1//0L12//2L50>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L12//2L50>>
.RW<< //ISPIN//+2 for \alpha spin, \minus 2 for \beta spin>>
.RW<<*//NATOMS//number of atoms (\le MAXATM)>>
.RW<<*//NDIM//declared dimensionality of matrices (overlap, density, etc.)>>
.RW<<*//NBAS//number of basis AOs (\le NDIM \le MAXBAS)>>
.RW<< //MXBO//maximum number of AOs per 2-c or 3-c NBO>>
.RW<< //MXAO//maximum AOs per atom>>
.RW<< //MXAOLM//maximum AOs of the same symmetry per atom>>
.RW<<*//MUNIT//0 for Hartree energy units, 1 for eV units, 2 for kcal/mol.>>
.RW-
.ET
.RL20
.OS<<3//#_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:
.TB
.FM<<0L1//0C14//2L50>>
.RW-
.RW<< //variable (FLAG)//condition that FLAG=.TRUE.>>
.RW=
.FM<<0L1//0L12//2L50>>
.RW<<*//ROHF//Restricted open-shell Hartree-Fock wavefunction>>
.RW<<*//UHF//Unrestricted Hartree-Fock wavefunction>>
.RW<<*//CI//Configuration Interaction wavefunction>>
.RW<<*//OPEN//open-shell calculation>>
.RW<<*//COMPLX//complex-valued wavefunction (not currently implemented)>>
.RW<< //ALPHA//\alpha spin set>>
.RW<< //BETA//\beta spin set>>
.RW<<*//MCSCF//Multi-Configuration Self-Consistent-Field wavefunction>>
.RW<<*//AUHF//Spin-Annihilated UHF wavefunction>>
.RW<<*//ORTHO//basis set is orthonormal>>
.RW-
.ET
Note (Section B.6.11) that both \alpha and \beta spin density matrices
should be available if OPEN is set `.TRUE.' for the open-shell case.
.RL30
.OS<<3//#_3. COMMON/NBOPT/#/>>
The INTEGER variables (flags) of this block are used for storing the keyword
options selected by the user in the $NBO keylist. In many cases, a variable
of the form IWOPT (``IW'' stands for ``I Want'') is set to one or zero
(or to some Hollerith content; see below) depending on whether
the ``requested option'' has been specified or not. The table also
lists the keyword (if any) that requests the option:
.LJ
.RL22
.TB
.FM<<0L1//0L10//2L10//2L42>>
.RW-
.RW<< //variable//keyword//requested option>>
.RW=
.FM<<0L1//0L10//2L10//2L40>>
.RW<<*//IWDM//BODM//1 to transform input bond-order matrix, 0 otherwise>>
.RW<< //IW3C//3CBOND//3-center bonds>>
.RW<< //IWAPOL// //`apolar' bonds, #Ic#N#dA#u = #Ic#N#dB#u (not used)>>
.RW<< //IWHYBS//$NBO//set equal to JPRINT(5)>>
.RW<< //IWPNAO//(PAOPNAO)//PAO\rarr PNAO transformation>>
.RW<< //IWTNAO//AONAO//AO\rarr NAO transformation>>
.RW<< //IWTNAB//NAONBO//NAO\rarr NBO transformation>>
.RW<< //IWTNBO//AONBO//AO\rarr NBO transformation>>
.RW<< //IWFOCK// //+1 if Fock matrix available on DAF, 0 otherwise>>
.RW<<*//IWCUBF//CUBICF//cubic #If#N functions>>
.RW<<*//IPSEUD// //effective core potential>>
.RW<< //KOPT// //(not used)>>
.RW<< //IPRINT//PRINT=n//print level>>
.RW<< //IWDETL//DETAIL//detailed output>>
.RW<< //IWMULP//MULAT//Mulliken population analysis>>
.RW<< //ICHOOS//$CHOOSE//directed NBO ($CHOOSE) search>>
.RW<< //JCORE//$CORE//user-specified core list>>
.RW<< //JPRINT(60)//various//printing option flags>>
.RW-
.ET
.FJ
.RL22
.BM60
The keyword associated with each element I=1-54
of the JPRINT array is shown below (55-60 are not currently used):
.LJ
.TB
.FM<<0L68>>
.RW<>
.FM<<2C3//2L12//2C3//2L10//2C3//2L10//2C3//2L10>>
.RW-
.RW<>
.RW=
.RW<<1//SKIPBO//15//FNLMO//29//FNHO//43//PLOT>>
.RW<<2//version//16//DMNBO//30//AOPNHO//44//AOPNAO>>
.RW<<3//E2PERT//17//DMNLMO//31//FNAO//45//NBOMO>>
.RW<<4//NPA//18//NAONLMO//32//(reserved)//46//DIPOLE>>
.RW<<5//NBO//19//SPNAO//33//NAONHO//47//NBONLMO>>
.RW<<6//NBOSUM//20//SPNHO//34//DMNHO//48//SPNLMO>>
.RW<<7//ARCHIVE//21//SPNBO//35//DMNAO//49//AOPNLMO>>
.RW<<8//NLMO//22//AOINFO//36//BEND//50//DIAO>>
.RW<<9//NAOMO//23//AONLMO//37//FNBO//51//DINAO>>
.RW<<10//NOBOND//24//NHONLMO//38//NHOMO//52//DINHO>>
.RW<<11//RPNAO//25//AOPNBO//39//SAO//53//DINBO>>
.RW<<12//BNDIDX//26//AOMO//40//FAO//54//DINLMO>>
.FM<<2C3//2L12//2C3//2L10//2C3//2L10//0C5//2L10>>
.RW<<13//NLMOMO//27//DMAO//41//NHONBO//55-60//(not used)>>
.RW<<14//RESONANCE//28//AONHO//42//BOAO// // >>
.RW-
.ET
.FJ
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:
.LJ
.LM+8
.RL10
.TB
.FM<<0C12//2L35>>
.RW-
.RW<>
.RW=
.RW<<0//Do nothing>>
.RW<<0 < #In#N//Print #In#N columns of the matrix>>
.RW<<-1000 < #In#N < 0//Write matrix to external file |#In#N|>>
.RW<>
.RW<<`FULL'//Print the full matrix to the output file>>
.RW<<`VAL'//Print only core plus valence orbitals>>
.RW<<`LEW'//Print only the occupied (Lewis) orbitals>>
.RW-
.ET
.FJ
.LM-8
.RL12
.OS<<3//#_4. COMMON/NBAO/#/>>
The INTEGER arrays of this block store information on the
atomic centers and angular symmetry of each AO:
.TB
.FM<<0L1//0L20//2L40>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L20//2L40>>
.RW<<*//LCTR(MAXBAS)//list of atomic centers of the basis AOs>>
.RW<< // //(LCTR(3)=2 if AO 3 is on atom 2)>>
.RW<<*//LANG(MAXBAS)//angular symmetry labels (Sec. B.7.5) of the basis AOs>>
.RW-
.ET
.RL16
.OS<<3//#_5. COMMON/NBATOM/#/>>
The INTEGER arrays of this block store information about the
orbitals on each atomic center:
.TB
.FM<<0L1//0L20//2L40>>
.RW-
.RW<< //variable//meaning>>
.RW=
.FM<<0L1//0L20//2L40>>
.RW<<*//IATNO(MAXATM)//atomic number for each atom>>
.RW<< //INO(MAXATM)//number of atomic hybrids on each atom>>
.RW<< //NORBS(MAXATM)//number of AOs on each atom>>
.RW<< //LL(MAXATM)//number of the first NAO on each atom>>
.RW<< //LU(MAXATM)//number of the last NAO on each atom>>
.RW<<*//IZNUC(MAXATM)//nuclear charge on each atom (\le IATNO)>>
.RW<< //IATCR(MAXATM)//atomic core list for modified $CORE table>>
.RW-
.ET
.RL27
.OS<<3//#_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):
.TB
.FM<<0L1//0L8//0C8//2L40>>
.RW-
.RW<< //LFN//value//file contents>>
.RW=
.RW<<*//LFNIN// //standard ESS input file>>
.RW<<*//LFNPR// //standard ESS output (print) file>>
.RW<< //LFNAO//31//AO info file>>
.RW<< //LFNPNA//32//AO\rarr PNAO transformation>>
.RW<< //LFNNAO//33//AO\rarr NAO transformation>>
.RW<< //LFNPNH//34//AO\rarr PNHO transformation>>
.RW<< //LFNNHO//35//AO\rarr NHO transformation>>
.RW<< //LFNPNB//36//AO\rarr PNBO transformation>>
.RW<< //LFNNBO//37//AO\rarr NBO transformation>>
.RW<< //LFNPNL//38//AO\rarr PNLMO transformation>>
.RW<< //LFNNLM//39//AO\rarr NLMO transformation>>
.RW<< //LFNMO//40//AO\rarr MO transformation (LCAO-MO coeffs.)>>
.RW<< //LFNDM//41//density matrix in AO basis>>
.RW<< //LFNNAB//42//NAO\rarr NBO transformation>>
.RW<< //LFNPPA//43//PAO\rarr PNAO transformation>>
.RW<< //LFNGEN//47//`archive' file>>
.RW<< //LFNDAF//48//direct access file (DAF)>>
.RW<< //LFNDEF//49//`default' for other file output>>
.RW-
.ET
.RL35
.LM-3
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.
.LM+3
.RL16
.OS<<3//#_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/ #Ichanges#N
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!):
.TB
.FM<<0L18//2L45>>
.RW-
.RW<>
.RW=
.FM<<0L18//2L45>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_8. COMMON/NBTHR/#/>>
The DOUBLE PRECISION variables of this block store the
default values of various
numerical thresh#|olds that can be set by the user:
.TB
.FM<<0L8//2L45>>
.RW-
.RW<>
.RW=
.FM<<0L8//2L45>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_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):
.TB
.FM<<0L18//2L45>>
.RW-
.RW<>
.RW=
.FM<<0L18//2L45>>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_10. COMMON/NBNAO/#/>>
The INTEGER arrays of this block store information pertaining
to the labelling of NAOs in the NPA output:
.TB
.FM<<0L18//2L45>>
.RW-
.RW<>
.RW=
.FM<<0L18//2L45>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_11. COMMON/NBMOL/#/>>
The INTEGER scalars, vectors, and arrays of this block
store information pertaining to ``molecular units'':
.TB
.FM<<0L26//2L40>>
.RW-
.RW<>
.RW=
.FM<<0L25//2L40>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_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:
.TB
.FM<<0L25//2L40>>
.RW-
.RW<>
.RW=
.FM<<0L25//2L40>>
.RW<>
.RW<>
.RW<>
.RW<< //(or number of lone pairs on I, if I = J)>>
.RW<>
.RW<>
.RW-
.ET
.RL16
.OS<<3//#_13. COMMON/NBDXYZ/#/>>
The DOUBLE PRECISION variables of this block store
information pertaining to the molecular dipole moment and charge
distribution:
.TB
.FM<<0L18//2L45>>
.RW-
.RW<>
.RW=
.FM<<0L18//2L45>>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL12
.OS<<3//#_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:
.TB
.FM<<0L12//2L50>>
.RW-
.RW<>
.RW=
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL13
.OS<<3//#_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:
.TB
.FM<<0L12//2L50>>
.RW-
.RW<>
.RW=
.RW<>
.RW<>
.RW<>
.RW<>
.RW-
.ET
.RL13
.OS<<3//#_16. COMMON/NBODAF/#/>>
The INTEGER variables of this block store information
related to the NBO direct access file (FILE48). The PARAMETER statement
#T
PARAMETER (NBDAR = 100)
#Nsets the maximum number of logical records accessible in FILE48:
.TB
.FM<<0L15//2L50>>
.RW-
.RW<>
.RW=
.RW<>
.RW<
