|
|
#HNBO 3.0 Program Manual#N
#N(#INatural Bond Orbital / Natural Population Analysis /
Natural Localized Molecular Orbital Programs#N)
E. D. Glendening, A. E. Reed, agger J. E. Carpenter, dagger
and F. Weinhold
#ITheoretical Chemistry Institute and Department of Chemis-
try, University of Wisconsin, Madison, Wisconsin 53706#N
92717.#N
0 The various natural localized sets can be considered
to result from a sequence of transformations of the in-
put atomic orbital basis set {
_______________
agger #C#RNote, however, that some electronic structure
packages do not make provision for calculating the spin
density matrices for some types of open-shell wavefunc-
tions (e.g., MCSCF wavefunctions calculated by the GUGA
formalism in the GAMESS system), so that NBO analysis
cannot be applied in these cases.#O
dagger #C#RIf the wavefunction is not calculated in an
atom-centered basis set, it would be necessary to first
compute a wavefunction for each isolated atom of the
molecule (in the actual basis set and geometry of the
molecular calculation), then select the most highly oc-
cupied natural orbitals of each atomic wavefunction to
compose a final set of linearly independent atom-
centered basis functions of the required dimensionali-
ty. Since atom-centered basis functions are the nearly
universal choice for molecular calculations, the
current
_________________________
July 11, 1995
- 2 -
NBO program makes no provision for this step.#O
Guide, Section C.
+0 +lf 0>>
+0 +lf 0//'
|<<3________________________
-dwid +0 ipen //+0 +dht ipen //+dhlfwid +0 ipen >>
input basis arr NAOs arr NHOs arr NBOs arr NLMOs
_________________________
Each natural localized set forms a complete orthonormal
set of one-electron functions for expanding the delo-
calized 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 or-
bital interactions in the usual way.
0 The optimal condensation of occupancy in the natural
localized orbitals leads to partitioning into high- and
low-occupancy orbital types (reduction in dimensionali-
ty of the orbitals having significant occupancy), as
reflected in the orbital labelling. The small set of
most highly-occupied NAOs, having a close correspon-
dence 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 , in the NHO basis give rise to a bond
(b ) and antibond (ab ) in the NBO basis,
b = ab =
the former a Lewis (L) and the latter a non-Lewis (NL)
orbital. The antibonds (valence shell non-Lewis orbi-
tals) typically play the primary role in departures
(delocalization) from the idealized Lewis structure.
0 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 ef-
fects are based on second-order perturbation theory, or
on the effect of deleting certain orbitals or matrix
elements and recalculating the total energy. NBO ener-
gy analysis is dependent on the specific ESS to which
the NBO program is attached, as described in the Appen-
July 11, 1995
- 3 -
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//'ext
_________________________
dix.
0 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 ver-
sions are described in individual Appendices.
#IA.1.2 #IStructure of the NBO Program#N
0 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).
0 The main NBO program is represented by modules la-
belled ``NBO'' and ``NBOEAN.'' These refer to the con-
struction 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.
0 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 en-
ergy value) upon request. Each such ESS device there-
fore requires special drivers to make this feedback
July 11, 1995
- 4 -
' 2//+0 +lf 0//'file' 2>>
#BFigure 1:#N Schematic diagram depicting flow of informa-
tion between the electronic structure system (ESS) and the
NBO program, and the commun#|ication lines connecting these
programs
_________________________
possible. Versions of the driver subroutines are in-
cluded for several popular packages. The driver rou-
tines are described in more detail in the Programmer's
agger #RPresent address: Bayer AG, Abteilung AV-IM-AM,
5090 Leverkusen, Bayerwerk, Federal Republic of Ger-
many.
dagger #RPresent address: Department of Chemistry,
University of California-Irvine, Irvine, California
#HTable of Contents#N
#HPREFACE: HOW TO USE THIS MANUAL#N
0 The NBO manual is divided into three major sections:
0 Section A (``General Introduction and Installation'')
contains general introductory and `one-time' informa-
tion for the novice user: what the program does, pro-
gram structure and relationship to driver electronic
structure package, initial installation, `quick start'
sample input data, and a brief tutorial on sample out-
put.
0 Section B (``NBO User's Guide'') is for the inter-
mediate 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
July 11, 1995
- 5 -
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,
_________________________
program to its full potential, to `turn off' or `turn
on' various NBO options for their specialized applica-
tions.
0 Section C (``NBO Programmer's Guide'') is for accom-
plished programmers who are interested in program logic
and the detailed layout of the source code. This sec-
tion describes the relationship of the source code sub-
programs to the published algorithms for NAO, NBO, and
NLMO determination, providing documentation at the lev-
el of individual common blocks, functions, and subrou-
tines. 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.
#HSection A: GENERAL INTRODUCTION AND INSTALLATION#N
#BA.1 INTRODUCTION TO THE NBO PROGRAM#N
#IA.1.1 #IWhat Does the NBO Program Do?#N
0 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 pro-
perties. 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 lpha
and g r This section provides a brief introduction
to NBO algorithms and nomenclature.
0 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 ma-
July 11, 1995
- 6 -
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.
#IA.1.3 #IInput and Output#N
0 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.
0 The following information is passed from the ESS to
the NBO program (transparent to the user):
The one-electron density matrix #BD#N (or density
matrices in the open-shell case) in the chosen atomic
orbital (AO) basis set;
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;
Atomic number (nuclear charge) of each atom.
Certain additional information is written on the FILE48
direct access file and may be used in response to
specific job options, such as the AO Fock matrix #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
_________________________
trix, and are hence ``natural'' in the sense of L mlaut
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 depar-
tures from this idealized localized picture.
July 11, 1995
- 7 -
plotting information is requested to be saved as input
for a contour plotting program.
0 The principal #_output#/ from the NBO program con-
sists 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.
#IA.1.4 #IGeneral Capabilities and Restrictions#N
0 Principal capabilities of the NBO program are:
Natural population, natural bond orbital, and natural
localized molecular orbital analysis of SCF, MCSCF, CI,
and M0t oller-Plesset wavefunctions (main subroutine:
NBO);
For RHF closed-shell and UHF wavefunctions only, ener-
getic analysis of the wavefunction in terms of the
interactions (Fock matrix elements) between NBOs (main
subroutine: NBOEAN);
Localized analysis of molecular dipole moment in terms
of NLMO and NBO bond moments and their interactions
(main subroutine: DIPANL).
0 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:
= overlap matrix = density matrix (or D) = Fock matrix
= dipole matrix (or DXYZ, or DX, DY, DZ) = Natural
Population Analysis = Natural Atomic Orbital = Natural
Bond Orbital = Natural Localized Molecular Orbital =
pre-orthogonal NAO (i.e., omit interatomic orthogonali-
zation) hsp
0 Most of the NBO storage is allocated dynamically, to
conform to the minimum required for the molecular sys-
tem under study. However, certain NBO common blocks of
fixed dimensionality are used for integer storage.
These are currently dimensioned to accomodate up to 99
July 11, 1995
- 8 -
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
M0t 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 poten-
tials (``pseudo#|potentials'') can be handled, includ-
ing 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.
#IA.1.5 #IReferences and Relationship to Previous
Versions#N
0 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, #IQuan-
tum Chemistry Program Exchange No. 408#N (1980); ``ver-
sion 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 frame-
work.
Principal contributors to the development of the NBO
methods and programs (1975-1990) are
Principal references to the development and applica-
tions of NAO/NBO/NLMO methods are:
J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc.
#B102#N, 7211-7218 (1980).
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).
A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B83#N,
July 11, 1995
- 9 -
1736-1740
(1985).
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.
A. E. Reed, L. A. Curtiss, and F. Weinhold, #IChem.
Rev. #B88#N, 899-926 (1988); F. Weinhold and J. E. Car-
penter, in, R. Naaman and Z. Vager (eds.), ``The Struc-
ture of Small Molecules and Ions,'' (Plenum, New York,
1988), pp. 227-236.
0 The principal enhancements of version 3.0 include:
#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.
#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 sum-
mary tables (Section A.3.2) include an SCF atomic orbi-
tal energy (if available), a conventional atomic orbi-
tal 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 = Ryd-
berg) to aid characterization of the NAO.
#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 ele-
ments, and 2nd-order energy analysis.
#IBond Bending Analysis.#N The program includes a new
analysis of hydrid directionality and bond ``bending''
(keyword BEND, Section A.3.4).
#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
July 11, 1995
- 10 -
localized
NLMOs and NBOs.
#IPrint options.#N The program offers new structured
printing options (Section B.2.4) that give greater con-
venience 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.
#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 orbi-
tals.
#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).
The program also includes three changes to correct
problems of the previous version (which may have
affected a small number of users):
#IUnpolarized Cores.#N NAOs identified as ``core''
orbitals are now auto#|matically carried over as unhy-
bridized 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 occupan-
cies are `accidentally' degenerate (usually, both very
close to 2.000...) within the numerical machine preci-
sion. A warning message is printed when the core occu-
pancy is less than 1.9990, indicating a possible ``core
polarization'' effect of physical significance.
#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 mes-
sage 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
July 11, 1995
- 11 -
the
basis of occupancy.]
#IAlternative Resonance Structures.#N The program now
institutes a search for alternative Lewis (`resonance')
structures when two or more structures may be competi-
tive, and returns the structure of lowest non-Lewis
occupancy. This corrects a possible dependence on
atomic numbering in cases of strong delocalization.
Despite these changes and extensions, version 3.0 has
been designed to be upward compatible with v. 2.0, as
nearly as possible. Previous users of NBO 2.0 should
find that their jobs run similarly (i.e., most keywords
continue to function as in previous versions). Thus,
experienced NBO users should find little difficulty in
adapting to, and experimenting with, the new capabili-
ties of the program.
#BA.2 INSTALLING THE NBO PROGRAM#N
0 The NBO programs and manual are provided on a distri-
bution tape. The tape contains three files: the
TechSet code of this manual (file NBO.MAN), a file con-
taining the core NBO source routines and supporting
driver routines (file NBO.SRC), and the Fortran ``ena-
bler'' program (file ENABLE.FOR).
0 In overview, the installation procedure involves the
following steps (the details of each step being depen-
dent on your operating system):
#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 ena-
bler 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.
July 11, 1995
- 12 -
#ICompiling the NBO routines.#N Using your system For-
tran 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 diffi-
culties in this step.]
#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 con-
sists 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.
#IRebuilding the integrated ESS/NBO program.#N Re-
compile your modified ESS programs and link the result-
ing 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 state-
ment (or deposited in one of the libraries accessed by
the linker, etc.).
Note that installation of the NBO programs into your
ESS system in no way affects the way your system
processes standard input files. The only change
involves enabling the reading of NBO keylists (if
detected in your input file), performance of the tasks
requested in the keylist, and return of control to the
parent ESS program in the state in which the NBO call
was encountered.
0 If you are interfacing the NBO programs to a new ESS
package (not represented in the driver routines pro-
vided with this distribution), see Section C for gui-
dance 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.
0 The TechSet-coded version of this manual, NBO.MAN,
can be printed on an HP LaserJet printer (`F' car-
tridge) with the TECHSET technical typesetting program
[ACS Software, American Chemical Society, Marketing
Communications Dept., 1155 Sixteenth Street, N.W.,
Washington, D.C. 20036].
#BA.3 TUTORIAL EXAMPLE FOR METHYLAMINE#N
July 11, 1995
- 13 -
#IA.3.1 Running the Example#N
0 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.
0 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 includ-
ing the line
#T
$NBO $END
#Nat the end of the file. This is an `empty' NBO keyl-
ist, specifying that NBO analysis should be carried out
at the #Idefault#N level.
0 The default NBO output produced by this example is
shown below, just as it appears in your output file.
The start of the NBO section is marked by a standard
header and storage info:
*******************************************************************************
N A T U R A L A T O M I C O R B I T A L
A N D
N A T U R A L B O N D O R B I T A L A N
A L Y S I S
*******************************************************************************
Job title: Methylamine...RHF/3-21G//Pople-Gordon stan-
dard geometry
Storage needed: 2505 in NPA, 2569 in NBO ( 750000
available)
#T @seg
#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 key-
words (none for the present default case) and shows an
estimate of the memory requirements (in double preci-
sion words) for the separate steps of the NBO process,
compared to the total allocated memory available
through your ESS process. Increase the memory allo-
cated to your ESS process if the estimated NBO requests
exceed the available storage. #IA.3.2 Natural
July 11, 1995
- 14 -
Population
Analysis#N
#N0 The next four NBO output segments summarize the
results of natural population analysis (NPA). The
first segment is the main NAO table, as shown below:
NATURAL POPULATIONS: Natural atomic orbital occupan-
cies
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
#T
@seg
#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
July 11, 1995
- 15 -
momentum
type `lang' (#Is#N, #Ip#dx#u#N, etc., in the coor-
dinate 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 popu-
lation' 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 occu-
pancies 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 orbi-
tals in describing molecular properties.
0 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.
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
July 11, 1995
- 16 -
#NThe next segment is an atomic summary showing the natural
atomic charges (nuclear charge minus summed natural popula-
tions of NAOs on the atom) and total core, valence, and Ryd-
berg populations on each atom:
#T
@seg
#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.]
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) ---
-----------------------------------------------------
#NNext follows a summary of the NMB and NRB populations for
the composite system, summed over atoms:
#T @seg
#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 den-
sity, whereas the 15 NMB functions account for 99.93% of the
total.]
#NFinally, the natural populations are summarized as an
effective valence electron configuration (``natural electron
configuration'') for each atom:
Atom # Natural Electron Configuration ---------
-
------------------------------------------------------------------
C 1 [core]2s( 1.09)2p( 3.35)
N 2 [core]2s( 1.43)2p( 4.47)
H 3 1s( 0.81)
H 4 1s( 0.78)
H 5 1s( 0.78)
H 6 1s( 0.64)
H 7 1s( 0.64)
#T
@seg
July 11, 1995
- 17 -
#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' configura-
tions. [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.]
#IA.3.3 Natural Bond Orbital Analysis#N
#N0 The next segments of the output summarize the
results of NBO analysis. The first segment
reports on details of the search for an NBO
natural Lewis structure:
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 17.95048 0.04952 2 6 0 1
0 0 0.02 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
#T @seg
#NNormally, there is but one cycle of the NBO search (cf.
the ``RESONANCE'' keyword, Section B.6.6). The table sum-
marizes a variety of information for each cycle: the occu-
pancy 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 orbi-
tals of the formal Lewis structure exceed the occupancy
thresh#|old (default, 1.90 electrons).
0 #NNext follows a more detailed breakdown of the Lewis and
non-Lewis occupancies into core, valence, and Rydberg shell
contributions:
WARNING: 1 low occupancy (<1.9990e) core orbital found on
July 11, 1995
- 18 -
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) -----
---------------------------------------------------
#T @seg
#NThis shows the general quality of the natural Lewis struc-
ture 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 local-
ized Lewis structure model. (In this case, the table also
includes a warning about a carbon core orbital with slightly
less than double occupancy.)
(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
July 11, 1995
- 19 -
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
July 11, 1995
- 20 -
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
July 11, 1995
- 21 -
-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%)
July 11, 1995
- 22 -
-1.0000 -0.0020
#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
@seg
#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 sam-
ple output is the 2-center bond (with 1.99858 electrons)
between carbon (atom 1) and nitrogen (atom 2), the gma
#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 #d
composition (percentage #Is#N-character, #Ip#N-character,
etc.) of each #Ih#N#dA#u. [For example, the gma #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,
gma #dCN#u = 0.633(#Isp#N#u3.61#d)#dC#u +
0.774(#Isp#N#u2.24#d)#dN#u
corresponding roughly to the qualitative concept of
interacting #Isp#N#u3#d hybrids (75% #Ip#N-character) and
the higher electronegativity (larger polarization coeffi-
cient) of N.] Below each NHO label is the set of coeffi-
cients 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 gma #dCN#u bond has largest coefficients
for the 2#und#d and 4#uth#d NAOs, corresponding to the
approximate description
#Ih#N#dC#u ~= minus 0.4653(2#Is#N)#dC#u minus
0.8808(2#Ip#N#dx#u)#dC#u
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
July 11, 1995
- 23 -
(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 gma #dCH#u NBOs, and the slightly higher occupancy
(0.01569 #Ivs.#N 0.0077 electrons) in the gma
*#<#dC#d1#uH#d3#u#u antibond (NBO 24) lying #Itrans#N to the
nitrogen lone pair. #IA.3.4 NHO Directional Analysis#N
0 The next segment of output summarizes the angular proper-
ties of the natural hybrid orbitals:
NHO Directionality and "Bond Bending" (deviations from line
of nuclear centers)
[Thresholds for printing: angular deviation > 1.0
degree]
hybrid p-character >
25.0%
orbital occupancy >
0.10e
Line of Centers Hybrid 1
Hybrid 2
--------------- -------------------
------------------
NBO Theta Phi Theta Phi Dev
Theta Phi Dev
===============================================================================
1. BD ( 1) C 1- N 2 90.0 5.4 -- -- --
90.0 182.4 3.0
3. BD ( 1) C 1- H 4 35.3 130.7 34.9 129.0 1.0
-- -- --
4. BD ( 1) C 1- H 5 144.7 130.7 145.1 129.0 1.0
-- -- --
5. BD ( 1) N 2- H 6 144.7 310.7 145.0 318.3 4.4
-- -- --
6. BD ( 1) N 2- H 7 35.3 310.7 35.0 318.3 4.4
-- -- --
9. LP ( 1) N 2 -- -- 90.0 74.8 --
-- -- --
#T @seg
#NThe `direction' of a hybrid is specified in terms of the
polar (heta ) and azimuthal (hi
) 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)
July 11, 1995
- 24 -
between
these two directions. For example, in the CH#d3#uNH#d2#u
case shown above, the nitrogen NHO of the gma #dCN#u bond
(NBO 1) is bent away from the line of C-N centers by
3.0 egree , whereas the carbon NHO is approximately aligned
with the C-N axis (within the 1.0 egree threshold for print-
ing). The N-H bonds (NBOs 5, 6) are bent even further
(4.4 egree ). The information in this table is often useful
in anticipating the direction of geometry changes resulting
from geometry optimization (viz., likely reduced pyramidali-
zation of the -NH#d2#u group to relieve the nitrogen bond
`kinks' found in the tetrahedral Pople-Gordon geometry).
#IA.3.5 Perturbation Theory Energy Analysis#N
0 The next segment summarizes the second-order perturbative
estimates of `donor-acceptor' (bond-antibond) interactions
in the NBO basis:
Second Order Perturbation Theory Analysis of Fock Matrix in
NBO Basis
Threshold for printing: 0.50 kcal/mol
E(2)
E(j)-E(i) F(i,j)
Donor NBO (i) Acceptor NBO (j)
kcal/mol a.u. a.u.
===============================================================================
within unit 1
2. BD ( 1) C 1- H 3 / 14. RY*( 1) N 2
0.84 2.18 0.038
3. BD ( 1) C 1- H 4 / 26. BD*( 1) C 1- H 5
0.52 1.39 0.024
3. BD ( 1) C 1- H 4 / 27. BD*( 1) N 2- H 6
3.03 1.37 0.057
4. BD ( 1) C 1- H 5 / 25. BD*( 1) C 1- H 4
0.52 1.39 0.024
4. BD ( 1) C 1- H 5 / 28. BD*( 1) N 2- H 7
3.03 1.37 0.057
5. BD ( 1) N 2- H 6 / 10. RY*( 1) C 1
0.56 1.78 0.028
5. BD ( 1) N 2- H 6 / 25. BD*( 1) C 1- H 4
2.85 1.51 0.059
6. BD ( 1) N 2- H 7 / 10. RY*( 1) C 1
0.56 1.78 0.028
6. BD ( 1) N 2- H 7 / 26. BD*( 1) C 1- H 5
2.85 1.51 0.059
7. CR ( 1) C 1 / 16. RY*( 3) N 2
0.61 13.11 0.080
7. CR ( 1) C 1 / 18. RY*( 1) H 3
1.40 11.99 0.116
7. CR ( 1) C 1 / 19. RY*( 1) H 4
1.55 11.99 0.122
July 11, 1995
- 25 -
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
#T @seg
#NThis is carried out by examining all possible interactions
between `filled' (donor) Lewis-type NBOs and `empty' (accep-
tor) non-Lewis NBOs, and estimating their energetic impor-
tance 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 `delo-
calization' 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 delo-
calization (``2e-stabilization'') #Ii arr j#N is estimated
as
E(2) = Delta E#dij#u = q#di#u quo <>
where #Iq#N#di#u is the donor orbital occupancy, \psilon
#di#u, \psilon #dj#u are diagonal elements (orbital ener-
gies) and F(i,j) is the off-diagonal NBO Fock matrix ele-
ment. [In the example above, the #In#N#dN#u arr gma
*#<#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. #IA.3.6 NBO Summary#N
0 Next appears a condensed summary of the principal NBOs,
showing the occupancy, orbital energy, and the qualitative
pattern of delocalization interactions associated with each:
Natural Bond Orbitals (Summary):
Princi-
pal Delocalizations
July 11, 1995
- 26 -
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
#T @seg
#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
July 11, 1995
- 27 -
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 gma *#<#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).]
#HSection B: NBO USER'S GUIDE#N
#BB.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO
KEYLISTS#N
0 Section B constitutes the general user's guide to the NBO
program. It assumes that the user has an installed elec-
tronic 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.
0 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 dis-
tinct keylist ($KEY) types are recognized ($NBO, $CORE,
$CHOOSE, and $DEL), and these will be described in turn in
Sections B.2-B.5. Some of the details of inserting NBO
keylists into the input file depend on the details of your
ESS method, and are described in the appropriate Appendix
for the ESS. However, the general form of NBO keylists and
the meaning and function of each keyword are identical for
all versions (insofar as the option is meaningful for the
ESS), and are described herein.
0 The four keylist types have common rules of syntax: Keyl-
ist delimiters are identified by a ``$'' prefix. Each keyl-
ist begins with the parent keylist name (e.g., ``$NBO''),
followed by any number of keywords, and ended with the word
``$END''; for example,
#T
July 11, 1995
- 28 -
$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 for-
mat,'' 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. Key-
words 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.
#BB.2 THE $NBO KEYLIST#N
#IB.2.1 Overview of $NBO keywords#N
0 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:
#IJob Control Keywords:#N #IJob Threshold Keywords:#N #IMa-
trix Output Keywords:#N #IOther Output Control Keywords:#N
#IPrint Level Control:#N PRINT=n
Keywords are first listed and described according to these
formal groupings in Sections B.2.2-B.2.6. Section B.6
illustrates the effect of commonly used $NBO keywords (as
well as other $KEY lists) on the successive stages of
NAO/NBO/NLMO transformation and subsequent energy or dipole
analysis, with sample output for these keyword options.
0 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.)
July 11, 1995
- 29 -
[0 Although the general user's interaction with the NBO pro-
grams 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 spe-
cialist.] #IB.2.2 Job Control Keywords#N
0 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 indica-
tion of where the option is useful):
#IOPTION DESCRIPTION#N
Request Natural Population Analysis and printing of NPA sum-
mary tables (Section A.3.2). This keyword also activates
calculation of NAOs, except for semi-empirical ESS methods.
Request calculation of NBOs and printing of the main NBO
table (Section A.3.3).
Request printing of the NBO summary table (Section A.3.6).
This combines elements of the NBO table and 2nd-order per-
turbation theory analysis table (see below) in a convenient
form for recognizing the principal delocalization patterns.
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 RESO-
NANCE 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 occu-
pancy 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 delo-
calized molecules.)
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.)
Request search for 3-center bonds (Section B.6.8). The nor-
mal default is to search for only 1- and 2-center NBOs.
(Useful for diborane and other electron-deficient `bridged'
species.)
Skip the computation of NBOs, i.e., only determine NAOs and
perform natural population analysis. (Useful when only NPA
is desired.)
Compute and print out the summary table of Natural Localized
Molecular Orbitals (Section B.6.2). NLMOs are similar to
July 11, 1995
- 30 -
Boys
or Edmiston-Ruedenberg LMOs, but more efficiently calcu-
lated. (Useful for `semi-localized' description of an SCF
or correlated wavefunction.) Activated automatically by all
keywords that pertain to NLMOs (e.g., AONLMO, SPNLMO,
DIPOLE).
Note that the SKIPBO keyword has higher precedence than
other keywords in this list, so that keywords with which it
is implicitly in conflict (e.g., NBO, 3CBOND, NLMO) will be
ignored if SKIPBO is included in the $NBO keylist. #IB.2.3
Job Threshold Keywords#N
0 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].)
#IOPTION DESCRIPTION#N
Request the NHO Directional Analysis table (Section A.3.4).
The three parameters [and default values] have the following
significance:
= threshold angular deviation for printing = threshold
percentage #Ip#N-character for printing = threshold NBO
occupancy for printing
#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 egree (ang), hybrids of at least 10% #Ip#N-character
(pct), and NBOs of occupancy at least 1.9 electrons (occ).
Request the Perturbation Theory Energy Analysis table (Sec-
tion A.3.5), where
= threshold energy (in kcal/mol) for printing
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 arr gma *#<#dCH#u interaction in the output of
Section A.3.5).
July 11, 1995
- 31 -
Request the Molecular Dipole Moment Analysis table (Section
B.6.3), where
= threshold dipole moment (Debye) for printing
The program will carry out a decomposition of the total
molecular dipole moment in terms of localized NLMO and NBO
contributions, including all terms whose contribution (in
vector norm) exceeds the `dval' threshold.
Example:#T DIPOLE=0.1
#NThis example would print out dipole contributions of all
NBOs (and their delocalization interactions) of magnitude ge
0.1hsp D.
#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 keyl-
ist
#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. #IB.2.4 Matrix Output Keywords#N
0 The keywords in this group activate the printing of vari-
ous matrices to the output file, or their writing to (or
reading from) external disk files. The large number of key-
words in this group provide great flexibility in printing
out the details of the successive transformations,
eps1 eps2
or the matrices of various operators in the natural local-
ized basis sets. This ordered sequence of transformations
forms the basis for naming the keywords.
#_Keyword Names#/
0 The keyword for printing the matrix for a particular basis
transformation, IN arr OUT, is constructed from the
corresponding acronymns for the two sets in the generic form
``INOUT''. For example, the transformation AO arr 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
July 11, 1995
- 32 -
(NAO,
NHO, NBO, NLMO, MO, or the pre-orthogonal PNAO, PNHO, PNBO,
PNLMO sets) in the overall sequence leading to canonical
MOs, i.e.,
AONAO AONHO AONBO AONLMO AOMO AOPNAO AOPNHO AOPNBO
AOPNLMO
and from each of the orthonormal natural localized sets to
sets lying to the right in the sequence, i.e.,
NAONHO NAONBO NAONLMO NAOMO
NHONBO NHONLMO NHOMO
NBONLMO NBOMO
NLMOMO
The matrix T#dIN,OUT#u for a specified IN arr OUT transform
has rows labelled by the IN set and columns labelled by the
OUT set.
0 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 local-
ized sets (NAO, NHO, NBO, or NLMO). The corresponding key-
word is constructed by combining the abbreviation (M) for
the operator with that for the set (SET) in the generic form
``MSET''. For example, to print the Fock matrix (F) in the
NBO set, use the keyword ``FNBO'', or to print the dipole
matrix in the NLMO basis, use ``DINLMO''. (For the dipole
matrix keywords, all three vector components will be
printed.) One can also print out elements of the overlap
matrix (S) in the input AO basis or any of the `pre-
orthogonal' sets (PNAO, PNHO, PNBO, or PNLMO), using, e.g.,
``SPNAO'' for the overlap matrix in the PNAO basis. The
complete set of allowed keywords for operator matrices is:
FAO FNAO FNHO FNBO FNLMO
DMAO DMNAO DMNHO DMNBO DMNLMO
DIAO DINAO DINHO DINBO DINLMO
SAO SPNAO SPNHO SPNBO SPNLMO
Other desired transformations can be readily obtained from
the keyword transformations by matrix multiplication.
#_Keyword Parameters#/
0 Each generic matrix keyword (``MATKEY'') can include a
July 11, 1995
- 33 -
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):
(print out the matrix in the standard output file, 'c'
columns)
(write out the matrix to disk file #In#N)
#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 out-
put file. Thus, ``MATKEY=P'' would be equivalent to ``MAT-
KEY'', 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 neces-
sarily those with pre#|dominant valence character. Simi-
larly, 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 methy-
lamine example. Judicious use of these print parameters
keeps printed output within reasonable bounds in calcula-
tions 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:
July 11, 1995
- 34 -
#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 exam-
ple, the keyword
#T
AONBO=W22
#Nwould write out the AO arr NBO transformation to LFN = 22
(rather than the default LFN = 37).
0 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 for-
mat), 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.
0 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 bypass-
ing the NBO optimization of these orbitals for the molecular
system). For example, the keyword ``NAONBO=R44'' would have
the effect of freezing the NAO arr NBO transformation coef-
ficients 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).
#IB.2.5 Other Output Control Keywords#N
0 The keywords in this group also help to control the I/O
produced by a specified set of job options, and thus supple-
ment 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:
#IOPTION DESCRIPTION#N
July 11, 1995
- 35 -
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 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.
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.)
Request writing of information concerning the AO basis set
(geometrical positions, orbital exponents, contraction coef-
ficients, etc.) to an external file, LFN 31. This is a por-
tion of the information needed by the ORB#|PLOT orbital con-
tour plotting programs (cf. ``PLOT'' keyword below.)
1. 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.
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 repeat-
ing the calculation of the wavefunction (Section B.7).
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). #IB.2.6 Print Level Keywords#N
0 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 out-
put (PRINT=0) to a considerable volume of detail (PRINT=4).
The keywords associated with each print level are tabulated
below [default value, PRINT=2]:
July 11, 1995
- 36 -
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.
0 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 Sec-
tion 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.'] #IB.2.7
Semi-Documented Additional Keywords#N
0 Some additional keywords are listed below that may of use
to specialists or program developers:
#IOPTION DESCRIPTION#N
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).
Set the projection threshold [default 0.20] to determine if
a `new' hybrid orbital has too high overlap with hybrids
previously found.
Print total gross Mulliken populations by atom.
Print gross Mulliken populations, by orbital and atom.
Revises PAO to PNAO transformation matrix by post-
multiplying by #BT#N#dRyd#u and #BT#N#dred#u [see the NPA
July 11, 1995
- 37 -
paper:
A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys.
#B83#N, 735-746 (1985)].
Input or output of pure AO (PAO) to pre-NAO (PNAO) transfor-
mation. 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.
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.
#BB.3 THE $CORE LIST#N
0 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 occu-
pancy 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 signifi-
cance.
0 [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' degen-
eracy in occupancy of core and valence lone pairs leads to
undesirable core-valence mixing; the present version expli-
citly isolates core pairs as unhybridized NAOs prior to the
main NBO search to prevent this unphysical effect.]
0 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.
0 The format of the $CORE modification list is:
July 11, 1995
- 38 -
The keyword ``$CORE''
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.
The keyword ``$END'', to indicate the end of core input.
The entire list may also be condensed to a single line, but
the word ``$CORE'' must occur as the first word of the line
and ``$END'' as the last word; that is, the core modifica-
tion keylist cannot continue on a line that contains other
keylist information.
0 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 orbi-
tals, 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 lpha and p n-shell calcula-
tion.
An example, appropriate for Ni(1)-C(2)-O(3) with the indi-
cated 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.
[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).]
#BB.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)#N
0 A $CHOOSE keylist requests that the NBO search be directed
July 11, 1995
- 39 -
to
find a particular Lewis structure (`resonance structure')
chosen by the user. (This is useful for testing the accu-
racy 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 algo-
rithm seek the best location for lone pairs, but it is usu-
ally safest to completely specify the resonance structure,
both lone pairs and bonds.
0 The format of the $CHOOSE list is:
The keyword ``$CHOOSE''
The keyword ``ALPHA'' (only for open-shell wavefunction)
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. Ter-
minate 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
single bond double bond triple bond quadruple bond
followed by the two atomic centers of the bond (e.g., ``D 9
16'' for a double bond between atoms 9 and 16).
If three-center NBOs are to be searched for, type the key-
word ``3CBOND'', followed by the list of 3-c bond specif-
iers, 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.)
The word ``END'' to signal the end of the lpha spin list.
The keyword ``BETA'' (for open-shell wavefunctions)
The input for m format as above. The overall $CHOOSE
list should always end with the ``$END'' keyword.
July 11, 1995
- 40 -
Two examples will serve to illustrate the $CHOOSE format
(each is rather artificial, inasmuch as the specified
$CHOOSE structure corresponds to the `normal' structure that
would be found by the NBO program):
The closed-shell H-bonded complex FH ots CO, with atom
numbering F(1)-H(2) ots 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).
The open-shell FH ots 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 lpha 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
#NNote that this example incorporates the idea of ``dif-
ferent Lewis structures for different spins,'' with a dis-
tinct pattern of localized 1-c (`lone') and 2-c (`bond')
functions for lpha and . 0 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. #BB.5 THE $DEL KEYLIST (NBO ENERGETIC
ANALYSIS)#N
July 11, 1995
- 41 -
#IB.5.1 Introduction to NBO Energetic Analysis#N
0 The fourth and final type of keylist is a `deletions'
($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) diagonal-
izing 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 differ-
ence 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 wavefunc-
tions only.
0 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 sin-
gle job, with each deletion included in the overall $DEL
keylist. The nine distinct types of deletions input are
described in Section B.5.2 below.
0 The deletions keylist begins with the ``$DEL'' keyword.
For the analysis of UHF wavefunctions, the deletions for the
lpha and b separately specified (see Section B.5.3).
Otherwise, the input for closed shells RHF and UHF is ident-
ical. 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.
|<<__________________________
#BWARNING#N
If symmetry is used, one must be careful to only do dele-
tions that will preserve the symmetry of the electronic
wavefunction!! If this is not done, the energy of the dele-
tion 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 sin-
gle C-H antibond.) The remedy is not to use symmetry in the
SCF calculation.
0 In describing the deletion types, use is made of the terms
``molecular unit'' and ``chemical fragment.'' The NBO pro-
gram 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
July 11, 1995
- 42 -
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 neces-
sarily) 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 molecu-
lar unit, identified by giving the atom numbers of which the
fragment consists. #IB.5.2 The Nine Deletion Types#N
0 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.]
|<<__________________________
#BWARNING#N
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 redistribu-
tion of the electron density of deleted orbitals) is small
compared to the net energy change of deletion. It is funda-
mentally erroneous to delete #Ihigh#N-occupancy (Lewis)
orbitals by this procedure.
#_(2) Deletion of specific Fock matrix elements.#/
This is called for by typing ``DELETE'', then the number of
elements to be deleted, then the keyword ``ELEMENT'' (or
``ELEMENTS''), then the list of the elements to be deleted
(each as a pair of integers).
Example: #TDELETE 3 ELEMENTS 1 15 3 19 23 2
July 11, 1995
- 43 -
#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:
(1) the dimensions of the block, separated by the word
``BY'' (e.g., ``6 BY 3'' if the first set has 6 orbitals and
the second set has 3 orbitals);
(2) the list of orbitals in the first set;
(3) the list of orbitals in the second set.
An example is shown below:
#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:
(3,9), (3,10), (3,11), (3,14), (3,19), (9,3), (10,3),
(11,3), (14,3), (19,3), (4,9), (4,10), (4,11), (4,14),
(4,19), (9,4), (10,4), (11,4), (14,4), (19,4), (1,20),
(1,24), (2,20), (2,24), (7,20), (7,24) (20,1), (24,1),
(20,2), (24,2), (20,7), (24,7)
[Usually, in studying the total delocalization from one
molecular unit to another, it is much easier to use deletion
type (8) below. Similarly, in studying the total delocali-
zation 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
July 11, 1995
- 44 -
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 vari-
ational expectation value of the determinant of doubly occu-
pied Lewis NBOs).
#_(5) Deletion of all vicinal delocalizations.#/
To delete all Fock matrix elements between Lewis NBOs and
the vicinal non-Lewis NBOs, simply enter ``NOVIC''.
#_(6) Deletion of all geminal delocalizations.#/
To delete all Fock matrix elements between Lewis NBOs and
the geminal non-Lewis NBOs, simply enter ``NOGEM''.
#_(7) Deletion of all starred (antibond/Rydberg) orbitals on
a particular molecular unit.#/
This is called for by typing ``DESTAR'', then the number of
molecular units to be de#|starred, then the keyword ``UNIT''
(or ``UNITS''), then the list of units.
Example: #TDESTAR 2 UNITS 3 4
#N
#_(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 delo-
calization, 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 delo-
calizations between units 1 and 2 (i.e., both 1 arr 2 and 2
arr 1). The effect is to remove all Fock matrix elements
between high-occupancy (core/lone pair/bond) NBOs of the
donor unit to the low-occupancy (antibond/Rydberg) NBOs of
the acceptor unit. The donor and acceptor units may be the
same.
#_(9) Zeroing all delocalization from one chemical fragment
to another.#/
This is called for by typing ``ZERO'', then the number of
July 11, 1995
- 45 -
inter-fragment
delocalizations to be zeroed, then the words ``ATOM
BLOCKS'', and then, for each delocalization, the following:
(1) the number of atoms in the two fragments, separated by
the word ``BY'' (e.g., ``6 BY 3'' if the first fragment
has 6 atoms and the second has 3 atoms);
(2) the list of atoms in the first fragment;
(3) the list of atoms in the second fragment.
For example, to zero all delocalizations between the frag-
ments 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) arr
(3,4,5) delocalizations, while the second removes the
(3,4,5) arr (1,2) delocalizations.
0 For additional examples of $DEL input, see Section B.6.10.
#IB.5.3 Input for UHF Analysis#N
0 Deletions of the alpha and beta Fock matrices can be done
independently. The deletions are input as above (Section
B.5.2) for RHF closed shell, but they must be specified
separately for alpha and beta in the UHF case.
0 The deletion to be done on the alpha Fock matrix must be
preceded by the keyword ``ALPHA'', and the deletion of the
beta Fock matrix must be preceded by the keyword ``BETA''.
(Actually, only the first letter ``A'' or ``B'' is searched
for by the program.) The ALPHA deletion must precede the
BETA deletion. The BETA deletion may be the same as the
ALPHA deletion, or different.
0 NOTE: The types of the lpha NBOs often differ from those
of the d tions lists are generally required. For example,
O#d2#u (triplet) has one bond in the lpha system and three
in the t m, if the unpaired electrons are in the lpha sys-
tem.
0 Here are three examples to illustrate UHF open-shell dele-
tions:
Example 1:
July 11, 1995
- 46 -
#T
ALPHA ZERO 1 DELOC FROM 1 TO 2
BETA NOSTAR
#NExample 2:
#T
ALPHA ZERO 1 DELOC FROM 1 TO 2
BETA ZERO 0 DELOC
#NExample 3:
#T
ALPHA DELETE 0 ORBITALS
BETA DELETE 1 ORBITAL 8
#NIf no deletion is done, this must be specified using zero
(0) with one of the deletion input formats, as shown in
Examples 2,3 above. #BB.6 NBO KEYLIST ILLUSTRATIONS#N
#IB.6.1 Introduction#N
0 This section illustrates the output produced by several
important keyword options of the NBO keylists ($NBO,
$CHOOSE, $DEL, $CORE lists), supplementing the illustrations
of Section A.3. Excerpts are provided rather than full out-
put, since, e.g., NPA analysis is unaffected by keywords
that modify the NBO search. Keywords of general applicabil-
ity are illustrated with the methylamine example (RHF/3-21G,
Pople-Gordon geometry) of Section A.3, which should be con-
sulted for further information. More specialized keywords
(RESONANCE, 3CBOND, etc.) are illustrated with prototype
molecules (benzene, diborane, etc.) chosen for the keyword.
0 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 key-
words. Section B.6.9 and B.6.10 similarly illustrate the
use of the $CHOOSE and $DEL keylists. Section B.6.11 illus-
trates the output for open-shell UHF cases, emphasizing
features associated with the ``different Lewis structures
for different spins'' representation of lpha and
S ction 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. #IB.6.2 NLMO Keyword#N
0 When the NLMO keyword is activated, the program computes
the NLMOs and prints out three tables summarizing their
form. For the RHF/3-21G methylamine example (cf. Section
A.3), the principal NLMO table is shown below:
NATURAL LOCALIZED MOLECULAR ORBITAL (NLMO) ANALYSIS:
Maximum off-diagonal element of DM in NLMO basis: 0.00000
Hybridization/Polarization Analysis of NLMOs in NAO Basis:
July 11, 1995
- 47 -
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%)
July 11, 1995
- 48 -
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%)
#T
@seg
#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 fol-
lows an NAO decomposition of the NLMO, showing the percen-
tage of the NLMO on each atom and the hybrid composition
ratios (effective #Isp#N#u #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 con-
tributions (~0.4% each) from C(1) and H(3), and smaller con-
tributions (~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]. #IB.6.3
DIPOLE Keyword#N
0 The DIPOLE keyword activates the NBO/NLMO analysis of the
molecular dipole moment, as shown below for the example of
RHF/3-21G methylamine (cf. Section A.3):
Dipole moment analysis:
[Print threshold: Net dipole > 0.02 Debye]
NLMO bond dipole
NBO bond dipole
July 11, 1995
- 49 -
------------------------- ------------------------
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
July 11, 1995
- 50 -
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
#T
@seg
#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 coor-
dinate 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' contri-
butions to give the net molecular moment). Each NLMO or NBO
bond dipole vector t mu #dAB #u is evaluated as
mab = mabe + mabn
where mabe = 2#Ie#N a t r#Nar b t is the electronic dipole
expectation value for an electron pair in the b 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 correc-
tions 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 { } of NBOs,
nlmo = this correction is (for each electron, lpha or
) .LM+10
+ s <> 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 t 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
July 11, 1995
- 51 -
has
also the largest off-diagonal delocalization correction in
the table, a 0.18 D correction due to the #In#N#dN#u arr
gma *#<#dCH#u delocalization into the vicinal C(1)-H(3)
antibond, NBO 24.
0 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).
0 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]. #IB.6.4 Matrix Output Keywords#N
0 Two simple examples will be given to illustrate the for-
matting of output for operators or basis set transformation
matrices using the matrix output keywords of Section B.2.4.
For the RHF/3-21G methylamine example of Section A.3, the
keyword ``FNHO'' would cause the Fock matrix in the NHO
basis to be printed out. Shown below is a reproduction of
the first eight columns (out of 28) of this output:
NHO Fock matrix:
NHO 1 2 3 4 5
6 7 8
---------- ------- ------- ------- ------- ------- ---
---- ------- -------
1. C1 ( N2 ) -0.0208 -0.7203 -0.0571 -0.0665 0.0438
0.0672 0.0438 0.0672
2. N2 ( C1 ) -0.7203 -0.3083 -0.0773 -0.0627 0.0835
0.0646 0.0835 0.0646
3. C1 ( H3 ) -0.0571 -0.0773 -0.1394 -0.6758 0.0638
0.0746 0.0638 0.0746
4. H3 ( C1 ) -0.0665 -0.0627 -0.6758 0.1349 0.0740
0.0672 0.0740 0.0672
5. C1 ( H4 ) 0.0438 0.0835 0.0638 0.0740 -0.1466
-0.6761 -0.0548 -0.0759
6. H4 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.6761
0.1541 -0.0759 -0.0697
7. C1 ( H5 ) 0.0438 0.0835 0.0638 0.0740 -0.0548
-0.0759 -0.1466 -0.6761
8. H5 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.0759
-0.0697 -0.6761 0.1541
9. N2 ( H6 ) 0.0926 0.1499 0.0240 -0.0113 0.0912
-0.0078 -0.0349 0.0134
10. H6 ( N2 ) 0.1083 0.0826 -0.0010 0.0232 -0.0118
-0.0242 0.0017 -0.0224
July 11, 1995
- 52 -
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
#T
@seg
#N
0 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
July 11, 1995
- 53 -
element,
between the C(1) hybrid pointing toward N(2) and the N(2)
hybrid pointing toward H(6), is 0.0926 a.u.
0 As a second example, the keyword ``NBOMO=PVAL'' would
print out the core + valence columns of the NBO arr MO
transformation, as reproduced below:
MOs in the NBO basis:
NBO 1 2 3 4 5
6 7 8
---------- ------- ------- ------- ------- ------- ---
---- ------- -------
1. C1 - N2 -0.0661 -0.0574 0.6288 -0.1243 0.0000
-0.3239 0.6816 0.0000
2. C1 - H3 -0.0018 -0.0578 0.2061 -0.4716 0.0000
0.7747 0.1386 0.0000
3. C1 - H4 0.0023 0.0579 -0.1836 0.4908 0.3813
0.2304 0.3921 0.5940
4. C1 - H5 0.0023 0.0579 -0.1836 0.4908 -0.3813
0.2304 0.3921 -0.5940
5. N2 - H6 0.0570 0.0000 -0.4742 -0.3567 -0.5937
-0.1954 0.3035 0.3814
6. N2 - H7 0.0570 0.0000 -0.4742 -0.3567 0.5937
-0.1954 0.3035 -0.3814
7. C1 (cr) -0.0021 0.9931 0.0692 -0.0920 0.0000
0.0006 0.0019 0.0000
8. N2 (cr) 0.9935 -0.0019 0.1048 0.0348 0.0000
-0.0131 0.0022 0.0000
9. N2 (lp) 0.0432 -0.0037 -0.1676 -0.1219 0.0000
0.3312 0.1525 0.0000
10. C1 (ry*) -0.0088 -0.0005 0.0114 0.0089 0.0000
-0.0016 -0.0086 0.0000
11. C1 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0109
0.0000 0.0000 -0.0070
12. C1 (ry*) -0.0063 0.0001 -0.0050 -0.0035 0.0000
-0.0030 0.0026 0.0000
13. C1 (ry*) 0.0020 -0.0002 -0.0003 -0.0003 0.0000
-0.0009 0.0002 0.0000
14. N2 (ry*) -0.0041 -0.0003 -0.0006 0.0016 0.0000
0.0192 0.0107 0.0000
15. N2 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0080
0.0000 0.0000 0.0124
16. N2 (ry*) 0.0035 -0.0060 -0.0039 0.0102 0.0000
-0.0023 0.0040 0.0000
17. N2 (ry*) -0.0018 0.0023 -0.0007 0.0013 0.0000
-0.0007 0.0005 0.0000
18. H3 (ry*) -0.0008 -0.0094 -0.0103 0.0146 0.0000
0.0017 -0.0021 0.0000
19. H4 (ry*) -0.0008 -0.0100 -0.0061 0.0119 0.0062
0.0004 -0.0054 -0.0098
20. H5 (ry*) -0.0008 -0.0100 -0.0061 0.0119 -0.0062
0.0004 -0.0054 0.0098
21. H6 (ry*) -0.0052 -0.0013 -0.0147 -0.0018 -0.0027
July 11, 1995
- 54 -
-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
July 11, 1995
- 55 -
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
#T
@seg
#N
0 In this transformation matrix, rows correspond to NBOs and
columns to MOs (in the ordering used elesewhere in the pro-
gram), 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
hi #d5#u ~= minus 0.594n + 0.381c
hi #d8#u ~= 0.381n + 0.594c
whereas hi
#d6#u is primarily the C-H(3) NBO and hi
#d9#u the N lone pair NBO. #IB.6.5 BNDIDX Keyword#N
0 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
July 11, 1995
- 56 -
tables
for the example of RHF/3-21G methylamine (Section A.3).
0 The first segment of BNDIDX output shows the Wiberg bond
index (the sum of squares of off-diagonal density matrix
elements between atoms), as formulated in terms of the NAO
basis set:
Wiberg bond index matrix in the NAO basis:
Atom 1 2 3 4 5 6
7
---- ------ ------ ------ ------ ------ ------ --
----
1. C 0.0000 0.9964 0.9472 0.9394 0.9394 0.0020
0.0020
2. N 0.9964 0.0000 0.0208 0.0052 0.0052 0.8611
0.8611
3. H 0.9472 0.0208 0.0000 0.0004 0.0004 0.0002
0.0002
4. H 0.9394 0.0052 0.0004 0.0000 0.0009 0.0079
0.0005
5. H 0.9394 0.0052 0.0004 0.0009 0.0000 0.0005
0.0079
6. H 0.0020 0.8611 0.0002 0.0079 0.0005 0.0000
0.0003
7. H 0.0020 0.8611 0.0002 0.0005 0.0079 0.0003
0.0000
Wiberg bond index, Totals by atom:
Atom 1
---- ------
1. C 3.8265
2. N 2.7499
3. H 0.9691
4. H 0.9544
5. H 0.9544
6. H 0.8720
7. H 0.8720
#T
@seg
#N
0 This index is intrinsically a positive quantity, making no
distinction between net bonding or antibonding character of
the density matrix elements.
0 The next segment tabulates the ``overlap-weighted NAO bond
order,'' as shown below:
July 11, 1995
- 57 -
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
#T
@seg
#N
0 This index corresponds to a sum of off-diagonal NAO den-
sity matrix elements between atoms, each multiplied by the
corresponding PNAO overlap integral.
0 Another type of BNDIDX output appears if the NLMO keyword
is included, summarizing a formal ``NLMO/NPA bond order''
that can be associated with each NLMO:
Individual LMO bond orders greater than 0.002 in magnitude,
with the overlap between the hybrids in the NLMO given:
Atom I / Atom J / NLMO / Bond Order / Hybrid Overlap /
1 2 1 0.8007741 0.7314361
1 2 5 0.0022694 0.1796696
1 2 6 0.0022694 0.1796696
July 11, 1995
- 58 -
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
#T
@seg
#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 nega-
tive bond order (-0.0098) between atoms N(2), H(3).
0 The NLMO bond order contributions are then summed for each
atom pair to give the net NLMO/NPA bond orders shown below:
Atom-Atom Net Linear NLMO/NPA Bond Orders:
Atom 1 2 3 4 5 6
7
---- ------ ------ ------ ------ ------ ------ --
----
1. C 0.0000 0.8174 0.7960 0.7732 0.7732 -0.0013
-0.0013
2. N 0.8174 0.0000 -0.0104 -0.0030 -0.0030 0.6337
0.6337
3. H 0.7960 -0.0104 0.0000 -0.0020 -0.0020 0.0001
0.0001
4. H 0.7732 -0.0030 -0.0020 0.0000 0.0020 0.0062
July 11, 1995
- 59 -
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
#T
@seg
#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 unsatisfac-
tory aspect of this method of assessing bond order.)
0 These bond indices are based on different assumptions, and
each has certain advantages and disadvantages. #ICaveat
emptor!#N #IB.6.6 RESONANCE Keyword: Benzene#N
0 When NBO analysis is performed on a wavefunction that can-
not be satisfactorily localized [i.e., in which one or more
NBOs of the natural Lewis structure fail to achieve the
threshold occupancy (1.90) for a satisfactory `pair'], the
NBO program aborts with a message indicating that the
wavefunction is unsuitable for localized analysis. For
example, when benzene (RHF/STO-3G level, idealized Pople-
Gordon geometry) is treated by the NBO program in default
mode, one obtains the output:
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 38.87476 3.12524 6 12 0 3
3 3 0.44
2(2) 1.90 38.87476 3.12524 6 12 0 3
3 3 0.44 ----------
-------------------------------------------------------------------
Only strongly delocalized resonance structures can be found.
The default procedure is to abort the NBO search.
#T
@seg
July 11, 1995
- 60 -
0 #NWhen the RESONANCE keyword is activated for this same
example, one obtains a summary of NBO search cycles as shown
below:
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 38.87476 3.12524 6 12 0 3
3 3 0.44
2(2) 1.90 38.87476 3.12524 6 12 0 3
3 3 0.44
3(1) 1.80 38.87476 3.12524 6 12 0 3
3 3 0.44
4(2) 1.80 38.87476 3.12524 6 12 0 3
3 3 0.44
5(1) 1.70 38.87476 3.12524 6 12 0 3
3 3 0.44
6(2) 1.70 38.87476 3.12524 6 12 0 3
3 3 0.44
7(1) 1.60 40.87476 1.12524 6 15 0 0
0 3 0.44
8(2) 1.60 40.87476 1.12524 6 15 0 0
0 3 0.44
9(1) 1.50 40.87476 1.12524 6 15 0 0
0 3 0.44
10(2) 1.50 40.87476 1.12524 6 15 0 0
0 3 0.44
11(1) 1.60 40.87476 1.12524 6 15 0 0
0 3 0.44 ----------
-------------------------------------------------------------------
Structure accepted: RESONANCE keyword permits strongly delo-
calized structure
#T
@seg
#N
0 As this table shows, the occupancy threshold was succes-
sively 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:
(Occupancy) Bond orbital/ Coefficients/ Hybrids -----
July 11, 1995
- 61 -
-----
---------------------------------------------------------------------
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
July 11, 1995
- 62 -
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(
July 11, 1995
- 63 -
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
July 11, 1995
- 64 -
( 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%)
July 11, 1995
- 65 -
-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
#T
@seg
July 11, 1995
- 66 -
#N
0 As one can see from this table, the set of NBOs obtained
by the program corresponds to one of the two equivalent
Kekulcute e structures, with reasonably well localized gma
#dCC#u and gma #dCH#u NBOs (1.98940 and 1.98977 electrons,
respectively), but three severely depleted i
#dCC#u bonds (1.66667e) and corresponding high occupancy
i *#<#dCC#u antibonds (0.33333e). Other sections of the NBO
output (not shown) will similarly exhibit the sharp distinc-
tions between benzene and more `typical' non-aromatic com-
pounds.
|<<__________________________
#-#BWARNING#N#+
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 lpha and h 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.
#IB.6.7 NOBOND Keyword#N
0 The NOBOND keyword forces the NBO program to analyze the
wavefunction in terms of 1-center functions only, thus forc-
ing 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+#dhsp F#uminus #d interactions.
0 The default NBO analysis of this example is shown below:
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 9.99942 0.00058 1 1 0 3
0 0 0.00 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
--------------------------------------------------------
July 11, 1995
- 67 -
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(
July 11, 1995
- 68 -
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%)
#T
@seg
#N
As the output shows, default NBO analysis leads to a polar
covalent description of HF. The gma #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.
0 When the NOBOND keyword is activated to bypass the search
for 2-center bonds, the NBO output is modified as shown
below:
/NOBOND / : No two-center NBO search
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.00 9.50378 0.49622 1 0 0 4
0 1 0.75 ----------
-------------------------------------------------------------------
Structure accepted: Search for bonds prevented by NOBOND
keyword
--------------------------------------------------------
Core 1.99993 ( 99.997% of 2)
Valence Lewis 7.50385 ( 93.798% of 8)
================== ============================
Total Lewis 9.50378 ( 95.038% of 10)
-----------------------------------------------------
Valence non-Lewis 0.49564 ( 4.956% of 10)
Rydberg non-Lewis 0.00058 ( 0.006% of 10)
================== ============================
Total non-Lewis 0.49622 ( 4.962% of 10) -----
July 11, 1995
- 69 -
---------------------------------------------------
(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
#T
@seg
#N
0 In this case, the NBO output indicates a rather poor Lewis
July 11, 1995
- 70 -
structure
(4.962% non-Lewis density), with a severely depleted
F#uminus #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. #IB.6.8 3CBOND Keyword:
Diborane#N
0 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#uminus #d fragments), with about 2.13
electrons unaccounted for (~15% non-Lewis occupancy), symp-
tomatic of general breakdown of the conventional Lewis
structure representation.
0 However, when the NBO search is extended to 3-center bonds
by activating the 3CBOND keyword, one obtains the NBO output
shown below:
/3CBOND / : Search for 3-center bonds
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 15.94335 0.05665 2 4 2 0
0 0 0.15
2(2) 1.90 15.94335 0.05665 2 4 2 0
0 0 0.15 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
WARNING: 1 low occupancy (<1.9990e) core orbital found on
B 1
1 low occupancy (<1.9990e) core orbital found on
B 2
--------------------------------------------------------
Core 3.99702 ( 99.925% of 4)
Valence Lewis 11.94633 ( 99.553% of 12)
================== ============================
Total Lewis 15.94335 ( 99.646% of 16)
July 11, 1995
- 71 -
-----------------------------------------------------
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
July 11, 1995
- 72 -
-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%)
July 11, 1995
- 73 -
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%)
July 11, 1995
- 74 -
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
July 11, 1995
- 75 -
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
#T
@seg
#N
0 The resulting NBO Lewis structure has improved signifi-
cantly [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 interac-
tions. 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 illus-
trates the kind of #Iqualitative#N improvement that indi-
cates when 3-center bonds are needed in the zeroth-order
picture of the bonding.
0 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.' #IB.6.9
NBO Directed Search ($CHOOSE Keylist)#N
0 To illustrate the $CHOOSE keylist for a directed NBO
search, we again make use of the methylamine example (Sec-
tion A.3). The vicinal #In#N#dN#u arr gma *#<#dCH#u delo-
calization, 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:
W10R'#-0hsp H#d4#u#+hsp '//
D11R'H#d5#u'//BD3'N#d2#u#<#+#++#-#-
July 11, 1995
- 76 -
'//W5R'H#d6#u'//D4R'H#d7#u'>>
nobond
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:
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
July 11, 1995
- 77 -
-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
July 11, 1995
- 78 -
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%)
July 11, 1995
- 79 -
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
July 11, 1995
- 80 -
-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
#T
@seg
#N
0 One can see that the $CHOOSE resonance structure is signi-
ficantly 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 $CHOOSE structure (compared to 0.05e, or 0.3%, for the
principal structure). Particularly defective is the hydride
`lone pair' (NBO 9), which has less than half the expected
occupancy (0.81453e). The C-N i
bond (NBO 1) is seen to be more than 92% polarized toward N,
indicative of essential lone pair character.
0 Note that structural elements shared by the two resonance
structures (e.g., the two N-H bonds, which are common to
both structures) need not have identical forms, since each
detail of the NBOs is optimized with respect to the overall
structure. #IB.6.10 NBO Energetic Analysis ($DEL Keylist)#N
0 The NBO energetic analysis with deletions ($DEL keylist)
will be illustrated with two simple examples for RHF/3-21G
methylamine (Section A.3).
0 The first example is the ``NOSTAR'' option (type 4, Sec-
tion B.5), requesting deletion of all non-Lewis orbitals,
July 11, 1995
- 81 -
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:
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
July 11, 1995
- 82 -
-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
#T
@seg
#N
0 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 occu-
pancy 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.
0 The next example is a more selective set of deletions
between `chemical fragments' (type 9), selected by the $DEL
July 11, 1995
- 83 -
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:
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
July 11, 1995
- 84 -
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
#T
July 11, 1995
- 85 -
@seg
#N
0 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 gma *#<#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 delo-
calization energy) associated with this deletion was 27.9
kcal/mol.
0 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 arr gma *#<#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 arr gma *#<#dC#d1#uH#d3#u#u
(9 arr 24) interaction that was noted in Section A.3.5.]
#IB.6.11 Open-Shell UHF Output: Methyl Radical#N
0 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 = 1.0736hsp ngstrom ). In
the open-shell case, one obtains two separate NPA and NBO
listings, one for the lpha and one for the s t,
corresponding to the ``different Lewis structures for dif-
ferent spins'' description. A portion of the NBO output for
the lpha spin manifold is reproduced below:
NATURAL BOND ORBITAL ANALYSIS, alpha spin orbitals:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 0.90 4.99903 0.00097 1 3 0 1
0 0 0.00 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
--------------------------------------------------------
Core 0.99984 ( 99.984% of 1)
July 11, 1995
- 86 -
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
July 11, 1995
- 87 -
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(
July 11, 1995
- 88 -
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
#T
@seg
#N
0 As can be seen in the output, the NBO spin-orbital occu-
pancy threshold was set at 0.90 (rather than 1.90), and the
occupancies of lpha 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 gma
#dCH#u bond hybrids (NBOs 1-3), whereas the out-of-plane
radical non-bonded orbital (NBO 5) has pure #Ip#N-character.
0 The NBO output for the z d') spin set then follows:
NATURAL BOND ORBITAL ANALYSIS, beta spin orbitals:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 0.90 3.99981 0.00019 1 3 0 0
0 0 0.00 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
--------------------------------------------------------
Core 0.99985 ( 99.985% of 1)
Valence Lewis 2.99996 ( 99.999% of 3)
================== ============================
Total Lewis 3.99981 ( 99.995% of 4)
-----------------------------------------------------
Valence non-Lewis 0.00002 ( 0.000% of 4)
Rydberg non-Lewis 0.00017 ( 0.004% of 4)
================== ============================
Total non-Lewis 0.00019 ( 0.005% of 4) -----
---------------------------------------------------
July 11, 1995
- 89 -
(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
July 11, 1995
- 90 -
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%)
#T
@seg
#N
0 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 gma #dCH#u bonds is somewhat altered
(about 55.8% on the C atom in the s t set, #Ivs.#N 61.1% in
the lpha set). [In other cases, the lpha and L wis
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.
|<<__________________________
#-#BWARNING#N#+
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 lpha and h ir total populations
are calculated correctly from the spinless density matrix,
July 11, 1995
- 91 -
NBOs
and NLMOs are not. NBO analysis of an open-shell spinless
density matrix is a fundamental misuse of the program.
#IB.6.12 Effective Core Potential: Cu#d2#u Dimer#N
0 To illustrate some of the variations of NBO output associ-
ated with use of effective core potentials (ECP) and inclu-
sion of #Id#N orbitals, we use the example of the copper
dimer Cu#d2#u (#IR#N = 2.2195hsp ngstrom ), 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.
0 Use of an ECP shows up most directly in the NPA portion of
the output, shown below:
NATURAL POPULATIONS: Natural atomic orbital occupancies
NAO Atom # lang Type(AO) Occupancy Energy -----
----------------------------------------------------
1 Cu 1 s Val( 4s) 0.94240 -0.26321
2 Cu 1 s Ryd( 5s) 0.00019 0.92165
3 Cu 1 px Ryd( 4p) 0.99604 -0.06989
4 Cu 1 px Ryd( 5p) 0.00001 0.09916
5 Cu 1 py Ryd( 4p) 0.99604 -0.06989
6 Cu 1 py Ryd( 5p) 0.00001 0.09916
7 Cu 1 pz Ryd( 5p) 0.05481 1.09062
8 Cu 1 pz Ryd( 4p) 0.00062 0.52821
9 Cu 1 dxy Val( 3d) 0.00000 -0.36077
10 Cu 1 dxy Ryd( 4d) 0.00000 0.72280
11 Cu 1 dxz Val( 3d) 1.99997 -1.29316
12 Cu 1 dxz Ryd( 4d) 0.00398 0.75681
13 Cu 1 dyz Val( 3d) 1.99997 -1.29316
14 Cu 1 dyz Ryd( 4d) 0.00398 0.75681
15 Cu 1 dx2y2 Val( 3d) 1.99939 -1.38791
16 Cu 1 dx2y2 Ryd( 4d) 0.00061 0.67825
17 Cu 1 dz2 Val( 3d) 1.99890 -1.26114
18 Cu 1 dz2 Ryd( 4d) 0.00308 1.16392
19 Cu 2 s Val( 4s) 0.94240 -0.26321
20 Cu 2 s Ryd( 5s) 0.00019 0.92165
21 Cu 2 px Ryd( 4p) 0.99604 -0.06989
22 Cu 2 px Ryd( 5p) 0.00001 0.09916
23 Cu 2 py Ryd( 4p) 0.99604 -0.06989
24 Cu 2 py Ryd( 5p) 0.00001 0.09916
25 Cu 2 pz Ryd( 5p) 0.05481 1.09062
26 Cu 2 pz Ryd( 4p) 0.00062 0.52821
27 Cu 2 dxy Val( 3d) 0.00000 -0.36077
28 Cu 2 dxy Ryd( 4d) 0.00000 0.72280
29 Cu 2 dxz Val( 3d) 1.99997 -1.29316
30 Cu 2 dxz Ryd( 4d) 0.00398 0.75681
July 11, 1995
- 92 -
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)
#T
@seg
#N
0 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,
July 11, 1995
- 93 -
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 accor-
dance 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.]
0 The main ECP effect in the NBO portion of the
output is the omission of core NBOs, as illus-
trated below:
NATURAL BOND ORBITAL ANALYSIS:
Occupancies Lewis Structure
Low High
Occ. ------------------- -----------------
occ occ
Cycle Thresh. Lewis Non-Lewis CR BD 3C LP
(L) (NL) Dev
=============================================================================
1(1) 1.90 57.99970 0.00030 0 3 0 8
0 0 0.00 ----------
-------------------------------------------------------------------
Structure accepted: No low occupancy Lewis orbitals
--------------------------------------------------------
Effective Core 36.00000
Valence Lewis 21.99970 ( 99.999% of 22)
================== ============================
Total Lewis 57.99970 ( 99.999% of 58)
-----------------------------------------------------
Valence non-Lewis 0.00000 ( 0.000% of 58)
Rydberg non-Lewis 0.00030 ( 0.001% of 58)
================== ============================
Total non-Lewis 0.00030 ( 0.001% of 58) -----
---------------------------------------------------
(Occupancy) Bond orbital/ Coefficients/ Hybrids -----
-----
---------------------------------------------------------------------
1. (2.00000) BD ( 1)Cu 1-Cu 2
( 50.00%) 0.7071*Cu 1 s( 94.13%)p 0.06(
5.54%)d 0.00( 0.33%)
0.9702 -0.0003
0.0000 0.0000 0.0000
July 11, 1995
- 94 -
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
July 11, 1995
- 95 -
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
July 11, 1995
- 96 -
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%)
July 11, 1995
- 97 -
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%)
July 11, 1995
- 98 -
Natural Bond Orbitals (Summary):
Princi-
pal 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
#T
July 11, 1995
- 99 -
@seg
#N
0 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.
0 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 gma #dCuCu#u bond (NBO 1) and the two i
#dCuCu#u bonds (NBOs 2, 3) have very slight admixtures (<
0.4%) of #Id#N character. The remaining orbitals of predom-
inant #Id#N character (NBOs 17-22 and 28-33) are of negligi-
ble occupancy. Note that the abbreviated ``#Isp#u #dd#umu
#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
#dd#umu #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 #dd#umu #d#N designa-
tion.
#BB.7 FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO
PROGRAM#N
#IB.7.1 Introduction#N
0 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.
0 Some knowledge of FILE47 is useful even if your NBO pro-
gram 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 subse-
quently 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
July 11, 1995
- 100 -
would
require access to the formatted one- and two-electron
integrals of the parent ESS package.]
0 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 pro-
gram directly to your ESS package by writing your own driver
routines. See the Programmer's Guide, Section C.13, for
direction.
0 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. #IB.7.2
Format of the FILE47 Input File#N
0 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, $CON-
TRACT, $DIPOLE) or the standard NBO keylists ($NBO, $CORE,
$CHOOSE) are optional, depending on the requested applica-
tion. If the $NBO keylist is not present in FILE47, the
default NBO analysis is performed.
0 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:
$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
July 11, 1995
- 101 -
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
July 11, 1995
- 102 -
$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
#T
@seg
#N
The nine lists of FILE47 are described in turn in the fol-
lowing sections, making use of this example for illustra-
tion. #IB.7.3 $GENNBO Keylist#N
0 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:
#IOPTION DESCRIPTION#N
Instructs GENNBO to reuse an old NBO direct-access file,
FILE48, rather than create a new FILE48 from the wavefunc-
tion 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.
Number of atoms in the molecule (required).
Number of basis functions (required).
Designates an open shell wavefunction. GENNBO will subse-
quently read in alpha and beta density, Fock, and MO coeffi-
cient matrices.
Indicates that the AO basis set is orthogonal (basis func-
tions 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,
July 11, 1995
- 103 -
AOPNHO,
AOPNBO, AOPNLMO).
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.
Indicates that the $DENSITY datalist contains the bond-order
matrix (``Fock-Dirac density matrix'') rather than the den-
sity matrix (i.e., matrix elements of the density operator).
(In orthogonal AO basis sets, the bond-order matrix and den-
sity matrix are identical, but in nonorthogonal basis sets
they must be distinguished.) By default, GENNBO assumes
this data#|list contains the density matrix elements. If
``BODM'' is included, the datalist elements are transformed
with the AO overlap matrix to produce the true density
matrix.
Indicates that the atomic coordinates ($COORD) and the
dipole integrals ($DIPOLE) are in atomic units, rather than
the default angstroms.
Indicates that the Fock matrix elements ($FOCK) have units
of electron volts (eV), rather than the default atomic units
(Hartrees).
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).
The methylamine sample $GENNBO keylist specifies 7 atoms, 28
basis functions, upper triangular matrix input, and $DENSITY
datalist containing the bond-order matrix. #IB.7.4 $COORD
Datalist#N
0 The $COORD datalist (required, unless REUSE is specified
in $GENNBO) contains the job title and information indicat-
ing the identity and coordinates of each atom, including
missing core electrons or effective core potentials.
0 The first line following the $COORD identifier is an arbi-
trary job title, up to 80 characters.
0 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
July 11, 1995
- 104 -
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. #IB.7.5 $BASIS Datalist#N
0 The $BASIS datalist (required, unless REUSE is specified
in $GENNBO) provides essential information about the AO
basis functions, specifying the atomic center and the angu-
lar symmetry ( , x
,
y , z
, etc.) of each AO. This information is contained in two
arrays in this datalist called CENTER and LABEL.
0 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.]
0 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 (= 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 + #Ik#N + #Im#N,
where #Ik#N is 0 (cartesian) or 50 (pure), and #Im#N is a
particular component of the symmetry (see table below). For
#Is#N or #Ip#N AOs, the cartesian and pure sets are identi-
cal, 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.
July 11, 1995
- 105 -
0 The labels associated with each allowed AO function type
are tabulated below, where #Ix, y, z#N refer to the speci-
fied cartesian axis system:
#_Pure #If#N ``cubic'' set:#/>> 351//#If#N(D1):
x(5x#u2#dminus 3r#u2#d)>> 352//#If#N(D2): y(5y#u2#dminus
3r#u2#d)>> 353//#If#N(D3): z(5z#u2#dminus 3r#u2#d)>>
354//#If#N(B): xyz>> 355//#If#N(E1): x(z#u2#dminus
y#u2#d)>> 356//#If#N(E2): y(z#u2#dminus x#u2#d)>>
357//#If#N(E3): z(x#u2#dminus y#u2#d)>> 356//#If#N(c3):
x(x#u2#dminus 3y#u2#d)>> 357//#If#N(s3): y(3x#u2#dminus
y#u2#d)>>
[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 , , x
, y
, z
,
, x
, y
, z
type, respectively.] #IB.7.6 $CONTRACT Datalist#N
0 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 for-
mat for orbital plotting with the ORBPLOT program. Omit the
$CONTRACT datalist if you do not intend to make orbital
plots.
0 Two integers must be initially given: NSHELL (the number
of shells of basis functions) and NEXP (the number of orbi-
tal 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.
0 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 func-
tions. 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
July 11, 1995
- 106 -
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.]
0 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.]
0 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, respec-
tively.]
0 EXP, CS, CP, CD, and CF are free format, real arrays con-
taining the orbital exponents, and the s, p, d, and f con-
traction 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.]
0 The information in the $CONTRACT datalist along with that
in the $BASIS datalist is enough to completely determine the
AO basis set. [For example, the second shell on the methy-
lamine sample contains 4 basis functions (NCOMP). These are
#Is#N, #Ip#N#dx#u, #Ip#N#dy#u, and #Ip#N#dz#u orbitals
(LABEL), all centered on atom 1 (CENTER), and each basis
function is a contraction of two primitive gaussians
(NPRIM). From NPTR, EXP, CS, and CP, we find the explicit
form of these functions:
hi #ds#u(#Br#N) hsp = hsp +
hi #dp#dx#u#u(#Br#N) = 1
+ 2
hi #dp#dy#u#u(#Br#N) = 3
+ 4
hi #dp#dz#u#u(#Br#N) = 5
+ 6
July 11, 1995
- 107 -
where #Br#N=(x,y,z) is measured in bohr units relative to
the cartesian coordinates of atom 1.] #IB.7.7 Matrix
Datalists#N
0 The remaining datalists ($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.
0 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 $NBO keywords that require each datalist to
be included in FILE47:
#I$NBO Keywords Requiring the Datalist#N
SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, AOPNHO, AOPNBO,
AOPNLMO
E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO
AOMO, NAOMO, NHOMO, NBOMO, NLMOMO
DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE
AOINFO, PLOT
0 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, $DEN-
SITY, and $FOCK data#|lists used for default PRINT=2
analysis), but the $DIPOLE data#|list might have been omit-
ted 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.
July 11, 1995
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#HSection C: NBO PROGRAMMER'S GUIDE#N
#BC.1 INTRODUCTION#N
0 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 familiar-
ity with published algorithms for NAO/NBO/NLMO determina-
tion. This section is intended for the accomplished pro-
grammer who wishes to inquire into the details of the NBO
numerical methods and find the specific source code associ-
ated with individual steps of the published NAO/NBO/NLMO
algorithms or segments of NBO output.
0 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 subrou-
tine or function, and should be consulted on questions per-
taining to individual subprograms.
0 In this Programmer's Guide, we focus on global aspects of
program organization and data structure. Individual subpro-
grams (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 associa-
tion 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 indivi-
dual subprograms, we use the abbreviation ``SR'' for ``sub-
routine'' and ``FN'' for ``function''.
0 Sections C.2-C.4 describe the overall NBO.SRC source lay-
out, labelled COMMON blocks, and I/O structures (including
the FILE48 direct access file). Sections C.5-C.11 then fol-
low the layout of the source code in describing the princi-
pal groupings of subprograms, with a brief description of
each subprogram. Section C.12 similarly describes subpro-
grams 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.
#BC.2 OVERVIEW OF NBO SOURCE PROGRAM GROUPS#N
0 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:
July 11, 1995
- 109 -
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 secon-
dary 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.
0 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.
0 A general overview of the subprograms of Groups I and II
is shown in the accompanying flow chart, indicating the log-
ical relationship of the routines to be discussed in Sec-
tions 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.
#HNBO Flow Chart for Group I, II Subprograms#N
|<<__________________________ #T
|<<___ __
RUNNBO
I II
|<<___ __ |<<___ __
NBO NBOEAN
|<<___ __ |<<___ __ |<<___ __ |<<___ __
(init.) NAODRV NBODRV NBODEL,DELETE,
NBOSET (& simulation) NEWDM,RNKEIG,
July 11, 1995
- 110 -
JOBOPT SIMTRN
NBODIM
|<<___ __ |<<___ __ |<<___ __ |<<___ __ |<<___ __ |<<___ __
(prepare) NAO NAOANL NATHYB NLMO DIPANL
SIMTRM (CHSDRV,
MULANA CHOOSE)
DFGORB
|<<___ __ |<<___ __ |<<___ __ |<<___ __
(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
#BC.3 LABELLED COMMON BLOCKS#N
0 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 pro-
vided 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 diffi-
culty in #Idecreasing#N either of these values, or in
increasing MAXBAS (up to 999). However, the program cannot
July 11, 1995
- 111 -
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:
The INTEGER variables of this block store general informa-
tion related to basis set dimensionality, spin manifold,
number of atoms, and energy units:
The LOGICAL variables of this block are set .TRUE. or
.FALSE. depending on whether the ``condition'' (type of
wavefunction, spin set, etc.) is satisfied:
Note (Section B.6.11) that both lpha and d nsity matrices
should be available if OPEN is set `.TRUE.' for the open-
shell case.
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:
The keyword associated with each element I=1-54 of the
JPRINT array is shown below (55-60 are not currently used):
In general, if the flag is set to zero, its associated key-
word 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 follow-
ing scheme:
July 11, 1995
- 112 -
The INTEGER arrays of this block store information on the
atomic centers and angular symmetry of each AO:
The INTEGER arrays of this block store information about the
orbitals on each atomic center:
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 con-
tents of the file associated with each LFN (cf. Section
B.2.4):
The remaining `secondary' COMMON blocks 7-18 contain vari-
ables 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.
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!):
The DOUBLE PRECISION variables of this block store the
default values of various numerical thresh#|olds that can be
set by the user:
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
July 11, 1995
- 113 -
localized
orbital labels (AO, NAO, NHO, NBO):
The INTEGER arrays of this block store information pertain-
ing to the labelling of NAOs in the NPA output:
The INTEGER scalars, vectors, and arrays of this block store
information pertaining to ``molecular units'':
The INTEGER variables of this block contain atom search
lists to direct the search for NBOs and information pertain-
ing to the `topology' (bond connectivity) of the molecule:
The DOUBLE PRECISION variables of this block store informa-
tion pertaining to the molecular dipole moment and charge
distribution:
The INTEGER variables of this block store general informa-
tion related to the `card image' (line) being processed by
the free-format input routines:
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:
The INTEGER variables of this block store information
related to the NBO direct access file (FILE48). The PARAME-
TER statement
#T
July 11, 1995
- 114 -
PARAMETER (NBDAR = 100)
#Nsets the maximum number of logical records accessible in
FILE48:
The INTEGER variables of this block provide scratch storage
for writing to the NBO direct access file (FILE48). The
PARAMETER statement
#T
PARAMETER (ISINGL = 2, LENGTH = 256)
#Nsets the FILE48 physical record LENGTH to 256 longwords
(1024 bytes):
The LOGICAL variables of this block store information
related to running the GENNBO program in stand-alone mode.
In each case, the variable is set .TRUE. if the specified
condition is met:
#BC.4 DIRECT ACCESS FILE AND OTHER I/O#N
0 The principal I/O routines of Groups III-V are described
in Sections C.7-C.9. The #Iinput#N to the NBO programs is
primarily from the standard ESS input file (LFN 5), and the
#Ioutput#N is primarily to the standard ESS output file (LFN
6). Other ``matrix output'' (read/write) I/O is by default
assigned to LFNs 31-49 (see Table of Section B.2.4), or to a
user-selectable LFN, based on keyword entries in the $NBO
keylist.
0 The remaining two files that are routinely created or
modified by the NBO programs are the FILE48 direct access
file (LFN 48) and the FILE47 `archive' file (LFN 47,
described in Section B.7). The latter file can also serve
as the main input file (reassigned as LFN 5) when the NBO
program is run in stand-alone GENNBO mode.
0 From the programmer's viewpoint, the most important infor-
mation concerns the organization of the FILE48 direct access
file. The records of this file are assigned as shown in the
following table. The items marked with an asterisk (*) must
be provided from the ESS program (e.g., through the FEAOIN
driver), and hence are of particular importance to the pro-
grammer:
July 11, 1995
- 115 -
[Cartesian coordinates (record 9) and dipole integrals
(records 50-52) should be in angstrom units.]
0 The direct access file serves as a principal medium of
communication between all segments of the NBO program.
Input received from the ESS program (Section C.11) is
immediately saved in the direct access file and subsequently
fetched by other subprograms, using the fetch/save I/O rou-
tines of Section C.7. Further information on the structure
of the direct access file is specified in COMMON blocks 16,
17 of Section C.3.
#BC.5 NAO/NBO/NLMO ROUTINES (GROUP I)#N
#IC.5.1 SR NBO Master Subroutine#N
0 The subroutine of highest precedence in the core NBO pro-
gram is SR NBO. This routine initially requests that the
input file be searched for the $NBO keylist (See NBOINP,
Section C.9). If found, SR NBO continues by calling three
main clusters of programs, as shown below:
|<<_________________________ |<<__________________________
|<<__________________________ |<<__________________________
#TV+30 SR NBO(CORE,MEMORY,NBOOPT)#N
In addition, SR NBO creates a new NBO direct access file
(DAF) each time it is called, and closes this file upon com-
pletion (See NBOPEN and NBCLOS, Section C.9).
0 SR NBO is provided a memory vector, CORE, which is
`MEMORY' double precision words in length. For modest-sized
calculations (e.g. 10 heavy atoms with a double-zeta basis
set), a vector of 50,000 words should be adequate. Although
SR NBO performs an initial partitioning of this memory vec-
tor, the majority of the dynamic memory allocation occurs in
the NAO and NBO/NLMO formation routines, described in Sec-
tions C.5.3 and C.5.4.
0 An array of job options, NBOOPT(10), is also passed to SR
NBO. These job options identify the current version of the
NBO program (i.e., the identity of the ESS calling program),
control program input and execution, and determine several
July 11, 1995
- 116 -
of
the default options of the NBO analysis, as summarized in
the following table. [Entries marked with an asterisk (*)
contain information pertaining to the identity or job
options of the calling ESS program, and thus are of special
concern to the programmer.]
#IDESCRIPTION#N
Do nothing (return control to calling program) Perform
Natural Population Analysis (NPA) only Perform NPA/NBO/NLMO
analyses, normal program run Perform NPA/NBO/NLMO analyses,
don't read $NBO keylist Initiate energetic analysis, read
one deletion from $DEL Complete energetic analysis, print
the energy change
SCF density MP first order density MP2 density MP3 density
MP4 density CI one-particle density CI density QCI/CC den-
sity Density correct to second order
Perform the NBO/NLMO dipole analysis (force the DIPOLE key-
word)
Allow strongly delocalized Lewis structures (force the RESO-
NANCE keyword)
Spin-annihilated UHF (AUHF) wavefunction (unused)
(unused)
General version of the NBO program (GENNBO) AMPAC version
GAMESS version HONDO version GAUSSIAN-8x version
These options are read by job initialization routines (Sec-
tion C.5.2) and stored in COMMON/NBOPT/, where they control
events throughout the program. [Note that NBOOPT(2) is only
used by the Gaussian versions.]
#IC.5.2 Job Initialization Routines#N
0 The routines of this section initialize the default
options and parameters, read and store the user's $NBO key-
word options:
This routine sets default option flags (COMMON/NBOPT/),
default logical file numbers (COMMON/NBIO/), and default
thresholds (COMMON/NBTHR/) for the NBO program. In addi-
tion, SR NBOSET interprets the NBOOPT array, setting option
flags appropriately.
July 11, 1995
- 117 -
This routine is primarily responsible for reading and set-
ting option flags (COMMON/NBOPT/) according to the keywords
specified in the $NBO keylist. It reads the $NBO keywords
using the free format routines described in Section C.8,
continuing until the word ``$END'' terminates the keylist.
Options which are incompatible with the chosen wavefunction
or program version are `shut off', and other options are
`turned on' in accord with the requested print level ($NBO
keyword PRINT). All keywords which are selected in the $NBO
keylist are echoed in the output file.
Determines the scratch memory requirements of the NBO pro-
gram, as determined by the options selected in the $NBO
keylist. Program execution halts if the memory requirements
exceed the available memory.
#IC.5.3 NAO Formation Routines#N
0 The principal task of this cluster of routines is to con-
trol the formation of the NAOs from the input AO basis. In
addition, these routines are responsible for the writing (to
an external file) or printing (to the output file) of a
variety of matrices in the AO, PNAO, and NAO basis sets,
according to job options requested in the $NBO keylist. The
first set of routines are called by SR NBO:
This is the principal controller routine for non-orthogonal
basis sets. The scratch vector A is partitioned within this
routine according to the memory requirements of the NAO sub-
programs.
This routine `simulates' SR NAODRV in the case of a semi-
empirical calculation, where the (orthonormal) basis AOs are
the presumed effective valence shell atomic orbitals, and no
NAO transformation is needed.
Performs the transformation and analysis of the open-shell
AO density matrix (alpha or beta spin) to the NAO basis.
This routine employs the AO to NAO transformation, T, deter-
mined by SR NAODRV:
Simulates SR DMNAO for the open-shell semi-empirical case,
when no transformation is required.
Principal driver program for NBO formation; Section C.5.4.
The next set of routines are called by the main NAO driver,
July 11, 1995
- 118 -
SR
NAODRV. They include the principal subroutine, SR NAO,
which generates the NAOs:
Performs the similarity transformation S#ut#d*A*S leading to
Mulliken populations, with S = overlap matrix, A = bond-
order matrix.
Evaluates Mulliken gross populations and performs Mayer-
Mulliken bond-order analysis (requires bond order matrix).
Performs the decomposition of `raw' cartesian #Id#N, #If#N,
or #Ig#N AO sets to pure angular symmetry AOs (e.g., 6
cartesian #Id#N arr 5 pure #Id#N + 1 #Is#N); cf. Section
B.7.5.
This is the principal routine for formation of NAOs, follow-
ing closely the algorithm described by A. E. Reed, R. B.
Weinstock, and F. Weinhold, #IJ. Chem. Phys. #B83#N, 735-746
(1985).
This is the principal routine for performing and printing
out natural population analysis (NPA). The routine assigns
orbital labels and energies and writes out the NPA, natural
electron configuration (NEC), NAO-Wiberg bond index and
overlap-weighted bond population tables. [Thresholds TEST,
TEST2, ALLOW, ALLOW2 test for numerical conservation of an
integer number of electrons.]
Forms and outputs NCOL columns of the transformation matrix
to MOs from a chosen localized set, specified by INDEX = 2
(NAO), 3 (NHO), 4 (NBO), or 5 (NLMO). Input matrix T is the
transformation from AOs to the basis set specified by INDEX,
and matrices TMO, C, and SCR are scratch arrays employed by
this routine.
#NThe remaining routines of this section are auxiliary sub-
routines called by SR NAO to perform individual steps of the
NAO algorithm:
Averages the AO density matrix elements over the 2+ 1 com-
ponents of for a particular atom, and loads the density
matrix and overlap integrals for the orbitals of LISTAO into
matrices A, B, respectively.
Solves the generalized eigenvalue problem (A minus
July 11, 1995
- 119 -
EVAL*B)*C
= 0 to diagonalize an atomic block.
Selects the `occupied' NAOs to be included in the natural
minimal basis set for a particular atom (up to Z = 105) and
angular momentum symmetry type (L), and stores them in
LSTOCC.
Recomputes symmetry-averaged occupancy weights for PNAOs.
This routine is only used in conjunction with the
`PAOPNAO=R' keyword.
This subroutine implements the occupancy-weighted symmetric
orthogonalization (OWSO), a key feature of the NAO algo-
rithm. [Note that BLK and BIGBLK share the same storage
area, though they are dimensioned differently. The routine
includes three numerical thresholds, WTTHR (10#uminus 3#d)
for occupancy weight, DIAGTH (10#uminus 12#d) for Jacobi
diagonalization, and DANGER (10#u3#d) for linear dependence
difficulties.]
Schmidt orthogonalization of column vectors of T.
#NComputes new Rydberg NAOs after Schmidt orthogonalization
of the Rydberg space to the NMB set.
#NDiagonalizes an atomic Rydberg block and updates the PNAO
transformation matrix.
Partitions Rydbergs into `significantly occupied' (> WTTHR)
and `negligibly occupied' (ts, assigning the latter to have
equal (non-zero) occupancy weighting. This avoids numerical
singularities associated with the OWSO occupancy weighting
for orbitals of negligible occupancy, effectively replacing
OWSO by ordinary L mlaut owdin-orthog#|onalization of these
`residual' Rydbergs among themselves. [Threshold WTTHR
(10#uminus 4#d) controls singularities of the inverse
square-root weighting matrix.]
Rediagonalizes the atomic density matrix blocks after sym-
metry averaging.
Finds the rediagonalization transformation for a specific
atomic subblock of the density matrix.
July 11, 1995
- 120 -
#IC.5.4 NBO/NLMO Formation Routines#N
0 The master routine of this cluster is SRhsp hsp
NBODRV(DM,T,A), which partitions the scratch storage vector
(A) according to the memory requirements of the NBO forma-
tion and analysis subprograms and controls the calculation
of the transformation (T) from NAOs to NBOs using the NAO
density matrix (DM). SR NBODRV calls either SR NATHYB (for
the default NBO search) or SR CHSDRV (for the $CHOOSE
directed NBO search) to form the NBOs. It also calls the
NLMO formation routine (SR NLMO) and dipole analysis routine
(SR DIPANL). According to job options selected in the $NBO
keylist, SR NBODRV also transforms and outputs a variety of
matrices in the PNHO, NHO, PNBO, NBO, PNLMO, and NLMO basis
sets. [Note that the first NATOMS*NATOMS elements of the A
vector store the Wiberg bond index elements determined in
the NAO routines; these should not be destroyed until calcu-
lation of NBOs is complete.]
0 The following routines are called by SR NBODRV:
#NThis routine performs the basic NBO search, the central
task of NBO analysis, closely following the description
given by J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc.
#B102#N, 7211-7218 (1980). The routine constructs the
orthogonal matrix (T) for the NAO to NBO transformation from
the input NAO density matrix (DM). The efficiency of the
search procedure is enhanced by using the NAO-Wiberg bond
index as a `GUIDE' to order the NBO search.
[Beware the IBXM bond orbital permutation list (!), which
reorders the LABEL array of COMMON/NBBAS/. The occupancy
threshold, THRESH, determines whether an NBO is accepted
during the search for bond orbitals (cf. SR CYCLES). Two
numerical thresholds (PRJTHR, PRJINC) control possible
linear dependencies: In the main loops over 1-c, 2-c (and
3-c) functions, each prospective NBO is checked for possible
redundancy with previous NHOs by the PRJEXP (projection
operator expectation value) test. The threshold PRJTHR for
a `new' hybrid is initially set conservatively low (0.20),
but will be auto-incremented by PRJINC (0.05) as needed to
prevent linear dependency; any numerical singularity
triggers IALARM and causes PRJTHR to be incremented and the
entire NBO search repeated.]
#NThis routine, the ``$CHOOSE driver,'' reads the $CHOOSE
keylist, setting up the arrays NTOPO and I3CTR of
COMMON/NBTOPO/ which will control the directed NBO search of
SR CHOOSE.
July 11, 1995
- 121 -
#NThis routine is essentially similar to SR NATHYB, but the
search loops are directed by the $CHOOSE specification.
Reorders (dangerous!) the NBOs according to bond type and
constituent atomic centers. NBOs are ordered BD (and 3C),
CR, LP, LP*, RY*, BD* (and 3C*). Note that this step is not
required for the proper execution of any of the NBO analysis
or NLMO formation routines, but it leads to more readable
output.
Examines PNHO overlaps to determine whether NBOs were prop-
erly labelled as `bonds' (unstarred, Lewis) or `antibonds'
(starred, non-Lewis) in the NBO formation routines (SR
NATHYB and SR CHOOSE). If incorrect nodal character is
recognized in a bond or antibond (generally indicative of an
excited state), a warning is printed and the orbital is
relabelled. Note that this will probably mix the NBO order-
ing set by SR SRTNBO.
Prints out the principal table (Section A.3.3) of NBO
analysis [using the IBXM ordering!], expressing each NHO in
#Isp#u #d#N form.
Analyzes input hybrid for polarization coefficient and per-
centages of each angular momentum component (accepts up to
#Ig#N orbitals).
Forms the NAO to NHO transformation (THYB) and saves it on
the DAF.
Computes hybrid directionality and bond bending angles as
determined from percentage #Ip#N-character for selected
NBOs, and prints the BEND table (Section A.3.4). [Keyword-
selectable thresh#|olds ATHR (angular deviation), PTHR (%
#Ip#N-character), and ETHR (occupancy) control printing.]
Finds direction and percentage #Ip#N-character of a given
hybrid.
Finds `molecular units' from NBO connectivity.
Classifies NBOs according to donor/acceptor type, number of
atomic centers, and parent molecular unit.
July 11, 1995
- 122 -
Performs the 2nd-order perturbation theory energy analysis
of the NBO Fock matrix and prints the table (Section A.3.5).
[Thresholds ETHR1 (intramolecular) and ETHR2 (intermolecu-
lar) control printing.]
Prepares and prints the NBO summary table (Section A.3.6).
Assembles the delocalization list, LIST(NL), for the
IBO#uth#d NBO. Only intramolecular and intermolecular delo-
calizations which are stronger than THR1 and THR2 (in
kcalhsp mol#uminus 1#d), respectively, are included in the
list.
Builds a character string containing delocalization informa-
tion for the NBO summary table.
This is the main routine for determination of the NLMOs,
following closely the description given by A. E. Reed and F.
Weinhold, #IJ. Chem. Phys. #B83#N, 1736-1740 (1985).
[Numerical thresholds DIFFER (10#uminus 5#d), DONE
(10#uminus 10#d), and EPS (10#uminus 11#d) control the modi-
fied Jacobi diagonalizations.]
#NPrints out details of the NAO arr NLMO transformation and
the NAO/NLMO bond order table (Section B.6.2).
Calculates and prints out the DIPOLE analysis table (Section
B.6.3).
Evaluates the #Ix,y,z#N (INDEX = 1,2,3) electronic dipole
moment contributions, including delocalization contribu-
tions, for each occupied NBO.
Evaluates the nuclear contributions (DX, DY, DZ) to the
molecular dipole moment.
The following routines are called by SR NATHYB and SR CHOOSE
in calculating the NBOs. Overall supervision of this set of
routines is exercised by SR CYCLES. Other routines are
associated with specific steps of the NBO algorithm:
Performs the first step in the search for NBOs. This rou-
tine identifies core orbitals and depletes the NAO density
matrix of their contributions.
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This function returns zero (no projection wanted) if still
on the same atomic center, or one (projection operator
should be formed) if this is a new center.
`Depletes' density matrix of contribution from bond orbital
(BORB), by subtracting its diagonal contribution from the
spectral expansion of the density operator. This insures
that the same electron pair will not be found twice in the
NBO loops.
Loads the appropriate atomic blocks of the density matrix
into the local (2-c, 3-c) density matrix subblock (BLK), in
preparation for diagonalization.
Determines how much of a prospective bond orbital (BORB) is
composed of hybrids already used. The projection operator
onto the space of previously accepted hybrids is used to
evaluate the expectation value of each hybrid component of
BORB.
Decomposes bond orbital (BORB) into constituent normalized
hybrids and stores them in the hybrid array (Q).
Performs symmetric (L mlaut owdin) orthogonalization on occu-
pied atomic hybrids (PNHOs) to give final NHOs. [Threshold
TOOSML (10#uminus 4#d) turns on the alarm (IALARM) to warn
of numerical instabilities due to linear dependence.]
Forms projection matrix to annihilate components of the
occupied atomic hybrids on a given center.
This routine augments the set of occupied atomic hybrids on
a center with a sufficient number of Rydberg AOs (in order
of occupancy) to complete the span of the basis set on that
atom.
Diagonalizes each 2x2 block of the density matrix in the
basis of final NHOs to get the optimal polarization coeffi-
cients for each NBO.
Constructs the final NAO to NBO transformation matrix (T)
from the final array of NHOs (Q) and polarization coeffi-
cients (POL).
July 11, 1995
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Controls the overall search for an acceptable resonance
structure, including the lowering of the occupancy threshold
(THRESH) for the RESONANCE keyword. Decides whether a
structure is acceptable, initiates reordered searches over
atoms for alternative resonance structures, and returns with
the best overall structure. Prints the initial table (Sec-
tion A.3.3) of the NBO output.
The final routines of this group are auxiliary to the forma-
tion of NLMOs, called by SR NLMO:
#NSymmetrizes the unitary transformation matrix (TSYM) to
preserve symmetries inherent in the density matrix, using
symmetric orthogonalization of columns (if necessary) to
preserve unitarity.
Symmetric orthogonalization of a set of column vectors (T).
[Thresholds DIAGTH (10#uminus 12#d) for off-diagonal Jacobi
diagonalization and DANGER (10#u3#d) to detect singularities
of the overlap matrix; all eigenvalues of S must be less
than DIAGTH*DANGER.] #BC.6 ENERGY ANALYSIS ROUTINES (GROUP
II)#N
The small set of routines in this group carry out the second
main task of NBO analysis, the NBO Energetic Analysis
(``deletions,'' associated with inclusion of a $DEL keylist;
Section B.5). These routines depend on the presence of a
Fock matrix, and are bypassed in any non-SCF calculation.
Overall control of Group II routines is with SR NBOEAN,
which in turn calls the remaining programs of this group:
The task performed by this subroutine is dependent of the
value of NBOOPT(1). If set to 2, this routine initiates (by
calling SR NBODEL) the calculation of the next NBO deletion
of the $DEL keylist. If set to 3, this routine completes
the NBO deletion by computing the energy for the deletion.
INTEGER variable IDONE is set to 1 if no additional dele-
tions are found in the $DEL keylist.
Controls the calculation of the new AO density matrix from
the requested deletion in the $DEL keylist. A modified NBO
Fock matrix is created (SR DELETE) and diagonalized (SR
JACOBI), leading to a new AO density matrix (SR NEWDM).
This routine also prints the NBO deletions table (Section
B.6.10).
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Reads the $DEL list for the next deletion, deletes (sets to
zero) the appropriate elements from the Fock matrix, and
prints out the deletion specification Section B.6.10).
Constructs a new density matrix corresponding to the deleted
Fock matrix.
Ranks the eigenvalues found in vector EIG (lowest eigenvalue
having first rank). I = ARCRNK(N) is the entry whose rank
is N.
Performs the similarity transform U#ut#d*F*U on a packed
upper-triangular matrix F. #BC.7 DIRECT ACCESS FILE ROU-
TINES (GROUP III)#N
0 The routines of Group III are involved in communication
between the NBO programs and the FILE48 direct access file
(DAF), whose contents are described in Section C.4. Two
levels of I/O routines are employed.
0 The higher-level `fetch/save' routines are called directly
by the NBO subroutines. In most cases, the function of the
fetch/save routines can be recognized by its name or argu-
ment list; e.g., ``FETITL(TITLE)'' fetches the job title
line, ``FEFAO(F,IWFOCK)'' fetches the AO Fock matrix (FAO),
and so forth. Each routine can also be associated with a
logical record number (IDAR) of the direct access file (Sec-
tion C.4), where the I/O item is stored. We list these rou-
tines in order of appearance, together with the associated
direct access file record number(s) IDAR, without further
description:
0 In turn, the fetch/save routines call the following
lower-level, primitive subprograms, which open, close, read,
write, and test the contents of the DAF (these are heavily
modified versions of the direct access file subroutines of
HONDO):
Opens a new or existing unformatted DAF depending in the
value of logical variable NEW. Record lengths are currently
set at 256 (LENGTH) single precision words (1024 bytes), and
up to 100 (NBDAR) logical records can be written. Note that
logical records and physical records of the DAF are not
equivalent; single logical records can span several physical
records and need not be ordered sequentially. The array
IONBO (in COMMON/NBODAF/) maps each logical record with its
associated physical records. The first physical record of
the DAF is reserved for COMMON/NBODAF/. [Note: Some
machines may require that you alter the parameters LENGTH
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(the
chosen record length) and ISINGL (a record length scaling
factor).#N]
Writes NX double precision words of array IX to logical
record number IDAR of the NBO DAF.
Reads NX double precision words of the logical record number
IDAR of the NBO DAF.
Rewrites common block /NBODAF/ on the first physical record
of the DAF, and closes the file.
Inquires whether information has been stored in logical
record IDAR of the direct access file, and sets IDAR=0 if
the record is empty. #BC.8 FREE FORMAT INPUT ROUTINES
(GROUP IV)#N
0 The routines of Group IV are the small set of system-
independent free-format input routines that are used in
reading the various keylists and datalists of the input
file. The routines of this group are the `primitives' that
read and interpret individual keywords or entries of a keyl-
ist. They are called by higher-level I/O routines (such as
SR JOBOPT of Group I) throughout the NBO program.
The free-format input primitive routines are:
Initializes input from the LFNIN input file.
Reads the next `card' (line) of the input file, and stores
this line in the integer array ICD in COMMON/NBCRD1/ with
all lower case characters converted to upper case. Logical
variable END in COMMON/NBCRD2/ is set to .TRUE. if the end-
of-file is encountered.
Searches input file LFNIN for the next string of non-blank
characters, and checks to see if they form an integer. If
so, the numerical value of the integer is placed in INT. If
not, the logical variable ERROR is set to .TRUE. and INT is
set positive (indicating an ``END'' terminating mark or
end-of-file was encountered) or negative (indicating that
the character string is not an integer).
Similar to SR IFLD, but for a real number REAL. This rou-
tine will accept real numbers in a variety of different
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formats.
For example, 1000 can be represented by 1000, 1000.0, 1.0E3,
D3, 1+3, etc.
Similar to SR IFLD and RFLD, but for a Hollerith array
KEYWD(LENG). The logical variable ENDD is set to .TRUE. if
the ``END'' terminating mark or the end-of-file is encoun-
tered. On return to the calling subroutine, LENG is set to
the length of the string in KEYWD or to zero if the end-of-
file is encountered.
Searches for the next non-blank field on the input file,
reading additional lines if necessary. Commas and equal
signs are treated as blanks, and any character string which
follows an exclamation point is treated as an arbitrary com-
ment, and is ignored. The contents of this field are stored
in the integer array LOOK of length LENGTH in
COMMON/NBCRD1/.
This logical function tests the equivalence of the first `L'
elements of the Hollerith strings IA and IB.
#BC.9 OTHER SYSTEM-INDEPENDENT I/O ROUTINES (GROUP V)#N
0 This section summarizes the I/O routines of Group V.
These routines perform a variety of auxiliary I/O tasks,
such as the reading or writing of matrices, or perform func-
tions closely related to I/O.
0 The first set of programs in this group are responsible
for searching for the $GENNBO, $NBO, $CORE, $CHOOSE, and
$DEL identifiers of the job input file LFNIN:
Searches for the $GENNBO identifier. In addition, this rou-
tine reads in the keywords of the $GENNBO keylist (see Sec-
tion B.7), setting the option flags of COMMON/NBOPT/ and
COMMON/NBGEN/ appropriately.
Searches for the $NBO identifier according to the program
version number, NBOOPT(10). The integer variable IDONE is
set to 0 if this identifier is located, or 1 otherwise.
Searches for the $CORE identifier according to the program
version number, IESS. The integer variable ICOR is set to 1
if this identifier is located, or 0 otherwise.
Searches for the $CHOOSE identifier according to the program
version number, IESS. The integer variable ICHS is set to 1
July 11, 1995
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if
this identifier is located, or 0 otherwise.
Searches for the $DEL identifier according to the program
version number, NBOOPT(10). The integer variable IDONE is
set to 0 if this identifier is located, or 1 otherwise.
0 The remaining routines of this group perform miscellaneous
I/O functions:
Initializes the atomic core array (IATCR on COMMON/NBATOM/),
and reads the entries of the $CORE keylist.
Writes the transformation from `pure' AOs to PNAOs, the NAO
labels (NAOCTR, NAOL, and LSTOCC from COMMON/NBBAS/), and
PNAO occupancies (diagonal PNAO density matrix elements) to
an external file (LFN = minus IFLG). Pure AOs (PAOs) are
obtained from `raw' cartesian AOs by the transformations of
SR DFGORB.
Reads the transformation from `pure' AOs (PAOs) to PNAOs,
NAO labels, and PNAO occupancies from an external file (LFN
= minus IFLG/1000) (cf. SR WRPPNA).
Writes the AO to NAO transformation (fetched from the DAF),
NAO labels, and the PNAO overlap matrix (also fetched from
the DAF) to an external file (LFN = minus IFLG). Note that
T is the PNAO overlap matrix when control is returned to the
calling routine.
Reads the AO to NAO transformation, NAO labels, and PNAO
overlap matrix from an external file (LFN = minus
IFLG/1000). The transformation and overlap matrices are
saved on the DAF, and the input AO density matrix is
transformed to the NAO basis. Note that T is the PNAO over-
lap matrix on return to the calling routine (cf. SR WRTNAO).
Writes the NAO to NBO transformation and NBO info (LABELS
and IBXM arrays of COMMON/NBBAS/) to an external file (LFN =
minus IFLG).
Reads the NAO to NBO transformation and NBO info from an
external disk file (LFN = minus IFLG/1000). The input NAO
density matrix is also transformed to the NBO basis, and the
NBO occupancies are stored in BNDOCC (cf. WRTNAB).
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Writes the AO to NBO transformation, the NBO occupancies,
and additional NBO info (NBOUNI, NBOTYP, LABEL, IBXM, and
IATNO arrays) to an external disk file (LFN = minus IFLG).
Similar to SR WRTNBO but for NLMOs. Note that the NLMO
labels are identical to the NBO labels.
Writes the atomic coordinates and AO basis set information
to the `AOINFO' file LFN. The information contained in this
file is identical to that of the $COORD, $BASIS, and $CON-
TRACT datalists of the GENNBO input file (see Section B.7).
For more information on the file format, see the subroutine
source code.
Writes the `ARCHIVE' file LFN (see Section B.7).
General utility to write matrix A(MR,1) to an external file
(LFN = minus IFLG) or print it to the output file (IFLG =
number of columns to print, `FULL', `VAL', or `LEW'). TITLE
is a CHARACTER*80 matrix label, and the rows of A are
labelled according to the value of INDEX = 0 (atoms), 1
(AOs), 2 (NAOs), 3 (NHOs), 4 (NBOs), or 5 (NLMOs). This
routine calls SR APRINT or SR AWRITE.
Prints MCOL columns of matrix A to the output file. The
format of the matrix is chosen according to the magnitude of
the largest matrix element in A (cf. SR AOUT).
Writes matrix A to external disk file LFN (cf. SR AOUT).
Reads NC columns of the matrix A(MR,1) from the external
file LFN. The job title in the external file is returned to
the calling subroutine in the Hollerith array, JOB(20), and
the LOGICAL variable ERROR is set to .TRUE. if an error
occurred while reading.
Prints the matrix A(MR,MC) to the standard output file.
This routine is called only when the print formats of SR
APRINT are unsuitable for matrix A.
Interprets the Hollerith array STRING(LEN), storing the
result in IFLG. The contents of STRING can be any of the
read/write/print parameters such as `W38', `PVAL', `R43',
etc., described in Section B.2.4, and the resulting value of
IFLG is determined according to the discussion of
July 11, 1995
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COMMON/NBOPT/
in Section C.3. When this routine is called, IFLG should be
set to its default value, LFN should be the default file for
writing or reading, and LOGICAL variable READ should be set
to .TRUE. if reading from an external file is allowed. The
LOGICAL variable ERROR is set to .TRUE. if STRING is unin-
terpretable.
Interprets IFLG as to whether the I/O item should be printed
(IOINQR = `PRNT'), read (IOINQR = `READ'), or written out
(IOINQR = `WRIT') to an external file.
Forms labels for AOs and stores them in COMMON/NBLBL/.
Forms labels for NAOs and stores them in COMMON/NBLBL/.
Forms labels for NBOs and stores them in COMMON/NBLBL/.
Forms labels for NHOs and stores them in COMMON/NBLBL/.
#BC.10 GENERAL UTILITY ROUTINES (GROUP VI)#N
#NThe utility routines of Group VI perform a variety of
mathematical and other general tasks (such as solving sets
of linear equations), and are called from routines
throughout the NBO program. They are grouped in alphabeti-
cal order (except for the final group of routines controlled
by the SR LINEQ driver):
Converts cartesian coordinates (X,Y,Z) to corresponding
polar angle THETA and azi#|muthal angle PHI in spherical
polar coordinates.
LOGICAL function BDFIND is set to .TRUE. if there is at
least one bond between atoms IAT, JAT.
Builds a `chemical formula' for the list of atoms in LISTA
having been identified as belonging to a particular `molecu-
lar unit'. The chemical formula is stored in the Hollerith
array ISTR(NL).
Consolidates an upper-triangular (AUT) and lower-triangular
(ALT) matrix in a single matrix, stored in AUT.
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2.
Converts the Hollerith array IJ(LEN) into an integer IK.
This is the inverse of SR IDIGIT.
Converts a 2-digit integer N to two Hollerith characters
NC1, NC2.
Copies matrix A to matrix B.
Stores the nominal ``core table,'' giving the number of core
#Is#N, #Ip#N, #Id#N, #If#N orbitals for elements 1-105 (H to
Lw, and elements 104, 105). This table controls the number
of high-occupancy unhybridized NAOs that will be isolated
and removed as core NBOs (taking account also of any effec-
tive core potential).
Decomposes a Hollerith variable I into its four individual
Hollerith `bytes' IBYTE(4).
Halts the execution of the NBO program if an unrecognizable
keyword is found in the $NBO keylist.
Converts the INTEGER variable KINT in the first ND elements
of the Hollerith array IK(MAXD). This is the inverse of SR
CONVIN.
This Hollerith function determines whether the IBO arr JBO
delocalization is vicinal (`v'), geminal (`g'), or remote
(`r'), based on the derived NBO connectivity.
3. Diagonalizes a real symmetric matrix by the Jacobi rota-
tions method. If ICONTR=0, a standard Jacobi diagonaliza-
tion (unconstrained 2x2 rotations) is carried out. If
ICONTR=1, the algorithm is prevented from mixing orbitals
that are degenerate within `DIFFER' if the off-diagonal ele-
ment connecting them is less than `DIFFER'. [Threshold
DIFFER (10#uminus 5#d) controls degenerate mixing, DONE
(10#uminus 13#d) is the maximum allowed off-diagonal ele-
ment, and EPS (0.5x10#uminus 13#d) is a number between DONE
and the machine pre#|cision.]
This routine carries out a `limited' transformation of a
matrix (T), using only the rows and columns specified by
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vector
M. The operations performed are T*A, A#ut#d*T*A, or
A#ut#d*T according to the value of IOPT.
Multiplies square matrices A*B (using scratch vector V) and
stores result in A.
Multiplies A#ut#d*B (using scratch vector V) and stores the
result in B. The algorithm assumes that A*B is a symmetric,
so about half the work is saved. [SR MATML2 is typically
the second step in a similarity transform of B by A, where B
(and thus A#ut#d*B*A) is symmetric.]
Returns the (Hollerith) atomic symbol for atomic number IZ
Normalizes the columns of A using the overlap matrix S.
4. Ranks the positive elements of integer LIST(N), lowest
values first. [RANK and ARCRNK are integer vectors, with I
= ARCRNK(N) if LIST(I) is the element of rank N.]
Packs the upper-triangular portion of the symmetric matrix
T(NBAS,NBAS) the first L2 elements of T.
Orders the entries of vector EIG, highest values first.
ARCRNK(I) is the old location of the I#uth#d highest value
in EIG. On return, EIG(I) is the I#uth#d highest value.
[Entries are not switched unless they differ by more than a
DIFFER (5x10#uminus 8#d) threshold.]
Performs the general similarity transform T#ut#d*A*T of A by
T, using scratch vector V.
Performs the `fast' similarity transform S#ut#d*A*S, assum-
ing the result is symmetric.
Transposes the matrix A: A arr A#ut#d.
Unpacks an upper triangular matrix (vector of length L2)
into a symmetric matrix T(NBAS,NBAS).
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Specifies the nominal ``valence table,'' giving the number
of valence AOs of each symmetry type for elements 1-105.
Evaluates Euclidean length of vector X.
This and the three following routines constitute the linear
equations package for solving the system A*X = B for matrix
X by the method of Gaussian elimination.
Supports SR LINEQ.
Supports SR LINEQ.
Supports SR LINEQ. #BC.11 SYSTEM-DEPENDENT DRIVER ROUTINES
(GROUP VII)#N
0 The routines of Group VII comprise the set of ESS-
dependent driver routines which initiate the NBO and NBO
energetic analyses and provide the NBO program with a
variety of information about the electronic wavefunction.
This section provides a brief, generic description of each
of the driver routines. If you intend to write a set of
routines for an ESS program not supported by this distribu-
tion, refer to the driver source code for additional gui-
dance. Also, see Section C.13 for helpful hints for attach-
ing the NBO program to an ESS package.
0 The driver routines are grouped together at the end of the
NBO source code. Since multiple versions of each driver are
provided (one for each supported ESS package and GENNBO),
all of the executable lines in these routines are `commented
out' with an asterisk in the first column. In addition,
every line of the drivers has an identifier `#IXXX#NDRV' in
columns 73-78, where `#IXXX#N' is a 3-letter identifier for
the associated ESS package. It is the responsibility of the
program ENABLE to `uncomment' the appropriate lines of the
code for the requested program version (see Section A.2).
0 The system-dependent driver routines are:
Determines the logical file numbers for the input and output
files (LFNIN and LFNPR) of the parent program, initializes
the NBOOPT job option array Section C.5.1), and initiates
the NBO analysis (SR NBO) and energetic analysis (SR
NBOEAN). This routine is the only routine of the NBO pro-
gram called directly by the parent ESS package.
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Interrogates the scratch files and COMMON blocks of the
parent program, providing the NBO program with required
information of the electronic wavefunction via the NBO COM-
MON blocks and FILE48 direct access file. (Note that for
GENNBO, this routine directs the input of information from
the GENNBO input file, FILE47.) The NBO COMMON blocks and
FILE48 records which must be initialized by SR FEAOIN are
discussed in Sections C.3, C.4. Additional information on
the COMMON blocks and scratch files of the parent ESS pack-
age is provided in the Appendices.
Performs one of two tasks, depending of the value of
NBOOPT(1). If NBOOPT(1) is set to 2, SR DELSCF provides the
parent ESS program with the modified density matrix gen-
erated by the NBO energetic analysis routines. The parent
program will then compute the ``deletion energy'' for this
modified wavefunction. If NBOOPT(1) is set to 3, SR DELSCF
fetches the deletion energy from the parent program and
writes it to the FILE48 direct access file. (The NBOOPT
array is discussed in Section C.5.1).
#BC.12 GENNBO AUXILIARY ROUTINES#N
0 An additional set of routines is provided for the GENNBO
stand-alone program. These routines are called by the
GENNBO driver routine FEAOIN and are responsible for reading
the datalists of the GENNBO input file. Each of these rou-
tines rewinds the input file before searching sequentially
for its associated datalist. Thus, the order of datalists
(as well as keylists) in the input file is immaterial. Each
routine also checks that all required information in the
datalist is given and stores this information on the FILE48
direct access file or in the NBO COMMON blocks.
0 Below we list each GENNBO auxiliary routine, indicating
its associated datalist, but without furthur explanation:
#BC.13 ATTACHING NBO TO A NEW ESS PROGRAM#N
This section briefly outlines the steps to be considered
when attaching the NBO program to a new ESS package that is
not supported by this distribution.
In general, you should try to identify the supported ESS
package that is most similar to the ESS package you wish to
use, and try to create driver routines modelled as closely
as possible on those provided for the ESS. [In fact, exa-
mining the source code for driver routines of #Iall#N sup-
ported ESS packages is good preparation for writing your own
drivers.]
July 11, 1995
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Decide where in the parent ESS package you wish to perform
the NBO analysis. This will necessarily be placed after the
calculation of the wavefunction (and the associated density
matrix), usually near the wavefunction analysis routines
(e.g., the perennial ``Mulliken population analysis'' sec-
tion) or wavefunction properties section of the code. If
possible, restrict the modification of your ESS source code
to insertion of a single ``CALL RUNNBO'' statement at some
point where the information required for NBO analysis is
known to be available.
Check carefully for possible conflicts between the parent
ESS program and the NBO program in (1) function or subrou-
tine names, (2) COMMON block names, and (3) logical file
assignments (LFNs) for I/O. NBO common block names all
begin with /NB.../, and default LFN assignments are in the
range 31-49. (Duplicate FN or SR names are detected by a
linker.)
Create new driver (interfacing) subroutines RUNNBO, FEAOIN,
and DELSCF to perform the functions briefly described in
Section C.11, using the drivers provided with this distribu-
tion as templates insofar as possible. The following are a
few helpful hints for each driver:
The RUNNBO routine should be relatively straightforward to
write, following an analogous example provided in this dis-
tribution. Note that you can simply omit the calls to SR
NBOEAN and SR DELSCF from RUNNBO if you do not plan to use
the NBO energetic analysis (for example, because the DELSCF
driver is unmanageable).
If your parent program is quite different from any of those
supported by this distribution, choose an alternate version
number [NBOOPT(10)], and carefully consider step 4 below.
Routine FEAOIN should fetch information about the electronic
wavefunction from your ESS package and load it into the NBO
COMMON blocks and FILE48 direct access file. This requires
intimate knowledge of where these items are stored in the
ESS program, so the FEAOIN examples of the distribution may
provide little direct guidance. See Sections C.3, C.4 for
description of the NBO COMMON blocks and file records which
must be initialized by this routine.
Note that the NBO analysis will perform properly without the
information stored on logical records 2, 5, 9, 30, 31, 40,
41, and 50-52 of the direct access file. If information is
not provided on these records, the NBO program will simply
shut off (with warnings) any requested keyword options which
are thereby incompatible. In addition, the overlap matrix
of record 10 need not be provided if the input basis set is
orthogonal, and the energies of record 8 are not required if
the NBO energetic analysis is not implemented for your ESS
July 11, 1995
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package.
Creating routine DELSCF will require intimate knowledge of
the SCF routines in the parent ESS program; again, versions
of DELSCF provided with this distribution may only be of
minimal assistance. As described in Section C.11, SR DELSCF
is responsible for providing a modified AO density matrix to
an SCF energy evaluator (one pass throught the SCF routines)
and returning this new energy to the NBO deletion routines
via the FILE48 direct access file. If you do not intend to
employ the NBO energetic analysis, you need not provide this
routine to the NBO program. [Note that the 2nd-order per-
turbation theory energy analysis will be carried out (pro-
vided the Fock matrix is available) even if you do not
include the NBOEAN and DELSCF energy analysis routines.]
In addition to the explicitly system-dependent subroutines
RUNNBO, FEAOIN, and DELSCF, there are a few routines within
the NBO program which can be considered #Iquasi#N-system
dependent, and might, therefore, require modification.
These are SR NBOSET (Section C.5.2) and the `INP' routines
NBOINP, CORINP, CHSINP, and DELINP (Section C.9):
SR NBOSET assigns the logical file numbers (LFNs) 31-49 to
be used by the NBO program. As mentioned above, if these
are in conflict with the files employed by the parent ESS
program, the conflicting LFNs will have to be reassigned in
this subroutine.
The `INP' routines may have to be modified according to the
manner in which the input file of the parent program should
be processed by the NBO program. More specifically, these
routines either rewind the input file before searching for
their associated keylist identifier, or they simply begin
searching the input file sequentially at the point where the
parent program left off, depending on the version number
specified in NBOOPT(10). Be sure this parameter is con-
sistent with the way you wish to modify the ESS input file
for NBO input.
001111111100// 011100001110// 011000000110// 110000000011//
110000000011// 110000000011// 110000000011// 011000000110//
011100001110// 001111111100// 000011110000// 000000000000//
000000000000// 000000000000// 000000000000// 000000000000//
000000000000// 000000000000// 000000000000// 000000000000//
000000000000// 000000000000// 000000000000// 000000000000//
000000000000// 000000000000// 000000000000// 000000000000>>
#HSection D: APPENDIX#N
#BD.1 INTRODUCTION#N
July 11, 1995
- 137 -
0 This Appendix contains system-dependent information about
NBO input and source code for the ESS (electronic structure
system) packages supported by this distribution. We assume
that the user has basic familiarity with the ESS program of
interest.
0 The Appendix is organized according to the ESS packages
supported, which are described in Sections D.2-D.7, as shown
below:
0 Each ESS section contains information on:
Sample input file for RHF/3-21G methylamine
NBO program installation
Communication between the NBO drivers and the ESS program
0 For most users, only the first section(s) on sample input
file will be required reading. For the programmer responsi-
ble for attaching the NBO program to an ESS package, the
final section on NBO drivers will be important only if the
available ESS version differs significantly from that
assumed in the installation instructions.
0 In the Appendix we use ``SR'' and ``FN'' to denote subrou-
tines and functions, respectively.
#BD.2 GAUSSIAN 88 VERSION#N
#ID.2.1 GAUSSIAN 88 sample input#N
0 A sample GAUSSIAN 88 input file to recreate the default
methylamine (RHF/3-21G at Pople-Gordon idealized geometry)
output displayed in Section A.3 is shown below:
# RHF/3-21G
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
0 1
C
N 1 CN
H 1 CH 2 tet
H 1 CH 2 tet 3 120. 0
H 1 CH 2 tet 3 240. 0
H 2 NH 1 tet 3 60. 0
H 2 NH 1 tet 3 300. 0
CN 1.47
CH 1.09
NH 1.01
tet 109.4712
July 11, 1995
- 138 -
$NBO $END
#T
@seg
0 #NThe keylists of the NBO program should always
appear at the bottom of the GAUSSIAN 88 input file and
should be ordered: $NBO, $CORE, $CHOOSE, $DEL. NBO job
options are selected by inserting their associated key-
words (Section B.2) into the $NBO keylist. All NBO
keywords are applicable to the electronic wavefunctions
computed by the GAUSSIAN 88 programs.
0 If the NBO program encounters the end-of-file while
searching for a keylist, the input file is rewound and
the search for the keylist is continued. This is par-
ticularly useful for jobs which call the NBO analysis
several times. For example, an MP2 calculation with
the GAUSSIAN 88 option DENSITY=ALL causes Link 601 to
loop over three densities (SCF, Rho2, and MP2), and
hence, the NBO analysis is called three times, once for
each density. A single $NBO keylist (and $CORE and
$CHOOSE keylists) will suffice as input for all three
analyses. Alternatively, separate $NBO keylists, one
for each density, could be inserted at the bottom of
the GAUSSIAN 88 input file.
- 138 -
0 The IOp parameters 40-43 of Link 601 exert additional
control over the NBO program, as listed below:
For example, to restrict the NBO output to the Natural
Population analysis (NPA) only, set IOp(40) to minus 1
in all Link 601 entries of a GAUSSIAN 88 non-standard
route, as shown below:
#T 6/40=-1/1;
#NBy default, the NBO analysis will be performed, read-
ing keywords from the $NBO keylist [IOp(40)=0], on the
density matrix for the current wavefunction. The
DIPOLE and RESONANCE keywords are generally activated
through the $NBO keylist rather than via the IOp param-
eters.
- 138 -
#ID.2.2 NBO energetic analysis#N
0 Due to the overlay structure of the GAUSSIAN 88 pro-
grams, a non-standard route must be employed to perform
the NBO energetic analysis. The following table lists
and describes the tasks of the GAUSSIAN 88 links in the
order that they appear in the non-standard route:
#IDESCRIPTION#N
Perform the normal NBO analysis, storing information
about the NBOs for the NBO energetic analysis on the
FILE48 direct access file.
Read the next deletion listed in the $DEL keylist. If
there are no more deletions, move to the next link.
Otherwise, compute the modified density matrix, store
it on the read-write files, and skip the next link in
the non-standard route.
Finish GAUSSIAN 88 execution.
Using the modified density matrix, compute the deletion
energy by a single pass through the SCF energy evalua-
tor. Store the deletion energy on the read-write
files.
Read the deletion energy from the read-write files and
complete the energetic analysis. Step backwards, in
the non-standard route, three links.
0 The following is a GAUSSIAN 88 input file that will
generate, in addition to the default NBO output, the
NLMO (Section B.6.2), the dipole moment (Section
B.6.3), and the NBO energetic (Section B.6.10) analyses
of methylamine:
# NONSTD 1//1; 2//2; 3/5=5,11=1,25=14,30=1/1,2,3,11,14;
4/7=1/1; 5//1; 6/7=2,8=2,9=2,10=2,19=1/1; 6/40=2/1(1);
99/5=1,9=1/99; 5/7=1,13=1/1; 6/40=3/1(-3);
Methylamine...RHF/3-21G//Pople-Gordon standard geometry
0 1
C
N 1 CN
H 1 CH 2 tet
H 1 CH 2 tet 3 120. 0
H 1 CH 2 tet 3 240. 0
H 2 NH 1 tet 3 60. 0
H 2 NH 1 tet 3 300. 0
CN 1.47
July 11, 1995
- 139 -
CH 1.09
NH 1.01
tet 109.4712
$NBO NLMO DIPOLE $END $DEL NOSTAR
ZERO 2 ATOM BLOCKS 4 BY 3
1 3 4 5
2 6 7
3 BY 4
2 6 7
1 3 4 5 $END
#T
@seg
0 #NNote that for the GAUSSIAN 88 version of the NBO pro-
gram, each deletion in the $DEL keylist must begin on a new
line of the input file (the first deletion can follow the
``$DEL'' keylist identifier, as shown above). The ``$END''
keylist terminator must also appear on its own line.
- 139 -
#ID.2.3 Geometry reoptimization with NBO deletions#N
0 The structural effects of electron delocalization can be
examined by coupling the NBO energetic analysis to the
Fletcher-Powell (numerical) geometry optimization routines
of the GAUSSIAN 88 package. The following GAUSSIAN 88 input
file will reoptimize selected internal coordinates of
RHF/3-21G methylamine in the absence of its strong
#In#N#dN#u arr gma #u*#d#d#> C C Run the NBO ener-
getic analysis. C
If(IOp(40).ge.2) then
IDens = 0 ! SCF density for dele-
tion runs
IOp(41) = IDens
Call RunNBO(Core,NGot,IOp,IContr)
go to 999
endIf C C <<< End of first NBO insert >> C C
Put density matrices first. C
IPA = IEnd1 + 1
.
.
.
- 140 -
Call
ElEner(IOut,ISelfE,SCFDen,ISCF,IROHF,NAE,NBE,NBasis,
$ Core(IPA),Core(IV),MDV) C C <<< Beginning of
second NBO insert >>> C C Run the NBO analysis. C
If(IOp(40).ne.-2) then
IOp(41) = IDens
Call RunNBO(Core,NGot,IOp,IContr)
endIf C C <<< End of second NBO insert >>> C
else if(IDens1.eq.IDSt.and.IDens1.eq.IDEnd) then
.
.
.
Call
PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
$
Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip)) C C
<<< Beginning of third NBO insert >>> C C The following
line has been changed from "Call ChainX(0)" in C order
to exit the NBO deletion loop after the deletions are done:
C
999 Call ChainX(IContr) C C <<< End of third NBO
insert >>> C
Return
End
#T
@seg
0 #NThe first NBO insert initiates the NBO energetic
analysis of SCF wavefunctions. The second insert lies
within a loop over densities, and thus, the NBO program is
called once for each density matrix analyzed by this link.
The third insert allows the NBO energetic analysis to exit
from the loop in the non-standard route.
The NBO program installation should continue as discussed in
Section A.2.
- 140 -
#ID.2.5 NBO communication with GAUSSIAN 88#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following GAUSSIAN 88 routines, read-write files, and
COMMON blocks:
#_GAUSSIAN 88 routines:#/#T
SR CharPn(IString)
SR DENGET(IOut,IODens,IMeth,LenDen,GotIt,P)
FN ILSW(IOPER,WHERE,WHAT)
FN InToWP(Nints)
FN ITqry(Ifile)
SR TRead(IARN,X,M,N,MM,NN,K)
SR TWrite(IARN,X,M,N,MM,NN,K)
#N#_GAUSSIAN 88 read-write files:#/
#_GAUSSIAN 88 COMMON blocks:#/#T
COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
+ ATMCHG(400),C(1200)
COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
+ KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
COMMON/B/EXX(6000),C1(6000),C2(6000),C3(6000),X(2000),Y(2000),
+
Z(2000),JAN(2000),SHELLA(2000),SHELLN(2000),SHELLT(2000),
+ SHELLC(2000),AOS(2000),AON(2000),NSHELL,MAXTYP
INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
DIMENSION C4(2000),SHLADF(2000)
EQUIVALENCE(C4(1),C3(2001)),(SHLADF(1),C3(4001))
#N #BD.3 GAUSSIAN 86 VERSION#N
#ID.3.1 GAUSSIAN 86 sample input#N
0 See Section D.2.1. Note that the NBO IOp parameters of
Link 601 are set to 40-43 (changed from 20-23 in previous
distributions of the NBO program).
#ID.3.2 NBO energetic analysis#N
0 See Section D.2.2.
#ID.3.3 Geometry reoptimization with NBO deletions#N
0 See Section D.2.3.
- 140 -
#ID.3.4 NBO program installation#N
0 The NBO interfacing (driver) routines provided in this
distribution were written for the Revision C version of
GAUSSIAN 86, dated 30-APR-1986. Section D.3.5 lists the
GAUSSIAN 86 dependent elements of the NBO driver routines
that may need slight modification for other versions of the
GAUSSIAN 86 programs.
0 Two modifications to SR MulDrv of Link 601 are required to
run the NBO analysis:
*Deck MulDrv
Subroutine MulDrv(Core)
.
.
.
If(NGot.lt.IEnd1) Write(IOut,2002) IEnd1, NGot
Len2 = (NGot-I2A+1)/NTT C C <<< Beginning of first
NBO insert >>> C
IF(IOp(40).GE.2.OR.IOp(41).NE.0) GO TO 999 C C <<<
End of first NBO insert >>> C C Do population analysis.
C
CALL
MULPOP(MaxAtm,IOP,IROHF,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,
.
.
.
Call
PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT,
$
Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip)) C C
<<< Beginning of second NBO insert >>> C
999 Call GetSCM(-1,Core(1),NGot,3HNBO,0)
Call RunNBO(Core,NGot,IOp,IContr) C C The follow-
ing line has been changed from "999 Call ChainX(0)" in C
order to exit the NBO deletion loop after deletions are com-
plete. C
Call ChainX(IContr) C C <<< End of second NBO
insert >>> C
Return
End
#T
@seg
- 140 -
0 #NThe first NBO insert allows Link 601 to by-pass the Mul-
liken Population and electric moment analysis routines if
the NBO energetic analysis is to be performed or if a corre-
lated wavefunction is being analyzed. The second insert
requests all available memory be allocated for the NBO pro-
gram and initiates the NBO analysis. Note that the call to
SR ChainX has been altered from the original code.
The NBO program installation should continue as discussed in
Section A.2.
- 140 -
#ID.3.5 NBO communication with GAUSSIAN 86#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following GAUSSIAN 86 routines, read-write files, and
COMMON blocks:
#_GAUSSIAN 86 routines:#/#T
SR CharPn(IString)
FN ILSW(IOPER,WHERE,WHAT)
FN InToWP(Nints)
FN ITqry(Ifile)
SR TRead(IARN,X,M,N,MM,NN,K)
SR TWrite(IARN,X,M,N,MM,NN,K)
#N#_GAUSSIAN 86 read-write files:#/
#_GAUSSIAN 86 COMMON blocks:#/#T
COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401),
+ ATMCHG(400),C(1200)
COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5),
+ KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400)
COMMON/B/EXX(1200),C1(1200),C2(1200),C3(1200),X(400),Y(400),
+
Z(400),JAN(400),SHELLA(400),SHELLN(400),SHELLT(400),
+ SHELLC(400),AOS(400),AON(400),NSHELL,MAXTYP
INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
DIMENSION C4(400),SHLADF(400)
EQUIVALENCE(C4(1),C3(401)),(SHLADF(1),C3(801))
#N #BD.4 GAUSSIAN 82 VERSION#N
#ID.4.1 GAUSSIAN 82 sample input#N
0 See Section D.2.1. Note that the NBO IOp parameters of
Link 601 are set to 40-43 (changed from 20-23 in previous
distributions of the NBO program).
#ID.4.2 NBO energetic analysis#N
0 See Section D.2.2.
#ID.4.3 Geometry reoptimization with NBO deletions#N
0 See Section D.2.3.
- 140 -
#ID.4.4 NBO program installation#N
0 The NBO interfacing (driver) routines provided in this
distribution were written for the Revision H version of
GAUSSIAN 82, dated 28-NOV-1983. Section D.4.5 lists the
GAUSSIAN 82 dependent elements of the NBO driver routines
that may need slight modification for other versions of the
GAUSSIAN 82 programs.
0 Two modifications to SR MulDrv of Link 601 are required to
run the NBO analysis:
*Deck MulDrv
Subroutine MulDrv(Core)
.
.
.
IF(IPRINT.NE.0)
$WRITE(IOUT,2001)I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,IEND C
C <<< Beginning of first NBO insert >>> C C The fol-
lowing line has been changed from "CALL GETSCM(IEND,...)", C
in order to ask for all available memory. C
CALL GETSCM(-1,CORE(1),JJJMEM,6HMULDRV,0) C
IF(IOP(40).GE.2.OR.IOP(41).NE.0) GO TO 100 C C <<<
End of first NBO insert >>> C C DO THE POPULATION
ANALYSIS.
CALL
MULPOP(IOP,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,IAN,AtmChg,
$ C,Core(I1),CORE(I2),CORE(I3),CORE(I4),CORE(I5),
$ CORE(I6),CORE(I7),CORE(I8),CORE(I9),CORE(I10)) C C
<<< Beginning of second NBO insert >>> C
100 CALL RUNNBO(CORE,JJJMEM,IOP,ICONTR) C C The fol-
lowing line has been changed from "CALL CHAINX(0)" in C
order to exit the NBO deletion loop after deletions are com-
plete. C
CALL CHAINX(ICONTR) C C <<< End of second NBO
insert >>> C
RETURN
END
#T
@seg
- 140 -
0 #NThe first NBO insert allows Link 601 to by-pass the Mul-
liken Population analysis routines if the NBO energetic
analysis is to be performed or if a correlated wavefunction
is being analyzed. The second insert initiates the NBO
analysis. Note that the calls to routines GETSCM and CHAINX
have been altered from the original code.
The NBO program installation should continue as discussed in
Section A.2.
- 140 -
#ID.4.5 NBO communication with GAUSSIAN 82#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following GAUSSIAN 82 routines, read-write files, and
COMMON blocks:
#_GAUSSIAN 82 routines:#/#T
SR CharPn(IString)
FN ILSW(IOPER,WHERE,WHAT)
FN InToWP(Nints)
FN ITqry(Ifile)
SR TRead(IARN,X,M,N,MM,NN,K)
SR TWrite(IARN,X,M,N,MM,NN,K)
#N#_GAUSSIAN 82 read-write files:#/
#_GAUSSIAN 82 COMMON blocks:#/#T
COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(101),
+ ATMCHG(100),C(300)
COMMON/LP2/NLP(400),CLP(400),ZLP(400),KFIRST(100,5),
+ KLAST(100,5),LMAX(100),LPSKIP(100),NFroz(100)
COMMON/B/EXX(240),C1(240),C2(240),C3(240),X(80),Y(80),
+ Z(80),JAN(80),SHELLA(80),SHELLN(80),SHELLT(80),
+ SHELLC(80),AOS(80),AON(80),NSHELL,MAXTYP
INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON
DIMENSION C4(80),SHLADF(80)
EQUIVALENCE(C4(1),C3(81)),(SHLADF(1),C3(161))
#N #BD.5 GAMESS VERSION#N
#ID.5.1 GAMESS sample input#N
0 A sample GAMESS input file to recreate the default methy-
lamine (RHF/3-21G at Pople-Gordon idealized geometry) output
displayed in Section A.3 is shown below:
$CONTRL SCFTYP=RHF RUNTYP=ENERGY $END
$DATA Methylamine...RHF/3-21G//Pople-Gordon standard
geometry CS 0
Carbon 6. -0.713673 -0.014253
0.000000
1 SV 3 N21
Nitrogen 7. 0.749817 0.123940
0.000000
1 SV 3 N21
Hydrogen 1. -0.978788 -1.071520
0.000000
1 SV 3 N21
July 11, 1995
- 141 -
Hydrogen 1. -1.123702 0.463146
-0.889982
1 SV 3 N21
Hydrogen 1. 1.129752 -0.318420
0.824662
1 SV 3 N21
$END
$GUESS GUESS=EXTGUESS $END
$NBO $END
#T
@seg
0 #NNBO job options are selected by inserting their associ-
ated keywords (Section B.2) into the $NBO keylist. All NBO
keywords are applicable to the electronic wavefunctions com-
puted by GAMESS.
0 The following is a modified GAMESS input file that will
generate, in addition to the default NBO output, the NLMO
(Section B.6.2), the dipole moment (Section B.6.3), and the
NBO energetic (Section B.6.10) analyses of methylamine:
$CONTRL SCFTYP=RHF RUNTYP=ENERGY $END
$DATA Methylamine...RHF/3-21G//Pople-Gordon standard
geometry CS 0
Carbon 6. -0.713673 -0.014253
0.000000
1 SV 3 N21
Nitrogen 7. 0.749817 0.123940
0.000000
1 SV 3 N21
Hydrogen 1. -0.978788 -1.071520
0.000000
1 SV 3 N21
Hydrogen 1. -1.123702 0.463146
-0.889982
1 SV 3 N21
Hydrogen 1. 1.129752 -0.318420
0.824662
1 SV 3 N21
$END
$GUESS GUESS=EXTGUESS $END
$NBO NLMO DIPOLE $END
$DEL NOSTAR
July 11, 1995
- 142 -
ZERO 2 ATOM BLOCKS 4 BY 3
1 3 4 5
2 6 7
3 BY 4
2 6 7
1 3 4 5
- 142 -
$END
#T
@seg
0 #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists
can be inserted in any order within the GAMESS input file;
the NBO program rewinds the input file each time it searches
for a keylist.
- 142 -
#ID.5.2 NBO program installation#N
0 The NBO interfacing (driver) routines provided in this
distribution were written for the GAMESS program dated 6-
DEC-1989. Section D.5.3 lists the GAMESS dependent elements
of the NBO driver routines that may need slight modification
for other versions of the GAMESS program.
0 Only one command line is added to the GAMESS source code
to run the NBO analysis. A call (``IF(RHO) CALL RUNNBO'')
should be inserted at the end of the GAMESS properties pack-
age (SR HFPROP in module PRPLIB), as shown below:
C*MODULE PRPLIB *DECK HFPROP
SUBROUTINE HFPROP(SCFTYP)
.
.
.
C C ----- SELECT DESIRED ELECTROSTATIC PROPERTIES -----
C
CALL PRSELC(SCFTYP) C
WRITE(IW,FMT='('' ...... END OF PROPERTY EVALUATION
......'')')
CALL TIMIT(1) C C <<< BEGINNING OF NBO INSERT >>>
C
IF(RHO) CALL RUNNBO C C <<< END OF NBO INSERT >>>
C
RETURN
END
#T
@seg
0 #NIf the density matrix is available (RHO = .TRUE.), the
NBO analysis is performed each time the properties package
is called within GAMESS. For example, the NBO analysis of
the computed wavefunction will be performed for every single
point calculation and for both the initial and final points
of a geometry optimization. The NBO output will appear
immediately after the Mulliken Population Analysis and the
electric properties in the GAMESS output file.
0 The NBO program installation should continue as discussed
- 142 -
in Section A.2.
#ID.5.3 NBO communication with GAMESS#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following GAMESS routines, records of the dictionary
file, and COMMON blocks:
#_GAMESS routines:#T#/
SR DAREAD(IDAF,IODA,V,LEN,NREC,NAV)
FN ENUC(N,Z,C)
ENTRY GOTFM(IPAR)
SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
SR SYMH(F,H,IA)
FN TRACEP(A,B,N)
SR VADD(A,I,B,J,C,K,N)
ENTRY VALFM(IPAR)
#_#NGAMESS dictionary file:#/
#_#NGAMESS COMMON blocks:#T#/
PARAMETER (MXGTOT=5000, MXSH=1000, MXATM=50)
COMMON /ECP2 /
CLP(400),ZLP(400),NLP(400),KFIRST(MXATM,6),
+
KLAST(MXATM,6),LMAX(MXATM),LPSKIP(MXATM),
+ IZCORE(MXATM)
COMMON /FMCOM / CORE(1)
COMMON /INFOA /
NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(MXATM),C(3,MXATM)
COMMON /INTFIL/ NINTMX,NHEX,NTUPL,PACK2E,INTG76
COMMON /IOFILE/ IR,IW,IP,IS,IPK,IDAF,NAV,IODA(99)
COMMON /NSHEL /
EX(MXGTOT),CS(MXGTOT),CP(MXGTOT),CD(MXGTOT),
+
KSTART(MXSH),KATOM(MXSH),KTYPE(MXSH),KNG(MXSH),
+ KLOC(MXSH),KMIN(MXSH),KMAX(MXSH),NSHELL
COMMON /OUTPUT/ NPRINT,ITOL,ICUT,NORMF,NORMP,NOPK
COMMON /RUNLAB/ TITLE(10),A(MXATM),B(MXATM),BFLAB(2047)
COMMON /SCFOPT/ SCFTYP,BLKTYP,MAXIT,MCONV,NCONV,NPUNCH
- 142 -
COMMON /XYZPRP/ X(3)
#BD.6 HONDO VERSION#N
#ID.6.1 HONDO sample input#N
0 A sample HONDO input file to recreate the default methy-
lamine (RHF/3-21G at Pople-Gordon idealized geometry) output
displayed in Section A.3 is shown below:
$CNTRL RUNFLG=0 $END
$BASIS Methylamine...RHF/3-21G//Pople-Gordon standard
geometry
0 0 15 1 N21 CS 0
Carbon 6. -0.713673 -0.014253
0.000000 Nitrogen 7. 0.749817 0.123940
0.000000 Hydrogen 1. -0.978788 -1.071520
0.000000 Hydrogen 1. -1.123702 0.463146
-0.889982 Hydrogen 1. 1.129752 -
0.318420 0.824662
$END
$GUESS NGUESS=4 $END
$INTGRL $END
$WFN WFNFLG=0 $END
$SCF NCO=9 $END
$NBO $END
#T
@seg
0 #NNBO job options are selected by inserting their associ-
ated keywords (Section B.2) into the $NBO keylist. All NBO
keywords are applicable to the electronic wavefunctions com-
puted by HONDO.
0 The following is a modified HONDO input file that will
generate, in addition to the default NBO output, the NLMO
(Section B.6.2), the dipole moment (Section B.6.3), and the
NBO energetic (Section B.6.10) analyses of methylamine:
$CNTRL RUNFLG=0 $END
$BASIS Methylamine...RHF/3-21G//Pople-Gordon standard
geometry
0 0 15 1 N21 CS 0
Carbon 6. -0.713673 -0.014253
0.000000 Nitrogen 7. 0.749817 0.123940
0.000000 Hydrogen 1. -0.978788 -1.071520
0.000000 Hydrogen 1. -1.123702 0.463146
-0.889982 Hydrogen 1. 1.129752 -
0.318420 0.824662
$END
$GUESS NGUESS=4 $END
July 11, 1995
- 143 -
$INTGRL $END
$WFN WFNFLG=0 $END
$SCF NCO=9 $END
$NBO NLMO DIPOLE $END
$DEL NOSTAR
ZERO 2 ATOM BLOCKS 4 BY 3
1 3 4 5
2 6 7
3 BY 4
2 6 7
1 3 4 5
- 143 -
$END
#T
@seg
0 #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists
can be inserted in any order within the HONDO input file;
the NBO program rewinds the input file each time it searches
for a keylist.
- 143 -
#ID.6.2 NBO program installation#N
0 The NBO interfacing (driver) routines provided in this
distribution were written for HONDO 7.0, dated 18-JAN-1988.
Section D.6.3 lists the HONDO dependent elements of the NBO
driver routines that may need slight modification for other
versions of the HONDO program.
0 Only one command line is added to the HONDO source code to
run the NBO analysis. A call (``CALL RUNNBO'') should be
inserted at the end of the HONDO properties package (SR
PROPTY in module PRP), as shown below:
SUBROUTINE PROPTY
.
.
.
C C ----- ELECTRON AND SPIN DENSITIES ----- C
IF(NODEN.EQ.0) CALL ELDENS C C <<< BEGINNING OF
NBO INSERT >>> C
CALL RUNNBO C C <<< END OF NBO INSERT >>> C
NCALL=0
IF(SOME) NCALL=1
CALL TIMIT(NCALL)
RETURN
.
.
.
END
#T
@seg
0 #NThe NBO analysis is performed each time the properties
package is called within HONDO. For example, the NBO
analysis of the computed wavefunction will be performed
(unless NOPROP=1 in the $CONTRL namelist) for every single
point calculation, for each point on a scan of a potential
energy surface, and for both the initial and final points of
a geometry optimization. The NBO output will appear immedi-
ately after the Mulliken Population Analysis and the elec-
tric properties in the HONDO output file.
0 The NBO program installation should continue as discussed
- 143 -
in Section A.2.
#ID.6.3 NBO communication with HONDO#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following HONDO routines, records of the dictionary
file, and COMMON blocks:
#_HONDO routines:#T#/
SR DAREAD(IDAF,IODA,IX,NX,IDAR)
SR DIPAMS(BMASS,NCALL,NCODE,SOME)
FN DOTTRI(A,B,N)
FN ENUC(N,Z,C)
SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK)
SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK)
SR SYMFCK(F,H,IA)
#_#NHONDO dictionary file:#/
#_#NHONDO COMMON blocks:#T#/
COMMON/IJPAIR/IA(1)
COMMON/INFOA/NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(50),C(3,50)
COMMON/INTFIL/NOPK,NOK,NOSQUR,NINTMX,NHEX,NTUPL,PACK2E
COMMON/IOFILE/IR,IW,IP,IJK,IPK,IDAF,NAV,IODA(99)
COMMON/MEMORY/MAXCOR,MAXLCM
COMMON/MOLNUC/NUC(50)
COMMON/NSHEL/EX(440),CS(440),CP(440),CD(440),CF(440),CG(440),
+ KSTART(120),KATOM(120),KTYPE(120),KNG(120),
+ KLOC(120),KMIN(120),KMAX(120),NSHELL
COMMON/RUNLAB/TITLE(10),ANAM(50),BNAM(50),BFLAB(512)
COMMON/SCFOPT/SCFTYP
COMMON/SCM/CORE(1)
COMMON/WFNOPT/WFNTYP
#N #BD.7 AMPAC VERSION#N
#ID.7.1 AMPAC sample input#N
0 A sample AMPAC input file that will create default methy-
lamine (AM1 at Pople-Gordon idealized geometry) output simi-
lar to the #Iab initio#N output displayed in Section A.3 is
shown below:
AM1
CH3NH2...AM1//Pople-Gordon standard geometry
C 0.000000 0 0.000000 0 0.000000 0 0 0
0
N 1.470000 0 0.000000 0 0.000000 0 1 0
0
H 1.090000 0 109.471230 0 0.000000 0 1 2
0
H 1.090000 0 109.471230 0 120.000000 0 1 2
July 11, 1995
- 144 -
3
H 1.090000 0 109.471230 0 240.000000 0 1 2
3
H 1.010000 0 109.471230 0 60.000000 0 2 1
3
H 1.010000 0 109.471230 0 300.000000 0 2 1
3
$NBO $END
#T
@seg
0 #NThe keylists of the NBO program should always appear at
the bottom of the AMPAC input file and should be ordered:
$NBO, $CORE, $CHOOSE, $DEL. NBO job options are selected by
inserting their associated keywords (Section B.2) into the
$NBO keylist.
0 Due to the implicit orthogonality of the basis functions,
the following NBO keywords are not applicable to the
wavefunctions computed by AMPAC (or other semi-empirical
packages):
#T
AOPNAO AOPNLMO NAONHO SPNAO
AONAO DINAO NAONLMO SPNHO
AOPNHO DMNAO NAOMO SPNBO
AOPNBO FNAO SAO SPNLMO
#NIn addition, the NBO keywords that require access to the
AO dipole integrals (DIPOLE, DIAO, DINAO, DINHO, DINBO,
DINLMO) are not applicable with AMPAC, since these integrals
are unavailable to the NBO program.
- 144 -
0 The following is a modified AMPAC input file that will
generate, in addition to the default NBO output, the NLMO
and the NBO energetic analyses of methylamine:
AM1
CH3NH2...AM1//Pople-Gordon standard geometry
C 0.000000 0 0.000000 0 0.000000 0 0 0
0
N 1.470000 0 0.000000 0 0.000000 0 1 0
0
H 1.090000 0 109.471230 0 0.000000 0 1 2
0
H 1.090000 0 109.471230 0 120.000000 0 1 2
3
H 1.090000 0 109.471230 0 240.000000 0 1 2
3
H 1.010000 0 109.471230 0 60.000000 0 2 1
3
H 1.010000 0 109.471230 0 300.000000 0 2 1
3
$NBO NLMO $END $DEL NOSTAR
ZERO 2 ATOM BLOCKS 3 BY 4
1 3 4 5
2 6 7
4 BY 3
2 6 7
1 3 4 5 $END
#T
@seg
- 144 -
#ID.7.2 Sample NBO output for AMPAC wavefunctions#N
0 Since the AMPAC output differs in significant respects
from the #Iab initio#N examples presented in Sections A,B,
we present some excerpts from the NBO output and a brief
discussion of the NBO analysis of the AM1 wavefunction for
methylamine (Pople-Gordon idealized geometry). The numeri-
cal values in these exerpts (summary tables) should be ade-
quate for checking purposes.
0 The summary of the Natural Population Analysis (NPA) for
methylamine is shown below:
Summary of Natural Population Analysis:
Natural Population
Natural ---------
--------------------------------------
Atom # Charge Core Valence Rydberg
Total ----------
-------------------------------------------------------------
C 1 -0.13281 2.00000 4.13281 0.00000
6.13281
N 2 -0.34739 2.00000 5.34739 0.00000
7.34739
H 3 0.03346 0.00000 0.96654 0.00000
0.96654
H 4 0.08488 0.00000 0.91512 0.00000
0.91512
H 5 0.08488 0.00000 0.91512 0.00000
0.91512
H 6 0.13849 0.00000 0.86151 0.00000
0.86151
H 7 0.13849 0.00000 0.86151 0.00000
0.86151
=======================================================================
* Total * 0.00000 4.00000 14.00000 0.00000
18.00000
#T
@seg
0 #NNote that the core electrons of all heavy atoms
(neglected in the semi-empirical AMPAC procedure) are incor-
porated into the NPA, along the lines of the treatment of
effective core potentials (Section B.6.12). Note also that
the numerical values of AM1 natural charges (and other quan-
tities) differ significantly from those presented in Section
A.3.2, reflecting a tendency toward somewhat reduced bond
polarities in AM1 wavefunctions.
July 11, 1995
- 145 -
- 145 -
The NBO summary table is shown below:
Natural Bond Orbitals (Summary):
Princi-
pal Delocalizations
NBO Occupancy Energy
(geminal,vicinal,remote)
===============================================================================
Molecular unit 1 (CH5N)
1. BD ( 1) C 1- N 2 1.99095 -20.60408
9(g),10(g),11(g),12(g),13(g)
2. BD ( 1) C 1- H 3 1.99184 -17.81012
8(g),10(g),11(g),9(g)
3. BD ( 1) C 1- H 4 1.98864 -17.75195
12(v),9(g),11(g),8(g)
4. BD ( 1) C 1- H 5 1.98864 -17.75195
13(v),9(g),10(g),8(g)
5. BD ( 1) N 2- H 6 1.98916 -19.74256
13(g),8(g),10(v)
6. BD ( 1) N 2- H 7 1.98916 -19.74256
12(g),8(g),11(v)
7. LP ( 1) N 2 1.98489 -15.52775 9(v)
8. BD*( 1) C 1- N 2 0.01048 4.75597
9. BD*( 1) C 1- H 3 0.02306 4.29359
10. BD*( 1) C 1- H 4 0.01070 4.57248
11. BD*( 1) C 1- H 5 0.01070 4.57248
12. BD*( 1) N 2- H 6 0.01090 5.27834
13. BD*( 1) N 2- H 7 0.01090 5.27834
-------------------------------
Total Lewis 17.92328 ( 99.5738%)
Valence non-Lewis 0.07672 ( 0.4262%)
Rydberg non-Lewis 0.00000 ( 0.0000%)
-------------------------------
Total unit 1 18.00000 (100.0000%)
Charge unit 1 0.00000
#T
@seg
0 #NNote that in this case the orbital energies and other
matrix elements of the Fock operator are printed in electron
volts, the energy units of the AMPAC package. Note also
that the physical pattern of delocalization effects differs
significantly from that shown in Section A.3.6, the AM1
results portraying numerous strong #Igeminal#N interactions
that are not present in the #Iab initio#N output. Other
differences between the AM1 and #Iab initio#N wavefunctions
will be evident throughout the NBO output.
- 145 -
July 11, 1995
- 146 -
0 Finally, we include the output segment showing the NBO
energetic analysis of methylamine:
NOSTAR: Delete all Rydberg/antibond NBOs Deletion of the
following orbitals from the NBO Fock matrix:
8 9 10 11 12 13
Occupations of bond orbitals:
Orbital No deletions This deletion
Change ----------
--------------------------------------------------------------------
1. BD ( 1) C 1- N 2 1.99095 2.00000
0.00905
2. BD ( 1) C 1- H 3 1.99184 2.00000
0.00816
3. BD ( 1) C 1- H 4 1.98864 2.00000
0.01136
4. BD ( 1) C 1- H 5 1.98864 2.00000
0.01136
5. BD ( 1) N 2- H 6 1.98916 2.00000
0.01084
6. BD ( 1) N 2- H 7 1.98916 2.00000
0.01084
7. LP ( 1) N 2 1.98489 2.00000
0.01511
8. BD*( 1) C 1- N 2 0.01048 0.00000
-0.01048
9. BD*( 1) C 1- H 3 0.02306 0.00000
-0.02306
10. BD*( 1) C 1- H 4 0.01070 0.00000
-0.01070
11. BD*( 1) C 1- H 5 0.01070 0.00000
-0.01070
12. BD*( 1) N 2- H 6 0.01090 0.00000
-0.01090
13. BD*( 1) N 2- H 7 0.01090 0.00000
-0.01090
NEXT STEP: Evaluate the energy of the new density matrix
that has been constructed from the deleted NBO
Fock matrix by doing one SCF cycle.
---------
---------------------------------------------------------------------
Energy of deletion : 22.024
Total SCF energy : -5.051
-------------------
Energy change : 27.075 kcal/mol,
27.075 kcal/mol ----------
--------------------------------------------------------------------
#T
@seg
July 11, 1995
- 147 -
0 #NNote that the ``energy of deletion'' (22.0 kcal/mol),
``total SCF energy'' (-5.1 kcal/mol) and ``energy change''
(27.1 kcal/mol) are all given in terms of heats of forma-
tion, the standard AM1 form of expressing molecular ener-
gies.
- 147 -
#ID.7.3 NBO program installation#N
0 The NBO interfacing (driver) routines provided in this
distribution were written for AMPAC, version 1.00. Section
D.7.4 lists the AMPAC dependent elements of the NBO driver
routines that may need slight modification for other ver-
sions of the AMPAC program.
0 Only one command line is added to the AMPAC source code to
run the NBO analysis. A command ``CALL RUNNBO'' should be
inserted in the AMPAC properties package (SR WRITE in module
WRITE), as shown below:
SUBROUTINE WRITE(TIME0,FUNCT)
.
.
.
X=MECI(EIGS,C,CBETA,EIGB, NORBS,NMOS,NCIS, .TRUE.)
ENDIF C C <<< BEGINNING OF NBO INSERT >>> C
CALL RUNNBO C C <<< END OF NBO INSERT >>> C
IF (INDEX(KEYWRD,'MULLIK') +INDEX(KEYWRD,'GRAPH') .NE.
0) THEN
IF (INDEX(KEYWRD,'MULLIK') .NE. 0) THEN
.
.
.
#T
@seg
0 #NThe NBO analysis is performed each time SR WRITE is
called. For example, the NBO analysis of the computed
wavefunction will be performed for every single point calcu-
lation and at the end of geometry optimizations. The NBO
output will appear immediately after the Mulliken Population
Analysis in the AMPAC output file.
0 The NBO program installation should continue as discussed
- 147 -
in Section A.2.
#ID.7.4 NBO communication with AMPAC#N
0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access
the following AMPAC routines and COMMON blocks:
#_AMPAC routines:#T#/
SR GMETRY(GEO,COORD)
SR HCORE(COORD,H,W,WJ,WK,ENUCLR)
SR FOCK2(F,PTOT,P,W,WJ,WK,NUMAT,NFIRST,NMIDLE,NLAST)
SR FOCK1(F,PTOT,PA,PB)
FN HELECT(N,P,H,F)
#_#NAMPAC COMMON blocks:#T#/
INCLUDE 'SIZES'
COMMON /ATHEAT/ ATHEAT
COMMON /DENSTY/ P(MPACK),PA(MPACK),PB(MPACK)
COMMON /ENUCLR/ ENUCLR
COMMON /FOKMAT/ F(MPACK),FB(MPACK)
COMMON /GEOKST/
NATOM,LABELS(NUMATM),NA(NUMATM),NB(NUMATM),
+ NC(NUMATM)
COMMON /GEOM / GEO(3,NUMATM)
COMMON /HMATRX/ H(MPACK)
COMMON /KEYWRD/ KEYWRD
COMMON /MOLKST/
NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
+
NLAST(NUMATM),NORBS,NELECS,NALPHA,NBETA,NCLOSE,
+ NOPEN,NDUMY,FRACT
COMMON /NATORB/ NATORB(107)
COMMON /TITLES/ COMENT(10),TITLE(10)
COMMON /VECTOR/
C(MORB2),EIGS(MAXORB),CBETA(MORB2),EIGB(MAXORB)
COMMON /WMATRX/ WJ(N2ELEC),WK(N2ELEC)
#N #N
#HINDEX#N
Acceptor orbital,A21
ACS Software,A11
AMPAC version,A2,A7,A8,B66,C17
Angular symmetry labels,A5,#IB68#N,C7
Antiperiplanar interaction,A19,A23,B50
Archive file (FILE47),A5,
#IB62-71#N,C8,C14,C31,C36
Arrays
IBXM,C9,C22,C23
JPRINT,C6
July 11, 1995
- 148 -
NBOOPT,C16,#IC17#N,C18,
C26,C30,C36,C39
Atom-centered basis functions,A1
Atomic charge,A14
Atomic orbitals,A1,A5,A6,B67-68
Contracted gaussian,A6,B69-70
Pure (PAO),#IB11#N,B67-68,C19,C30
Slater-type,A6
#Isee#N Atomic shell
#Isee#N Core orbitals
#Isee#N Pre-orthogonal orbitals
Atomic shell
Core,A7,A8,A13,A14,A16,C24
Rydberg,A2,A8,A13,A14,A16,C25
Valence,A8,A13,A14,A16
Atomic units,A13,B65,C4,C13
Attaching NBO to ESS program,
A10-11,C36,C38-39
AUHF method
#Isee#N Wavefunction type
Azimuthal angle (hi
),A20,C33
Basis set
#Isee#N Atomic orbitals
Benzene (C#d6#uH#d6#u),B3,B32-36
Bond bending,A8,A20
#Isee#N Hybrid direction
BONDO program,A7
Bond order,B29-31
Matrix,B11,B65,C19
Boys LMOs,B3
Brunck, T. K.,A7
Canonical MOs,B6,B27-28,B71,C20
Carpenter, J. E.,A7
Chemical fragment,#IB16#N,B19
$CHOOSE list
#Isee#N Keylists
Comments (!),B1,B63,C29
Comment statements,C1
COMMON blocks
/NBAO/,C7
/NBATOM/,C7
/NBBAS/,C9,C22,C31,C30
/NBCRD1/,C11,C29
/NBCRD2/,C12,C29
/NBDAF/,C12,C27,C28
/NBDXYZ/,C11
/NBFLAG/,C5
/NBGEN/,C13,C30
/NBINFO/,C4
/NBIO/,C8,C18
/NBLBL/,C10,C32
July 11, 1995
- 149 -
/NBMOL/,C10
/NBNAO/,C10
/NBONAV/,C12
/NBOPT/,C6-7,C18,C30
/NBTHR/,C9,C18
/NBTOPO/,C11,C22
Contour plotting program,A8,B9,B69
Contracted gaussian orbitals
#Isee#N Atomic orbitals
Copper dimer (Cu#d2#u),B56-61
$CORE list
#Isee#N Keylists
Core orbitals,A6,A7,A8,A16,
B12-13,B56-61,B66,C24,C30,C33
Core polarization,A8,B12
Core table,B12,C33
DAF
#Isee#N Direct access file
Datalists,B63-64
$BASIS,#IB67-68#N,B71,C31,C37
$CONTRACT,#IB69-70#N,C31,C37
$COORD,B63,B65,#IB66#N,C31,C37
$DENSITY,B71
$DIPOLE,B65,B71,C37
$FOCK,B65,B71,C37
$LCAOMO,B71,C37
Matrix,B71
$OVERLAP,B65,B71,C37
#Id#N-orbitals,B53,B56,B61
Default output,A12,B10
Deletion types,B17-19
$DEL (deletions) list
#Isee#N Keylists
Delocalization,A1,A2,A21,B3,B32,B51
Delocalization tail,A22,B23
Density matrix,A1,A5,A6,B6-7,C13
#Isee#N Bond-order matrix
#Isee#N Spin density matrices
Depletion of density matrix,C24
Diborane (B#d2#uH#d6#u),B40-43
Dictionary file,A4
Different Lewis structures for
different spin
#Isee#N Open-shell calculation
Dimension specification,C4
Dipole moment,A5,A6,A8,B5,B6-7,
#IB24-25#N,B65,B71,C11,C15,C24
Direct access file (FILE48),A3,A4,A5,
B9,B65,C12,#IC14-15#N,C16,C27,
C28,C36-39
Directed NBO search
#Isee#N Keylists, $CHOOSE
Directional analysis
July 11, 1995
- 150 -
#Isee#N Hybrid direction
Distribution tape,A10
Donor orbital,A21,A22
Double-bond, no-bond resonance,B44-47
Driver routines,A3
#Isee#N Subroutines RUNNBO, etc.
Edmiston-Ruedenberg LMOs,B3
Effective core potential (ECP),
A8,#IB56-61#N,B66
Electronic structure system (ESS),A3
Common blocks,A4
Connection to NBO program,A3,A4,A7,
A10-11,B56,B62,C36,C38-39
Input file,A5,A11,A12
Output file,A5,A12
Scratch files,A4
#Isee#N AMPAC, GAUSSIAN-8X, #Ietc.#N
ENABLE program,A10,C36
Energetic analysis,A3,A5,#IB16-19#N,
C2,C26,C38,C39
#Isee#N Perturbation theory...
Excited state,A6,A8,A15,B56,C23
#If#N-orbitals
#Isee#N Angular symmetry labels
#Isee#N Keyword CUBICF
Fenske-Hall method
#Isee#N MEDVL
Fetch/Save routines,C15,C27
FILE48
#Isee#N Direct access file
FILE47
#Isee#N Archive file
Flow chart,A4,C3,C16
Fock matrix,A2,A5,A6,A8,A14,A21,
B6,B16-20,B26,B48-51,B65,B71,
C2,C23,C26,C39
Fortran 77,A6,A10
Foster, J.P.,C22
Free format,B1,C29
Freezing a transformation,B8
Functions
EQUAL,C29
IHTYP,C34
IOINQR,C32
IWPRJ,C24
NAMEAT,C34
VECLEN,C35
GAMESS version,A1,A2,A7,A10,A12,C17
Gaussian elimination,C35
GAUSSIAN-8X version,A2,A7,
A10,B56,C17
July 11, 1995
- 151 -
Geminal interaction,A22,B18,C33
Generalized eigenvalue problem,C20
GENNBO input file
#Isee#N Archive file
GENNBO stand-alone program
A10,B9,B62-71,C13,C36,C37,C38
Geometry,B66
Glendening, E. D.,A7
Groups of routines
I (NAO/NBO/NLMO),C2,C16-25
II (energy analysis),C2,C26
III (direct access file),C2,C27-28
IV (free format input),C2,C29
V (other I/O),C2,C30-32
VI (general utility),C2,C33-35
VII (system-dependent),C2,C36
GUGA formalism,A1
GVB method
#Isee#N Wavefunction type
Hay-Wadt ECP,B56
HONDO version,A2,A10,C17,C27
Hybrid composition,A19,B23
Hybrid direction,A8,#IA20#N,B4,C23
Hydrogen fluoride (HF),B37-39
I/O routines
#Isee#N Groups of routines
INP routines,C30,C39
Input file,A5,B62,C14
Installation procedure,A10-11
Ionic hybrids,B37-39
Job control keywords,B2,B3
Job initialization routines,C16,C18
Job threshold keywords,B2,B4-5
Kekulcute e structure,B36
Keylist,A5,A11,A12,#IB1#N
Keylists
$CHOOSE,B1,B2,B12,#IB14-15#N,#IB44-47#N,
B62,B63,B65,C6,C22,C30
$CORE,B1,B2,#IB12-B13#N,
B62,B63,B65,C3,C6-7,C30
$DEL,B1,B2,B12,#IB16-20#N,
#IB48-51#N,B62,C17,C26,C30
$GENNBO,#IB65#N,B66,C30
$NBO,B1,#IB2-11#N,B21-43,B62,B63,
B65,B69,C6,C17,C18,C22,C30
Keyword names (matrix output),B6-7
Keyword parameters (matrix output),B7-8
Keywords
AOINFO,B2,#IB9#N,B69,B71,C6,C31
AOMO,B2,B6,B71,C6
July 11, 1995
- 152 -
AONAO,B2,B6,C6,C30-31
AONBO,B2,B6,C6,C31
AONHO,B2,B6,C6
AONLMO,B2,B3,B6,C6,C31
AOPNAO,B2,B6,B71,C6
AOPNBO,B2,B6,B71,C6
AOPNHO,B2,B6,B71,C6
AOPNLMO,B2,B6,B71,C6
ARCHIVE,B2,#IB9#N,#IB62-71#N,C6,C31
BEND,A8,#IA20#N,B2,#IB4#N,B5,B10,C6,C23
BNDIDX,B2,#IB9#N,B10,B21,
#IB29-B31#N,C6
BOAO,B11,C6
BODM,#IB65#N,C6,C13
BOHR,#IB65#N,B66,,C13
CUBICF,#IB65#N,B68,C6
DESTAR,B18
DETAIL,B2,#IB9#N,C6
DIAO,B2,B7,B71,C6
DINAO,B2,B7,B71,C6
DINBO,B2,B7,B71,C6
DINHO,B2,B7,B71,C6
DINLMO,B2,B6,B7,B71,C6
DIPOLE,A8,B2,B3,#IB5#N,B10,B21,
#IB24-25#N,B71,C6,C17,C24
DMAO,B2,B7,C6
DMNAO,B2,B7,C6
DMNBO,B2,B7,C6
DMNHO,B2,B7,C6
DMNLMO,B2,B7,C6
E2PERT,#IA21#N,B2,#IB4#N,B5,B10,B71,C6
EV,B65
FAO,B2,B7,B71,C6
FNAO,B2,B7,B71,C6
FNBO,B2,B6-8,B7,B71,C6
FNHO,B2,B7,#IB26#N,B71,C6
FNLMO,B2,B7,B71,C6
LFNPR,B2,#IB9#N,C8
Matrix output,B6-8,B26-28
MULAT,B11,C6
MULORB,B11
NAOMO,B2,B6-8,B71,C6
NAONBO,B6-8,C6
NAONHO,B6-8,C6
NAONLMO,B6-8,C6
NATOMS,B65
NBAS,B65
NBODAF,B2,B9
NBO,#IA16-19#N,B2,#IB3#N,B10,C6
NBOMO,B2,B6-8,#IB27-28#N,B71,C6
NBONLMO,B2,B6-8,C6
NBOSUM,#IA22-23#N,B2,#IB3#N,B10,C6,C23
NHOMO,B2,B6-8,B71,C6
NHONBO,B2,B6-8,C6
July 11, 1995
- 153 -
NHONLMO,B2,B6-8,C6
NLMO,B2,#IB3#N,B5,B10,#IB22-23#N,C6
NLMOMO,B2,B6-8,B71,C6
NOBOND,B2,#IB3#N,B21,#IB37-39#N,C6
NOGEM,B18
NOSTAR,B18,#IB48-49#N
NOVIC,B18
NPA,#IA13-15#N,B2,#IB3#N,B10,C6,C20
OPEN,B65
ORTHO,B65
PAOPNAO,B11,C6
PLOT,A8,B2,#IB9#N,B69,B71,C6
PRINT,B2,B5,#IB10#N,B71,C18,C6
PRJTHR,B11
RESONANCE,A16,B2,#IB3#N,B21,
#IB32-36#N,C6,C17,C25
REUSE,#IB65#N,B66,B67,C13
RPNAO,B11,C6
SAO,B2,B7,B71,C6
SKIPBO,B2,#IB3#N,B10,C6
SPNAO,B2,B6-8,B7,B71,C6
SPNBO,B2,B7,B71,C6
SPNHO,B2,B7,B71,C6
SPNLMO,B2,B3,B7,B71,C6
3CBOND,B2,#IB3#N,B14,B21,#IB40-43#N,C6
THRESH,B11
UPPER,B65,B71,C13
ZERO,B19,#IB49-51#N
Kinks
#Isee#N Hybrid direction, Bond bending
Labelled COMMON blocks,A3,A6,C4-13
#Isee#N COMMON blocks
Lewis orbitals
#Isee#N Natural bond orbitals
Linear equations package,C35
Linear independence,A1,C22,C24
Logical file number (LFN),C8,C38,C39
L mlaut owdin, P.-O.,A1
L mlaut owdin orthogonalization,C21
Matrix multiplication,C34
Matrix output keywords,
B2,#IB6-8#N,B9,#IB26-28#N,C7
Mayer-Mulliken bond-order,C19
MCSCF method
#Isee#N Wavefunction type
MEDVL version,A10
Memory allocation,
A6,A12,C16,C18,C19,C22
Methylamine (CH#d3#uNH#d2#u),
A12-23,B21-31,B44-51,B63-71
Methyl radical (CH#d3#u),B52-55
Molecular units,#IB16#N,B18,B19,C10,C23
July 11, 1995
- 154 -
M0t oller-Plesset method
#Isee#N Wavefunction type
MOPAC version,A10
Mulliken population analysis,
A10,B11,C19,C38
Multiple bonds,A19,B14,B44-47,B56-61
Naaman, R.,A7
NAO formation routines,C16,C19-21
Natural atomic orbital (NAO)
Formation,A1,A7,C16,C19-21
Labels,A13-14,C10
Listing,A13,C10
Summary table,A7
#Isee#N Natural population analysis
Natural bond orbital (NBO)
Analysis,A1-2,A16-19
Formalism,A1-A2,A7
Labels,A8,A19,B27-28,B43,C9,C10,C32
Lewis,A2,A16,A19,A21,A23,B48-51,B17
Listing,#IA17-19#N,B2
Non-Lewis,A2,A16,A19,
A21,A23,B17,B18,B48-51
Summary table,#IA22-23#N,C23
3-center,A16,#IB40-43#N
#Isee#N Perturbation theory...
#Isee#N NBO/NLMO formation routines
Natural electron configuration (NEC),
A7,#IA15#N,C20
Natural hybrid orbital (NHO)
Directional analysis,A20
Formation,A1-2
Labels,B26,C10
Listing,A-19
#Isee#N Natural bond orbitals
#Isee#N Hybrid direction
Natural Lewis structure,A1-2,A16,
A19,B3,B18,B48,B49
Energy,B18,B48
Natural localized molecular orbital (NLMO)
Formation,A7,B3,C25
Listing,B3,#IB22-23#N
Natural minimal basis (NMB) set,A2,A14
Natural population analysis (NPA),
A3,A6,A7,#IA13-14#N,B3,
B10,B21,B56-57,C20
Natural Rydberg basis (NRB) set,A2,A18
NBO direct access file
#Isee#N Direct access file
$NBO keylist
#Isee#N Keylists
NBO energetic analysis
#Isee#N Energetic analysis
#Isee#N Perturbation theory...
July 11, 1995
- 155 -
NBO.MAN file,A10,A11
NBO/NLMO formation routines,
C16,C22-25
NBO program,Section C
I/O,A5,A12,C27-32
Installation,A10-11
Organization,A3-4,C2-4
Restrictions,A6
#Isee#N Electronic structure system
NBO.SRC file,A10,C1,C2
NBO summary table,#IA22-23#N,C23
NLMO/NPA bond order,B30-31
Non-Lewis orbitals
#Isee#N Natural Bond Orbital
Open-shell calculation,
A1,A5,B14,B25,#IB52-55#N,B65,C5
#Isee#N Wavefunction type
Orbital contour plotting program,
A8,B9,B69
Orthogonalization,C20
L mlaut owdin (symmetric),C24
Occupancy-weighted (OWSO),C20,C21
Schmidt,C20
Output control keywords,B2,#IB9-10#N
Output file,A8,A12,C1
Overlap matrix,A5,A6,A8,B6,B71,C38
singularities,C25
Overlap-weighted NAO bond order,B30
Perturbation theory energy analysis,
A8,#IA21#N,B3,B4,C23,C39
Phi,A20,C33
PNAO, PNBO, PNHO, PNLMO
#Isee#N Pre-orthogonal orbitals
Polar angle (heta ),A20,C33
Polarization coefficients,A2,A19,C25
Pople-Gordon geometry,A12,A20,B21,B32
Population analysis
#Isee#N Mulliken population analysis
#Isee#N Natural population analysis
Population inversion,A14,B57
Pre-orthogonal orbitals,
A1-2,A6,A8,B6,B65,B71
Print parameters,B2,#IB7-8#N,
B11,B27-28,C7,C10
Program groups,C2
#Isee#N Groups of routines
Program limits
Atoms,A6,C4
Basis functions,A6,C4
Program precedence,C2,C3
Pseudopotential
#Isee#N Effective core potential
July 11, 1995
- 156 -
Pure AOs,B11
#Isee#N Atomic orbital
QCPE,A7,A8
Read (R) parameter
#Isee#N Print parameters
Read-write file,A4
Reed, A. E.,A7,B11,B31,C19
References,A7
Remote interaction,A22,C33
Resonance structures,A9,B14-15,B32-33,
B38,B39,B44-47,C11,C25
Rewind input file,C39
RHF method
#Isee#N Wavefunction type
Rives, A. B.,A7
ROHF method
#Isee#N Wavefunction type
Schleyer, P. v.R.,B31
2nd-order perturbation theory analysis
#Isee#N Perturbation theory energy...
Semi-documented keywords,B2,#IB11#N
Similarity transformation,C19,C26,C34
Slater-type orbitals
#Isee#N AO basis functions
Spin
#Isee#N Open-shell calculations
Spin-annihilated UHF (AUHF) method
#Isee#N Wavefunction type
Spin density matrices,A1,B52-55,C5
Storage
#Isee#N Memory allocation
Subroutines,C2,C3
ANGLES,C33
ANLYZE,C23
AOUT,C31
APRINT,C31,C32
AREAD,C31
ATDIAG,C20
AUGMNT,C25
AWRITE,C31
BDFIND,C33
BLDSTR,C23
CHEM,C33
CHOOSE,C22,C23,C24
CHSDRV,C22
CHSINP,C30
CONSOL,C33
CONVIN,C33
CONVRT,C33
COPY,C33
CORE,C24
July 11, 1995
- 157 -
CORINP,C30
CORTBL,C33
CYCLES,C22,C25
DEBYTE,C33
DELETE,C26
DELINP,C30
DELSCF,A3,A4,A5,C2,#IC36#N,C38,C39
DEPLET,C24
DFGORB,C19,C30
DIPANL,A6,C22,C24
DIPELE,C24
DIPNUC,C24
DMNAO,C19
DMSIM,C19
FACTOR,C35
FEAOIN,A3,A4,A5,C2,C6,
C14,#IC36#N,C38,C39
FEAOMO,C27
FEAOM,C27
FEBAS,C27
FECOOR,C27
FEDNAO,C27
FEDRAW,C27
FEDXYZ,C27
FEE0,C27
FEFAO,C27
FEFNBO,C27
FEINFO,C27
FENBO,C27
Subroutines (#Icontinued#N)
FENEWD,C27
FENLMO,C27
FEPNAO,C27
FEPPAO,C27
FESNAO,C27
FESRAW,C27
FETITL,C27
FETLMO,C27
FETNAB,C27
FETNAO,C27
FETNBO,C27
FETNHO,C27
FNBOAN,C23
FNDFLD,C29
FNDMOL,C23
FNDSOL,C35
FORMT,C25
FRMHYB,C23
FRMPRJ,C25
FRMTMO,C20
GENINP,C30
GETDEL,C23
HALT,C33
HFLD,C29
July 11, 1995
- 158 -
HTYPE,C23
HYBCMP,C23
HYBDIR,C23
IDIGIT,C33
IFLD,C29
INTERP,C32
JACOBI,C25,C34
JOBOPT,C18,C29
LBLAO,C32
LBLNAO,C32
LBLNBO,C32
LBLNHO,C32
LIMTRN,C34
LINEQ,C33,C35
LMOANL,C24
LOADAV,C20
LOAD,C24
MATML2,C34
MATMLT,C34
MULANA,C19
NAOANL,C21
NAODRV,C2,C19
NAOSIM,C19
NAO,C19
NATHYB,C22,C23,C24
NBCLOS,C16,C28
NBINQR,C28
NBOCLA,C23
NBODEL,C26
NBODIM,C18
NBODRV,C2,C19,C22
NBOEAN,A3,A4,A6,C3,C26,C36,C39
NBOINP,C30
NBOPEN,C16,C27
NBOSET,C18,C39
NBO,A3,A4,C2,C16,C36
NBOSUM,C23
NBREAD,C28
NBWRIT,C28
NEWDM,C26
NEWRYD,C20
NEWWTS,C20
NLMO,C22,C24
NORMLZ,C34
ORDER,C34
ORTHYB,C24
OUTPUT,C32
PACK,C34
PRJEXP,C24
RANK,C34
RDCARD,C29
RDCORE,C30
RDPPNA,C30
RDTNAB,C31
July 11, 1995
- 159 -
RDTNAO,C31
REDBLK,C21
REDIAG,C21
REPOL,C25
RFLD,C29
RNKEIG,C26
RUNNBO,A3,A4,#IC36#N,C38,C39
RYDIAG,C20
RYDSEL,C21
SETBAS,C20
SHMDT,C20
SIMLTR,C26
SIMTRM,C19
SIMTRN,C34
SIMTRS,C34
SRTNBO,C22
STASH,C24
STRTIN,C29
SUBST,C35
SVDNAO,C27
SVE0,C27
SVFNBO,C27
SVNBO,C27
SVNEWD,C27
SVNLMO,C27
SVPNAO,C27
SVPPAO,C27
SVSNAO,C27
SVTLMO,C27
Subroutines (#Icontinued#N)
SVTNAB,C27
SVTNAO,C27
SVTNHO,C27
SYMORT,C25
SYMUNI,C25
TRANSP,C34
UNPACK,C35
VALTBL,C35
WRARC,C31
WRBAS,C31
WRMLMO,C31
WRPPNA,C30
WRTNAB,C31
WRTNAO,C30,C31
WRTNBO,C312
XCITED,C23
Symmetric orthogonalization,C24,C25
Symmetry,B16
System-dependent driver routines,C36
TechSet,A11,A20
Theta,A20,C33
3-center bonds
#Isee#N Natural bond orbitals
July 11, 1995
- 160 -
Thresholds,C9
ALLOW2,C20
ALLOW,C20
ANG,B4
ATHR,C23
DANGER,C20,C25
DIAGTH,C20,C25
DIFFER,C24,C34,C34
DONE,C34
DVAL,B5,B25
EPS,C24,C34
ETHR1,C23
ETHR2,C23
ETHR,C23
EVAL,B4
OCC,B4
PCT,B4
PRJINC,C22
PRJTHR,B11,C22
PTHR,C23
TEST2,C20
TEST,C20
THRESH,C22
THR1,C23
THR2,C23
THRESH,B11,C25
TOOSML,C24
WORTH,C20
WTTHR,C20,C21
2e-stabilization,A21
UHF method
#Isee#N Wavefunction type
Upper triangular matrix,
B65,B71,C13,C33,C34
Vager, Z.,A7
Valency index
#Isee#N Bond order
Versions, previous,#IA7#N,A9,B13
Vicinal interaction,A22-23,B18,
B23,B25,B51,C33
Warnings,B16,B17,B36,B55
Wavefunction type
AUHF,C5,C17
CI,A6,C5,C17
Complex,A6,C5
Correlated,B25
GVB,A6
MCSCF,A1,A6,C5
M0t oller-Plesset,A6,C17
RHF,A6,A12,B16,B56,C2
ROHF,A6,C5
July 11, 1995
- 161 -
SCF,A6,B16,B25,C17
Semi-empirical,A7,A8,B66
UHF,A6,B16,B20,B52-55,C2,C5
Weinhold, F.,A7,B11,C19,C22
Weinstock, R. B.,A7,B11,C19
Wiberg bond index,A16,B9,B29,C20,C22
Write (W) parameter
#Isee#N Print parameters
July 11, 1995
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