|
|
#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,9agger J. E. Carpenter,9dagger
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 {
_______________
9agger #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
9dagger #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//15//75//8//35>>|7____________________99____________________
-dwid +0 ipen //+0 +dht ipen //+dhlfwid +0 ipen >>
input basis7 arr NAOs7 arr NHOs7 arr NBOs7 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
9 agger #RPresent address: Bayer AG, Abteilung AV-IM-AM,
5090 Leverkusen, Bayerwerk, Federal Republic of Ger-
many.
9 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
and777777 t99a999999 s99p99i99n99.99999999999999999a99g99g777777r 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 L8mlaut
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
3.09egree , whereas the carbon NHO is approximately aligned
with the C-N axis (within the 1.09egree threshold for print-
ing). The N-H bonds (NBOs 5, 6) are bent even further
(4.49egree ). 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'') #Ii7 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#u7 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
29egree (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#u7 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, IN7 arr OUT, is constructed from the
corresponding acronymns for the two sets in the generic form
``INOUT''. For example, the transformation AO7 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
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(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 IN7 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
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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 AO7 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 NAO7 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. _R_e_q_u_e_s_t _w_r_i_t_i_n_g _o_f #_I_a_l_l#_N _f_i_l_e_s _r_e_q_u_i_r_e_d _b_y _o_r_b_i_t_a_l
_c_o_n_t_o_u_r _p_l_o_t_t_i_n_g _p_r_o_g_r_a_m_s _O_R_B#|_P_L_O_T. _T_h_i_s _a_c_t_i_v_a_t_e_s _t_h_e
_A_O_I_N_F_O _k_e_y_w_o_r_d, _a_s _w_e_l_l _a_s _a_l_l _t_h_e _n_e_c_e_s_s_a_r_y _m_a_t_r_i_x _o_u_t_p_u_t
_k_e_y_w_o_r_d_s (_A_O_N_B_O=_W_3_7, _e_t_c.) _t_h_a_t _c_o_u_l_d _b_e _r_e_q_u_i_r_e_d _f_o_r
_O_R_B_P_L_O_T.
_R_e_q_u_e_s_t _w_r_i_t_i_n_g _t_h_e _F_I_L_E_4_7 `_a_r_c_h_i_v_e' _f_i_l_e _t_o _e_x_t_e_r_n_a_l _d_i_s_k
_f_i_l_e _L_F_N = #_I_n#_N (_o_r, _i_f ``=_n'' _i_s _n_o_t _p_r_e_s_e_n_t, _t_o _t_h_e
_d_e_f_a_u_l_t _L_F_N = _4_7). _T_h_i_s _f_i_l_e _c_a_n _s_e_r_v_e _a_s _t_h_e _i_n_p_u_t _f_i_l_e _t_o
_r_u_n _t_h_e _G_E_N_N_B_O _p_r_o_g_r_a_m _i_n _s_t_a_n_d-_a_l_o_n_e _m_o_d_e, _t_o _r_e_p_e_a_t _t_h_e
_N_B_O _a_n_a_l_y_s_i_s (_p_o_s_s_i_b_l_y _w_i_t_h _n_e_w _j_o_b _o_p_t_i_o_n_s) _w_i_t_h_o_u_t _r_e_p_e_a_t_-
_i_n_g _t_h_e _c_a_l_c_u_l_a_t_i_o_n _o_f _t_h_e _w_a_v_e_f_u_n_c_t_i_o_n (_S_e_c_t_i_o_n _B._7).
_R_e_q_u_e_s_t _w_r_i_t_i_n_g _t_h_e _N_B_O _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e (_D_A_F) _t_o _e_x_t_e_r_n_a_l
_d_i_s_k _f_i_l_e _L_F_N = #_I_n#_N (_o_r, _i_f ``=_n'' _i_s _n_o_t _p_r_e_s_e_n_t, _t_o _t_h_e
_d_e_f_a_u_l_t _L_F_N =_4_8). #_I_B._2._6 _P_r_i_n_t _L_e_v_e_l _K_e_y_w_o_r_d_s#_N
_0 _T_h_e _k_e_y_w_o_r_d ``_P_R_I_N_T=_n'' (#_I_n#_N = _0-_4) _c_a_n _b_e _u_s_e_d _t_o _g_i_v_e
_c_o_n_v_e_n_i_e_n_t, _f_l_e_x_i_b_l_e _c_o_n_t_r_o_l _o_f _a_l_l _N_B_O _o_u_t_p_u_t _i_n _t_e_r_m_s _o_f _a
_s_p_e_c_i_f_i_e_d _p_r_i_n_t _l_e_v_e_l #_I_n#_N. _T_h_i_s _k_e_y_w_o_r_d _a_c_t_i_v_a_t_e_s _g_r_o_u_p_s
_o_f _k_e_y_w_o_r_d_s _i_n _a _h_e_i_r_a_r_c_h_i_c_a_l _m_a_n_n_e_r, _a_n_d _t_h_u_s _i_n_c_r_e_m_e_n_t_a_l_l_y
_i_n_c_r_e_a_s_e_s _t_h_e _v_o_l_u_m_e _o_f _o_u_t_p_u_t, _r_a_n_g_i_n_g _f_r_o_m #_I_n_o#_N _N_B_O _o_u_t_-
_p_u_t (_P_R_I_N_T=_0) _t_o _a _c_o_n_s_i_d_e_r_a_b_l_e _v_o_l_u_m_e _o_f _d_e_t_a_i_l (_P_R_I_N_T=_4).
_T_h_e _k_e_y_w_o_r_d_s _a_s_s_o_c_i_a_t_e_d _w_i_t_h _e_a_c_h _p_r_i_n_t _l_e_v_e_l _a_r_e _t_a_b_u_l_a_t_e_d
_b_e_l_o_w [_d_e_f_a_u_l_t _v_a_l_u_e, _P_R_I_N_T=_2]:
July 11, 1995
- 36 -
_F_o_r _e_a_c_h _p_r_i_n_t _l_e_v_e_l #_I_n#_N, _t_h_e _N_B_O _o_u_t_p_u_t _w_i_l_l _i_n_c_l_u_d_e
_i_t_e_m_s _a_c_t_i_v_a_t_e_d _b_y _t_h_e _l_i_s_t_e_d _k_e_y_w_o_r_d_s, _a_s _w_e_l_l _a_s _a_l_l _i_t_e_m_s
_f_r_o_m _l_o_w_e_r _p_r_i_n_t _l_e_v_e_l_s.
_0 _W_h_e_n _a_d_d_i_t_i_o_n_a_l _k_e_y_w_o_r_d_s _a_r_e _i_n_c_l_u_d_e_d _w_i_t_h _a ``_P_R_I_N_T=_n''
_k_e_y_w_o_r_d _i_n _t_h_e $_N_B_O _k_e_y_l_i_s_t, _t_h_e _N_B_O _o_u_t_p_u_t _i_n_c_l_u_d_e_s _t_h_e
_a_d_d_i_t_i_o_n_a_l _k_e_y_w_o_r_d _i_t_e_m_s _a_s _w_e_l_l _a_s _t_h_o_s_e _i_m_p_l_i_e_d _b_y _t_h_e
_p_r_i_n_t _l_e_v_e_l. _T_h_i_s _c_a_n _b_e _u_s_e_d _t_o _t_a_i_l_o_r _t_h_e _N_B_O _o_u_t_p_u_t _t_o
_v_i_r_t_u_a_l_l_y _a_n_y _s_e_l_e_c_t_i_o_n _o_f _o_u_t_p_u_t _i_t_e_m_s. _F_o_r _e_x_a_m_p_l_e, _t_h_e
_k_e_y_l_i_s_t
#_T
$_N_B_O _P_R_I_N_T=_2 _N_L_M_O _F_N_B_O=_P _N_A_O_M_O=_P_1_1 $_E_N_D
#_N_w_o_u_l_d _a_d_d _t_o _t_h_e _s_t_a_n_d_a_r_d _m_e_t_h_y_l_a_m_i_n_e _o_u_t_p_u_t _f_i_l_e _o_f _S_e_c_-
_t_i_o_n _A._3 _a_n _N_L_M_O _s_u_m_m_a_r_y _t_a_b_l_e, _t_h_e _F_o_c_k _m_a_t_r_i_x _i_n _t_h_e _N_B_O
_b_a_s_i_s, _a_n_d _t_h_e _t_r_a_n_s_f_o_r_m_a_t_i_o_n _c_o_e_f_f_i_c_i_e_n_t_s _f_o_r _t_h_e _f_i_r_s_t _1_1
_m_o_l_e_c_u_l_a_r _o_r_b_i_t_a_l_s _i_n _t_e_r_m_s _o_f _N_A_O_s. _S_i_m_i_l_a_r_l_y, _t_o _p_r_o_d_u_c_e
_t_h_e _N_P_A _l_i_s_t_i_n_g _o_n_l_y, _o_n_e _c_o_u_l_d _u_s_e
#_T
$_N_B_O _P_R_I_N_T=_1 _S_K_I_P_B_O $_E_N_D
#_N_o_r
#_T
$_N_B_O _P_R_I_N_T=_0 _N_P_A $_E_N_D
#_N[_T_h_e_r_e _i_s _a_c_t_u_a_l_l_y _a _s_l_i_g_h_t _d_i_f_f_e_r_e_n_c_e _b_e_t_w_e_e_n _t_h_e _t_w_o
_e_x_a_m_p_l_e_s: _T_h_e _N_B_O_s _a_r_e _d_e_t_e_r_m_i_n_e_d _b_y _d_e_f_a_u_l_t (_o_n_c_e _t_h_e $_N_B_O
_k_e_y_l_i_s_t _i_s _e_n_c_o_u_n_t_e_r_e_d), _e_v_e_n _i_f _a_l_l _o_u_t_p_u_t _i_s _s_u_p_p_r_e_s_s_e_d
_w_i_t_h _P_R_I_N_T=_0; _i_n _t_h_e _f_i_r_s_t _e_x_a_m_p_l_e, _t_h_e _k_e_y_w_o_r_d _S_K_I_P_B_O
_b_y_p_a_s_s_e_s _N_B_O _d_e_t_e_r_m_i_n_a_t_i_o_n, _w_h_e_r_e_a_s _i_n _t_h_e _s_e_c_o_n_d _e_x_a_m_p_l_e
_t_h_e _N_B_O_s _a_r_e _s_t_i_l_l _d_e_t_e_r_m_i_n_e_d `_i_n _b_a_c_k_g_r_o_u_n_d.'] #_I_B._2._7
_S_e_m_i-_D_o_c_u_m_e_n_t_e_d _A_d_d_i_t_i_o_n_a_l _K_e_y_w_o_r_d_s#_N
_0 _S_o_m_e _a_d_d_i_t_i_o_n_a_l _k_e_y_w_o_r_d_s _a_r_e _l_i_s_t_e_d _b_e_l_o_w _t_h_a_t _m_a_y _o_f _u_s_e
_t_o _s_p_e_c_i_a_l_i_s_t_s _o_r _p_r_o_g_r_a_m _d_e_v_e_l_o_p_e_r_s:
#_I_O_P_T_I_O_N _D_E_S_C_R_I_P_T_I_O_N#_N
_S_e_t _t_h_e _t_h_r_e_s_h_o_l_d _o_f _o_r_b_i_t_a_l _o_c_c_u_p_a_n_c_y _d_e_s_i_r_e_d _f_o_r _b_o_n_d
_o_r_b_i_t_a_l _s_e_l_e_c_t_i_o_n. _I_f _t_h_i_s _i_s _n_o_t _i_n_c_l_u_d_e_d, _t_h_e _d_e_f_a_u_l_t
_o_c_c_u_p_a_n_c_y [_1._9_0] _w_i_l_l _b_e _u_s_e_d (_o_r _v_a_l_u_e_s _d_e_c_r_e_a_s_i_n_g _f_r_o_m
_1._9_0 _t_o _1._5_0 _b_y _0._1_0 _s_t_e_p_s, _i_f _t_h_e _R_E_S_O_N_A_N_C_E _k_e_y_w_o_r_d _i_s
_i_n_c_l_u_d_e_d).
_S_e_t _t_h_e _p_r_o_j_e_c_t_i_o_n _t_h_r_e_s_h_o_l_d [_d_e_f_a_u_l_t _0._2_0] _t_o _d_e_t_e_r_m_i_n_e _i_f
_a `_n_e_w' _h_y_b_r_i_d _o_r_b_i_t_a_l _h_a_s _t_o_o _h_i_g_h _o_v_e_r_l_a_p _w_i_t_h _h_y_b_r_i_d_s
_p_r_e_v_i_o_u_s_l_y _f_o_u_n_d.
_P_r_i_n_t _t_o_t_a_l _g_r_o_s_s _M_u_l_l_i_k_e_n _p_o_p_u_l_a_t_i_o_n_s _b_y _a_t_o_m.
_P_r_i_n_t _g_r_o_s_s _M_u_l_l_i_k_e_n _p_o_p_u_l_a_t_i_o_n_s, _b_y _o_r_b_i_t_a_l _a_n_d _a_t_o_m.
_R_e_v_i_s_e_s _P_A_O _t_o _P_N_A_O _t_r_a_n_s_f_o_r_m_a_t_i_o_n _m_a_t_r_i_x _b_y _p_o_s_t-
_m_u_l_t_i_p_l_y_i_n_g _b_y #_B_T#_N#_d_R_y_d#_u _a_n_d #_B_T#_N#_d_r_e_d#_u [_s_e_e _t_h_e _N_P_A
July 11, 1995
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_p_a_p_e_r:
_A. _E. _R_e_e_d, _R. _B. _W_e_i_n_s_t_o_c_k, _a_n_d _F. _W_e_i_n_h_o_l_d, _J. _C_h_e_m. _P_h_y_s.
#_B_8_3#_N, _7_3_5-_7_4_6 (_1_9_8_5)].
_I_n_p_u_t _o_r _o_u_t_p_u_t _o_f _p_u_r_e _A_O (_P_A_O) _t_o _p_r_e-_N_A_O (_P_N_A_O) _t_r_a_n_s_f_o_r_-
_m_a_t_i_o_n. _T_h_e _P_A_O_s _a_r_e _A_O_s _o_f _p_u_r_e _a_n_g_u_l_a_r _m_o_m_e_n_t_u_m _s_y_m_m_e_t_r_y
(_r_a_t_h_e_r _t_h_a_n _c_a_r_t_e_s_i_a_n _g_a_u_s_s_i_a_n_s). _T_h_i_s _k_e_y_w_o_r_d _c_a_n _b_e _u_s_e_d
_w_i_t_h _r_e_a_d (`_R'), _w_r_i_t_e (`_W', _d_e_f_a_u_l_t _L_F_N _4_3) _o_r _p_r_i_n_t (`_P')
_p_a_r_a_m_e_t_e_r_s.
_P_r_i_n_t _o_u_t _t_h_e _b_o_n_d-_o_r_d_e_r _m_a_t_r_i_x (_F_o_c_k-_D_i_r_a_c _d_e_n_s_i_t_y _m_a_t_r_i_x)
_i_n _t_h_e _b_a_s_i_s _s_e_t _o_f _i_n_p_u_t _A_O_s. _T_h_i_s _k_e_y_w_o_r_d _c_a_n _b_e _u_s_e_d
_w_i_t_h _w_r_i_t_e (`_W', _d_e_f_a_u_l_t _L_F_N _4_9) _o_r _p_r_i_n_t (`_P') _p_a_r_a_m_e_t_e_r_s.
#_B_B._3 _T_H_E $_C_O_R_E _L_I_S_T#_N
_0 _I_n _t_h_e _L_e_w_i_s _s_t_r_u_c_t_u_r_e _p_i_c_t_u_r_e, _t_h_e _i_n_n_e_r `_c_o_r_e' _e_l_e_c_t_r_o_n
_p_a_i_r_s _a_r_e _p_i_c_t_u_r_e_d _a_s _o_c_c_u_p_y_i_n_g _o_r_b_i_t_a_l_s _h_a_v_i_n_g _e_s_s_e_n_t_i_a_l_l_y
_i_s_o_l_a_t_e_d _a_t_o_m_i_c _o_r_b_i_t_a_l _c_h_a_r_a_c_t_e_r. _I_n _N_B_O _p_a_r_l_a_n_c_e, _t_h_e_s_e
_c_o_r_e _o_r_b_i_t_a_l_s _c_o_r_r_e_s_p_o_n_d _t_o _1-_c_e_n_t_e_r _u_n_h_y_b_r_i_d_i_z_e_d _N_A_O_s _o_f
_n_e_a_r-_m_a_x_i_m_u_m _o_c_c_u_p_a_n_c_y, _w_h_i_c_h _a_r_e _i_s_o_l_a_t_e_d _o_n _e_a_c_h _c_e_n_t_e_r
_b_e_f_o_r_e _t_h_e _m_a_i_n _N_B_O _s_e_a_r_c_h _b_e_g_i_n_s _f_o_r _l_o_c_a_l_i_z_e_d _v_a_l_e_n_c_e
_e_l_e_c_t_r_o_n _p_a_i_r_s. _A _w_a_r_n_i_n_g _m_e_s_s_a_g_e _i_s _p_r_i_n_t_e_d _i_f _t_h_e _o_c_c_u_-
_p_a_n_c_y _o_f _a _p_r_e_s_u_m_e_d _c_l_o_s_e_d-_s_h_e_l_l _c_o_r_e _N_B_O _f_a_l_l_s _b_e_l_o_w _1._9_9_9_0
_e_l_e_c_t_r_o_n_s (_o_r _0._9_9_9_0 _i_n _t_h_e _o_p_e_n-_s_h_e_l_l _c_a_s_e), _i_n_d_i_c_a_t_i_v_e _o_f
_a _p_o_s_s_i_b_l_e _c_o_r_e-_v_a_l_e_n_c_e _m_i_x_i_n_g _e_f_f_e_c_t _o_f _p_h_y_s_i_c_a_l _s_i_g_n_i_f_i_-
_c_a_n_c_e.
_0 [_I_n _p_r_e_v_i_o_u_s _v_e_r_s_i_o_n_s _o_f _t_h_e _N_B_O _p_r_o_g_r_a_m, _c_o_r_e _o_r_b_i_t_a_l_s
_h_a_v_i_n_g _t_h_e _e_x_p_e_c_t_e_d _p_u_r_e _a_t_o_m_i_c _c_h_a_r_a_c_t_e_r _a_r_e _f_o_u_n_d _i_n
_e_s_s_e_n_t_i_a_l_l_y _a_l_l _c_a_s_e_s, _e_x_c_e_p_t _w_h_e_r_e _a_n `_a_c_c_i_d_e_n_t_a_l' _d_e_g_e_n_-
_e_r_a_c_y _i_n _o_c_c_u_p_a_n_c_y _o_f _c_o_r_e _a_n_d _v_a_l_e_n_c_e _l_o_n_e _p_a_i_r_s _l_e_a_d_s _t_o
_u_n_d_e_s_i_r_a_b_l_e _c_o_r_e-_v_a_l_e_n_c_e _m_i_x_i_n_g; _t_h_e _p_r_e_s_e_n_t _v_e_r_s_i_o_n _e_x_p_l_i_-
_c_i_t_l_y _i_s_o_l_a_t_e_s _c_o_r_e _p_a_i_r_s _a_s _u_n_h_y_b_r_i_d_i_z_e_d _N_A_O_s _p_r_i_o_r _t_o _t_h_e
_m_a_i_n _N_B_O _s_e_a_r_c_h _t_o _p_r_e_v_e_n_t _t_h_i_s _u_n_p_h_y_s_i_c_a_l _e_f_f_e_c_t.]
_0 _T_h_e _N_B_O _p_r_o_g_r_a_m _c_o_n_t_a_i_n_s _a _t_a_b_l_e _g_i_v_i_n_g _t_h_e _n_o_m_i_n_a_l _n_u_m_b_e_r
_o_f _c_o_r_e _o_r_b_i_t_a_l_s _t_o _b_e _i_s_o_l_a_t_e_d _o_n _e_a_c_h _t_y_p_e _o_f _a_t_o_m (_e._g.,
_1#_I_s#_N _f_o_r _f_i_r_s_t-_r_o_w _a_t_o_m_s _L_i-_N_e, _1#_I_s#_N, _2#_I_s#_N, _2#_I_p#_N _f_o_r
_s_e_c_o_n_d-_r_o_w _a_t_o_m_s _N_a-_A_r, _e_t_c.). _A_t _t_i_m_e_s, _h_o_w_e_v_e_r, _i_t _i_s
_i_n_t_e_r_e_s_t_i_n_g _t_o _e_x_a_m_i_n_e _t_h_e _e_f_f_e_c_t _o_f _a_l_l_o_w_i_n_g _c_o_r_e _o_r_b_i_t_a_l_s
_t_o _m_i_x _i_n_t_o _t_h_e _b_o_n_d_i_n_g _h_y_b_r_i_d_s, _o_r _t_o _h_y_b_r_i_d_i_z_e (_p_o_l_a_r_i_z_e)
_a_m_o_n_g _t_h_e_m_s_e_l_v_e_s. _T_h_i_s _c_a_n _b_e _a_c_c_o_m_p_l_i_s_h_e_d _b_y _i_n_c_l_u_d_i_n_g _a
$_C_O_R_E _k_e_y_l_i_s_t _t_o _s_p_e_c_i_f_y _t_h_e _n_u_m_b_e_r _o_f _c_o_r_e _o_r_b_i_t_a_l_s _t_o _b_e
_i_s_o_l_a_t_e_d _o_n _e_a_c_h _a_t_o_m_i_c _c_e_n_t_e_r, _t_h_u_s _m_o_d_i_f_y_i_n_g _t_h_e _n_o_m_i_n_a_l
_c_o_r_e _t_a_b_l_e. _U_n_l_i_k_e _o_t_h_e_r _N_B_O _k_e_y_l_i_s_t_s, _t_h_e $_C_O_R_E _l_i_s_t
_i_n_c_l_u_d_e_s _o_n_l_y _i_n_t_e_g_e_r_s (_r_a_t_h_e_r _t_h_a_n _k_e_y_w_o_r_d_s) _t_o _s_p_e_c_i_f_y _t_h_e
_c_o_r_e _m_o_d_i_f_i_c_a_t_i_o_n_s, _b_u_t _t_h_e _r_u_l_e_s _a_r_e _o_t_h_e_r_w_i_s_e _s_i_m_i_l_a_r _t_o
_t_h_o_s_e _f_o_r _o_t_h_e_r _k_e_y_l_i_s_t_s. _T_h_e $_C_O_R_E _l_i_s_t (_i_f _i_n_c_l_u_d_e_d) _m_u_s_t
_f_o_l_l_o_w _t_h_e $_N_B_O _k_e_y_l_i_s_t _a_n_d _p_r_e_c_e_d_e _t_h_e $_C_H_O_O_S_E _o_r $_D_E_L
_k_e_y_l_i_s_t_s.
_0 _T_h_e _f_o_r_m_a_t _o_f _t_h_e $_C_O_R_E _m_o_d_i_f_i_c_a_t_i_o_n _l_i_s_t _i_s:
July 11, 1995
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_T_h_e _k_e_y_w_o_r_d ``$_C_O_R_E''
_P_a_i_r_s _o_f _i_n_t_e_g_e_r_s, _o_n_e _p_a_i_r _f_o_r _e_a_c_h _c_e_n_t_e_r. _T_h_e _f_i_r_s_t
_i_n_t_e_g_e_r _i_n_d_i_c_a_t_e_s _t_h_e _a_t_o_m_i_c _c_e_n_t_e_r (_i_n _t_h_e _n_u_m_b_e_r_i_n_g _o_f _t_h_e
_m_a_i_n _E_S_S) _a_n_d _t_h_e _s_e_c_o_n_d _i_s _t_h_e _n_u_m_b_e_r _o_f _c_o_r_e _o_r_b_i_t_a_l_s _t_o
_b_e _i_s_o_l_a_t_e_d _o_n _t_h_a_t _a_t_o_m. _N_o_t_e _t_h_a_t _a_t_o_m_i_c _c_e_n_t_e_r_s _n_o_t
_i_n_c_l_u_d_e_d _i_n _t_h_e _C_O_R_E _l_i_s_t _a_r_e _a_s_s_i_g_n_e_d _d_e_f_a_u_l_t _c_o_r_e_s.
_T_h_e _k_e_y_w_o_r_d ``$_E_N_D'', _t_o _i_n_d_i_c_a_t_e _t_h_e _e_n_d _o_f _c_o_r_e _i_n_p_u_t.
_T_h_e _e_n_t_i_r_e _l_i_s_t _m_a_y _a_l_s_o _b_e _c_o_n_d_e_n_s_e_d _t_o _a _s_i_n_g_l_e _l_i_n_e, _b_u_t
_t_h_e _w_o_r_d ``$_C_O_R_E'' _m_u_s_t _o_c_c_u_r _a_s _t_h_e _f_i_r_s_t _w_o_r_d _o_f _t_h_e _l_i_n_e
_a_n_d ``$_E_N_D'' _a_s _t_h_e _l_a_s_t _w_o_r_d; _t_h_a_t _i_s, _t_h_e _c_o_r_e _m_o_d_i_f_i_c_a_-
_t_i_o_n _k_e_y_l_i_s_t _c_a_n_n_o_t _c_o_n_t_i_n_u_e _o_n _a _l_i_n_e _t_h_a_t _c_o_n_t_a_i_n_s _o_t_h_e_r
_k_e_y_l_i_s_t _i_n_f_o_r_m_a_t_i_o_n.
_0 _T_h_e _c_o_r_e _o_r_b_i_t_a_l_s _a_r_e _i_s_o_l_a_t_e_d _b_y _o_c_c_u_p_a_n_c_y, _t_h_e _m_o_s_t
_o_c_c_u_p_i_e_d _N_A_O_s _b_e_i_n_g _f_i_r_s_t _s_e_l_e_c_t_e_d, _a_n_d _f_u_l_l _s_u_b_s_h_e_l_l_s _a_r_e
_i_s_o_l_a_t_e_d _a_t _a _t_i_m_e. _T_h_u_s, _f_o_r _e_x_a_m_p_l_e, _t_o _s_e_l_e_c_t _t_h_e _f_i_v_e
_o_r_b_i_t_a_l_s _o_f _t_h_e #_I_n#_N = _1 _a_n_d #_I_n#_N = _2 _s_h_e_l_l_s _a_s _c_o_r_e _o_r_b_i_-
_t_a_l_s, _i_t _w_o_u_l_d _m_a_k_e _n_o _d_i_f_f_e_r_e_n_c_e _t_o _s_e_l_e_c_t ``_3'' _o_r ``_4''
(_i_n_s_t_e_a_d _o_f ``_5''), _s_i_n_c_e _a_l_l _t_h_r_e_e _o_f _t_h_e_s_e _c_h_o_i_c_e_s _w_o_u_l_d
_s_p_e_c_i_f_y _a _c_o_r_e _c_o_n_t_a_i_n_i_n_g _a _1#_I_s#_N, _2#_I_s#_N, _a_n_d _a_l_l _t_h_r_e_e
_2#_I_p#_N _o_r_b_i_t_a_l_s. _T_h_e $_C_O_R_E _m_o_d_i_f_i_c_a_t_i_o_n _l_i_s_t _i_s _r_e_a_d _o_n_l_y
_o_n_c_e, _a_n_d _a_p_p_l_i_e_s _t_o _b_o_t_h _l_p_h_a _a_n_d7777777777777 t99a999999 s99p99i99n9999 m99a99n99i99f99o99l99d99s9999 i99n9999 a99n9999 o99_p7777777777777_n-_s_h_e_l_l _c_a_l_c_u_l_a_-
_t_i_o_n.
_A_n _e_x_a_m_p_l_e, _a_p_p_r_o_p_r_i_a_t_e _f_o_r _N_i(_1)-_C(_2)-_O(_3) _w_i_t_h _t_h_e _i_n_d_i_-
_c_a_t_e_d _n_u_m_b_e_r_i_n_g _o_f _a_t_o_m_s, _i_s _s_h_o_w_n _b_e_l_o_w:
#_T
$_C_O_R_E
_1 _5
$_E_N_D
#_N_T_h_i_s _w_o_u_l_d _d_i_r_e_c_t _t_h_e _N_B_O _p_r_o_g_r_a_m _t_o _i_s_o_l_a_t_e _o_n_l_y _5 _c_o_r_e
_o_r_b_i_t_a_l_s _o_n _N_i_c_k_e_l (_a_t_o_m _1), _r_a_t_h_e_r _t_h_a_n _t_h_e _n_o_m_i_n_a_l _9 _c_o_r_e
_o_r_b_i_t_a_l_s. _I_n _o_t_h_e_r _w_o_r_d_s, _o_n_l_y _1#_I_s#_N, _2#_I_s#_N, _a_n_d _2#_I_p#_N
_o_r_b_i_t_a_l_s _w_i_l_l _b_e _c_o_n_s_i_d_e_r_e_d _a_s _c_o_r_e _o_r_b_i_t_a_l_s _i_n _t_h_e _s_e_a_r_c_h
_f_o_r _N_B_O_s _o_f _N_i_C_O, _a_l_l_o_w_i_n_g _t_h_e _3#_I_s#_N _a_n_d _3#_I_p#_N _o_r_b_i_t_a_l_s _t_o
_m_i_x _w_i_t_h _v_a_l_e_n_c_e _N_A_O_s _i_n _b_o_n_d _f_o_r_m_a_t_i_o_n. _S_i_n_c_e _t_h_e _c_a_r_b_o_n
_a_n_d _o_x_y_g_e_n _a_t_o_m_s _w_e_r_e _n_o_t _i_n_c_l_u_d_e_d _i_n _t_h_e _m_o_d_i_f_i_c_a_t_i_o_n _l_i_s_t,
_t_h_e _n_o_m_i_n_a_l _s_e_t _o_f _c_o_r_e _o_r_b_i_t_a_l_s (_1#_I_s#_N _o_n_l_y) _i_s _i_s_o_l_a_t_e_d
_o_n _e_a_c_h _o_f _t_h_e_s_e _a_t_o_m_s.
[_T_h_e _a_l_t_e_r_n_a_t_i_v_e _e_x_a_m_p_l_e
#_T
$_C_O_R_E _1 _0 _2 _0 _3 _0 $_E_N_D
#_N(_n_o _c_o_r_e_s) _w_o_u_l_d _a_l_l_o_w _a_l_l _N_A_O_s _t_o _b_e _i_n_c_l_u_d_e_d _i_n _t_h_e _N_B_O
_s_e_a_r_c_h; _t_h_i_s _w_o_u_l_d _b_e _e_q_u_i_v_a_l_e_n_t _t_o _t_h_e _d_e_f_a_u_l_t _t_r_e_a_t_m_e_n_t _i_n
_t_h_e _e_a_r_l_i_e_r _v_e_r_s_i_o_n _o_f _t_h_e _p_r_o_g_r_a_m (_s_e_e _S_e_c_t_i_o_n _A._1._5).]
#_B_B._4 _T_H_E $_C_H_O_O_S_E _K_E_Y_L_I_S_T (_D_I_R_E_C_T_E_D _N_B_O _S_E_A_R_C_H)#_N
_0 _A $_C_H_O_O_S_E _k_e_y_l_i_s_t _r_e_q_u_e_s_t_s _t_h_a_t _t_h_e _N_B_O _s_e_a_r_c_h _b_e _d_i_r_e_c_t_e_d
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_t_o
_f_i_n_d _a _p_a_r_t_i_c_u_l_a_r _L_e_w_i_s _s_t_r_u_c_t_u_r_e (`_r_e_s_o_n_a_n_c_e _s_t_r_u_c_t_u_r_e')
_c_h_o_s_e_n _b_y _t_h_e _u_s_e_r. (_T_h_i_s _i_s _u_s_e_f_u_l _f_o_r _t_e_s_t_i_n_g _t_h_e _a_c_c_u_-
_r_a_c_y _o_f _a_l_t_e_r_n_a_t_i_v_e _r_e_s_o_n_a_n_c_e _s_t_r_u_c_t_u_r_e _r_e_p_r_e_s_e_n_t_a_t_i_o_n_s _o_f
_t_h_e _w_a_v_e_f_u_n_c_t_i_o_n, _r_e_l_a_t_i_v_e _t_o _t_h_e _o_p_t_i_m_a_l _L_e_w_i_s _s_t_r_u_c_t_u_r_e
_r_e_t_u_r_n_e_d _i_n _a _f_r_e_e _N_B_O _s_e_a_r_c_h.) _I_n _t_h_e $_C_H_O_O_S_E _l_i_s_t, _a
_r_e_s_o_n_a_n_c_e _s_t_r_u_c_t_u_r_e _i_s _s_p_e_c_i_f_i_e_d _b_y _i_n_d_i_c_a_t_i_n_g _w_h_e_r_e _l_o_n_e
_p_a_i_r_s _a_n_d _b_o_n_d_s (_i_n_c_l_u_d_i_n_g _m_u_l_t_i_p_l_e _b_o_n_d_s) _a_r_e _t_o _b_e _f_o_u_n_d
_i_n _t_h_e _m_o_l_e_c_u_l_e. _I_n _s_o_m_e _c_a_s_e_s, _t_h_e _u_s_e_r _m_a_y _w_i_s_h _t_o
_s_p_e_c_i_f_y _o_n_l_y _t_h_e _l_o_c_a_t_i_o_n _o_f _b_o_n_d_s, _l_e_t_t_i_n_g _t_h_e _N_B_O _a_l_g_o_-
_r_i_t_h_m _s_e_e_k _t_h_e _b_e_s_t _l_o_c_a_t_i_o_n _f_o_r _l_o_n_e _p_a_i_r_s, _b_u_t _i_t _i_s _u_s_u_-
_a_l_l_y _s_a_f_e_s_t _t_o _c_o_m_p_l_e_t_e_l_y _s_p_e_c_i_f_y _t_h_e _r_e_s_o_n_a_n_c_e _s_t_r_u_c_t_u_r_e,
_b_o_t_h _l_o_n_e _p_a_i_r_s _a_n_d _b_o_n_d_s.
_0 _T_h_e _f_o_r_m_a_t _o_f _t_h_e $_C_H_O_O_S_E _l_i_s_t _i_s:
_T_h_e _k_e_y_w_o_r_d ``$_C_H_O_O_S_E''
_T_h_e _k_e_y_w_o_r_d ``_A_L_P_H_A'' (_o_n_l_y _f_o_r _o_p_e_n-_s_h_e_l_l _w_a_v_e_f_u_n_c_t_i_o_n)
_I_f _o_n_e-_c_e_n_t_e_r (`_l_o_n_e') _N_B_O_s _a_r_e _t_o _b_e _s_e_a_r_c_h_e_d _f_o_r, _t_y_p_e _t_h_e
_k_e_y_w_o_r_d ``_L_O_N_E'' _f_o_l_l_o_w_e_d _b_y _a _l_i_s_t _o_f _p_a_i_r_s _o_f _n_u_m_b_e_r_s, _t_h_e
_f_i_r_s_t _n_u_m_b_e_r _o_f _e_a_c_h _p_a_i_r _b_e_i_n_g _t_h_e _a_t_o_m_i_c _c_e_n_t_e_r _a_n_d _t_h_e
_s_e_c_o_n_d _t_h_e _n_u_m_b_e_r _o_f _v_a_l_e_n_c_e _l_o_n_e _p_a_i_r_s _o_n _t_h_a_t _a_t_o_m. _T_e_r_-
_m_i_n_a_t_e _t_h_e _l_i_s_t _w_i_t_h ``_E_N_D''. (_N_o_t_e _t_h_a_t _o_n_l_y _t_h_e _o_c_c_u_p_i_e_d
#_I_v_a_l_e_n_c_e#_N _l_o_n_e _p_a_i_r_s _s_h_o_u_l_d _b_e _e_n_t_e_r_e_d, _s_i_n_c_e _t_h_e _n_u_m_b_e_r
_o_f _c_o_r_e _o_r_b_i_t_a_l_s _o_n _e_a_c_h _c_e_n_t_e_r _i_s _p_r_e_s_u_m_e_d _k_n_o_w_n.)
_I_f _t_w_o-_c_e_n_t_e_r (`_b_o_n_d') _N_B_O_s _a_r_e _t_o _b_e _s_e_a_r_c_h_e_d _f_o_r, _t_y_p_e _t_h_e
_k_e_y_w_o_r_d ``_B_O_N_D'', _f_o_l_l_o_w_e_d _b_y _t_h_e _l_i_s_t _o_f _b_o_n_d _s_p_e_c_i_f_i_e_r_s,
_a_n_d _t_e_r_m_i_n_a_t_e_d _b_y ``_E_N_D''. _E_a_c_h _b_o_n_d _s_p_e_c_i_f_i_e_r _i_s _o_n_e _o_f
_t_h_e _l_e_t_t_e_r_s
_s_i_n_g_l_e _b_o_n_d _d_o_u_b_l_e _b_o_n_d _t_r_i_p_l_e _b_o_n_d _q_u_a_d_r_u_p_l_e _b_o_n_d
_f_o_l_l_o_w_e_d _b_y _t_h_e _t_w_o _a_t_o_m_i_c _c_e_n_t_e_r_s _o_f _t_h_e _b_o_n_d (_e._g., ``_D _9
_1_6'' _f_o_r _a _d_o_u_b_l_e _b_o_n_d _b_e_t_w_e_e_n _a_t_o_m_s _9 _a_n_d _1_6).
_I_f _t_h_r_e_e-_c_e_n_t_e_r _N_B_O_s _a_r_e _t_o _b_e _s_e_a_r_c_h_e_d _f_o_r, _t_y_p_e _t_h_e _k_e_y_-
_w_o_r_d ``_3_C_B_O_N_D'', _f_o_l_l_o_w_e_d _b_y _t_h_e _l_i_s_t _o_f _3-_c _b_o_n_d _s_p_e_c_i_f_-
_i_e_r_s, _a_n_d _t_e_r_m_i_n_a_t_e_d _b_y ``_E_N_D''. _E_a_c_h _3-_c _b_o_n_d _s_p_e_c_i_f_i_e_r _i_s
_a_g_a_i_n _o_n_e _o_f _t_h_e _l_e_t_t_e_r_s ``_S'' (_s_i_n_g_l_e), ``_D'' (_d_o_u_b_l_e),
``_T'' (_t_r_i_p_l_e), _o_r ``_Q'' (_q_u_a_d_r_u_p_l_e), _f_o_l_l_o_w_e_d _b_y _t_h_r_e_e
_i_n_t_e_g_e_r_s _f_o_r _t_h_e _t_h_r_e_e _a_t_o_m_i_c _c_e_n_t_e_r_s (_e._g., ``_S _4 _8 _1_0''
_f_o_r _a _s_i_n_g_l_e _t_h_r_e_e-_c_e_n_t_e_r _b_o_n_d _4-_8-_1_0). (_N_o_t_e _t_h_a_t _t_h_e
_3_C_B_O_N_D _k_e_y_w_o_r_d _o_f _t_h_e $_N_B_O _k_e_y_l_i_s_t _i_s _i_m_p_l_i_c_i_t_l_y _a_c_t_i_v_a_t_e_d
_i_f _3-_c _b_o_n_d_s _a_r_e _i_n_c_l_u_d_e_d _i_n _a $_C_H_O_O_S_E _l_i_s_t.)
_T_h_e _w_o_r_d ``_E_N_D'' _t_o _s_i_g_n_a_l _t_h_e _e_n_d _o_f _t_h_e _l_p_h_a _s_p_i_n _l_i_s_t.
_T_h_e _k_e_y_w_o_r_d ``_B_E_T_A'' (_f_o_r _o_p_e_n-_s_h_e_l_l _w_a_v_e_f_u_n_c_t_i_o_n_s)
_T_h_e _i_n_p_u_t _f_o_r777777 t99a999999 s99p99i99n99,9999 s99a99_m777777 _f_o_r_m_a_t _a_s _a_b_o_v_e. _T_h_e _o_v_e_r_a_l_l $_C_H_O_O_S_E
_l_i_s_t _s_h_o_u_l_d _a_l_w_a_y_s _e_n_d _w_i_t_h _t_h_e ``$_E_N_D'' _k_e_y_w_o_r_d.
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_T_w_o _e_x_a_m_p_l_e_s _w_i_l_l _s_e_r_v_e _t_o _i_l_l_u_s_t_r_a_t_e _t_h_e $_C_H_O_O_S_E _f_o_r_m_a_t
(_e_a_c_h _i_s _r_a_t_h_e_r _a_r_t_i_f_i_c_i_a_l, _i_n_a_s_m_u_c_h _a_s _t_h_e _s_p_e_c_i_f_i_e_d
$_C_H_O_O_S_E _s_t_r_u_c_t_u_r_e _c_o_r_r_e_s_p_o_n_d_s _t_o _t_h_e `_n_o_r_m_a_l' _s_t_r_u_c_t_u_r_e _t_h_a_t
_w_o_u_l_d _b_e _f_o_u_n_d _b_y _t_h_e _N_B_O _p_r_o_g_r_a_m):
_T_h_e _c_l_o_s_e_d-_s_h_e_l_l _H-_b_o_n_d_e_d _c_o_m_p_l_e_x _F_H9_o_t_s _C_O, _w_i_t_h _a_t_o_m
_n_u_m_b_e_r_i_n_g _F(_1)-_H(_2)9_o_t_s _C(_3)-_O(_4), _m_i_g_h_t _b_e _s_p_e_c_i_f_i_e_d _a_s
#_T
$_C_H_O_O_S_E
_L_O_N_E _1 _3
_3 _1
_4 _1 _E_N_D
_B_O_N_D _S _1 _2
_T _3 _4 _E_N_D
$_E_N_D
#_N_T_h_i_s _w_o_u_l_d _d_i_r_e_c_t _t_h_e _N_B_O _p_r_o_g_r_a_m _t_o _s_e_a_r_c_h _f_o_r _t_h_r_e_e _l_o_n_e
_p_a_i_r_s _o_n _a_t_o_m _F(_1), _o_n_e _l_o_n_e _p_a_i_r _o_n _a_t_o_m _C(_3), _o_n_e _l_o_n_e
_p_a_i_r _o_n _a_t_o_m _O(_4), _o_n_e _b_o_n_d _b_e_t_w_e_e_n _F(_1)-_H(_2), _a_n_d _t_h_r_e_e
_b_o_n_d_s _b_e_t_w_e_e_n _C(_3)-_O(_4).
_T_h_e _o_p_e_n-_s_h_e_l_l _F_H9_o_t_s _O#_d_2#_u _c_o_m_p_l_e_x, _w_i_t_h _a_t_o_m _n_u_m_b_e_r_i_n_g
_F(_1)-_H(_2)#+...#-_O(_3)-_O(_4), _a_n_d _w_i_t_h _t_h_e _u_n_p_a_i_r_e_d _e_l_e_c_t_r_o_n_s
_o_n _O#_d_2#_u _b_e_i_n_g _o_f _l_p_h_a _s_p_i_n, _m_i_g_h_t _b_e _s_p_e_c_i_f_i_e_d _a_s
#_T
$_C_H_O_O_S_E
_A_L_P_H_A
_L_O_N_E _1 _3
_3 _3
_4 _3 _E_N_D
_B_O_N_D _S _1 _2
_S _3 _4 _E_N_D
_E_N_D
_B_E_T_A
_L_O_N_E _1 _3
_3 _1
_4 _1 _E_N_D
_B_O_N_D _S _1 _2
_T _3 _4 _E_N_D
_E_N_D
$_E_N_D
#_N_N_o_t_e _t_h_a_t _t_h_i_s _e_x_a_m_p_l_e _i_n_c_o_r_p_o_r_a_t_e_s _t_h_e _i_d_e_a _o_f ``_d_i_f_-
_f_e_r_e_n_t _L_e_w_i_s _s_t_r_u_c_t_u_r_e_s _f_o_r _d_i_f_f_e_r_e_n_t _s_p_i_n_s,'' _w_i_t_h _a _d_i_s_-
_t_i_n_c_t _p_a_t_t_e_r_n _o_f _l_o_c_a_l_i_z_e_d _1-_c (`_l_o_n_e') _a_n_d _2-_c (`_b_o_n_d')
_f_u_n_c_t_i_o_n_s _f_o_r _l_p_h_a _a_n_d7777 t99a999999 s99p99i99n99.7777 _0 _A_s _w_i_t_h _o_t_h_e_r _k_e_y_l_i_s_t_s, _t_h_e
$_C_H_O_O_S_E _k_e_y_l_i_s_t _c_a_n _b_e _c_o_n_d_e_n_s_e_d _t_o _a _s_m_a_l_l_e_r _n_u_m_b_e_r _o_f
_l_i_n_e_s, _a_s _l_o_n_g _a_s _n_o _l_i_n_e _i_s _s_h_a_r_e_d _w_i_t_h _a_n_o_t_h_e_r _k_e_y_l_i_s_t.
_T_h_e _o_r_d_e_r _o_f _k_e_y_w_o_r_d_s _w_i_t_h_i_n _t_h_e $_C_H_O_O_S_E _k_e_y_l_i_s_t _s_h_o_u_l_d _b_e
_a_s _s_h_o_w_n _a_b_o_v_e (_i._e., _A_L_P_H_A _b_e_f_o_r_e _B_E_T_A, _L_O_N_E _b_e_f_o_r_e _B_O_N_D,
_e_t_c.), _b_u_t _t_h_e _o_r_d_e_r _o_f _e_n_t_r_i_e_s _w_i_t_h_i_n _a _L_O_N_E _o_r _B_O_N_D _l_i_s_t
_i_s _i_m_m_a_t_e_r_i_a_l. _A $_C_O_R_E _k_e_y_l_i_s_t (_i_f _p_r_e_s_e_n_t) _m_u_s_t _p_r_e_c_e_d_e
_t_h_e $_C_H_O_O_S_E _l_i_s_t. #_B_B._5 _T_H_E $_D_E_L _K_E_Y_L_I_S_T (_N_B_O _E_N_E_R_G_E_T_I_C
_A_N_A_L_Y_S_I_S)#_N
July 11, 1995
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#_I_B._5._1 _I_n_t_r_o_d_u_c_t_i_o_n _t_o _N_B_O _E_n_e_r_g_e_t_i_c _A_n_a_l_y_s_i_s#_N
_0 _T_h_e _f_o_u_r_t_h _a_n_d _f_i_n_a_l _t_y_p_e _o_f _k_e_y_l_i_s_t _i_s _a `_d_e_l_e_t_i_o_n_s'
($_D_E_L) _k_e_y_l_i_s_t, _t_o _a_c_t_i_v_a_t_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s. _T_h_i_s
_a_n_a_l_y_s_i_s _i_s _p_e_r_f_o_r_m_e_d _b_y (_1) _d_e_l_e_t_i_n_g _s_p_e_c_i_f_i_e_d _e_l_e_m_e_n_t_s (_o_r
_b_l_o_c_k_s _o_f _e_l_e_m_e_n_t_s) _f_r_o_m _t_h_e _N_B_O _F_o_c_k _m_a_t_r_i_x, (_2) _d_i_a_g_o_n_a_l_-
_i_z_i_n_g _t_h_i_s _n_e_w _F_o_c_k _m_a_t_r_i_x _t_o _o_b_t_a_i_n _a _n_e_w _d_e_n_s_i_t_y _m_a_t_r_i_x,
_a_n_d (_3) _p_a_s_s_i_n_g _t_h_i_s _d_e_n_s_i_t_y _m_a_t_r_i_x _t_o _t_h_e _S_C_F _r_o_u_t_i_n_e_s _f_o_r
_a _s_i_n_g_l_e _p_a_s_s _t_h_r_o_u_g_h _t_h_e _S_C_F _e_n_e_r_g_y _e_v_a_l_u_a_t_o_r. _T_h_e _d_i_f_f_e_r_-
_e_n_c_e _b_e_t_w_e_e_n _t_h_i_s `_d_e_l_e_t_i_o_n' _e_n_e_r_g_y _a_n_d _t_h_e _o_r_i_g_i_n_a_l _S_C_F
_e_n_e_r_g_y _p_r_o_v_i_d_e_s _a _u_s_e_f_u_l _m_e_a_s_u_r_e _o_f _t_h_e _e_n_e_r_g_y _c_o_n_t_r_i_b_u_t_i_o_n
_o_f _t_h_e _d_e_l_e_t_e_d _t_e_r_m_s. _S_i_n_c_e _a _F_o_c_k _m_a_t_r_i_x _i_s _r_e_q_u_i_r_e_d, _t_h_e
_e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s _i_s _p_e_r_f_o_r_m_e_d _f_o_r _R_H_F _a_n_d _U_H_F _w_a_v_e_f_u_n_c_-
_t_i_o_n_s _o_n_l_y.
_0 _I_n_p_u_t _f_o_r _t_h_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s _i_s _t_h_r_o_u_g_h _t_h_e $_D_E_L
_k_e_y_l_i_s_t, _w_h_i_c_h _s_p_e_c_i_f_i_e_s _t_h_e _d_e_l_e_t_i_o_n_s _t_o _b_e _p_e_r_f_o_r_m_e_d.
_M_u_l_t_i_p_l_e _a_n_a_l_y_s_e_s (_d_e_l_e_t_i_o_n_s) _c_a_n _b_e _p_e_r_f_o_r_m_e_d _d_u_r_i_n_g _a _s_i_n_-
_g_l_e _j_o_b, _w_i_t_h _e_a_c_h _d_e_l_e_t_i_o_n _i_n_c_l_u_d_e_d _i_n _t_h_e _o_v_e_r_a_l_l $_D_E_L
_k_e_y_l_i_s_t. _T_h_e _n_i_n_e _d_i_s_t_i_n_c_t _t_y_p_e_s _o_f _d_e_l_e_t_i_o_n_s _i_n_p_u_t _a_r_e
_d_e_s_c_r_i_b_e_d _i_n _S_e_c_t_i_o_n _B._5._2 _b_e_l_o_w.
_0 _T_h_e _d_e_l_e_t_i_o_n_s _k_e_y_l_i_s_t _b_e_g_i_n_s _w_i_t_h _t_h_e ``$_D_E_L'' _k_e_y_w_o_r_d.
_F_o_r _t_h_e _a_n_a_l_y_s_i_s _o_f _U_H_F _w_a_v_e_f_u_n_c_t_i_o_n_s, _t_h_e _d_e_l_e_t_i_o_n_s _f_o_r _t_h_e
_l_p_h_a _a_n_d777777777777 t99a999999 s99p99i99n9999 m99a99n99i99f99o99l99d99s9999 m99u99s99t9999 _b777777777777 _s_e_p_a_r_a_t_e_l_y _s_p_e_c_i_f_i_e_d (_s_e_e _S_e_c_t_i_o_n _B._5._3).
_O_t_h_e_r_w_i_s_e, _t_h_e _i_n_p_u_t _f_o_r _c_l_o_s_e_d _s_h_e_l_l_s _R_H_F _a_n_d _U_H_F _i_s _i_d_e_n_t_-
_i_c_a_l. _T_h_e _i_n_p_u_t _i_s _f_r_e_e _f_o_r_m_a_t _a_n_d _t_h_e _i_n_p_u_t _f_o_r _a _s_i_n_g_l_e
_d_e_l_e_t_i_o_n _c_a_n _b_e _s_p_r_e_a_d _o_v_e_r _a_s _m_a_n_y _l_i_n_e_s _a_s _d_e_s_i_r_e_d. _T_h_e
_d_e_s_i_r_e_d _d_e_l_e_t_i_o_n_s _s_h_o_u_l_d _b_e _l_i_s_t_e_d _o_n_e _a_f_t_e_r _t_h_e _o_t_h_e_r.
_A_f_t_e_r _t_h_e _l_a_s_t _d_e_l_e_t_i_o_n, _t_h_e _w_o_r_d ``$_E_N_D'' _s_i_g_n_a_l_s _t_h_e _e_n_d
_o_f _t_h_e _k_e_y_l_i_s_t.
|<<_3//_1_8//_7_2//+_0//+_1_3>>|7______________________99______________________
#_B_W_A_R_N_I_N_G#_N
_I_f _s_y_m_m_e_t_r_y _i_s _u_s_e_d, _o_n_e _m_u_s_t _b_e _c_a_r_e_f_u_l _t_o _o_n_l_y _d_o _d_e_l_e_-
_t_i_o_n_s _t_h_a_t _w_i_l_l _p_r_e_s_e_r_v_e _t_h_e _s_y_m_m_e_t_r_y _o_f _t_h_e _e_l_e_c_t_r_o_n_i_c
_w_a_v_e_f_u_n_c_t_i_o_n!! _I_f _t_h_i_s _i_s _n_o_t _d_o_n_e, _t_h_e _e_n_e_r_g_y _o_f _t_h_e _d_e_l_e_-
_t_i_o_n _w_i_l_l _b_e _i_n_c_o_r_r_e_c_t _b_e_c_a_u_s_e _t_h_e _a_s_s_u_m_p_t_i_o_n _i_s _m_a_d_e _i_n
_e_v_a_l_u_a_t_i_n_g _t_h_e _e_n_e_r_g_y _t_h_a_t _t_h_e _o_r_i_g_i_n_a_l _s_y_m_m_e_t_r_y _s_t_i_l_l
_e_x_i_s_t_s, _a_n_d _t_h_e _v_a_r_i_a_t_i_o_n_a_l _p_r_i_n_c_i_p_l_e _m_a_y _b_e _v_i_o_l_a_t_e_d. (_F_o_r
_e_x_a_m_p_l_e, _i_f _s_y_m_m_e_t_r_y _i_s _u_s_e_d _f_o_r _e_t_h_a_n_e, _i_s _i_s _p_e_r_m_i_s_s_i_b_l_e
_t_o _d_o _a ``_N_O_S_T_A_R'' _d_e_l_e_t_i_o_n, _b_u_t _n_o_t _t_h_e _d_e_l_e_t_i_o_n _o_f _a _s_i_n_-
_g_l_e _C-_H _a_n_t_i_b_o_n_d.) _T_h_e _r_e_m_e_d_y _i_s _n_o_t _t_o _u_s_e _s_y_m_m_e_t_r_y _i_n _t_h_e
_S_C_F _c_a_l_c_u_l_a_t_i_o_n.
_0 _I_n _d_e_s_c_r_i_b_i_n_g _t_h_e _d_e_l_e_t_i_o_n _t_y_p_e_s, _u_s_e _i_s _m_a_d_e _o_f _t_h_e _t_e_r_m_s
``_m_o_l_e_c_u_l_a_r _u_n_i_t'' _a_n_d ``_c_h_e_m_i_c_a_l _f_r_a_g_m_e_n_t.'' _T_h_e _N_B_O _p_r_o_-
_g_r_a_m _l_o_o_k_s _a_t _t_h_e _c_h_e_m_i_c_a_l _b_o_n_d_i_n_g _p_a_t_t_e_r_n _p_r_o_d_u_c_e_d _b_y _t_h_e
_b_o_n_d_i_n_g _N_B_O_s _a_n_d _i_d_e_n_t_i_f_i_e_s _t_h_e _g_r_o_u_p_s _o_f _a_t_o_m_s _t_h_a_t _a_r_e
_l_i_n_k_e_d _t_o_g_e_t_h_e_r _i_n _d_i_s_t_i_n_c_t ``_m_o_l_e_c_u_l_a_r _u_n_i_t_s'' (_u_s_u_a_l_l_y
July 11, 1995
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_s_y_n_o_n_y_m_o_u_s
_w_i_t_h ``_m_o_l_e_c_u_l_e_s'' _i_n _t_h_e _c_h_e_m_i_c_a_l _s_e_n_s_e). _T_h_e _f_i_r_s_t _a_t_o_m
_t_h_a_t _i_s _n_o_t _i_n _m_o_l_e_c_u_l_a_r _u_n_i_t _1 _w_i_l_l _b_e _i_n _m_o_l_e_c_u_l_a_r _u_n_i_t _2,
_a_n_d _s_o _f_o_r_t_h. _F_o_r _e_x_a_m_p_l_e, _i_f _t_h_e _l_i_s_t _o_f _a_t_o_m_s _i_s _C(_1),
_H(_2), _F(_3), _O(_4), _a_n_d _b_o_n_d_i_n_g _N_B_O_s _a_r_e _f_o_u_n_d _b_e_t_w_e_e_n _C(_1)-
_O(_4) _a_n_d _H(_2)-_F(_3), _t_h_e_n _m_o_l_e_c_u_l_a_r _u_n_i_t _1 _w_i_l_l _b_e _C_O _a_n_d
_m_o_l_e_c_u_l_a_r _u_n_i_t _2 _w_i_l_l _b_e _H_F. _A ``_c_h_e_m_i_c_a_l _f_r_a_g_m_e_n_t'' _i_s
_t_a_k_e_n _t_o _b_e _a_n_y _s_u_b_s_e_t _o_f _t_h_e _a_t_o_m_s, _u_s_u_a_l_l_y (_b_u_t _n_o_t _n_e_c_e_s_-
_s_a_r_i_l_y) _i_n _t_h_e _s_a_m_e _m_o_l_e_c_u_l_a_r _u_n_i_t, _a_n_d _u_s_u_a_l_l_y (_b_u_t _n_o_t
_n_e_c_e_s_s_a_r_i_l_y) _c_o_n_n_e_c_t_e_d _b_y _b_o_n_d _N_B_O_s. _T_y_p_i_c_a_l_l_y, _a _c_h_e_m_i_c_a_l
_f_r_a_g_m_e_n_t _m_i_g_h_t _b_e _s_p_e_c_i_f_i_e_d _t_o _b_e _a _s_i_n_g_l_e _a_t_o_m, _t_h_e _f_o_u_r
_a_t_o_m_s _o_f _a _m_e_t_h_y_l _g_r_o_u_p, _o_r _a_n_y _o_t_h_e_r `_r_a_d_i_c_a_l' _o_f _a _m_o_l_e_c_u_-
_l_a_r _u_n_i_t, _i_d_e_n_t_i_f_i_e_d _b_y _g_i_v_i_n_g _t_h_e _a_t_o_m _n_u_m_b_e_r_s _o_f _w_h_i_c_h _t_h_e
_f_r_a_g_m_e_n_t _c_o_n_s_i_s_t_s. #_I_B._5._2 _T_h_e _N_i_n_e _D_e_l_e_t_i_o_n _T_y_p_e_s#_N
_0 _T_h_e _k_e_y_w_o_r_d_s _a_n_d _f_o_r_m_a_t _t_o _s_p_e_c_i_f_y _e_a_c_h _o_f _t_h_e _n_i_n_e
_a_l_l_o_w_e_d _d_e_l_e_t_i_o_n _t_y_p_e_s _a_r_e _d_e_s_c_r_i_b_e_d _b_e_l_o_w:
#_(_1) _D_e_l_e_t_i_o_n _o_f _e_n_t_i_r_e _o_r_b_i_t_a_l_s.#/
_T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_D_E_L_E_T_E'', _t_h_e_n _t_h_e _n_u_m_b_e_r _o_f
_o_r_b_i_t_a_l_s _t_o _b_e _d_e_l_e_t_e_d, _t_h_e_n _t_h_e _k_e_y_w_o_r_d ``_O_R_B_I_T_A_L'' (_o_r
``_O_R_B_I_T_A_L_S''), _t_h_e_n _t_h_e _l_i_s_t _o_f _t_h_e _o_r_b_i_t_a_l_s _t_o _b_e _d_e_l_e_t_e_d.
_E_x_a_m_p_l_e: #_T_D_E_L_E_T_E _3 _O_R_B_I_T_A_L_S _1_5 _1_8 _2_9
#_N[_S_e_e _a_l_s_o _d_e_l_e_t_i_o_n _t_y_p_e_s (_4) _a_n_d (_7) _f_o_r _d_e_l_e_t_i_n_g _s_e_t_s _o_f
_o_r_b_i_t_a_l_s.]
|<<_3//_1_8//_7_2//+_0//+_1_1>>|7______________________99______________________
#_B_W_A_R_N_I_N_G#_N
_T_h_e ``_s_i_n_g_l_e-_p_a_s_s'' _m_e_t_h_o_d _o_f _e_v_a_l_u_a_t_i_n_g _d_e_l_e_t_i_o_n _e_n_e_r_g_i_e_s
_i_s _a_p_p_r_o_p_r_i_a_t_e _o_n_l_y _f_o_r _d_e_l_e_t_i_o_n_s _o_f #_I_l_o_w#_N-_o_c_c_u_p_a_n_c_y
(_n_o_n-_L_e_w_i_s) _o_r_b_i_t_a_l_s, _f_o_r _w_h_i_c_h _t_h_e _l_o_s_s _o_f _s_e_l_f-_c_o_n_s_i_s_t_e_n_c_y
_i_n _t_h_e _C_o_u_l_o_m_b _a_n_d _e_x_c_h_a_n_g_e _p_o_t_e_n_t_i_a_l_s (_d_u_e _t_o _r_e_d_i_s_t_r_i_b_u_-
_t_i_o_n _o_f _t_h_e _e_l_e_c_t_r_o_n _d_e_n_s_i_t_y _o_f _d_e_l_e_t_e_d _o_r_b_i_t_a_l_s) _i_s _s_m_a_l_l
_c_o_m_p_a_r_e_d _t_o _t_h_e _n_e_t _e_n_e_r_g_y _c_h_a_n_g_e _o_f _d_e_l_e_t_i_o_n. _I_t _i_s _f_u_n_d_a_-
_m_e_n_t_a_l_l_y _e_r_r_o_n_e_o_u_s _t_o _d_e_l_e_t_e #_I_h_i_g_h#_N-_o_c_c_u_p_a_n_c_y (_L_e_w_i_s)
_o_r_b_i_t_a_l_s _b_y _t_h_i_s _p_r_o_c_e_d_u_r_e.
#_(_2) _D_e_l_e_t_i_o_n _o_f _s_p_e_c_i_f_i_c _F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s.#/
_T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_D_E_L_E_T_E'', _t_h_e_n _t_h_e _n_u_m_b_e_r _o_f
_e_l_e_m_e_n_t_s _t_o _b_e _d_e_l_e_t_e_d, _t_h_e_n _t_h_e _k_e_y_w_o_r_d ``_E_L_E_M_E_N_T'' (_o_r
``_E_L_E_M_E_N_T_S''), _t_h_e_n _t_h_e _l_i_s_t _o_f _t_h_e _e_l_e_m_e_n_t_s _t_o _b_e _d_e_l_e_t_e_d
(_e_a_c_h _a_s _a _p_a_i_r _o_f _i_n_t_e_g_e_r_s).
_E_x_a_m_p_l_e: #_T_D_E_L_E_T_E _3 _E_L_E_M_E_N_T_S _1 _1_5 _3 _1_9 _2_3 _2
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#_N_T_h_i_s _e_x_a_m_p_l_e _w_o_u_l_d _r_e_s_u_l_t _i_n _t_h_e _z_e_r_o_i_n_g _o_f _t_h_e _f_o_l_l_o_w_i_n_g
_F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s: (_1,_1_5), (_1_5,_1), (_3,_1_9), (_1_9,_3),
(_2_3,_2), (_2,_2_3). [_S_e_e _a_l_s_o _d_e_l_e_t_i_o_n _t_y_p_e_s (_3), (_5), (_6),
(_8), (_9) _f_o_r _d_e_l_e_t_i_n_g _s_e_t_s _o_f _e_l_e_m_e_n_t_s.]
#_(_3) _D_e_l_e_t_i_o_n _o_f _o_f_f-_d_i_a_g_o_n_a_l _b_l_o_c_k_s _o_f _t_h_e _F_o_c_k _m_a_t_r_i_x.#/
_E_a_c_h _b_l_o_c_k _i_s _s_p_e_c_i_f_i_e_d _b_y _t_w_o _s_e_t_s _o_f _o_r_b_i_t_a_l_s, _a_n_d _a_l_l
_F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s _i_n _c_o_m_m_o_n _b_e_t_w_e_e_n _t_h_e_s_e _t_w_o _s_e_t_s _a_r_e
_s_e_t _t_o _z_e_r_o. _T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_Z_E_R_O'', _t_h_e_n
_t_h_e _n_u_m_b_e_r _o_f _o_f_f-_d_i_a_g_o_n_a_l _b_l_o_c_k_s _t_o _b_e _z_e_r_o_e_d, _a_n_d _t_h_e_n,
_f_o_r _e_a_c_h _b_l_o_c_k, _t_h_e _f_o_l_l_o_w_i_n_g:
(_1) _t_h_e _d_i_m_e_n_s_i_o_n_s _o_f _t_h_e _b_l_o_c_k, _s_e_p_a_r_a_t_e_d _b_y _t_h_e _w_o_r_d
``_B_Y'' (_e._g., ``_6 _B_Y _3'' _i_f _t_h_e _f_i_r_s_t _s_e_t _h_a_s _6 _o_r_b_i_t_a_l_s _a_n_d
_t_h_e _s_e_c_o_n_d _s_e_t _h_a_s _3 _o_r_b_i_t_a_l_s);
(_2) _t_h_e _l_i_s_t _o_f _o_r_b_i_t_a_l_s _i_n _t_h_e _f_i_r_s_t _s_e_t;
(_3) _t_h_e _l_i_s_t _o_f _o_r_b_i_t_a_l_s _i_n _t_h_e _s_e_c_o_n_d _s_e_t.
_A_n _e_x_a_m_p_l_e _i_s _s_h_o_w_n _b_e_l_o_w:
#_T
_Z_E_R_O _2 _B_L_O_C_K_S _2 _B_Y _5
_3 _4
_9 _1_0 _1_1 _1_4 _1_9
_3 _B_Y _2
_1 _2 _7
_2_0 _2_4
#_N_T_h_i_s _w_i_l_l _s_e_t _t_h_e _f_o_l_l_o_w_i_n_g _F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s _t_o _z_e_r_o:
(_3,_9), (_3,_1_0), (_3,_1_1), (_3,_1_4), (_3,_1_9), (_9,_3), (_1_0,_3),
(_1_1,_3), (_1_4,_3), (_1_9,_3), (_4,_9), (_4,_1_0), (_4,_1_1), (_4,_1_4),
(_4,_1_9), (_9,_4), (_1_0,_4), (_1_1,_4), (_1_4,_4), (_1_9,_4), (_1,_2_0),
(_1,_2_4), (_2,_2_0), (_2,_2_4), (_7,_2_0), (_7,_2_4) (_2_0,_1), (_2_4,_1),
(_2_0,_2), (_2_4,_2), (_2_0,_7), (_2_4,_7)
[_U_s_u_a_l_l_y, _i_n _s_t_u_d_y_i_n_g _t_h_e _t_o_t_a_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n _f_r_o_m _o_n_e
_m_o_l_e_c_u_l_a_r _u_n_i_t _t_o _a_n_o_t_h_e_r, _i_t _i_s _m_u_c_h _e_a_s_i_e_r _t_o _u_s_e _d_e_l_e_t_i_o_n
_t_y_p_e (_8) _b_e_l_o_w. _S_i_m_i_l_a_r_l_y, _i_n _s_t_u_d_y_i_n_g _t_h_e _t_o_t_a_l _d_e_l_o_c_a_l_i_-
_z_a_t_i_o_n _f_r_o_m _o_n_e _c_h_e_m_i_c_a_l _f_r_a_g_m_e_n_t _t_o _a_n_o_t_h_e_r, _i_t _i_s _e_a_s_i_e_r
_t_o _u_s_e _d_e_l_e_t_i_o_n _t_y_p_e (_9).]
#_(_4) _D_e_l_e_t_i_o_n _o_f _a_l_l _R_y_d_b_e_r_g _a_n_d _a_n_t_i_b_o_n_d _o_r_b_i_t_a_l_s.#/
_T_h_e _R_y_d_b_e_r_g _a_n_d _a_n_t_i_b_o_n_d _o_r_b_i_t_a_l_s _a_r_e _t_h_e _n_o_n-_L_e_w_i_s _N_B_O
_o_r_b_i_t_a_l_s _t_h_a_t _h_a_v_e _s_t_a_r_s _i_n _t_h_e_i_r _l_a_b_e_l_s (_R_Y*, _B_D*) _i_n _t_h_e
_N_B_O _a_n_a_l_y_s_i_s _o_u_t_p_u_t. _T_o _d_e_l_e_t_e _a_l_l _t_h_e_s_e _o_r_b_i_t_a_l_s, _s_i_m_p_l_y
_e_n_t_e_r ``_N_O_S_T_A_R''. _T_h_e _r_e_s_u_l_t _o_f _t_h_i_s _d_e_l_e_t_i_o_n _i_s _t_h_e _e_n_e_r_g_y
_o_f _t_h_e _i_d_e_a_l_i_z_e_d _N_B_O _n_a_t_u_r_a_l _L_e_w_i_s _s_t_r_u_c_t_u_r_e, _w_i_t_h _a_l_l _L_e_w_i_s
_N_B_O_s _d_o_u_b_l_y _o_c_c_u_p_i_e_d. (_U_n_l_i_k_e _o_t_h_e_r _d_e_l_e_t_i_o_n_s, _i_n _w_h_i_c_h
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_t_h_e_r_e
_i_s _a _s_l_i_g_h_t _l_o_s_s _o_f _v_a_r_i_a_t_i_o_n_a_l _s_e_l_f-_c_o_n_s_i_s_t_e_n_c_y _d_u_e _t_o _t_h_e
_r_e_d_i_s_t_r_i_b_u_t_e_d _o_c_c_u_p_a_n_c_y _o_f _t_h_e _d_e_l_e_t_e_d _o_r_b_i_t_a_l_s, _t_h_e _r_e_s_u_l_t
_o_f _a ``_N_O_S_T_A_R'' _d_e_l_e_t_i_o_n _c_o_r_r_e_s_p_o_n_d_s _r_i_g_o_r_o_u_s_l_y _t_o _t_h_e _v_a_r_i_-
_a_t_i_o_n_a_l _e_x_p_e_c_t_a_t_i_o_n _v_a_l_u_e _o_f _t_h_e _d_e_t_e_r_m_i_n_a_n_t _o_f _d_o_u_b_l_y _o_c_c_u_-
_p_i_e_d _L_e_w_i_s _N_B_O_s).
#_(_5) _D_e_l_e_t_i_o_n _o_f _a_l_l _v_i_c_i_n_a_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s.#/
_T_o _d_e_l_e_t_e _a_l_l _F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s _b_e_t_w_e_e_n _L_e_w_i_s _N_B_O_s _a_n_d
_t_h_e _v_i_c_i_n_a_l _n_o_n-_L_e_w_i_s _N_B_O_s, _s_i_m_p_l_y _e_n_t_e_r ``_N_O_V_I_C''.
#_(_6) _D_e_l_e_t_i_o_n _o_f _a_l_l _g_e_m_i_n_a_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s.#/
_T_o _d_e_l_e_t_e _a_l_l _F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s _b_e_t_w_e_e_n _L_e_w_i_s _N_B_O_s _a_n_d
_t_h_e _g_e_m_i_n_a_l _n_o_n-_L_e_w_i_s _N_B_O_s, _s_i_m_p_l_y _e_n_t_e_r ``_N_O_G_E_M''.
#_(_7) _D_e_l_e_t_i_o_n _o_f _a_l_l _s_t_a_r_r_e_d (_a_n_t_i_b_o_n_d/_R_y_d_b_e_r_g) _o_r_b_i_t_a_l_s _o_n
_a _p_a_r_t_i_c_u_l_a_r _m_o_l_e_c_u_l_a_r _u_n_i_t.#/
_T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_D_E_S_T_A_R'', _t_h_e_n _t_h_e _n_u_m_b_e_r _o_f
_m_o_l_e_c_u_l_a_r _u_n_i_t_s _t_o _b_e _d_e#|_s_t_a_r_r_e_d, _t_h_e_n _t_h_e _k_e_y_w_o_r_d ``_U_N_I_T''
(_o_r ``_U_N_I_T_S''), _t_h_e_n _t_h_e _l_i_s_t _o_f _u_n_i_t_s.
_E_x_a_m_p_l_e: #_T_D_E_S_T_A_R _2 _U_N_I_T_S _3 _4
#_N
#_(_8) _Z_e_r_o_i_n_g _a_l_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n _f_r_o_m _o_n_e _m_o_l_e_c_u_l_a_r _u_n_i_t _t_o
_a_n_o_t_h_e_r.#/
_T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_Z_E_R_O'', _t_h_e_n _t_h_e _n_u_m_b_e_r _o_f
_d_e_l_o_c_a_l_i_z_a_t_i_o_n_s _t_o _z_e_r_o, _t_h_e_n _t_h_e _k_e_y_w_o_r_d ``_D_E_L_O_C_A_L_I_Z_A_T_I_O_N''
(_c_a_n _b_e _a_b_b_r_e_v_i_a_t_e_d _t_o ``_D_E_L_O_C''), _a_n_d _t_h_e_n, _f_o_r _e_a_c_h _d_e_l_o_-
_c_a_l_i_z_a_t_i_o_n, _t_h_e _w_o_r_d ``_F_R_O_M'', _t_h_e _n_u_m_b_e_r _o_f _t_h_e _d_o_n_o_r _u_n_i_t,
_t_h_e _w_o_r_d ``_T_O'', _a_n_d _t_h_e _n_u_m_b_e_r _o_f _t_h_e _a_c_c_e_p_t_o_r _u_n_i_t.
_E_x_a_m_p_l_e: #_T_Z_E_R_O _2 _D_E_L_O_C _F_R_O_M _1 _T_O _2 _F_R_O_M _2 _T_O _1
#_N_T_h_e _a_b_o_v_e _e_x_a_m_p_l_e _w_o_u_l_d _z_e_r_o #_I_a_l_l#_N _i_n_t_e_r_m_o_l_e_c_u_l_a_r _d_e_l_o_-
_c_a_l_i_z_a_t_i_o_n_s _b_e_t_w_e_e_n _u_n_i_t_s _1 _a_n_d _2 (_i._e., _b_o_t_h _17 _a_r_r _2 _a_n_d _2
7_a_r_r _1). _T_h_e _e_f_f_e_c_t _i_s _t_o _r_e_m_o_v_e _a_l_l _F_o_c_k _m_a_t_r_i_x _e_l_e_m_e_n_t_s
_b_e_t_w_e_e_n _h_i_g_h-_o_c_c_u_p_a_n_c_y (_c_o_r_e/_l_o_n_e _p_a_i_r/_b_o_n_d) _N_B_O_s _o_f _t_h_e
_d_o_n_o_r _u_n_i_t _t_o _t_h_e _l_o_w-_o_c_c_u_p_a_n_c_y (_a_n_t_i_b_o_n_d/_R_y_d_b_e_r_g) _N_B_O_s _o_f
_t_h_e _a_c_c_e_p_t_o_r _u_n_i_t. _T_h_e _d_o_n_o_r _a_n_d _a_c_c_e_p_t_o_r _u_n_i_t_s _m_a_y _b_e _t_h_e
_s_a_m_e.
#_(_9) _Z_e_r_o_i_n_g _a_l_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n _f_r_o_m _o_n_e _c_h_e_m_i_c_a_l _f_r_a_g_m_e_n_t
_t_o _a_n_o_t_h_e_r.#/
_T_h_i_s _i_s _c_a_l_l_e_d _f_o_r _b_y _t_y_p_i_n_g ``_Z_E_R_O'', _t_h_e_n _t_h_e _n_u_m_b_e_r _o_f
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_i_n_t_e_r-_f_r_a_g_m_e_n_t
_d_e_l_o_c_a_l_i_z_a_t_i_o_n_s _t_o _b_e _z_e_r_o_e_d, _t_h_e_n _t_h_e _w_o_r_d_s ``_A_T_O_M
_B_L_O_C_K_S'', _a_n_d _t_h_e_n, _f_o_r _e_a_c_h _d_e_l_o_c_a_l_i_z_a_t_i_o_n, _t_h_e _f_o_l_l_o_w_i_n_g:
(_1) _t_h_e _n_u_m_b_e_r _o_f _a_t_o_m_s _i_n _t_h_e _t_w_o _f_r_a_g_m_e_n_t_s, _s_e_p_a_r_a_t_e_d _b_y
_t_h_e _w_o_r_d ``_B_Y'' (_e._g., ``_6 _B_Y _3'' _i_f _t_h_e _f_i_r_s_t _f_r_a_g_m_e_n_t
_h_a_s _6 _a_t_o_m_s _a_n_d _t_h_e _s_e_c_o_n_d _h_a_s _3 _a_t_o_m_s);
(_2) _t_h_e _l_i_s_t _o_f _a_t_o_m_s _i_n _t_h_e _f_i_r_s_t _f_r_a_g_m_e_n_t;
(_3) _t_h_e _l_i_s_t _o_f _a_t_o_m_s _i_n _t_h_e _s_e_c_o_n_d _f_r_a_g_m_e_n_t.
_F_o_r _e_x_a_m_p_l_e, _t_o _z_e_r_o _a_l_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s _b_e_t_w_e_e_n _t_h_e _f_r_a_g_-
_m_e_n_t_s _d_e_f_i_n_e_d _b_y _a_t_o_m_s (_1,_2) _a_n_d _b_y _a_t_o_m_s (_3,_4,_5), _t_h_e $_D_E_L
_e_n_t_r_i_e_s _w_o_u_l_d _b_e
#_T
_Z_E_R_O _2 _A_T_O_M _B_L_O_C_K_S
_2 _B_Y _3
_1 _2
_3 _4 _5
_3 _B_Y _2
_3 _4 _5
_1 _2
#_N_I_n _t_h_i_s _e_x_a_m_p_l_e, _t_h_e _f_i_r_s_t _b_l_o_c_k _r_e_m_o_v_e_s _t_h_e (_1,_2)7 _a_r_r
(_3,_4,_5) _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s, _w_h_i_l_e _t_h_e _s_e_c_o_n_d _r_e_m_o_v_e_s _t_h_e
(_3,_4,_5)7 _a_r_r (_1,_2) _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s.
_0 _F_o_r _a_d_d_i_t_i_o_n_a_l _e_x_a_m_p_l_e_s _o_f $_D_E_L _i_n_p_u_t, _s_e_e _S_e_c_t_i_o_n _B._6._1_0.
#_I_B._5._3 _I_n_p_u_t _f_o_r _U_H_F _A_n_a_l_y_s_i_s#_N
_0 _D_e_l_e_t_i_o_n_s _o_f _t_h_e _a_l_p_h_a _a_n_d _b_e_t_a _F_o_c_k _m_a_t_r_i_c_e_s _c_a_n _b_e _d_o_n_e
_i_n_d_e_p_e_n_d_e_n_t_l_y. _T_h_e _d_e_l_e_t_i_o_n_s _a_r_e _i_n_p_u_t _a_s _a_b_o_v_e (_S_e_c_t_i_o_n
_B._5._2) _f_o_r _R_H_F _c_l_o_s_e_d _s_h_e_l_l, _b_u_t _t_h_e_y _m_u_s_t _b_e _s_p_e_c_i_f_i_e_d
_s_e_p_a_r_a_t_e_l_y _f_o_r _a_l_p_h_a _a_n_d _b_e_t_a _i_n _t_h_e _U_H_F _c_a_s_e.
_0 _T_h_e _d_e_l_e_t_i_o_n _t_o _b_e _d_o_n_e _o_n _t_h_e _a_l_p_h_a _F_o_c_k _m_a_t_r_i_x _m_u_s_t _b_e
_p_r_e_c_e_d_e_d _b_y _t_h_e _k_e_y_w_o_r_d ``_A_L_P_H_A'', _a_n_d _t_h_e _d_e_l_e_t_i_o_n _o_f _t_h_e
_b_e_t_a _F_o_c_k _m_a_t_r_i_x _m_u_s_t _b_e _p_r_e_c_e_d_e_d _b_y _t_h_e _k_e_y_w_o_r_d ``_B_E_T_A''.
(_A_c_t_u_a_l_l_y, _o_n_l_y _t_h_e _f_i_r_s_t _l_e_t_t_e_r ``_A'' _o_r ``_B'' _i_s _s_e_a_r_c_h_e_d
_f_o_r _b_y _t_h_e _p_r_o_g_r_a_m.) _T_h_e _A_L_P_H_A _d_e_l_e_t_i_o_n _m_u_s_t _p_r_e_c_e_d_e _t_h_e
_B_E_T_A _d_e_l_e_t_i_o_n. _T_h_e _B_E_T_A _d_e_l_e_t_i_o_n _m_a_y _b_e _t_h_e _s_a_m_e _a_s _t_h_e
_A_L_P_H_A _d_e_l_e_t_i_o_n, _o_r _d_i_f_f_e_r_e_n_t.
_0 _N_O_T_E: _T_h_e _t_y_p_e_s _o_f _t_h_e _l_p_h_a _N_B_O_s _o_f_t_e_n _d_i_f_f_e_r _f_r_o_m _t_h_o_s_e
_o_f _t_h_e77777777777777777777777 t99a999999 _d77_t_i_o_n_s _l_i_s_t_s _a_r_e _g_e_n_e_r_a_l_l_y _r_e_q_u_i_r_e_d. _F_o_r _e_x_a_m_p_l_e,
_O#_d_2#_u (_t_r_i_p_l_e_t) _h_a_s _o_n_e _b_o_n_d _i_n _t_h_e _l_p_h_a _s_y_s_t_e_m _a_n_d _t_h_r_e_e
_i_n _t_h_e7778 t99a999999 s99y99s99_t7778_m, _i_f _t_h_e _u_n_p_a_i_r_e_d _e_l_e_c_t_r_o_n_s _a_r_e _i_n _t_h_e _l_p_h_a _s_y_s_-
_t_e_m.
_0 _H_e_r_e _a_r_e _t_h_r_e_e _e_x_a_m_p_l_e_s _t_o _i_l_l_u_s_t_r_a_t_e _U_H_F _o_p_e_n-_s_h_e_l_l _d_e_l_e_-
_t_i_o_n_s:
_E_x_a_m_p_l_e _1:
July 11, 1995
- 46 -
#_T
_A_L_P_H_A _Z_E_R_O _1 _D_E_L_O_C _F_R_O_M _1 _T_O _2
_B_E_T_A _N_O_S_T_A_R
#_N_E_x_a_m_p_l_e _2:
#_T
_A_L_P_H_A _Z_E_R_O _1 _D_E_L_O_C _F_R_O_M _1 _T_O _2
_B_E_T_A _Z_E_R_O _0 _D_E_L_O_C
#_N_E_x_a_m_p_l_e _3:
#_T
_A_L_P_H_A _D_E_L_E_T_E _0 _O_R_B_I_T_A_L_S
_B_E_T_A _D_E_L_E_T_E _1 _O_R_B_I_T_A_L _8
#_N_I_f _n_o _d_e_l_e_t_i_o_n _i_s _d_o_n_e, _t_h_i_s _m_u_s_t _b_e _s_p_e_c_i_f_i_e_d _u_s_i_n_g _z_e_r_o
(_0) _w_i_t_h _o_n_e _o_f _t_h_e _d_e_l_e_t_i_o_n _i_n_p_u_t _f_o_r_m_a_t_s, _a_s _s_h_o_w_n _i_n
_E_x_a_m_p_l_e_s _2,_3 _a_b_o_v_e. #_B_B._6 _N_B_O _K_E_Y_L_I_S_T _I_L_L_U_S_T_R_A_T_I_O_N_S#_N
#_I_B._6._1 _I_n_t_r_o_d_u_c_t_i_o_n#_N
_0 _T_h_i_s _s_e_c_t_i_o_n _i_l_l_u_s_t_r_a_t_e_s _t_h_e _o_u_t_p_u_t _p_r_o_d_u_c_e_d _b_y _s_e_v_e_r_a_l
_i_m_p_o_r_t_a_n_t _k_e_y_w_o_r_d _o_p_t_i_o_n_s _o_f _t_h_e _N_B_O _k_e_y_l_i_s_t_s ($_N_B_O,
$_C_H_O_O_S_E, $_D_E_L, $_C_O_R_E _l_i_s_t_s), _s_u_p_p_l_e_m_e_n_t_i_n_g _t_h_e _i_l_l_u_s_t_r_a_t_i_o_n_s
_o_f _S_e_c_t_i_o_n _A._3. _E_x_c_e_r_p_t_s _a_r_e _p_r_o_v_i_d_e_d _r_a_t_h_e_r _t_h_a_n _f_u_l_l _o_u_t_-
_p_u_t, _s_i_n_c_e, _e._g., _N_P_A _a_n_a_l_y_s_i_s _i_s _u_n_a_f_f_e_c_t_e_d _b_y _k_e_y_w_o_r_d_s
_t_h_a_t _m_o_d_i_f_y _t_h_e _N_B_O _s_e_a_r_c_h. _K_e_y_w_o_r_d_s _o_f _g_e_n_e_r_a_l _a_p_p_l_i_c_a_b_i_l_-
_i_t_y _a_r_e _i_l_l_u_s_t_r_a_t_e_d _w_i_t_h _t_h_e _m_e_t_h_y_l_a_m_i_n_e _e_x_a_m_p_l_e (_R_H_F/_3-_2_1_G,
_P_o_p_l_e-_G_o_r_d_o_n _g_e_o_m_e_t_r_y) _o_f _S_e_c_t_i_o_n _A._3, _w_h_i_c_h _s_h_o_u_l_d _b_e _c_o_n_-
_s_u_l_t_e_d _f_o_r _f_u_r_t_h_e_r _i_n_f_o_r_m_a_t_i_o_n. _M_o_r_e _s_p_e_c_i_a_l_i_z_e_d _k_e_y_w_o_r_d_s
(_R_E_S_O_N_A_N_C_E, _3_C_B_O_N_D, _e_t_c.) _a_r_e _i_l_l_u_s_t_r_a_t_e_d _w_i_t_h _p_r_o_t_o_t_y_p_e
_m_o_l_e_c_u_l_e_s (_b_e_n_z_e_n_e, _d_i_b_o_r_a_n_e, _e_t_c.) _c_h_o_s_e_n _f_o_r _t_h_e _k_e_y_w_o_r_d.
_0 _S_e_c_t_i_o_n_s _B._6._2-_B._6._8 _i_l_l_u_s_t_r_a_t_e _r_e_p_r_e_s_e_n_t_a_t_i_v_e _e_x_a_m_p_l_e_s
_f_r_o_m _t_h_e $_N_B_O _k_e_y_w_o_r_d _g_r_o_u_p_s, _i_n_c_l_u_d_i_n_g _N_L_M_O, _D_I_P_O_L_E,
_B_N_D_I_D_X, _R_E_S_O_N_A_N_C_E, _N_O_B_O_N_D, _3_C_B_O_N_D, _a_n_d _m_a_t_r_i_x _o_u_t_p_u_t _k_e_y_-
_w_o_r_d_s. _S_e_c_t_i_o_n _B._6._9 _a_n_d _B._6._1_0 _s_i_m_i_l_a_r_l_y _i_l_l_u_s_t_r_a_t_e _t_h_e
_u_s_e _o_f _t_h_e $_C_H_O_O_S_E _a_n_d $_D_E_L _k_e_y_l_i_s_t_s. _S_e_c_t_i_o_n _B._6._1_1 _i_l_l_u_s_-
_t_r_a_t_e_s _t_h_e _o_u_t_p_u_t _f_o_r _o_p_e_n-_s_h_e_l_l _U_H_F _c_a_s_e_s, _e_m_p_h_a_s_i_z_i_n_g
_f_e_a_t_u_r_e_s _a_s_s_o_c_i_a_t_e_d _w_i_t_h _t_h_e ``_d_i_f_f_e_r_e_n_t _L_e_w_i_s _s_t_r_u_c_t_u_r_e_s
_f_o_r _d_i_f_f_e_r_e_n_t _s_p_i_n_s'' _r_e_p_r_e_s_e_n_t_a_t_i_o_n _o_f _l_p_h_a _a_n_d77777777778 t99a999999 s99p99i99n9999 m99a99n99i99f99o99l99d99s99.
_S77777777778_c_t_i_o_n _B._6._1_2 _s_h_o_w_s _t_h_e _e_f_f_e_c_t _o_f _u_s_i_n_g _e_f_f_e_c_t_i_v_e _c_o_r_e
_p_o_t_e_n_t_i_a_l_s _f_o_r _C_u#_d_2#_u, _a_l_s_o _i_l_l_u_s_t_r_a_t_i_n_g _a_s_p_e_c_t_s _o_f _t_h_e
_i_n_c_l_u_s_i_o_n _o_f #_I_d#_N _f_u_n_c_t_i_o_n_s. #_I_B._6._2 _N_L_M_O _K_e_y_w_o_r_d#_N
_0 _W_h_e_n _t_h_e _N_L_M_O _k_e_y_w_o_r_d _i_s _a_c_t_i_v_a_t_e_d, _t_h_e _p_r_o_g_r_a_m _c_o_m_p_u_t_e_s
_t_h_e _N_L_M_O_s _a_n_d _p_r_i_n_t_s _o_u_t _t_h_r_e_e _t_a_b_l_e_s _s_u_m_m_a_r_i_z_i_n_g _t_h_e_i_r
_f_o_r_m. _F_o_r _t_h_e _R_H_F/_3-_2_1_G _m_e_t_h_y_l_a_m_i_n_e _e_x_a_m_p_l_e (_c_f. _S_e_c_t_i_o_n
_A._3), _t_h_e _p_r_i_n_c_i_p_a_l _N_L_M_O _t_a_b_l_e _i_s _s_h_o_w_n _b_e_l_o_w:
_N_A_T_U_R_A_L _L_O_C_A_L_I_Z_E_D _M_O_L_E_C_U_L_A_R _O_R_B_I_T_A_L (_N_L_M_O) _A_N_A_L_Y_S_I_S:
_M_a_x_i_m_u_m _o_f_f-_d_i_a_g_o_n_a_l _e_l_e_m_e_n_t _o_f _D_M _i_n _N_L_M_O _b_a_s_i_s: _0._0_0_0_0_0
_H_y_b_r_i_d_i_z_a_t_i_o_n/_P_o_l_a_r_i_z_a_t_i_o_n _A_n_a_l_y_s_i_s _o_f _N_L_M_O_s _i_n _N_A_O _B_a_s_i_s:
July 11, 1995
- 47 -
_N_L_M_O/_O_c_c_u_p_a_n_c_y/_P_e_r_c_e_n_t
_f_r_o_m _P_a_r_e_n_t _N_B_O/ _A_t_o_m_i_c _H_y_b_r_i_d _C_o_n_t_r_i_b_u_t_i_o_n_s ----------
---------------------------------------------------------------------
_1. (_2._0_0_0_0_0) _9_9._9_2_9_0% _B_D ( _1) _C _1- _N _2
_4_0._0_3_9% _C _1 _s( _2_1._5_4%)_p _3._6_4(
_7_8._4_6%)
_5_9._8_9_1% _N _2 _s( _3_0._9_8%)_p _2._2_3(
_6_9._0_2%)
_0._0_1_5% _H _3 _s(_1_0_0._0_0%)
_0._0_2_1% _H _6 _s(_1_0_0._0_0%)
_0._0_2_1% _H _7 _s(_1_0_0._0_0%)
_2. (_2._0_0_0_0_0) _9_9._9_3_0_1% _B_D ( _1) _C _1- _H _3
_5_9._6_7_5% _C _1 _s( _2_5._4_4%)_p _2._9_3(
_7_4._5_6%)
_0._0_4_0% _N _2 _s( _1._9_9%)_p_4_9._2_2(
_9_8._0_1%)
_4_0._2_5_8% _H _3 _s(_1_0_0._0_0%)
_3. (_2._0_0_0_0_0) _9_9._6_9_9_6% _B_D ( _1) _C _1- _H _4
_6_0._8_4_8% _C _1 _s( _2_5._2_5%)_p _2._9_6(
_7_4._7_5%)
_0._0_9_3% _N _2 _s( _1_3._0_8%)_p _6._6_5(
_8_6._9_2%)
_0._0_1_4% _H _3 _s(_1_0_0._0_0%)
_3_8._8_6_1% _H _4 _s(_1_0_0._0_0%)
_0._0_1_7% _H _5 _s(_1_0_0._0_0%)
_0._1_5_8% _H _6 _s(_1_0_0._0_0%)
_4. (_2._0_0_0_0_0) _9_9._6_9_9_6% _B_D ( _1) _C _1- _H _5
_6_0._8_4_8% _C _1 _s( _2_5._2_5%)_p _2._9_6(
_7_4._7_5%)
_0._0_9_3% _N _2 _s( _1_3._0_8%)_p _6._6_5(
_8_6._9_2%)
_0._0_1_4% _H _3 _s(_1_0_0._0_0%)
_0._0_1_7% _H _4 _s(_1_0_0._0_0%)
_3_8._8_6_1% _H _5 _s(_1_0_0._0_0%)
_0._1_5_8% _H _7 _s(_1_0_0._0_0%)
_5. (_2._0_0_0_0_0) _9_9._7_2_0_6% _B_D ( _1) _N _2- _H _6
_0._1_1_3% _C _1 _s( _5._1_5%)_p_1_8._4_1(
_9_4._8_5%)
_6_7._9_2_9% _N _2 _s( _2_5._8_2%)_p _2._8_7(
_7_4._1_8%)
_0._1_3_7% _H _4 _s(_1_0_0._0_0%)
_0._0_1_4% _H _5 _s(_1_0_0._0_0%)
_3_1._7_9_3% _H _6 _s(_1_0_0._0_0%)
_6. (_2._0_0_0_0_0) _9_9._7_2_0_6% _B_D ( _1) _N _2- _H _7
_0._1_1_3% _C _1 _s( _5._1_5%)_p_1_8._4_1(
_9_4._8_5%)
_6_7._9_2_9% _N _2 _s( _2_5._8_2%)_p _2._8_7(
_7_4._1_8%)
_0._0_1_4% _H _4 _s(_1_0_0._0_0%)
_0._1_3_7% _H _5 _s(_1_0_0._0_0%)
_3_1._7_9_3% _H _7 _s(_1_0_0._0_0%)
_7. (_2._0_0_0_0_0) _9_9._9_4_9_9% _C_R ( _1) _C _1
_9_9._9_5_1% _C _1 _s(_1_0_0._0_0%)_p _0._0_0(
_0._0_0%)
July 11, 1995
- 48 -
_0._0_1_3% _H _3 _s(_1_0_0._0_0%)
_0._0_1_3% _H _4 _s(_1_0_0._0_0%)
_0._0_1_3% _H _5 _s(_1_0_0._0_0%)
_8. (_2._0_0_0_0_0) _9_9._9_7_6_3% _C_R ( _1) _N _2
_0._0_1_0% _C _1 _s( _2_2._3_0%)_p _3._4_8(
_7_7._7_0%)
_9_9._9_8_0% _N _2 _s(_1_0_0._0_0%)_p _0._0_0(
_0._0_0%)
_9. (_2._0_0_0_0_0) _9_8._8_9_7_2% _L_P ( _1) _N _2
_0._4_4_0% _C _1 _s( _1._0_5%)_p_9_4._1_5(
_9_8._9_5%)
_9_8._8_9_7% _N _2 _s( _1_7._8_5%)_p _4._6_0(
_8_2._1_5%)
_0._4_8_9% _H _3 _s(_1_0_0._0_0%)
_0._0_8_5% _H _4 _s(_1_0_0._0_0%)
_0._0_8_5% _H _5 _s(_1_0_0._0_0%)
#_T
@_s_e_g
#_N_F_o_r _e_a_c_h _o_f _t_h_e _n_i_n_e _o_c_c_u_p_l_i_e_d _N_L_M_O_s, _t_h_e _t_a_b_l_e _s_h_o_w_s
_f_i_r_s_t _t_h_e _N_L_M_O _o_c_c_u_p_a_n_c_y (_n_e_c_e_s_s_a_r_i_l_y _2._0_0_0_0 _a_t _S_C_F _l_e_v_e_l,
_a_s _i_n _t_h_e _p_r_e_s_e_n_t _e_x_a_m_p_l_e), _t_h_e _p_e_r_c_e_n_t_a_g_e _o_f _t_h_e _t_o_t_a_l _N_L_M_O
_c_o_m_p_o_s_i_t_i_o_n _r_e_p_r_e_s_e_n_t_e_d _b_y _t_h_i_s _p_a_r_e_n_t _N_B_O (_u_s_u_a_l_l_y > _9_9%),
_a_n_d _t_h_e _l_a_b_e_l _o_f _t_h_e `_p_a_r_e_n_t' _N_B_O. _B_e_l_o_w _t_h_i_s, _t_h_e_r_e _f_o_l_-
_l_o_w_s _a_n _N_A_O _d_e_c_o_m_p_o_s_i_t_i_o_n _o_f _t_h_e _N_L_M_O, _s_h_o_w_i_n_g _t_h_e _p_e_r_c_e_n_-
_t_a_g_e _o_f _t_h_e _N_L_M_O _o_n _e_a_c_h _a_t_o_m _a_n_d _t_h_e _h_y_b_r_i_d _c_o_m_p_o_s_i_t_i_o_n
_r_a_t_i_o_s (_e_f_f_e_c_t_i_v_e #_I_s_p#_N#_u #_d _c_h_a_r_a_c_t_e_r _a_n_d _p_e_r_c_e_n_t_a_g_e #_I_s-
#_N _a_n_d #_I_p#_N-_c_h_a_r_a_c_t_e_r) _o_f _t_h_e _N_A_O_s. _F_o_r _e_x_a_m_p_l_e, _N_L_M_O _9 _i_s
_t_h_e _m_o_s_t _d_e_l_o_c_a_l_i_z_e_d _N_L_M_O _o_f _t_h_e _t_a_b_l_e, _h_a_v_i_n_g _o_n_l_y _a_b_o_u_t _a
_9_8._9% _c_o_n_t_r_i_b_u_t_i_o_n _f_r_o_m _t_h_e _l_o_c_a_l_i_z_e_d _N(_2) _p_a_r_e_n_t _l_o_n_e _p_a_i_r
_N_B_O, _w_i_t_h `_d_e_l_o_c_a_l_i_z_a_t_i_o_n _t_a_i_l_s' _c_o_m_p_o_s_e_d _p_r_i_m_a_r_i_l_y _o_f _c_o_n_-
_t_r_i_b_u_t_i_o_n_s (~_0._4% _e_a_c_h) _f_r_o_m _C(_1) _a_n_d _H(_3), _a_n_d _s_m_a_l_l_e_r _c_o_n_-
_t_r_i_b_u_t_i_o_n_s (~_0._0_9%) _f_r_o_m _H(_4) _a_n_d _H(_5). _T_h_i_s _c_o_r_r_e_s_p_o_n_d_s _t_o
_w_h_a_t _m_i_g_h_t _h_a_v_e _b_e_e_n _a_n_t_i_c_i_p_a_t_e_d _f_r_o_m _t_h_e _N_B_O _s_u_m_m_a_r_y _t_a_b_l_e
(_S_e_c_t_i_o_n _A._3._6) _o_r _p_e_r_t_u_r_b_a_t_i_o_n _t_h_e_o_r_y _e_n_e_r_g_y _a_n_a_l_y_s_i_s _t_a_b_l_e
(_S_e_c_t_i_o_n _A._3._5), _w_h_i_c_h _s_h_o_w_e_d _t_h_a_t _t_h_e _N(_2) _l_o_n_e _p_a_i_r, _N_B_O
_9, _i_s _p_r_i_n_c_i_p_a_l_l_y _d_e_l_o_c_a_l_i_z_e_d _o_n_t_o _N_B_O _2_4, _t_h_e _v_i_c_i_n_a_l
_C(_1)-_H(_3) _a_n_t_i_b_o_n_d [_w_i_t_h _l_e_s_s_e_r _d_e_l_o_c_a_l_i_z_a_t_i_o_n_s _o_n_t_o _N_B_O_s
_2_5, _2_6, _t_h_e _C(_1)-_H(_4) _a_n_d _C(_1)-_H(_5) _a_n_t_i_b_o_n_d_s]. #_I_B._6._3
_D_I_P_O_L_E _K_e_y_w_o_r_d#_N
_0 _T_h_e _D_I_P_O_L_E _k_e_y_w_o_r_d _a_c_t_i_v_a_t_e_s _t_h_e _N_B_O/_N_L_M_O _a_n_a_l_y_s_i_s _o_f _t_h_e
_m_o_l_e_c_u_l_a_r _d_i_p_o_l_e _m_o_m_e_n_t, _a_s _s_h_o_w_n _b_e_l_o_w _f_o_r _t_h_e _e_x_a_m_p_l_e _o_f
_R_H_F/_3-_2_1_G _m_e_t_h_y_l_a_m_i_n_e (_c_f. _S_e_c_t_i_o_n _A._3):
_D_i_p_o_l_e _m_o_m_e_n_t _a_n_a_l_y_s_i_s:
[_P_r_i_n_t _t_h_r_e_s_h_o_l_d: _N_e_t _d_i_p_o_l_e > _0._0_2 _D_e_b_y_e]
_N_L_M_O _b_o_n_d _d_i_p_o_l_e
_N_B_O _b_o_n_d _d_i_p_o_l_e
July 11, 1995
- 49 -
------------------------- ------------------------
_O_r_b_i_t_a_l _x _y _z _T_o_t_a_l _x
_y _z _T_o_t_a_l
===============================================================================
_1. _B_D ( _1) _C _1- _N _2 -_0._7_6 -_0._0_8 _0._0_0 _0._7_6 -_0._7_6
-_0._0_9 _0._0_0 _0._7_7
_2. _B_D ( _1) _C _1- _H _3 _0._4_9 _1._9_0 _0._0_0 _1._9_6 _0._5_0
_1._9_0 _0._0_0 _1._9_7
_d_e_l_o_c _1_4: _0._0_3
-_0._0_1 _0._0_0 _0._0_3
_d_e_l_o_c _2_5: -_0._0_1
_0._0_0 _0._0_2 _0._0_2
_d_e_l_o_c _2_6: -_0._0_1
_0._0_0 -_0._0_2 _0._0_2
_3. _B_D ( _1) _C _1- _H _4 _0._6_7 -_0._7_7 -_1._5_0 _1._8_1 _0._7_1
-_0._7_9 -_1._5_0 _1._8_4
_d_e_l_o_c _2_7: -_0._0_5
_0._0_0 _0._0_0 _0._0_5
_d_e_l_o_c _2_6: -_0._0_2
_0._0_3 -_0._0_3 _0._0_4
_d_e_l_o_c _2_4: -_0._0_1
-_0._0_2 _0._0_0 _0._0_2
_4. _B_D ( _1) _C _1- _H _5 _0._6_7 -_0._7_7 _1._5_0 _1._8_1 _0._7_1
-_0._7_9 _1._5_0 _1._8_4
_d_e_l_o_c _2_8: -_0._0_5
_0._0_0 _0._0_0 _0._0_5
_d_e_l_o_c _2_5: -_0._0_2
_0._0_3 _0._0_3 _0._0_4
_d_e_l_o_c _2_4: -_0._0_1
-_0._0_2 _0._0_0 _0._0_2
_5. _B_D ( _1) _N _2- _H _6 -_0._4_5 _0._4_4 _0._8_6 _1._0_6 -_0._5_0
_0._4_4 _0._8_9 _1._1_1
_d_e_l_o_c _2_5: _0._0_6
-_0._0_1 -_0._0_2 _0._0_6
_6. _B_D ( _1) _N _2- _H _7 -_0._4_5 _0._4_4 -_0._8_6 _1._0_6 -_0._5_0
_0._4_4 -_0._8_9 _1._1_1
_d_e_l_o_c _2_6: _0._0_6
-_0._0_1 _0._0_2 _0._0_6
_7. _C_R ( _1) _C _1 _0._0_0 _0._0_0 _0._0_0 _0._0_0 _0._0_0
_0._0_0 _0._0_0 _0._0_0
_8. _C_R ( _1) _N _2 _0._0_0 _0._0_1 _0._0_0 _0._0_1 _0._0_0
_0._0_0 _0._0_0 _0._0_0
_9. _L_P ( _1) _N _2 -_0._6_3 -_2._8_5 _0._0_0 _2._9_1 -_0._8_8
-_2._9_3 _0._0_0 _3._0_6
_d_e_l_o_c _2_4: _0._1_6
_0._0_9 _0._0_0 _0._1_8
July 11, 1995
- 50 -
_d_e_l_o_c _2_5: _0._0_3 _0._0_1 _0._0_1 _0._0_3
_d_e_l_o_c _2_6: _0._0_3
_0._0_1 -_0._0_1 _0._0_3
_d_e_l_o_c _1_0: _0._0_2
-_0._0_2 _0._0_0 _0._0_3
----------
------------------------------------------
_N_e_t _d_i_p_o_l_e _m_o_m_e_n_t -_0._4_5 -_1._6_7 _0._0_0 _1._7_3 -_0._7_1
-_1._8_2 _0._0_0 _1._9_5 _D_e_l_o_c_a_l_i_z_a_t_i_o_n _c_o_r_r_e_c_t_i_o_n
_0._2_7 _0._1_4 _0._0_0 _0._3_0
----------
------------------------------------------
_T_o_t_a_l _d_i_p_o_l_e _m_o_m_e_n_t -_0._4_5 -_1._6_7 _0._0_0 _1._7_3 -_0._4_5
-_1._6_7 _0._0_0 _1._7_3
#_T
@_s_e_g
#_N_T_h_e _b_o_t_t_o_m _l_i_n_e _o_f _t_h_e _t_a_b_l_e _s_h_o_w_s _t_h_e _i_n_d_i_v_i_d_u_a_l (_x,_y,_z)
_v_e_c_t_o_r _c_o_m_p_o_n_e_n_t_s (_m_i_n_u_s _0._4_5,_m_i_n_u_s _1._6_7,_0._0_0) _a_n_d _l_e_n_g_t_h
(_1._7_3 _D) _o_f _t_h_e _t_o_t_a_l _m_o_l_e_c_u_l_a_r _d_i_p_o_l_e _m_o_m_e_n_t, _i_n _t_h_e _c_o_o_r_-
_d_i_n_a_t_e _s_y_s_t_e_m _o_f _t_h_e _E_S_S _p_r_o_g_r_a_m. _T_h_i_s _i_s _d_e_c_o_m_p_o_s_e_d _i_n _t_h_e
_m_a_i_n _b_o_d_y _o_f _t_h_e _t_a_b_l_e _i_n_t_o _t_h_e _i_n_d_i_v_i_d_u_a_l _c_o_n_t_r_i_b_u_t_i_o_n_s _o_f
``_N_L_M_O _b_o_n_d _d_i_p_o_l_e_s'' (_w_h_i_c_h _s_t_r_i_c_t_l_y _a_d_d _t_o _g_i_v_e _t_h_e _n_e_t
_m_o_l_e_c_u_l_e _d_i_p_o_l_e _a_t _t_h_e _S_C_F _l_e_v_e_l) _a_n_d ``_N_B_O _b_o_n_d _d_i_p_o_l_e_s''
(_w_h_i_c_h _m_u_s_t _b_e _a_d_d_e_d _w_i_t_h _t_h_e_i_r _o_f_f-_d_i_a_g_o_n_a_l `_d_e_l_o_c' _c_o_n_t_r_i_-
_b_u_t_i_o_n_s _t_o _g_i_v_e _t_h_e _n_e_t _m_o_l_e_c_u_l_a_r _m_o_m_e_n_t). _E_a_c_h _N_L_M_O _o_r _N_B_O
_b_o_n_d _d_i_p_o_l_e _v_e_c_t_o_r _t _m_u #_d_A_B #_u _i_s _e_v_a_l_u_a_t_e_d _a_s
_m_a_b = _m_a_b_e + _m_a_b_n
_w_h_e_r_e _m_a_b_e = _2#_I_e#_N77a9999 b9999 _a77 _t _r#_N_a_r _b _t _i_s _t_h_e _e_l_e_c_t_r_o_n_i_c _d_i_p_o_l_e
_e_x_p_e_c_t_a_t_i_o_n _v_a_l_u_e _f_o_r _a_n _e_l_e_c_t_r_o_n _p_a_i_r _i_n _t_h_e _b _N_L_M_O _o_r
_N_B_O, _a_n_d _m_a_b_n _i_s _t_h_e _n_u_c_l_e_a_r _c_o_n_t_r_i_b_u_t_i_o_n _o_f _c_o_m_p_e_n_s_a_t_i_n_g
_u_n_i_t _p_o_s_i_t_i_v_e _c_h_a_r_g_e_s _a_t _t_h_e _p_o_s_i_t_i_o_n_s _o_f _n_u_c_l_e_i _A _a_n_d _B (_o_r
_b_o_t_h _o_n _A _f_o_r _a _1-_c_e_n_t_e_r _N_B_O). _T_h_e `_d_e_l_o_c' _c_o_n_t_r_i_b_u_t_i_o_n_s
_b_e_l_o_w _e_a_c_h _N_B_O _b_o_n_d _d_i_p_o_l_e _s_h_o_w _t_h_e _o_f_f-_d_i_a_g_o_n_a_l _c_o_r_r_e_c_t_i_o_n_s
_t_o _a_n _a_d_d_i_t_i_v_e _b_o_n_d _d_i_p_o_l_e _a_p_p_r_o_x_i_m_a_t_i_o_n (_i._e., _t_h_e _c_o_r_r_e_c_-
_t_i_o_n_s _t_o _l_o_c_a_l_i_z_e_d _N_B_O _b_o_n_d _d_i_p_o_l_e_s _t_o _g_e_t _t_h_e _N_L_M_O _b_o_n_d
_d_i_p_o_l_e_s) _t_o _a_c_c_o_u_n_t _f_o_r _t_h_e _d_e_l_o_c_a_l_i_z_a_t_i_o_n _f_r_o_m _p_a_r_e_n_t _N_B_O
#_I_i#_N _o_n_t_o _o_t_h_e_r (_p_r_i_m_a_r_i_l_y, _n_o_n-_L_e_w_i_s) _N_B_O_s #_I_j#_N; _i_n _t_e_r_m_s
_o_f _t_h_e _e_x_p_a_n_s_i_o_n _o_f _a_n _N_L_M_O _i_n _t_h_e _s_e_t { } _o_f _N_B_O_s,
_n_l_m_o = _t_h_i_s _c_o_r_r_e_c_t_i_o_n _i_s (_f_o_r _e_a_c_h _e_l_e_c_t_r_o_n, _l_p_h_a _o_r7777 t99a
s
p
i
n
)7777._L_M+_1_0
+ _s <<_k>> _w_h_e_r_e _t_h_e _p_r_i_m_e_s _o_n _t_h_e _s_u_m_m_a_t_i_o_n _d_e_n_o_t_e _o_m_i_s_s_i_o_n
_o_f _t_e_r_m_s #_I_k#_N _e_q_u_a_l _t_o #_I_i#_N _o_r #_I_j#_N. _F_o_r _e_x_a_m_p_l_e, _i_n _t_h_e
_a_b_o_v_e _t_a_b_l_e _t_h_e _l_a_r_g_e_s_t _i_n_d_i_v_i_d_u_a_l _c_o_n_t_r_i_b_u_t_i_o_n _t_o _t _m_u _i_s
_f_r_o_m _t_h_e _n_i_t_r_o_g_e_n _l_o_n_e _p_a_i_r, _t_a_b_l_e _e_n_t_r_y _9, _w_h_i_c_h _h_a_s _a_n
_N_L_M_O _d_i_p_o_l_e _o_f _2._9_1 _D_e_b_y_e _o_r _N_B_O _d_i_p_o_l_e _o_f _3._0_6. _T_h_e _l_a_t_t_e_r
July 11, 1995
- 51 -
_h_a_s
_a_l_s_o _t_h_e _l_a_r_g_e_s_t _o_f_f-_d_i_a_g_o_n_a_l _d_e_l_o_c_a_l_i_z_a_t_i_o_n _c_o_r_r_e_c_t_i_o_n _i_n
_t_h_e _t_a_b_l_e, _a _0._1_8 _D _c_o_r_r_e_c_t_i_o_n _d_u_e _t_o _t_h_e #_I_n#_N#_d_N#_u7 _a_r_r
_g_m_a *#<#_d_C_H#_u _d_e_l_o_c_a_l_i_z_a_t_i_o_n _i_n_t_o _t_h_e _v_i_c_i_n_a_l _C(_1)-_H(_3)
_a_n_t_i_b_o_n_d, _N_B_O _2_4.
_0 _F_o_r _a _p_o_s_t-_S_C_F (_c_o_r_r_e_l_a_t_e_d) _c_a_l_c_u_l_a_t_i_o_n, _t_h_e _d_i_p_o_l_e _t_a_b_l_e
_w_o_u_l_d _a_l_s_o _i_n_c_l_u_d_e _a_n _a_d_d_i_t_i_o_n_a_l _l_i_n_e _f_o_r _t_h_e _c_o_r_r_e_c_t_i_o_n _d_u_e
_t_o _n_o_n-_a_d_d_i_t_i_v_i_t_y _o_f _t_h_e _N_L_M_O _b_o_n_d _d_i_p_o_l_e_s. _F_o_r _a_n _i_o_n_i_c
_s_p_e_c_i_e_s, _t_h_e_r_e _w_o_u_l_d _a_l_s_o _b_e _a_n _a_d_d_i_t_i_o_n_a_l _l_i_n_e _f_o_r _t_h_e
``_r_e_s_i_d_u_a_l _n_u_c_l_e_a_r _c_h_a_r_g_e'' _c_o_n_t_r_i_b_u_t_i_o_n; _h_e_r_e, _o_n_e _m_u_s_t _b_e
_a_w_a_r_e _t_h_a_t _t_h_e _d_i_p_o_l_e _m_o_m_e_n_t _i_s _c_a_l_c_u_l_a_t_e_d _w_i_t_h _r_e_s_p_e_c_t _t_o
_t_h_e _o_r_i_g_i_n _o_f _t_h_e _c_a_r_t_e_s_i_a_n _c_o_o_r_d_i_n_a_t_e _s_y_s_t_e_m _c_h_o_s_e_n _b_y _t_h_e
_E_S_S _p_r_o_g_r_a_m (_s_i_n_c_e _t_h_e _d_i_p_o_l_e _m_o_m_e_n_t _i_s _o_r_i_g_i_n-_d_e_p_e_n_d_e_n_t _i_n
_t_h_i_s _c_a_s_e).
_0 _N_o_t_e _t_h_a_t _t_h_e _a_m_o_u_n_t _o_f _d_e_t_a_i_l _i_n _t_h_e _d_i_p_o_l_e _t_a_b_l_e _c_a_n _b_e
_a_l_t_e_r_e_d _b_y _u_s_i_n_g _t_h_e ``_D_I_P_O_L_E=_t_h_r'' _f_o_r_m _o_f _t_h_e _k_e_y_w_o_r_d _t_o
_a_l_t_e_r _t_h_e _t_h_r_e_s_h_o_l_d _d_i_p_o_l_e (`_t_h_r') _f_o_r _p_r_i_n_t_i_n_g [_d_e_f_a_u_l_t:
_0._0_2 _D]. #_I_B._6._4 _M_a_t_r_i_x _O_u_t_p_u_t _K_e_y_w_o_r_d_s#_N
_0 _T_w_o _s_i_m_p_l_e _e_x_a_m_p_l_e_s _w_i_l_l _b_e _g_i_v_e_n _t_o _i_l_l_u_s_t_r_a_t_e _t_h_e _f_o_r_-
_m_a_t_t_i_n_g _o_f _o_u_t_p_u_t _f_o_r _o_p_e_r_a_t_o_r_s _o_r _b_a_s_i_s _s_e_t _t_r_a_n_s_f_o_r_m_a_t_i_o_n
_m_a_t_r_i_c_e_s _u_s_i_n_g _t_h_e _m_a_t_r_i_x _o_u_t_p_u_t _k_e_y_w_o_r_d_s _o_f _S_e_c_t_i_o_n _B._2._4.
_F_o_r _t_h_e _R_H_F/_3-_2_1_G _m_e_t_h_y_l_a_m_i_n_e _e_x_a_m_p_l_e _o_f _S_e_c_t_i_o_n _A._3, _t_h_e
_k_e_y_w_o_r_d ``_F_N_H_O'' _w_o_u_l_d _c_a_u_s_e _t_h_e _F_o_c_k _m_a_t_r_i_x _i_n _t_h_e _N_H_O
_b_a_s_i_s _t_o _b_e _p_r_i_n_t_e_d _o_u_t. _S_h_o_w_n _b_e_l_o_w _i_s _a _r_e_p_r_o_d_u_c_t_i_o_n _o_f
_t_h_e _f_i_r_s_t _e_i_g_h_t _c_o_l_u_m_n_s (_o_u_t _o_f _2_8) _o_f _t_h_i_s _o_u_t_p_u_t:
_N_H_O _F_o_c_k _m_a_t_r_i_x:
_N_H_O _1 _2 _3 _4 _5
_6 _7 _8
---------- ------- ------- ------- ------- ------- ---
---- ------- -------
_1. _C_1 ( _N_2 ) -_0._0_2_0_8 -_0._7_2_0_3 -_0._0_5_7_1 -_0._0_6_6_5 _0._0_4_3_8
_0._0_6_7_2 _0._0_4_3_8 _0._0_6_7_2
_2. _N_2 ( _C_1 ) -_0._7_2_0_3 -_0._3_0_8_3 -_0._0_7_7_3 -_0._0_6_2_7 _0._0_8_3_5
_0._0_6_4_6 _0._0_8_3_5 _0._0_6_4_6
_3. _C_1 ( _H_3 ) -_0._0_5_7_1 -_0._0_7_7_3 -_0._1_3_9_4 -_0._6_7_5_8 _0._0_6_3_8
_0._0_7_4_6 _0._0_6_3_8 _0._0_7_4_6
_4. _H_3 ( _C_1 ) -_0._0_6_6_5 -_0._0_6_2_7 -_0._6_7_5_8 _0._1_3_4_9 _0._0_7_4_0
_0._0_6_7_2 _0._0_7_4_0 _0._0_6_7_2
_5. _C_1 ( _H_4 ) _0._0_4_3_8 _0._0_8_3_5 _0._0_6_3_8 _0._0_7_4_0 -_0._1_4_6_6
-_0._6_7_6_1 -_0._0_5_4_8 -_0._0_7_5_9
_6. _H_4 ( _C_1 ) _0._0_6_7_2 _0._0_6_4_6 _0._0_7_4_6 _0._0_6_7_2 -_0._6_7_6_1
_0._1_5_4_1 -_0._0_7_5_9 -_0._0_6_9_7
_7. _C_1 ( _H_5 ) _0._0_4_3_8 _0._0_8_3_5 _0._0_6_3_8 _0._0_7_4_0 -_0._0_5_4_8
-_0._0_7_5_9 -_0._1_4_6_6 -_0._6_7_6_1
_8. _H_5 ( _C_1 ) _0._0_6_7_2 _0._0_6_4_6 _0._0_7_4_6 _0._0_6_7_2 -_0._0_7_5_9
-_0._0_6_9_7 -_0._6_7_6_1 _0._1_5_4_1
_9. _N_2 ( _H_6 ) _0._0_9_2_6 _0._1_4_9_9 _0._0_2_4_0 -_0._0_1_1_3 _0._0_9_1_2
-_0._0_0_7_8 -_0._0_3_4_9 _0._0_1_3_4
_1_0. _H_6 ( _N_2 ) _0._1_0_8_3 _0._0_8_2_6 -_0._0_0_1_0 _0._0_2_3_2 -_0._0_1_1_8
-_0._0_2_4_2 _0._0_0_1_7 -_0._0_2_2_4
July 11, 1995
- 52 -
_1_1. _N_2 ( _H_7 ) _0._0_9_2_6 _0._1_4_9_9 _0._0_2_4_0 -_0._0_1_1_3 -_0._0_3_4_9
_0._0_1_3_4 _0._0_9_1_2 -_0._0_0_7_8
_1_2. _H_7 ( _N_2 ) _0._1_0_8_3 _0._0_8_2_6 -_0._0_0_1_0 _0._0_2_3_2 _0._0_0_1_7
-_0._0_2_2_4 -_0._0_1_1_8 -_0._0_2_4_2
_1_3. _C_1 (_c_r) _0._3_9_6_2 _0._4_1_6_8 _0._4_4_0_0 _0._3_8_9_3 -_0._4_4_4_7
-_0._3_8_6_9 -_0._4_4_4_7 -_0._3_8_6_9
_1_4. _N_2 (_c_r) _0._6_1_4_7 _0._7_0_8_3 _0._0_0_3_9 _0._0_2_4_9 -_0._0_1_3_0
-_0._0_2_5_1 -_0._0_1_3_0 -_0._0_2_5_1
_1_5. _N_2 (_l_p) _0._0_7_6_2 _0._0_9_5_5 -_0._1_0_4_3 _0._0_2_5_4 -_0._0_3_8_6
_0._0_1_6_0 -_0._0_3_8_6 _0._0_1_6_0
_1_6. _C_1 (_r_y*) -_0._1_3_2_0 _0._0_9_2_4 _0._0_7_0_5 -_0._0_8_1_5 _0._0_0_2_2
-_0._0_0_3_7 _0._0_0_2_2 -_0._0_0_3_7
_1_7. _C_1 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_7_1_9
-_0._0_9_1_0 -_0._0_7_1_9 _0._0_9_1_0
_1_8. _C_1 (_r_y*) -_0._1_0_2_3 _0._0_7_6_4 -_0._0_6_4_3 _0._0_7_9_5 -_0._0_0_7_4
_0._0_1_0_5 -_0._0_0_7_4 _0._0_1_0_5
_1_9. _C_1 (_r_y*) _0._0_2_6_6 -_0._0_2_1_3 _0._0_0_1_9 -_0._0_0_5_7 _0._0_6_6_7
-_0._0_7_8_8 _0._0_6_6_7 -_0._0_7_8_8
_2_0. _N_2 (_r_y*) _0._0_1_5_1 -_0._0_1_7_7 -_0._0_3_5_1 -_0._0_1_7_2 -_0._0_1_7_9
-_0._0_1_4_6 -_0._0_1_7_9 -_0._0_1_4_6
_2_1. _N_2 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 -_0._0_1_5_8
-_0._0_2_4_9 _0._0_1_5_8 _0._0_2_4_9
_2_2. _N_2 (_r_y*) _0._1_7_9_9 -_0._1_4_4_0 -_0._0_0_6_4 _0._0_2_9_5 _0._0_0_3_8
-_0._0_2_8_9 _0._0_0_3_8 -_0._0_2_8_9
_2_3. _N_2 (_r_y*) _0._0_1_8_3 -_0._0_1_3_6 -_0._0_0_5_1 _0._0_2_1_3 _0._0_0_3_2
-_0._0_0_9_5 _0._0_0_3_2 -_0._0_0_9_5
_2_4. _H_3 (_r_y*) _0._0_2_5_3 -_0._0_0_3_8 _0._2_8_3_4 -_0._3_4_9_7 -_0._0_2_4_8
_0._0_0_4_7 -_0._0_2_4_8 _0._0_0_4_7
_2_5. _H_4 (_r_y*) _0._0_2_2_3 -_0._0_0_7_1 _0._0_2_1_1 -_0._0_0_6_8 -_0._2_7_8_9
_0._3_5_5_3 -_0._0_2_2_7 _0._0_0_6_9
_2_6. _H_5 (_r_y*) _0._0_2_2_3 -_0._0_0_7_1 _0._0_2_1_1 -_0._0_0_6_8 -_0._0_2_2_7
_0._0_0_6_9 -_0._2_7_8_9 _0._3_5_5_3
_2_7. _H_6 (_r_y*) _0._0_1_2_4 _0._0_1_7_2 -_0._0_0_6_7 _0._0_2_1_9 -_0._0_0_8_0
_0._0_0_9_7 _0._0_0_5_7 -_0._0_2_2_2
_2_8. _H_7 (_r_y*) _0._0_1_2_4 _0._0_1_7_2 -_0._0_0_6_7 _0._0_2_1_9 _0._0_0_5_7
-_0._0_2_2_2 -_0._0_0_8_0 _0._0_0_9_7
#_T
@_s_e_g
#_N
_0 _T_h_e _N_H_O _l_a_b_e_l_s _o_n _e_a_c_h _r_o_w _i_d_e_n_t_i_f_y _t_h_e _a_t_o_m _t_o _w_h_i_c_h _t_h_e
_N_H_O _b_e_l_o_n_g_s, _a_n_d (_i_n _p_a_r_e_n_t_h_e_s_e_s) _t_h_e _a_t_o_m _t_o_w_a_r_d _w_h_i_c_h _t_h_e
_h_y_b_r_i_d _i_s _p_o_i_n_t_e_d, _i_f _a _b_o_n_d _h_y_b_r_i_d, _o_r _a _1-_c_e_n_t_e_r _l_a_b_e_l
(_c_r, _l_p, _l_p*, _o_r _r_y*), _i_f _a _n_o_n-_b_o_n_d_e_d _h_y_b_r_i_d. _T_h_u_s, ``_C _1
(_N _2)'' (_N_H_O _1) _i_s _t_h_e _b_o_n_d_i_n_g _h_y_b_r_i_d _o_n _C(_1) _d_i_r_e_c_t_e_d
_t_o_w_a_r_d _N(_2), ``_N _2(_l_p)'' (_N_B_O _1_5) _i_s _a _n_o_n-_b_o_n_d_e_d (_l_o_n_e
_p_a_i_r) _h_y_b_r_i_d _o_n _N(_2), _e_t_c. _T_h_i_s _l_a_b_e_l _a_l_l_o_w_s _o_n_e _t_o _f_i_n_d
_t_h_e _p_r_e_c_i_s_e _f_o_r_m _o_f _t_h_e _N_H_O _i_n _t_h_e _m_a_i_n _l_i_s_t_i_n_g _o_f _N_B_O_s.
_T_h_e _F_N_H_O _m_a_t_r_i_x _s_h_o_w_s, _f_o_r _e_x_a_m_p_l_e, _t_h_a_t _t_h_e (_1,_2) _F_o_c_k
_m_a_t_r_i_x _e_l_e_m_e_n_t _b_e_t_w_e_e_n _t_h_e _d_i_r_e_c_t_l_y _i_n_t_e_r_a_c_t_i_n_g _N_H_O_s _f_o_r_m_i_n_g
_t_h_e _C-_N _b_o_n_d _N_B_O _i_s -_0._7_2_0_3 _a._u., _w_h_e_r_e_a_s _t_h_e (_1,_9) _m_a_t_r_i_x
July 11, 1995
- 53 -
_e_l_e_m_e_n_t,
_b_e_t_w_e_e_n _t_h_e _C(_1) _h_y_b_r_i_d _p_o_i_n_t_i_n_g _t_o_w_a_r_d _N(_2) _a_n_d _t_h_e _N(_2)
_h_y_b_r_i_d _p_o_i_n_t_i_n_g _t_o_w_a_r_d _H(_6), _i_s _0._0_9_2_6 _a._u.
_0 _A_s _a _s_e_c_o_n_d _e_x_a_m_p_l_e, _t_h_e _k_e_y_w_o_r_d ``_N_B_O_M_O=_P_V_A_L'' _w_o_u_l_d
_p_r_i_n_t _o_u_t _t_h_e _c_o_r_e + _v_a_l_e_n_c_e _c_o_l_u_m_n_s _o_f _t_h_e _N_B_O7 _a_r_r _M_O
_t_r_a_n_s_f_o_r_m_a_t_i_o_n, _a_s _r_e_p_r_o_d_u_c_e_d _b_e_l_o_w:
_M_O_s _i_n _t_h_e _N_B_O _b_a_s_i_s:
_N_B_O _1 _2 _3 _4 _5
_6 _7 _8
---------- ------- ------- ------- ------- ------- ---
---- ------- -------
_1. _C_1 - _N_2 -_0._0_6_6_1 -_0._0_5_7_4 _0._6_2_8_8 -_0._1_2_4_3 _0._0_0_0_0
-_0._3_2_3_9 _0._6_8_1_6 _0._0_0_0_0
_2. _C_1 - _H_3 -_0._0_0_1_8 -_0._0_5_7_8 _0._2_0_6_1 -_0._4_7_1_6 _0._0_0_0_0
_0._7_7_4_7 _0._1_3_8_6 _0._0_0_0_0
_3. _C_1 - _H_4 _0._0_0_2_3 _0._0_5_7_9 -_0._1_8_3_6 _0._4_9_0_8 _0._3_8_1_3
_0._2_3_0_4 _0._3_9_2_1 _0._5_9_4_0
_4. _C_1 - _H_5 _0._0_0_2_3 _0._0_5_7_9 -_0._1_8_3_6 _0._4_9_0_8 -_0._3_8_1_3
_0._2_3_0_4 _0._3_9_2_1 -_0._5_9_4_0
_5. _N_2 - _H_6 _0._0_5_7_0 _0._0_0_0_0 -_0._4_7_4_2 -_0._3_5_6_7 -_0._5_9_3_7
-_0._1_9_5_4 _0._3_0_3_5 _0._3_8_1_4
_6. _N_2 - _H_7 _0._0_5_7_0 _0._0_0_0_0 -_0._4_7_4_2 -_0._3_5_6_7 _0._5_9_3_7
-_0._1_9_5_4 _0._3_0_3_5 -_0._3_8_1_4
_7. _C_1 (_c_r) -_0._0_0_2_1 _0._9_9_3_1 _0._0_6_9_2 -_0._0_9_2_0 _0._0_0_0_0
_0._0_0_0_6 _0._0_0_1_9 _0._0_0_0_0
_8. _N_2 (_c_r) _0._9_9_3_5 -_0._0_0_1_9 _0._1_0_4_8 _0._0_3_4_8 _0._0_0_0_0
-_0._0_1_3_1 _0._0_0_2_2 _0._0_0_0_0
_9. _N_2 (_l_p) _0._0_4_3_2 -_0._0_0_3_7 -_0._1_6_7_6 -_0._1_2_1_9 _0._0_0_0_0
_0._3_3_1_2 _0._1_5_2_5 _0._0_0_0_0
_1_0. _C_1 (_r_y*) -_0._0_0_8_8 -_0._0_0_0_5 _0._0_1_1_4 _0._0_0_8_9 _0._0_0_0_0
-_0._0_0_1_6 -_0._0_0_8_6 _0._0_0_0_0
_1_1. _C_1 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_1_0_9
_0._0_0_0_0 _0._0_0_0_0 -_0._0_0_7_0
_1_2. _C_1 (_r_y*) -_0._0_0_6_3 _0._0_0_0_1 -_0._0_0_5_0 -_0._0_0_3_5 _0._0_0_0_0
-_0._0_0_3_0 _0._0_0_2_6 _0._0_0_0_0
_1_3. _C_1 (_r_y*) _0._0_0_2_0 -_0._0_0_0_2 -_0._0_0_0_3 -_0._0_0_0_3 _0._0_0_0_0
-_0._0_0_0_9 _0._0_0_0_2 _0._0_0_0_0
_1_4. _N_2 (_r_y*) -_0._0_0_4_1 -_0._0_0_0_3 -_0._0_0_0_6 _0._0_0_1_6 _0._0_0_0_0
_0._0_1_9_2 _0._0_1_0_7 _0._0_0_0_0
_1_5. _N_2 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_0_8_0
_0._0_0_0_0 _0._0_0_0_0 _0._0_1_2_4
_1_6. _N_2 (_r_y*) _0._0_0_3_5 -_0._0_0_6_0 -_0._0_0_3_9 _0._0_1_0_2 _0._0_0_0_0
-_0._0_0_2_3 _0._0_0_4_0 _0._0_0_0_0
_1_7. _N_2 (_r_y*) -_0._0_0_1_8 _0._0_0_2_3 -_0._0_0_0_7 _0._0_0_1_3 _0._0_0_0_0
-_0._0_0_0_7 _0._0_0_0_5 _0._0_0_0_0
_1_8. _H_3 (_r_y*) -_0._0_0_0_8 -_0._0_0_9_4 -_0._0_1_0_3 _0._0_1_4_6 _0._0_0_0_0
_0._0_0_1_7 -_0._0_0_2_1 _0._0_0_0_0
_1_9. _H_4 (_r_y*) -_0._0_0_0_8 -_0._0_1_0_0 -_0._0_0_6_1 _0._0_1_1_9 _0._0_0_6_2
_0._0_0_0_4 -_0._0_0_5_4 -_0._0_0_9_8
_2_0. _H_5 (_r_y*) -_0._0_0_0_8 -_0._0_1_0_0 -_0._0_0_6_1 _0._0_1_1_9 -_0._0_0_6_2
_0._0_0_0_4 -_0._0_0_5_4 _0._0_0_9_8
_2_1. _H_6 (_r_y*) -_0._0_0_5_2 -_0._0_0_1_3 -_0._0_1_4_7 -_0._0_0_1_8 -_0._0_0_2_7
July 11, 1995
- 54 -
-_0._0_0_1_6
-_0._0_0_9_7 -_0._0_1_5_9
_2_2. _H_7 (_r_y*) -_0._0_0_5_2 -_0._0_0_1_3 -_0._0_1_4_7 -_0._0_0_1_8 _0._0_0_2_7
-_0._0_0_1_6 -_0._0_0_9_7 _0._0_1_5_9
_2_3. _C_1 - _N_2 * -_0._0_0_1_9 -_0._0_0_3_5 -_0._0_0_2_6 _0._0_0_2_5 _0._0_0_0_0
_0._0_0_4_3 _0._0_0_4_9 _0._0_0_0_0
_2_4. _C_1 - _H_3 * -_0._0_0_1_3 -_0._0_0_2_4 _0._0_0_5_9 -_0._0_0_1_8 _0._0_0_0_0
-_0._0_3_4_9 -_0._0_1_3_9 _0._0_0_0_0
_2_5. _C_1 - _H_4 * _0._0_0_0_9 _0._0_0_2_8 -_0._0_1_3_8 _0._0_0_3_3 -_0._0_4_0_8
-_0._0_1_8_8 _0._0_0_6_1 _0._0_1_4_8
_2_6. _C_1 - _H_5 * _0._0_0_0_9 _0._0_0_2_8 -_0._0_1_3_8 _0._0_0_3_3 _0._0_4_0_8
-_0._0_1_8_8 _0._0_0_6_1 -_0._0_1_4_8
_2_7. _N_2 - _H_6 * -_0._0_0_1_0 _0._0_0_5_1 -_0._0_0_4_7 _0._0_1_8_2 _0._0_1_7_9
_0._0_1_2_2 _0._0_1_5_4 _0._0_3_2_2
_2_8. _N_2 - _H_7 * -_0._0_0_1_0 _0._0_0_5_1 -_0._0_0_4_7 _0._0_1_8_2 -_0._0_1_7_9
_0._0_1_2_2 _0._0_1_5_4 -_0._0_3_2_2
_N_B_O _9 _1_0 _1_1 _1_2 _1_3
_1_4 _1_5
---------- ------- ------- ------- ------- ------- ---
---- -------
_1. _C_1 - _N_2 _0._1_0_6_2 -_0._0_1_4_3 _0._0_0_0_6 _0._0_0_0_0 _0._0_0_4_9
_0._0_0_0_0 -_0._0_0_6_1
_2. _C_1 - _H_3 -_0._3_3_4_3 -_0._0_0_4_4 _0._0_0_1_5 _0._0_0_0_0 _0._0_0_0_7
_0._0_0_0_0 -_0._0_0_8_0
_3. _C_1 - _H_4 -_0._1_1_8_6 -_0._0_1_8_6 _0._0_1_0_3 _0._0_2_5_8 -_0._0_0_4_8
-_0._0_2_7_2 -_0._0_1_0_4
_4. _C_1 - _H_5 -_0._1_1_8_6 -_0._0_1_8_6 _0._0_1_0_3 -_0._0_2_5_8 -_0._0_0_4_8
_0._0_2_7_2 -_0._0_1_0_4
_5. _N_2 - _H_6 -_0._1_1_6_7 -_0._0_0_2_4 -_0._0_1_4_5 -_0._0_2_9_3 -_0._0_1_6_2
-_0._0_2_5_3 _0._0_0_4_0
_6. _N_2 - _H_7 -_0._1_1_6_7 -_0._0_0_2_4 -_0._0_1_4_5 _0._0_2_9_3 -_0._0_1_6_2
_0._0_2_5_3 _0._0_0_4_0
_7. _C_1 (_c_r) _0._0_0_3_7 -_0._0_1_3_4 -_0._0_0_8_2 _0._0_0_0_0 _0._0_0_0_8
_0._0_0_0_0 -_0._0_0_0_8
_8. _N_2 (_c_r) -_0._0_1_8_9 -_0._0_0_5_5 _0._0_0_3_0 _0._0_0_0_0 -_0._0_0_2_6
_0._0_0_0_0 _0._0_0_3_5
_9. _N_2 (_l_p) _0._9_0_0_7 -_0._0_1_4_4 _0._0_0_5_5 _0._0_0_0_0 _0._0_9_2_5
_0._0_0_0_0 _0._0_1_3_0
_1_0. _C_1 (_r_y*) -_0._0_1_2_8 -_0._0_9_9_3 _0._0_5_5_3 _0._0_0_0_0 _0._0_5_3_6
_0._0_0_0_0 _0._3_3_0_1
_1_1. _C_1 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_8_3_6 _0._0_0_0_0
_0._1_8_4_5 _0._0_0_0_0
_1_2. _C_1 (_r_y*) -_0._0_0_3_9 -_0._0_6_1_2 _0._0_7_4_8 _0._0_0_0_0 -_0._1_1_6_0
_0._0_0_0_0 _0._1_2_1_3
_1_3. _C_1 (_r_y*) -_0._0_0_1_8 _0._0_9_3_6 _0._0_1_9_2 _0._0_0_0_0 _0._1_0_2_2
_0._0_0_0_0 -_0._1_5_1_6
_1_4. _N_2 (_r_y*) -_0._0_0_8_6 -_0._0_2_3_2 _0._0_0_7_1 _0._0_0_0_0 -_0._0_4_6_1
_0._0_0_0_0 -_0._0_1_7_8
_1_5. _N_2 (_r_y*) _0._0_0_0_0 _0._0_0_0_0 _0._0_0_0_0 _0._0_1_7_6 _0._0_0_0_0
-_0._0_8_5_6 _0._0_0_0_0
_1_6. _N_2 (_r_y*) _0._0_0_0_6 _0._0_3_9_5 -_0._0_8_3_6 _0._0_0_0_0 _0._0_2_2_1
_0._0_0_0_0 -_0._1_5_6_5
_1_7. _N_2 (_r_y*) _0._0_0_0_3 _0._0_6_1_4 -_0._0_2_2_2 _0._0_0_0_0 _0._0_1_1_4
July 11, 1995
- 55 -
_0._0_0_0_0
_0._0_5_8_4
_1_8. _H_3 (_r_y*) -_0._0_2_1_8 -_0._2_4_8_3 -_0._2_2_3_2 _0._0_0_0_0 _0._4_8_2_7
_0._0_0_0_0 _0._0_0_0_1
_1_9. _H_4 (_r_y*) _0._0_0_6_0 -_0._1_9_7_3 -_0._3_2_2_4 -_0._3_3_7_2 -_0._2_0_6_9
-_0._2_1_5_1 -_0._0_4_8_3
_2_0. _H_5 (_r_y*) _0._0_0_6_0 -_0._1_9_7_3 -_0._3_2_2_4 _0._3_3_7_2 -_0._2_0_6_9
_0._2_1_5_1 -_0._0_4_8_3
_2_1. _H_6 (_r_y*) _0._0_0_2_7 -_0._2_8_6_9 _0._2_1_3_2 _0._2_2_9_7 -_0._0_3_7_2
-_0._3_5_4_3 -_0._1_7_3_7
_2_2. _H_7 (_r_y*) _0._0_0_2_7 -_0._2_8_6_9 _0._2_1_3_2 -_0._2_2_9_7 -_0._0_3_7_2
_0._3_5_4_3 -_0._1_7_3_7
_2_3. _C_1 - _N_2 * -_0._0_0_3_1 -_0._2_3_5_7 _0._2_5_9_8 _0._0_0_0_0 -_0._1_0_9_6
_0._0_0_0_0 _0._8_0_5_1
_2_4. _C_1 - _H_3 * -_0._0_7_9_9 -_0._3_2_1_4 -_0._2_6_5_4 _0._0_0_0_0 _0._6_6_8_7
_0._0_0_0_0 _0._1_1_3_3
_2_5. _C_1 - _H_4 * -_0._0_3_6_9 _0._2_5_5_9 _0._3_8_9_0 _0._4_6_9_9 _0._2_9_6_8
_0._3_1_9_3 -_0._0_4_7_7
_2_6. _C_1 - _H_5 * -_0._0_3_6_9 _0._2_5_5_9 _0._3_8_9_0 -_0._4_6_9_9 _0._2_9_6_8
-_0._3_1_9_3 -_0._0_4_7_7
_2_7. _N_2 - _H_6 * -_0._0_0_3_1 _0._4_3_3_9 -_0._3_1_1_2 -_0._3_2_8_0 _0._0_4_7_4
_0._4_5_1_9 _0._2_1_6_8
_2_8. _N_2 - _H_7 * -_0._0_0_3_1 _0._4_3_3_9 -_0._3_1_1_2 _0._3_2_8_0 _0._0_4_7_4
-_0._4_5_1_9 _0._2_1_6_8
#_T
@_s_e_g
#_N
_0 _I_n _t_h_i_s _t_r_a_n_s_f_o_r_m_a_t_i_o_n _m_a_t_r_i_x, _r_o_w_s _c_o_r_r_e_s_p_o_n_d _t_o _N_B_O_s _a_n_d
_c_o_l_u_m_n_s _t_o _M_O_s (_i_n _t_h_e _o_r_d_e_r_i_n_g _u_s_e_d _e_l_e_s_e_w_h_e_r_e _i_n _t_h_e _p_r_o_-
_g_r_a_m), _a_n_d _e_a_c_h _b_a_s_i_s _N_B_O _i_s _f_u_r_t_h_e_r _i_d_e_n_t_i_f_i_e_d _w_i_t_h _a _r_o_w
_l_a_b_e_l. _T_h_e _p_r_i_n_t _p_a_r_a_m_e_t_e_r ``_P_V_A_L'' _s_p_e_c_i_f_i_e_d _t_h_a_t _o_n_l_y _1_5
_M_O_s (_t_h_e _n_u_m_b_e_r _o_f _c_o_r_e + _v_a_l_e_n_c_e _o_r_b_i_t_a_l_s) _s_h_o_u_l_d _b_e
_p_r_i_n_t_e_d, _c_o_r_r_e_s_p_o_n_d_i_n_g _t_o _t_h_e _n_i_n_e _o_c_c_u_p_i_e_d _M_O_s _1-_9 _a_n_d _t_h_e
_l_o_w_e_s_t _s_i_x _v_i_r_t_u_a_l _M_O_s _1_0-_1_5. _T_h_e _m_a_t_r_i_x _a_l_l_o_w_s _o_n_e _t_o _s_e_e
_t_h_e _c_o_m_p_o_s_i_t_i_o_n _o_f _e_a_c_h _c_a_n_o_n_i_c_a_l _M_O _i_n _t_e_r_m_s _o_f _l_o_c_a_l_i_z_e_d
_b_o_n_d _N_B_O_s. _F_o_r _e_x_a_m_p_l_e, _M_O_s _5 _a_n_d _8 _c_a_n _b_e _a_p_p_r_o_x_i_m_a_t_e_l_y
_d_e_s_c_r_i_b_e_d _a_s
_h_i #_d_5#_u ~= _m_i_n_u_s _0._5_9_4_n + _0._3_8_1_c
_h_i #_d_8#_u ~= _0._3_8_1_n + _0._5_9_4_c
_w_h_e_r_e_a_s _h_i
#_d_6#_u _i_s _p_r_i_m_a_r_i_l_y _t_h_e _C-_H(_3) _N_B_O _a_n_d _h_i
#_d_9#_u _t_h_e _N _l_o_n_e _p_a_i_r _N_B_O. #_I_B._6._5 _B_N_D_I_D_X _K_e_y_w_o_r_d#_N
_0 _T_h_e _B_N_D_I_D_X _k_e_y_w_o_r_d _a_c_t_i_v_a_t_e_s _t_h_e _p_r_i_n_t_i_n_g _o_f _s_e_v_e_r_a_l _t_y_p_e_s
_o_f `_b_o_n_d _o_r_d_e_r' _a_n_d _v_a_l_e_n_c_y _i_n_d_i_c_e_s, _b_a_s_e_d _o_n _d_i_f_f_e_r_e_n_t
_a_s_s_u_m_p_t_i_o_n_s _a_n_d _f_o_r_m_u_l_a_s, _b_u_t _a_l_l _h_a_v_i_n_g _s_o_m_e _c_o_n_n_e_c_t_i_o_n _t_o
_t_h_e _N_A_O/_N_B_O/_N_L_M_O _f_o_r_m_a_l_i_s_m. _W_e _i_l_l_u_s_t_r_a_t_e _t_h_e_s_e _b_o_n_d _o_r_d_e_r
July 11, 1995
- 56 -
_t_a_b_l_e_s
_f_o_r _t_h_e _e_x_a_m_p_l_e _o_f _R_H_F/_3-_2_1_G _m_e_t_h_y_l_a_m_i_n_e (_S_e_c_t_i_o_n _A._3).
_0 _T_h_e _f_i_r_s_t _s_e_g_m_e_n_t _o_f _B_N_D_I_D_X _o_u_t_p_u_t _s_h_o_w_s _t_h_e _W_i_b_e_r_g _b_o_n_d
_i_n_d_e_x (_t_h_e _s_u_m _o_f _s_q_u_a_r_e_s _o_f _o_f_f-_d_i_a_g_o_n_a_l _d_e_n_s_i_t_y _m_a_t_r_i_x
_e_l_e_m_e_n_t_s _b_e_t_w_e_e_n _a_t_o_m_s), _a_s _f_o_r_m_u_l_a_t_e_d _i_n _t_e_r_m_s _o_f _t_h_e _N_A_O
_b_a_s_i_s _s_e_t:
_W_i_b_e_r_g _b_o_n_d _i_n_d_e_x _m_a_t_r_i_x _i_n _t_h_e _N_A_O _b_a_s_i_s:
_A_t_o_m _1 _2 _3 _4 _5 _6
_7
---- ------ ------ ------ ------ ------ ------ --
----
_1. _C _0._0_0_0_0 _0._9_9_6_4 _0._9_4_7_2 _0._9_3_9_4 _0._9_3_9_4 _0._0_0_2_0
_0._0_0_2_0
_2. _N _0._9_9_6_4 _0._0_0_0_0 _0._0_2_0_8 _0._0_0_5_2 _0._0_0_5_2 _0._8_6_1_1
_0._8_6_1_1
_3. _H _0._9_4_7_2 _0._0_2_0_8 _0._0_0_0_0 _0._0_0_0_4 _0._0_0_0_4 _0._0_0_0_2
_0._0_0_0_2
_4. _H _0._9_3_9_4 _0._0_0_5_2 _0._0_0_0_4 _0._0_0_0_0 _0._0_0_0_9 _0._0_0_7_9
_0._0_0_0_5
_5. _H _0._9_3_9_4 _0._0_0_5_2 _0._0_0_0_4 _0._0_0_0_9 _0._0_0_0_0 _0._0_0_0_5
_0._0_0_7_9
_6. _H _0._0_0_2_0 _0._8_6_1_1 _0._0_0_0_2 _0._0_0_7_9 _0._0_0_0_5 _0._0_0_0_0
_0._0_0_0_3
_7. _H _0._0_0_2_0 _0._8_6_1_1 _0._0_0_0_2 _0._0_0_0_5 _0._0_0_7_9 _0._0_0_0_3
_0._0_0_0_0
_W_i_b_e_r_g _b_o_n_d _i_n_d_e_x, _T_o_t_a_l_s _b_y _a_t_o_m:
_A_t_o_m _1
---- ------
_1. _C _3._8_2_6_5
_2. _N _2._7_4_9_9
_3. _H _0._9_6_9_1
_4. _H _0._9_5_4_4
_5. _H _0._9_5_4_4
_6. _H _0._8_7_2_0
_7. _H _0._8_7_2_0
#_T
@_s_e_g
#_N
_0 _T_h_i_s _i_n_d_e_x _i_s _i_n_t_r_i_n_s_i_c_a_l_l_y _a _p_o_s_i_t_i_v_e _q_u_a_n_t_i_t_y, _m_a_k_i_n_g _n_o
_d_i_s_t_i_n_c_t_i_o_n _b_e_t_w_e_e_n _n_e_t _b_o_n_d_i_n_g _o_r _a_n_t_i_b_o_n_d_i_n_g _c_h_a_r_a_c_t_e_r _o_f
_t_h_e _d_e_n_s_i_t_y _m_a_t_r_i_x _e_l_e_m_e_n_t_s.
_0 _T_h_e _n_e_x_t _s_e_g_m_e_n_t _t_a_b_u_l_a_t_e_s _t_h_e ``_o_v_e_r_l_a_p-_w_e_i_g_h_t_e_d _N_A_O _b_o_n_d
_o_r_d_e_r,'' _a_s _s_h_o_w_n _b_e_l_o_w:
July 11, 1995
- 57 -
_A_t_o_m-_a_t_o_m _o_v_e_r_l_a_p-_w_e_i_g_h_t_e_d _N_A_O _b_o_n_d _o_r_d_e_r:
_A_t_o_m _1 _2 _3 _4 _5 _6
_7
---- ------ ------ ------ ------ ------ ------ --
----
_1. _C _0._0_0_0_0 _0._7_8_1_5 _0._7_6_1_4 _0._7_6_3_3 _0._7_6_3_3 -_0._0_1_0_3
-_0._0_1_0_3
_2. _N _0._7_8_1_5 _0._0_0_0_0 -_0._0_2_2_5 -_0._0_0_9_7 -_0._0_0_9_7 _0._6_6_8_8
_0._6_6_8_8
_3. _H _0._7_6_1_4 -_0._0_2_2_5 _0._0_0_0_0 -_0._0_0_3_9 -_0._0_0_3_9 -_0._0_0_1_9
-_0._0_0_1_9
_4. _H _0._7_6_3_3 -_0._0_0_9_7 -_0._0_0_3_9 _0._0_0_0_0 _0._0_0_2_4 _0._0_0_3_8
-_0._0_0_3_2
_5. _H _0._7_6_3_3 -_0._0_0_9_7 -_0._0_0_3_9 _0._0_0_2_4 _0._0_0_0_0 -_0._0_0_3_2
_0._0_0_3_8
_6. _H -_0._0_1_0_3 _0._6_6_8_8 -_0._0_0_1_9 _0._0_0_3_8 -_0._0_0_3_2 _0._0_0_0_0
-_0._0_0_6_9
_7. _H -_0._0_1_0_3 _0._6_6_8_8 -_0._0_0_1_9 -_0._0_0_3_2 _0._0_0_3_8 -_0._0_0_6_9
_0._0_0_0_0
_A_t_o_m-_a_t_o_m _o_v_e_r_l_a_p-_w_e_i_g_h_t_e_d _N_A_O _b_o_n_d _o_r_d_e_r, _T_o_t_a_l_s _b_y _a_t_o_m:
_A_t_o_m _1
---- ------
_1. _C _3._0_4_8_8
_2. _N _2._0_7_7_2
_3. _H _0._7_2_7_3
_4. _H _0._7_5_2_7
_5. _H _0._7_5_2_7
_6. _H _0._6_5_0_3
_7. _H _0._6_5_0_3
#_T
@_s_e_g
#_N
_0 _T_h_i_s _i_n_d_e_x _c_o_r_r_e_s_p_o_n_d_s _t_o _a _s_u_m _o_f _o_f_f-_d_i_a_g_o_n_a_l _N_A_O _d_e_n_-
_s_i_t_y _m_a_t_r_i_x _e_l_e_m_e_n_t_s _b_e_t_w_e_e_n _a_t_o_m_s, _e_a_c_h _m_u_l_t_i_p_l_i_e_d _b_y _t_h_e
_c_o_r_r_e_s_p_o_n_d_i_n_g _P_N_A_O _o_v_e_r_l_a_p _i_n_t_e_g_r_a_l.
_0 _A_n_o_t_h_e_r _t_y_p_e _o_f _B_N_D_I_D_X _o_u_t_p_u_t _a_p_p_e_a_r_s _i_f _t_h_e _N_L_M_O _k_e_y_w_o_r_d
_i_s _i_n_c_l_u_d_e_d, _s_u_m_m_a_r_i_z_i_n_g _a _f_o_r_m_a_l ``_N_L_M_O/_N_P_A _b_o_n_d _o_r_d_e_r''
_t_h_a_t _c_a_n _b_e _a_s_s_o_c_i_a_t_e_d _w_i_t_h _e_a_c_h _N_L_M_O:
_I_n_d_i_v_i_d_u_a_l _L_M_O _b_o_n_d _o_r_d_e_r_s _g_r_e_a_t_e_r _t_h_a_n _0._0_0_2 _i_n _m_a_g_n_i_t_u_d_e,
_w_i_t_h _t_h_e _o_v_e_r_l_a_p _b_e_t_w_e_e_n _t_h_e _h_y_b_r_i_d_s _i_n _t_h_e _N_L_M_O _g_i_v_e_n:
_A_t_o_m _I / _A_t_o_m _J / _N_L_M_O / _B_o_n_d _O_r_d_e_r / _H_y_b_r_i_d _O_v_e_r_l_a_p /
_1 _2 _1 _0._8_0_0_7_7_4_1 _0._7_3_1_4_3_6_1
_1 _2 _5 _0._0_0_2_2_6_9_4 _0._1_7_9_6_6_9_6
_1 _2 _6 _0._0_0_2_2_6_9_4 _0._1_7_9_6_6_9_6
July 11, 1995
- 58 -
_1 _2 _9 _0._0_0_8_8_0_6_1 _0._3_0_5_3_7_3_0
_1 _3 _2 _0._8_0_5_1_6_4_7 _0._7_8_6_2_2_6_3
_1 _3 _9 -_0._0_0_8_8_0_6_1 -_0._5_7_6_2_5_7_5
_1 _4 _3 _0._7_7_7_2_1_7_9 _0._7_8_7_4_3_1_2
_1 _4 _5 -_0._0_0_2_2_6_9_4 -_0._5_3_9_6_9_4_7
_1 _5 _4 _0._7_7_7_2_1_7_9 _0._7_8_7_4_3_1_2
_1 _5 _6 -_0._0_0_2_2_6_9_4 -_0._5_3_9_6_9_4_7
_1 _6 _3 -_0._0_0_3_1_6_5_2 -_0._0_9_2_0_5_2_4
_1 _6 _5 _0._0_0_2_2_6_9_4 _0._0_8_5_2_0_7_0
_1 _7 _4 -_0._0_0_3_1_6_5_2 -_0._0_9_2_0_5_2_4
_1 _7 _6 _0._0_0_2_2_6_9_4 _0._0_8_5_2_0_7_0
_2 _3 _9 -_0._0_0_9_7_8_4_1 -_0._0_9_3_0_2_0_4
_2 _4 _5 -_0._0_0_2_7_4_3_7 -_0._0_7_0_1_7_1_7
_2 _5 _6 -_0._0_0_2_7_4_3_7 -_0._0_7_0_1_7_1_7
_2 _6 _5 _0._6_3_5_8_5_1_2 _0._7_2_8_6_0_6_1
_2 _7 _6 _0._6_3_5_8_5_1_2 _0._7_2_8_6_0_6_1
_4 _6 _3 _0._0_0_3_1_6_5_2 _0._0_4_2_9_2_0_2
_4 _6 _5 _0._0_0_2_7_4_3_7 _0._0_3_9_9_3_5_2
_5 _7 _4 _0._0_0_3_1_6_5_2 _0._0_4_2_9_2_0_2
_5 _7 _6 _0._0_0_2_7_4_3_7 _0._0_3_9_9_3_5_2
#_T
@_s_e_g
#_N_T_h_i_s _N_L_M_O _b_o_n_d _o_r_d_e_r _i_s _c_a_l_c_u_l_a_t_e_d _b_y _t_h_e _m_e_t_h_o_d _d_e_s_c_r_i_b_e_d
_b_y _A. _E. _R_e_e_d _a_n_d _P. _v._R. _S_c_h_l_e_y_e_r [#_I_I_n_o_r_g. _C_h_e_m. #_B_2_7#_N,
_3_9_6_9-_3_9_8_7 (_1_9_8_8); #_I_J. _A_m. _C_h_e_m. _S_o_c.#_N (_t_o _b_e _p_u_b_l_i_s_h_e_d)],
_b_a_s_e_d _o_n _t_h_e _s_h_a_r_e_d _o_c_c_u_p_a_n_c_i_e_s _a_n_d _h_y_b_r_i_d _o_v_e_r_l_a_p_s (_l_a_s_t
_c_o_l_u_m_n) _o_f _N_A_O_s _c_o_m_p_o_s_i_n_g _t_h_e _N_L_M_O. _I_n _t_h_e _a_b_o_v_e _t_a_b_l_e, _f_o_r
_e_x_a_m_p_l_e, _N_L_M_O _1 _o_c_c_u_r_s _o_n_l_y _i_n _t_h_e _f_i_r_s_t _l_i_n_e, _c_o_n_t_r_i_b_u_t_i_n_g
_a _b_o_n_d _o_f _f_o_r_m_a_l _o_r_d_e_r _0._8_0_1 _b_e_t_w_e_e_n _C(_1) _a_n_d _N(_2), _w_h_e_r_e_a_s
_N_L_M_O _9 (_t_h_e _n_i_t_r_o_g_e_n _l_o_n_e _p_a_i_r) _c_o_n_t_r_i_b_u_t_e_s _a _s_l_i_g_h_t
_s_t_r_e_n_g_t_h_e_n_i_n_g (+_0._0_0_8_8) _o_f _t_h_e _C(_1)-_N(_2) _b_o_n_d, _a _w_e_a_k_e_n_i_n_g
(-_0._0_0_8_8) _o_f _t_h_e _v_i_c_i_n_a_l _C(_1)-_H(_3) _b_o_n_d, _a_n_d _a _s_l_i_g_h_t _n_e_g_a_-
_t_i_v_e _b_o_n_d _o_r_d_e_r (-_0._0_0_9_8) _b_e_t_w_e_e_n _a_t_o_m_s _N(_2), _H(_3).
_0 _T_h_e _N_L_M_O _b_o_n_d _o_r_d_e_r _c_o_n_t_r_i_b_u_t_i_o_n_s _a_r_e _t_h_e_n _s_u_m_m_e_d _f_o_r _e_a_c_h
_a_t_o_m _p_a_i_r _t_o _g_i_v_e _t_h_e _n_e_t _N_L_M_O/_N_P_A _b_o_n_d _o_r_d_e_r_s _s_h_o_w_n _b_e_l_o_w:
_A_t_o_m-_A_t_o_m _N_e_t _L_i_n_e_a_r _N_L_M_O/_N_P_A _B_o_n_d _O_r_d_e_r_s:
_A_t_o_m _1 _2 _3 _4 _5 _6
_7
---- ------ ------ ------ ------ ------ ------ --
----
_1. _C _0._0_0_0_0 _0._8_1_7_4 _0._7_9_6_0 _0._7_7_3_2 _0._7_7_3_2 -_0._0_0_1_3
-_0._0_0_1_3
_2. _N _0._8_1_7_4 _0._0_0_0_0 -_0._0_1_0_4 -_0._0_0_3_0 -_0._0_0_3_0 _0._6_3_3_7
_0._6_3_3_7
_3. _H _0._7_9_6_0 -_0._0_1_0_4 _0._0_0_0_0 -_0._0_0_2_0 -_0._0_0_2_0 _0._0_0_0_1
_0._0_0_0_1
_4. _H _0._7_7_3_2 -_0._0_0_3_0 -_0._0_0_2_0 _0._0_0_0_0 _0._0_0_2_0 _0._0_0_6_2
July 11, 1995
- 59 -
_0._0_0_0_0
_5. _H _0._7_7_3_2 -_0._0_0_3_0 -_0._0_0_2_0 _0._0_0_2_0 _0._0_0_0_0 _0._0_0_0_0
_0._0_0_6_2
_6. _H -_0._0_0_1_3 _0._6_3_3_7 _0._0_0_0_1 _0._0_0_6_2 _0._0_0_0_0 _0._0_0_0_0
-_0._0_0_0_1
_7. _H -_0._0_0_1_3 _0._6_3_3_7 _0._0_0_0_1 _0._0_0_0_0 _0._0_0_6_2 -_0._0_0_0_1
_0._0_0_0_0
#_T
@_s_e_g
#_N_F_o_r _e_x_a_m_p_l_e, _t_h_e _t_a_b_l_e _a_t_t_r_i_b_u_t_e_s _a _f_o_r_m_a_l _b_o_n_d _o_r_d_e_r _o_f
_0._8_1_7_4 _t_o _t_h_e _C(_1)-_N(_2) _b_o_n_d _o_f _m_e_t_h_y_l_a_m_i_n_e, _t_h_e _h_i_g_h_e_s_t
_b_o_n_d _o_r_d_e_r _i_n _t_h_i_s _m_o_l_e_c_u_l_e. (_T_h_e _h_i_g_h_e_r _v_a_l_u_e _f_o_r _C(_1)-
_H(_3) _t_h_a_n _f_o_r _t_h_e _o_t_h_e_r _t_w_o _C_H _b_o_n_d_s _r_e_f_l_e_c_t_s _a_n _u_n_s_a_t_i_s_f_a_c_-
_t_o_r_y _a_s_p_e_c_t _o_f _t_h_i_s _m_e_t_h_o_d _o_f _a_s_s_e_s_s_i_n_g _b_o_n_d _o_r_d_e_r.)
_0 _T_h_e_s_e _b_o_n_d _i_n_d_i_c_e_s _a_r_e _b_a_s_e_d _o_n _d_i_f_f_e_r_e_n_t _a_s_s_u_m_p_t_i_o_n_s, _a_n_d
_e_a_c_h _h_a_s _c_e_r_t_a_i_n _a_d_v_a_n_t_a_g_e_s _a_n_d _d_i_s_a_d_v_a_n_t_a_g_e_s. #_I_C_a_v_e_a_t
_e_m_p_t_o_r!#_N #_I_B._6._6 _R_E_S_O_N_A_N_C_E _K_e_y_w_o_r_d: _B_e_n_z_e_n_e#_N
_0 _W_h_e_n _N_B_O _a_n_a_l_y_s_i_s _i_s _p_e_r_f_o_r_m_e_d _o_n _a _w_a_v_e_f_u_n_c_t_i_o_n _t_h_a_t _c_a_n_-
_n_o_t _b_e _s_a_t_i_s_f_a_c_t_o_r_i_l_y _l_o_c_a_l_i_z_e_d [_i._e., _i_n _w_h_i_c_h _o_n_e _o_r _m_o_r_e
_N_B_O_s _o_f _t_h_e _n_a_t_u_r_a_l _L_e_w_i_s _s_t_r_u_c_t_u_r_e _f_a_i_l _t_o _a_c_h_i_e_v_e _t_h_e
_t_h_r_e_s_h_o_l_d _o_c_c_u_p_a_n_c_y (_1._9_0) _f_o_r _a _s_a_t_i_s_f_a_c_t_o_r_y `_p_a_i_r'], _t_h_e
_N_B_O _p_r_o_g_r_a_m _a_b_o_r_t_s _w_i_t_h _a _m_e_s_s_a_g_e _i_n_d_i_c_a_t_i_n_g _t_h_a_t _t_h_e
_w_a_v_e_f_u_n_c_t_i_o_n _i_s _u_n_s_u_i_t_a_b_l_e _f_o_r _l_o_c_a_l_i_z_e_d _a_n_a_l_y_s_i_s. _F_o_r
_e_x_a_m_p_l_e, _w_h_e_n _b_e_n_z_e_n_e (_R_H_F/_S_T_O-_3_G _l_e_v_e_l, _i_d_e_a_l_i_z_e_d _P_o_p_l_e-
_G_o_r_d_o_n _g_e_o_m_e_t_r_y) _i_s _t_r_e_a_t_e_d _b_y _t_h_e _N_B_O _p_r_o_g_r_a_m _i_n _d_e_f_a_u_l_t
_m_o_d_e, _o_n_e _o_b_t_a_i_n_s _t_h_e _o_u_t_p_u_t:
_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:
_O_c_c_u_p_a_n_c_i_e_s _L_e_w_i_s _S_t_r_u_c_t_u_r_e
_L_o_w _H_i_g_h
_O_c_c. ------------------- -----------------
_o_c_c _o_c_c
_C_y_c_l_e _T_h_r_e_s_h. _L_e_w_i_s _N_o_n-_L_e_w_i_s _C_R _B_D _3_C _L_P
(_L) (_N_L) _D_e_v
=============================================================================
_1(_1) _1._9_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_2(_2) _1._9_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4 ----------
-------------------------------------------------------------------
_O_n_l_y _s_t_r_o_n_g_l_y _d_e_l_o_c_a_l_i_z_e_d _r_e_s_o_n_a_n_c_e _s_t_r_u_c_t_u_r_e_s _c_a_n _b_e _f_o_u_n_d.
_T_h_e _d_e_f_a_u_l_t _p_r_o_c_e_d_u_r_e _i_s _t_o _a_b_o_r_t _t_h_e _N_B_O _s_e_a_r_c_h.
#_T
@_s_e_g
July 11, 1995
- 60 -
_0 #_N_W_h_e_n _t_h_e _R_E_S_O_N_A_N_C_E _k_e_y_w_o_r_d _i_s _a_c_t_i_v_a_t_e_d _f_o_r _t_h_i_s _s_a_m_e
_e_x_a_m_p_l_e, _o_n_e _o_b_t_a_i_n_s _a _s_u_m_m_a_r_y _o_f _N_B_O _s_e_a_r_c_h _c_y_c_l_e_s _a_s _s_h_o_w_n
_b_e_l_o_w:
_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:
_O_c_c_u_p_a_n_c_i_e_s _L_e_w_i_s _S_t_r_u_c_t_u_r_e
_L_o_w _H_i_g_h
_O_c_c. ------------------- -----------------
_o_c_c _o_c_c
_C_y_c_l_e _T_h_r_e_s_h. _L_e_w_i_s _N_o_n-_L_e_w_i_s _C_R _B_D _3_C _L_P
(_L) (_N_L) _D_e_v
=============================================================================
_1(_1) _1._9_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_2(_2) _1._9_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_3(_1) _1._8_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_4(_2) _1._8_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_5(_1) _1._7_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_6(_2) _1._7_0 _3_8._8_7_4_7_6 _3._1_2_5_2_4 _6 _1_2 _0 _3
_3 _3 _0._4_4
_7(_1) _1._6_0 _4_0._8_7_4_7_6 _1._1_2_5_2_4 _6 _1_5 _0 _0
_0 _3 _0._4_4
_8(_2) _1._6_0 _4_0._8_7_4_7_6 _1._1_2_5_2_4 _6 _1_5 _0 _0
_0 _3 _0._4_4
_9(_1) _1._5_0 _4_0._8_7_4_7_6 _1._1_2_5_2_4 _6 _1_5 _0 _0
_0 _3 _0._4_4
_1_0(_2) _1._5_0 _4_0._8_7_4_7_6 _1._1_2_5_2_4 _6 _1_5 _0 _0
_0 _3 _0._4_4
_1_1(_1) _1._6_0 _4_0._8_7_4_7_6 _1._1_2_5_2_4 _6 _1_5 _0 _0
_0 _3 _0._4_4 ----------
-------------------------------------------------------------------
_S_t_r_u_c_t_u_r_e _a_c_c_e_p_t_e_d: _R_E_S_O_N_A_N_C_E _k_e_y_w_o_r_d _p_e_r_m_i_t_s _s_t_r_o_n_g_l_y _d_e_l_o_-
_c_a_l_i_z_e_d _s_t_r_u_c_t_u_r_e
#_T
@_s_e_g
#_N
_0 _A_s _t_h_i_s _t_a_b_l_e _s_h_o_w_s, _t_h_e _o_c_c_u_p_a_n_c_y _t_h_r_e_s_h_o_l_d _w_a_s _s_u_c_c_e_s_-
_s_i_v_e_l_y _l_o_w_e_r_e_d _f_r_o_m _1._9_0 _t_o _1._5_0 _b_y _0._1_e _f_o_r _e_a_c_h _c_y_c_l_e, _a_n_d
_t_h_e _N_B_O _s_e_a_r_c_h _r_e_p_e_a_t_e_d. _I_n _t_h_i_s _c_a_s_e, _t_h_e `_b_e_s_t' _L_e_w_i_s
_s_t_r_u_c_t_u_r_e (_l_o_w_e_s_t _o_v_e_r_a_l_l _n_o_n-_L_e_w_i_s _o_c_c_u_p_a_n_c_y, _1._1_2_5_2_4_e) _w_a_s
_f_o_u_n_d _i_n _c_y_c_l_e _7, _w_i_t_h _o_c_c_u_p_a_n_c_y _t_h_r_e_s_h#|_o_l_d _1._6_0_e. _T_h_e _N_B_O
_p_r_o_g_r_a_m _t_h_e_r_e_f_o_r_e _r_e_s_e_t _t_h_e _t_h_r_e_s_h#|_o_l_d _t_o _t_h_i_s _v_a_l_u_e _a_n_d
_c_a_l_c_u_l_a_t_e_d _t_h_e _s_e_t _o_f _N_B_O_s _c_o_r_r_e_s_p_o_n_d_i_n_g _t_o _t_h_i_s `_b_e_s_t'
_L_e_w_i_s _s_t_r_u_c_t_u_r_e, _a_s _s_h_o_w_n _b_e_l_o_w:
(_O_c_c_u_p_a_n_c_y) _B_o_n_d _o_r_b_i_t_a_l/ _C_o_e_f_f_i_c_i_e_n_t_s/ _H_y_b_r_i_d_s -----
July 11, 1995
- 61 -
-----
---------------------------------------------------------------------
_1. (_1._9_8_9_4_0) _B_D ( _1) _C _1- _C _2
( _5_0._0_0%) _0._7_0_7_1* _C _1 _s( _3_4._2_3%)_p _1._9_2(
_6_5._7_7%)
_0._0_0_0_0 _0._5_8_5_1
-_0._8_1_0_9 _0._0_0_9_7 _0._0_0_0_0
( _5_0._0_0%) _0._7_0_7_1* _C _2 _s( _3_4._2_3%)_p _1._9_2(
_6_5._7_7%)
_0._0_0_0_0 _0._5_8_5_1
_0._8_1_0_9 _0._0_0_9_7 _0._0_0_0_0
_2. (_1._9_8_9_4_0) _B_D ( _1) _C _1- _C _6
( _5_0._0_0%) _0._7_0_7_1* _C _1 _s( _3_4._2_3%)_p _1._9_2(
_6_5._7_7%)
_0._0_0_0_0 _0._5_8_5_1
_0._4_1_3_8 -_0._6_9_7_4 _0._0_0_0_0
( _5_0._0_0%) _0._7_0_7_1* _C _6 _s( _3_4._2_3%)_p _1._9_2(
_6_5._7_7%)
_0._0_0_0_0 _0._5_8_5_1
-_0._3_9_7_1 _0._7_0_7_1 _0._0_0_0_0
_3. (_1._6_6_6_6_7) _B_D ( _2) _C _1- _C _6
( _5_0._0_0%) _0._7_0_7_1* _C _1 _s( _0._0_0%)_p
_1._0_0(_1_0_0._0_0%)
_0._0_0_0_0 _0._0_0_0_0
_0._0_0_0_0 _0._0_0_0_0 _1._0_0_0_0
( _5_0._0_0%) _0._7_0_7_1* _C _6 _s( _0._0_0%)_p
_1._0_0(_1_0_0._0_0%)
_0._0_0_0_0 _0._0_0_0_0
_0._0_0_0_0 _0._0_0_0_0 _1._0_0_0_0
_4. (_1._9_8_9_7_7) _B_D ( _1) _C _1- _H _7
( _5_1._7_3%) _0._7_1_9_3* _C _1 _s( _3_1._5_3%)_p _2._1_7(
_6_8._4_7%)
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.
|<<3//18//72//+1//+11>>|7______________________99______________________
#-#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 and777778 t99a999999 s99p99i99n99,9999 t99h777778 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#u7 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#u7 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#u7 arr gma *#<#dC#d1#uH#d3#u#u
(97arr 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 the77778 t99a999999 s99p99i99n9999 s77778t,
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 the77777 t99a999999 (99`99i99o99n99i99z77777d') 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 the77 t99a999999 s77t set, #Ivs.#N 61.1% in
the lpha set). [In other cases, the lpha and7777 t99a999999 N99B99O9999 L7777wis
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.
|<<3//18//72//+1//+11>>|7______________________99______________________
#-#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 and777777777777777 t99a999999 s99p99i99n99.999999 A99l99t99h99o99u99g99h9999 N99A99O99s9999 a99n99d9999 t99h777777777777777ir 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
- 108 -
#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
|<<3//10//80//+2//+42>>|7______________________99______________________ #T
|< 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 and77778 t99a999999 s99p99i99n9999 d77778nsity 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
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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
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[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:
|<<3//27//63//+1//+5>>|7_____________________99_____________________ |<<3//10//30//+8//+14>>|7______________________99______________________
|<<3//35//55//+8//+14>>|7______________________99______________________ |<<3//60//80//+8//+14>>|7______________________99______________________
#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
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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
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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
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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#N7 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
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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 L8mlaut 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
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#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
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#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
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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 NAO7arr 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.
July 11, 1995
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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 (L8mlaut 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).
July 11, 1995
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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
July 11, 1995
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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
July 11, 1995
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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
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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.
_C_o_n_v_e_r_t_s _t_h_e _H_o_l_l_e_r_i_t_h _a_r_r_a_y _I_J(_L_E_N) _i_n_t_o _a_n _i_n_t_e_g_e_r _I_K.
_T_h_i_s _i_s _t_h_e _i_n_v_e_r_s_e _o_f _S_R _I_D_I_G_I_T.
_C_o_n_v_e_r_t_s _a _2-_d_i_g_i_t _i_n_t_e_g_e_r _N _t_o _t_w_o _H_o_l_l_e_r_i_t_h _c_h_a_r_a_c_t_e_r_s
_N_C_1, _N_C_2.
_C_o_p_i_e_s _m_a_t_r_i_x _A _t_o _m_a_t_r_i_x _B.
_S_t_o_r_e_s _t_h_e _n_o_m_i_n_a_l ``_c_o_r_e _t_a_b_l_e,'' _g_i_v_i_n_g _t_h_e _n_u_m_b_e_r _o_f _c_o_r_e
#_I_s#_N, #_I_p#_N, #_I_d#_N, #_I_f#_N _o_r_b_i_t_a_l_s _f_o_r _e_l_e_m_e_n_t_s _1-_1_0_5 (_H _t_o
_L_w, _a_n_d _e_l_e_m_e_n_t_s _1_0_4, _1_0_5). _T_h_i_s _t_a_b_l_e _c_o_n_t_r_o_l_s _t_h_e _n_u_m_b_e_r
_o_f _h_i_g_h-_o_c_c_u_p_a_n_c_y _u_n_h_y_b_r_i_d_i_z_e_d _N_A_O_s _t_h_a_t _w_i_l_l _b_e _i_s_o_l_a_t_e_d
_a_n_d _r_e_m_o_v_e_d _a_s _c_o_r_e _N_B_O_s (_t_a_k_i_n_g _a_c_c_o_u_n_t _a_l_s_o _o_f _a_n_y _e_f_f_e_c_-
_t_i_v_e _c_o_r_e _p_o_t_e_n_t_i_a_l).
_D_e_c_o_m_p_o_s_e_s _a _H_o_l_l_e_r_i_t_h _v_a_r_i_a_b_l_e _I _i_n_t_o _i_t_s _f_o_u_r _i_n_d_i_v_i_d_u_a_l
_H_o_l_l_e_r_i_t_h `_b_y_t_e_s' _I_B_Y_T_E(_4).
_H_a_l_t_s _t_h_e _e_x_e_c_u_t_i_o_n _o_f _t_h_e _N_B_O _p_r_o_g_r_a_m _i_f _a_n _u_n_r_e_c_o_g_n_i_z_a_b_l_e
_k_e_y_w_o_r_d _i_s _f_o_u_n_d _i_n _t_h_e $_N_B_O _k_e_y_l_i_s_t.
_C_o_n_v_e_r_t_s _t_h_e _I_N_T_E_G_E_R _v_a_r_i_a_b_l_e _K_I_N_T _i_n _t_h_e _f_i_r_s_t _N_D _e_l_e_m_e_n_t_s
_o_f _t_h_e _H_o_l_l_e_r_i_t_h _a_r_r_a_y _I_K(_M_A_X_D). _T_h_i_s _i_s _t_h_e _i_n_v_e_r_s_e _o_f _S_R
_C_O_N_V_I_N.
_T_h_i_s _H_o_l_l_e_r_i_t_h _f_u_n_c_t_i_o_n _d_e_t_e_r_m_i_n_e_s _w_h_e_t_h_e_r _t_h_e _I_B_O7_a_r_r _J_B_O
_d_e_l_o_c_a_l_i_z_a_t_i_o_n _i_s _v_i_c_i_n_a_l (`_v'), _g_e_m_i_n_a_l (`_g'), _o_r _r_e_m_o_t_e
(`_r'), _b_a_s_e_d _o_n _t_h_e _d_e_r_i_v_e_d _N_B_O _c_o_n_n_e_c_t_i_v_i_t_y.
_3. _D_i_a_g_o_n_a_l_i_z_e_s _a _r_e_a_l _s_y_m_m_e_t_r_i_c _m_a_t_r_i_x _b_y _t_h_e _J_a_c_o_b_i _r_o_t_a_-
_t_i_o_n_s _m_e_t_h_o_d. _I_f _I_C_O_N_T_R=_0, _a _s_t_a_n_d_a_r_d _J_a_c_o_b_i _d_i_a_g_o_n_a_l_i_z_a_-
_t_i_o_n (_u_n_c_o_n_s_t_r_a_i_n_e_d _2_x_2 _r_o_t_a_t_i_o_n_s) _i_s _c_a_r_r_i_e_d _o_u_t. _I_f
_I_C_O_N_T_R=_1, _t_h_e _a_l_g_o_r_i_t_h_m _i_s _p_r_e_v_e_n_t_e_d _f_r_o_m _m_i_x_i_n_g _o_r_b_i_t_a_l_s
_t_h_a_t _a_r_e _d_e_g_e_n_e_r_a_t_e _w_i_t_h_i_n `_D_I_F_F_E_R' _i_f _t_h_e _o_f_f-_d_i_a_g_o_n_a_l _e_l_e_-
_m_e_n_t _c_o_n_n_e_c_t_i_n_g _t_h_e_m _i_s _l_e_s_s _t_h_a_n `_D_I_F_F_E_R'. [_T_h_r_e_s_h_o_l_d
_D_I_F_F_E_R (_1_0#_u_m_i_n_u_s _5#_d) _c_o_n_t_r_o_l_s _d_e_g_e_n_e_r_a_t_e _m_i_x_i_n_g, _D_O_N_E
(_1_0#_u_m_i_n_u_s _1_3#_d) _i_s _t_h_e _m_a_x_i_m_u_m _a_l_l_o_w_e_d _o_f_f-_d_i_a_g_o_n_a_l _e_l_e_-
_m_e_n_t, _a_n_d _E_P_S (_0._5_x_1_0#_u_m_i_n_u_s _1_3#_d) _i_s _a _n_u_m_b_e_r _b_e_t_w_e_e_n _D_O_N_E
_a_n_d _t_h_e _m_a_c_h_i_n_e _p_r_e#|_c_i_s_i_o_n.]
_T_h_i_s _r_o_u_t_i_n_e _c_a_r_r_i_e_s _o_u_t _a `_l_i_m_i_t_e_d' _t_r_a_n_s_f_o_r_m_a_t_i_o_n _o_f _a
_m_a_t_r_i_x (_T), _u_s_i_n_g _o_n_l_y _t_h_e _r_o_w_s _a_n_d _c_o_l_u_m_n_s _s_p_e_c_i_f_i_e_d _b_y
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_v_e_c_t_o_r
_M. _T_h_e _o_p_e_r_a_t_i_o_n_s _p_e_r_f_o_r_m_e_d _a_r_e _T*_A, _A#_u_t#_d*_T*_A, _o_r
_A#_u_t#_d*_T _a_c_c_o_r_d_i_n_g _t_o _t_h_e _v_a_l_u_e _o_f _I_O_P_T.
_M_u_l_t_i_p_l_i_e_s _s_q_u_a_r_e _m_a_t_r_i_c_e_s _A*_B (_u_s_i_n_g _s_c_r_a_t_c_h _v_e_c_t_o_r _V) _a_n_d
_s_t_o_r_e_s _r_e_s_u_l_t _i_n _A.
_M_u_l_t_i_p_l_i_e_s _A#_u_t#_d*_B (_u_s_i_n_g _s_c_r_a_t_c_h _v_e_c_t_o_r _V) _a_n_d _s_t_o_r_e_s _t_h_e
_r_e_s_u_l_t _i_n _B. _T_h_e _a_l_g_o_r_i_t_h_m _a_s_s_u_m_e_s _t_h_a_t _A*_B _i_s _a _s_y_m_m_e_t_r_i_c,
_s_o _a_b_o_u_t _h_a_l_f _t_h_e _w_o_r_k _i_s _s_a_v_e_d. [_S_R _M_A_T_M_L_2 _i_s _t_y_p_i_c_a_l_l_y
_t_h_e _s_e_c_o_n_d _s_t_e_p _i_n _a _s_i_m_i_l_a_r_i_t_y _t_r_a_n_s_f_o_r_m _o_f _B _b_y _A, _w_h_e_r_e _B
(_a_n_d _t_h_u_s _A#_u_t#_d*_B*_A) _i_s _s_y_m_m_e_t_r_i_c.]
_R_e_t_u_r_n_s _t_h_e (_H_o_l_l_e_r_i_t_h) _a_t_o_m_i_c _s_y_m_b_o_l _f_o_r _a_t_o_m_i_c _n_u_m_b_e_r _I_Z
_N_o_r_m_a_l_i_z_e_s _t_h_e _c_o_l_u_m_n_s _o_f _A _u_s_i_n_g _t_h_e _o_v_e_r_l_a_p _m_a_t_r_i_x _S.
_4. _R_a_n_k_s _t_h_e _p_o_s_i_t_i_v_e _e_l_e_m_e_n_t_s _o_f _i_n_t_e_g_e_r _L_I_S_T(_N), _l_o_w_e_s_t
_v_a_l_u_e_s _f_i_r_s_t. [_R_A_N_K _a_n_d _A_R_C_R_N_K _a_r_e _i_n_t_e_g_e_r _v_e_c_t_o_r_s, _w_i_t_h _I
= _A_R_C_R_N_K(_N) _i_f _L_I_S_T(_I) _i_s _t_h_e _e_l_e_m_e_n_t _o_f _r_a_n_k _N.]
_P_a_c_k_s _t_h_e _u_p_p_e_r-_t_r_i_a_n_g_u_l_a_r _p_o_r_t_i_o_n _o_f _t_h_e _s_y_m_m_e_t_r_i_c _m_a_t_r_i_x
_T(_N_B_A_S,_N_B_A_S) _t_h_e _f_i_r_s_t _L_2 _e_l_e_m_e_n_t_s _o_f _T.
_O_r_d_e_r_s _t_h_e _e_n_t_r_i_e_s _o_f _v_e_c_t_o_r _E_I_G, _h_i_g_h_e_s_t _v_a_l_u_e_s _f_i_r_s_t.
_A_R_C_R_N_K(_I) _i_s _t_h_e _o_l_d _l_o_c_a_t_i_o_n _o_f _t_h_e _I#_u_t_h#_d _h_i_g_h_e_s_t _v_a_l_u_e
_i_n _E_I_G. _O_n _r_e_t_u_r_n, _E_I_G(_I) _i_s _t_h_e _I#_u_t_h#_d _h_i_g_h_e_s_t _v_a_l_u_e.
[_E_n_t_r_i_e_s _a_r_e _n_o_t _s_w_i_t_c_h_e_d _u_n_l_e_s_s _t_h_e_y _d_i_f_f_e_r _b_y _m_o_r_e _t_h_a_n _a
_D_I_F_F_E_R (_5_x_1_0#_u_m_i_n_u_s _8#_d) _t_h_r_e_s_h_o_l_d.]
_P_e_r_f_o_r_m_s _t_h_e _g_e_n_e_r_a_l _s_i_m_i_l_a_r_i_t_y _t_r_a_n_s_f_o_r_m _T#_u_t#_d*_A*_T _o_f _A _b_y
_T, _u_s_i_n_g _s_c_r_a_t_c_h _v_e_c_t_o_r _V.
_P_e_r_f_o_r_m_s _t_h_e `_f_a_s_t' _s_i_m_i_l_a_r_i_t_y _t_r_a_n_s_f_o_r_m _S#_u_t#_d*_A*_S, _a_s_s_u_m_-
_i_n_g _t_h_e _r_e_s_u_l_t _i_s _s_y_m_m_e_t_r_i_c.
_T_r_a_n_s_p_o_s_e_s _t_h_e _m_a_t_r_i_x _A: _A7_a_r_r _A#_u_t#_d.
_U_n_p_a_c_k_s _a_n _u_p_p_e_r _t_r_i_a_n_g_u_l_a_r _m_a_t_r_i_x (_v_e_c_t_o_r _o_f _l_e_n_g_t_h _L_2)
_i_n_t_o _a _s_y_m_m_e_t_r_i_c _m_a_t_r_i_x _T(_N_B_A_S,_N_B_A_S).
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_S_p_e_c_i_f_i_e_s _t_h_e _n_o_m_i_n_a_l ``_v_a_l_e_n_c_e _t_a_b_l_e,'' _g_i_v_i_n_g _t_h_e _n_u_m_b_e_r
_o_f _v_a_l_e_n_c_e _A_O_s _o_f _e_a_c_h _s_y_m_m_e_t_r_y _t_y_p_e _f_o_r _e_l_e_m_e_n_t_s _1-_1_0_5.
_E_v_a_l_u_a_t_e_s _E_u_c_l_i_d_e_a_n _l_e_n_g_t_h _o_f _v_e_c_t_o_r _X.
_T_h_i_s _a_n_d _t_h_e _t_h_r_e_e _f_o_l_l_o_w_i_n_g _r_o_u_t_i_n_e_s _c_o_n_s_t_i_t_u_t_e _t_h_e _l_i_n_e_a_r
_e_q_u_a_t_i_o_n_s _p_a_c_k_a_g_e _f_o_r _s_o_l_v_i_n_g _t_h_e _s_y_s_t_e_m _A*_X = _B _f_o_r _m_a_t_r_i_x
_X _b_y _t_h_e _m_e_t_h_o_d _o_f _G_a_u_s_s_i_a_n _e_l_i_m_i_n_a_t_i_o_n.
_S_u_p_p_o_r_t_s _S_R _L_I_N_E_Q.
_S_u_p_p_o_r_t_s _S_R _L_I_N_E_Q.
_S_u_p_p_o_r_t_s _S_R _L_I_N_E_Q. #_B_C._1_1 _S_Y_S_T_E_M-_D_E_P_E_N_D_E_N_T _D_R_I_V_E_R _R_O_U_T_I_N_E_S
(_G_R_O_U_P _V_I_I)#_N
_0 _T_h_e _r_o_u_t_i_n_e_s _o_f _G_r_o_u_p _V_I_I _c_o_m_p_r_i_s_e _t_h_e _s_e_t _o_f _E_S_S-
_d_e_p_e_n_d_e_n_t _d_r_i_v_e_r _r_o_u_t_i_n_e_s _w_h_i_c_h _i_n_i_t_i_a_t_e _t_h_e _N_B_O _a_n_d _N_B_O
_e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_e_s _a_n_d _p_r_o_v_i_d_e _t_h_e _N_B_O _p_r_o_g_r_a_m _w_i_t_h _a
_v_a_r_i_e_t_y _o_f _i_n_f_o_r_m_a_t_i_o_n _a_b_o_u_t _t_h_e _e_l_e_c_t_r_o_n_i_c _w_a_v_e_f_u_n_c_t_i_o_n.
_T_h_i_s _s_e_c_t_i_o_n _p_r_o_v_i_d_e_s _a _b_r_i_e_f, _g_e_n_e_r_i_c _d_e_s_c_r_i_p_t_i_o_n _o_f _e_a_c_h
_o_f _t_h_e _d_r_i_v_e_r _r_o_u_t_i_n_e_s. _I_f _y_o_u _i_n_t_e_n_d _t_o _w_r_i_t_e _a _s_e_t _o_f
_r_o_u_t_i_n_e_s _f_o_r _a_n _E_S_S _p_r_o_g_r_a_m _n_o_t _s_u_p_p_o_r_t_e_d _b_y _t_h_i_s _d_i_s_t_r_i_b_u_-
_t_i_o_n, _r_e_f_e_r _t_o _t_h_e _d_r_i_v_e_r _s_o_u_r_c_e _c_o_d_e _f_o_r _a_d_d_i_t_i_o_n_a_l _g_u_i_-
_d_a_n_c_e. _A_l_s_o, _s_e_e _S_e_c_t_i_o_n _C._1_3 _f_o_r _h_e_l_p_f_u_l _h_i_n_t_s _f_o_r _a_t_t_a_c_h_-
_i_n_g _t_h_e _N_B_O _p_r_o_g_r_a_m _t_o _a_n _E_S_S _p_a_c_k_a_g_e.
_0 _T_h_e _d_r_i_v_e_r _r_o_u_t_i_n_e_s _a_r_e _g_r_o_u_p_e_d _t_o_g_e_t_h_e_r _a_t _t_h_e _e_n_d _o_f _t_h_e
_N_B_O _s_o_u_r_c_e _c_o_d_e. _S_i_n_c_e _m_u_l_t_i_p_l_e _v_e_r_s_i_o_n_s _o_f _e_a_c_h _d_r_i_v_e_r _a_r_e
_p_r_o_v_i_d_e_d (_o_n_e _f_o_r _e_a_c_h _s_u_p_p_o_r_t_e_d _E_S_S _p_a_c_k_a_g_e _a_n_d _G_E_N_N_B_O),
_a_l_l _o_f _t_h_e _e_x_e_c_u_t_a_b_l_e _l_i_n_e_s _i_n _t_h_e_s_e _r_o_u_t_i_n_e_s _a_r_e `_c_o_m_m_e_n_t_e_d
_o_u_t' _w_i_t_h _a_n _a_s_t_e_r_i_s_k _i_n _t_h_e _f_i_r_s_t _c_o_l_u_m_n. _I_n _a_d_d_i_t_i_o_n,
_e_v_e_r_y _l_i_n_e _o_f _t_h_e _d_r_i_v_e_r_s _h_a_s _a_n _i_d_e_n_t_i_f_i_e_r `#_I_X_X_X#_N_D_R_V' _i_n
_c_o_l_u_m_n_s _7_3-_7_8, _w_h_e_r_e `#_I_X_X_X#_N' _i_s _a _3-_l_e_t_t_e_r _i_d_e_n_t_i_f_i_e_r _f_o_r
_t_h_e _a_s_s_o_c_i_a_t_e_d _E_S_S _p_a_c_k_a_g_e. _I_t _i_s _t_h_e _r_e_s_p_o_n_s_i_b_i_l_i_t_y _o_f _t_h_e
_p_r_o_g_r_a_m _E_N_A_B_L_E _t_o `_u_n_c_o_m_m_e_n_t' _t_h_e _a_p_p_r_o_p_r_i_a_t_e _l_i_n_e_s _o_f _t_h_e
_c_o_d_e _f_o_r _t_h_e _r_e_q_u_e_s_t_e_d _p_r_o_g_r_a_m _v_e_r_s_i_o_n (_s_e_e _S_e_c_t_i_o_n _A._2).
_0 _T_h_e _s_y_s_t_e_m-_d_e_p_e_n_d_e_n_t _d_r_i_v_e_r _r_o_u_t_i_n_e_s _a_r_e:
_D_e_t_e_r_m_i_n_e_s _t_h_e _l_o_g_i_c_a_l _f_i_l_e _n_u_m_b_e_r_s _f_o_r _t_h_e _i_n_p_u_t _a_n_d _o_u_t_p_u_t
_f_i_l_e_s (_L_F_N_I_N _a_n_d _L_F_N_P_R) _o_f _t_h_e _p_a_r_e_n_t _p_r_o_g_r_a_m, _i_n_i_t_i_a_l_i_z_e_s
_t_h_e _N_B_O_O_P_T _j_o_b _o_p_t_i_o_n _a_r_r_a_y _S_e_c_t_i_o_n _C._5._1), _a_n_d _i_n_i_t_i_a_t_e_s
_t_h_e _N_B_O _a_n_a_l_y_s_i_s (_S_R _N_B_O) _a_n_d _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s (_S_R
_N_B_O_E_A_N). _T_h_i_s _r_o_u_t_i_n_e _i_s _t_h_e _o_n_l_y _r_o_u_t_i_n_e _o_f _t_h_e _N_B_O _p_r_o_-
_g_r_a_m _c_a_l_l_e_d _d_i_r_e_c_t_l_y _b_y _t_h_e _p_a_r_e_n_t _E_S_S _p_a_c_k_a_g_e.
July 11, 1995
- 134 -
_I_n_t_e_r_r_o_g_a_t_e_s _t_h_e _s_c_r_a_t_c_h _f_i_l_e_s _a_n_d _C_O_M_M_O_N _b_l_o_c_k_s _o_f _t_h_e
_p_a_r_e_n_t _p_r_o_g_r_a_m, _p_r_o_v_i_d_i_n_g _t_h_e _N_B_O _p_r_o_g_r_a_m _w_i_t_h _r_e_q_u_i_r_e_d
_i_n_f_o_r_m_a_t_i_o_n _o_f _t_h_e _e_l_e_c_t_r_o_n_i_c _w_a_v_e_f_u_n_c_t_i_o_n _v_i_a _t_h_e _N_B_O _C_O_M_-
_M_O_N _b_l_o_c_k_s _a_n_d _F_I_L_E_4_8 _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e. (_N_o_t_e _t_h_a_t _f_o_r
_G_E_N_N_B_O, _t_h_i_s _r_o_u_t_i_n_e _d_i_r_e_c_t_s _t_h_e _i_n_p_u_t _o_f _i_n_f_o_r_m_a_t_i_o_n _f_r_o_m
_t_h_e _G_E_N_N_B_O _i_n_p_u_t _f_i_l_e, _F_I_L_E_4_7.) _T_h_e _N_B_O _C_O_M_M_O_N _b_l_o_c_k_s _a_n_d
_F_I_L_E_4_8 _r_e_c_o_r_d_s _w_h_i_c_h _m_u_s_t _b_e _i_n_i_t_i_a_l_i_z_e_d _b_y _S_R _F_E_A_O_I_N _a_r_e
_d_i_s_c_u_s_s_e_d _i_n _S_e_c_t_i_o_n_s _C._3, _C._4. _A_d_d_i_t_i_o_n_a_l _i_n_f_o_r_m_a_t_i_o_n _o_n
_t_h_e _C_O_M_M_O_N _b_l_o_c_k_s _a_n_d _s_c_r_a_t_c_h _f_i_l_e_s _o_f _t_h_e _p_a_r_e_n_t _E_S_S _p_a_c_k_-
_a_g_e _i_s _p_r_o_v_i_d_e_d _i_n _t_h_e _A_p_p_e_n_d_i_c_e_s.
_P_e_r_f_o_r_m_s _o_n_e _o_f _t_w_o _t_a_s_k_s, _d_e_p_e_n_d_i_n_g _o_f _t_h_e _v_a_l_u_e _o_f
_N_B_O_O_P_T(_1). _I_f _N_B_O_O_P_T(_1) _i_s _s_e_t _t_o _2, _S_R _D_E_L_S_C_F _p_r_o_v_i_d_e_s _t_h_e
_p_a_r_e_n_t _E_S_S _p_r_o_g_r_a_m _w_i_t_h _t_h_e _m_o_d_i_f_i_e_d _d_e_n_s_i_t_y _m_a_t_r_i_x _g_e_n_-
_e_r_a_t_e_d _b_y _t_h_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s _r_o_u_t_i_n_e_s. _T_h_e _p_a_r_e_n_t
_p_r_o_g_r_a_m _w_i_l_l _t_h_e_n _c_o_m_p_u_t_e _t_h_e ``_d_e_l_e_t_i_o_n _e_n_e_r_g_y'' _f_o_r _t_h_i_s
_m_o_d_i_f_i_e_d _w_a_v_e_f_u_n_c_t_i_o_n. _I_f _N_B_O_O_P_T(_1) _i_s _s_e_t _t_o _3, _S_R _D_E_L_S_C_F
_f_e_t_c_h_e_s _t_h_e _d_e_l_e_t_i_o_n _e_n_e_r_g_y _f_r_o_m _t_h_e _p_a_r_e_n_t _p_r_o_g_r_a_m _a_n_d
_w_r_i_t_e_s _i_t _t_o _t_h_e _F_I_L_E_4_8 _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e. (_T_h_e _N_B_O_O_P_T
_a_r_r_a_y _i_s _d_i_s_c_u_s_s_e_d _i_n _S_e_c_t_i_o_n _C._5._1).
#_B_C._1_2 _G_E_N_N_B_O _A_U_X_I_L_I_A_R_Y _R_O_U_T_I_N_E_S#_N
_0 _A_n _a_d_d_i_t_i_o_n_a_l _s_e_t _o_f _r_o_u_t_i_n_e_s _i_s _p_r_o_v_i_d_e_d _f_o_r _t_h_e _G_E_N_N_B_O
_s_t_a_n_d-_a_l_o_n_e _p_r_o_g_r_a_m. _T_h_e_s_e _r_o_u_t_i_n_e_s _a_r_e _c_a_l_l_e_d _b_y _t_h_e
_G_E_N_N_B_O _d_r_i_v_e_r _r_o_u_t_i_n_e _F_E_A_O_I_N _a_n_d _a_r_e _r_e_s_p_o_n_s_i_b_l_e _f_o_r _r_e_a_d_i_n_g
_t_h_e _d_a_t_a_l_i_s_t_s _o_f _t_h_e _G_E_N_N_B_O _i_n_p_u_t _f_i_l_e. _E_a_c_h _o_f _t_h_e_s_e _r_o_u_-
_t_i_n_e_s _r_e_w_i_n_d_s _t_h_e _i_n_p_u_t _f_i_l_e _b_e_f_o_r_e _s_e_a_r_c_h_i_n_g _s_e_q_u_e_n_t_i_a_l_l_y
_f_o_r _i_t_s _a_s_s_o_c_i_a_t_e_d _d_a_t_a_l_i_s_t. _T_h_u_s, _t_h_e _o_r_d_e_r _o_f _d_a_t_a_l_i_s_t_s
(_a_s _w_e_l_l _a_s _k_e_y_l_i_s_t_s) _i_n _t_h_e _i_n_p_u_t _f_i_l_e _i_s _i_m_m_a_t_e_r_i_a_l. _E_a_c_h
_r_o_u_t_i_n_e _a_l_s_o _c_h_e_c_k_s _t_h_a_t _a_l_l _r_e_q_u_i_r_e_d _i_n_f_o_r_m_a_t_i_o_n _i_n _t_h_e
_d_a_t_a_l_i_s_t _i_s _g_i_v_e_n _a_n_d _s_t_o_r_e_s _t_h_i_s _i_n_f_o_r_m_a_t_i_o_n _o_n _t_h_e _F_I_L_E_4_8
_d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e _o_r _i_n _t_h_e _N_B_O _C_O_M_M_O_N _b_l_o_c_k_s.
_0 _B_e_l_o_w _w_e _l_i_s_t _e_a_c_h _G_E_N_N_B_O _a_u_x_i_l_i_a_r_y _r_o_u_t_i_n_e, _i_n_d_i_c_a_t_i_n_g
_i_t_s _a_s_s_o_c_i_a_t_e_d _d_a_t_a_l_i_s_t, _b_u_t _w_i_t_h_o_u_t _f_u_r_t_h_u_r _e_x_p_l_a_n_a_t_i_o_n:
#_B_C._1_3 _A_T_T_A_C_H_I_N_G _N_B_O _T_O _A _N_E_W _E_S_S _P_R_O_G_R_A_M#_N
_T_h_i_s _s_e_c_t_i_o_n _b_r_i_e_f_l_y _o_u_t_l_i_n_e_s _t_h_e _s_t_e_p_s _t_o _b_e _c_o_n_s_i_d_e_r_e_d
_w_h_e_n _a_t_t_a_c_h_i_n_g _t_h_e _N_B_O _p_r_o_g_r_a_m _t_o _a _n_e_w _E_S_S _p_a_c_k_a_g_e _t_h_a_t _i_s
_n_o_t _s_u_p_p_o_r_t_e_d _b_y _t_h_i_s _d_i_s_t_r_i_b_u_t_i_o_n.
_I_n _g_e_n_e_r_a_l, _y_o_u _s_h_o_u_l_d _t_r_y _t_o _i_d_e_n_t_i_f_y _t_h_e _s_u_p_p_o_r_t_e_d _E_S_S
_p_a_c_k_a_g_e _t_h_a_t _i_s _m_o_s_t _s_i_m_i_l_a_r _t_o _t_h_e _E_S_S _p_a_c_k_a_g_e _y_o_u _w_i_s_h _t_o
_u_s_e, _a_n_d _t_r_y _t_o _c_r_e_a_t_e _d_r_i_v_e_r _r_o_u_t_i_n_e_s _m_o_d_e_l_l_e_d _a_s _c_l_o_s_e_l_y
_a_s _p_o_s_s_i_b_l_e _o_n _t_h_o_s_e _p_r_o_v_i_d_e_d _f_o_r _t_h_e _E_S_S. [_I_n _f_a_c_t, _e_x_a_-
_m_i_n_i_n_g _t_h_e _s_o_u_r_c_e _c_o_d_e _f_o_r _d_r_i_v_e_r _r_o_u_t_i_n_e_s _o_f #_I_a_l_l#_N _s_u_p_-
_p_o_r_t_e_d _E_S_S _p_a_c_k_a_g_e_s _i_s _g_o_o_d _p_r_e_p_a_r_a_t_i_o_n _f_o_r _w_r_i_t_i_n_g _y_o_u_r _o_w_n
_d_r_i_v_e_r_s.]
July 11, 1995
- 135 -
_D_e_c_i_d_e _w_h_e_r_e _i_n _t_h_e _p_a_r_e_n_t _E_S_S _p_a_c_k_a_g_e _y_o_u _w_i_s_h _t_o _p_e_r_f_o_r_m
_t_h_e _N_B_O _a_n_a_l_y_s_i_s. _T_h_i_s _w_i_l_l _n_e_c_e_s_s_a_r_i_l_y _b_e _p_l_a_c_e_d _a_f_t_e_r _t_h_e
_c_a_l_c_u_l_a_t_i_o_n _o_f _t_h_e _w_a_v_e_f_u_n_c_t_i_o_n (_a_n_d _t_h_e _a_s_s_o_c_i_a_t_e_d _d_e_n_s_i_t_y
_m_a_t_r_i_x), _u_s_u_a_l_l_y _n_e_a_r _t_h_e _w_a_v_e_f_u_n_c_t_i_o_n _a_n_a_l_y_s_i_s _r_o_u_t_i_n_e_s
(_e._g., _t_h_e _p_e_r_e_n_n_i_a_l ``_M_u_l_l_i_k_e_n _p_o_p_u_l_a_t_i_o_n _a_n_a_l_y_s_i_s'' _s_e_c_-
_t_i_o_n) _o_r _w_a_v_e_f_u_n_c_t_i_o_n _p_r_o_p_e_r_t_i_e_s _s_e_c_t_i_o_n _o_f _t_h_e _c_o_d_e. _I_f
_p_o_s_s_i_b_l_e, _r_e_s_t_r_i_c_t _t_h_e _m_o_d_i_f_i_c_a_t_i_o_n _o_f _y_o_u_r _E_S_S _s_o_u_r_c_e _c_o_d_e
_t_o _i_n_s_e_r_t_i_o_n _o_f _a _s_i_n_g_l_e ``_C_A_L_L _R_U_N_N_B_O'' _s_t_a_t_e_m_e_n_t _a_t _s_o_m_e
_p_o_i_n_t _w_h_e_r_e _t_h_e _i_n_f_o_r_m_a_t_i_o_n _r_e_q_u_i_r_e_d _f_o_r _N_B_O _a_n_a_l_y_s_i_s _i_s
_k_n_o_w_n _t_o _b_e _a_v_a_i_l_a_b_l_e.
_C_h_e_c_k _c_a_r_e_f_u_l_l_y _f_o_r _p_o_s_s_i_b_l_e _c_o_n_f_l_i_c_t_s _b_e_t_w_e_e_n _t_h_e _p_a_r_e_n_t
_E_S_S _p_r_o_g_r_a_m _a_n_d _t_h_e _N_B_O _p_r_o_g_r_a_m _i_n (_1) _f_u_n_c_t_i_o_n _o_r _s_u_b_r_o_u_-
_t_i_n_e _n_a_m_e_s, (_2) _C_O_M_M_O_N _b_l_o_c_k _n_a_m_e_s, _a_n_d (_3) _l_o_g_i_c_a_l _f_i_l_e
_a_s_s_i_g_n_m_e_n_t_s (_L_F_N_s) _f_o_r _I/_O. _N_B_O _c_o_m_m_o_n _b_l_o_c_k _n_a_m_e_s _a_l_l
_b_e_g_i_n _w_i_t_h /_N_B.../, _a_n_d _d_e_f_a_u_l_t _L_F_N _a_s_s_i_g_n_m_e_n_t_s _a_r_e _i_n _t_h_e
_r_a_n_g_e _3_1-_4_9. (_D_u_p_l_i_c_a_t_e _F_N _o_r _S_R _n_a_m_e_s _a_r_e _d_e_t_e_c_t_e_d _b_y _a
_l_i_n_k_e_r.)
_C_r_e_a_t_e _n_e_w _d_r_i_v_e_r (_i_n_t_e_r_f_a_c_i_n_g) _s_u_b_r_o_u_t_i_n_e_s _R_U_N_N_B_O, _F_E_A_O_I_N,
_a_n_d _D_E_L_S_C_F _t_o _p_e_r_f_o_r_m _t_h_e _f_u_n_c_t_i_o_n_s _b_r_i_e_f_l_y _d_e_s_c_r_i_b_e_d _i_n
_S_e_c_t_i_o_n _C._1_1, _u_s_i_n_g _t_h_e _d_r_i_v_e_r_s _p_r_o_v_i_d_e_d _w_i_t_h _t_h_i_s _d_i_s_t_r_i_b_u_-
_t_i_o_n _a_s _t_e_m_p_l_a_t_e_s _i_n_s_o_f_a_r _a_s _p_o_s_s_i_b_l_e. _T_h_e _f_o_l_l_o_w_i_n_g _a_r_e _a
_f_e_w _h_e_l_p_f_u_l _h_i_n_t_s _f_o_r _e_a_c_h _d_r_i_v_e_r:
_T_h_e _R_U_N_N_B_O _r_o_u_t_i_n_e _s_h_o_u_l_d _b_e _r_e_l_a_t_i_v_e_l_y _s_t_r_a_i_g_h_t_f_o_r_w_a_r_d _t_o
_w_r_i_t_e, _f_o_l_l_o_w_i_n_g _a_n _a_n_a_l_o_g_o_u_s _e_x_a_m_p_l_e _p_r_o_v_i_d_e_d _i_n _t_h_i_s _d_i_s_-
_t_r_i_b_u_t_i_o_n. _N_o_t_e _t_h_a_t _y_o_u _c_a_n _s_i_m_p_l_y _o_m_i_t _t_h_e _c_a_l_l_s _t_o _S_R
_N_B_O_E_A_N _a_n_d _S_R _D_E_L_S_C_F _f_r_o_m _R_U_N_N_B_O _i_f _y_o_u _d_o _n_o_t _p_l_a_n _t_o _u_s_e
_t_h_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s (_f_o_r _e_x_a_m_p_l_e, _b_e_c_a_u_s_e _t_h_e _D_E_L_S_C_F
_d_r_i_v_e_r _i_s _u_n_m_a_n_a_g_e_a_b_l_e).
_I_f _y_o_u_r _p_a_r_e_n_t _p_r_o_g_r_a_m _i_s _q_u_i_t_e _d_i_f_f_e_r_e_n_t _f_r_o_m _a_n_y _o_f _t_h_o_s_e
_s_u_p_p_o_r_t_e_d _b_y _t_h_i_s _d_i_s_t_r_i_b_u_t_i_o_n, _c_h_o_o_s_e _a_n _a_l_t_e_r_n_a_t_e _v_e_r_s_i_o_n
_n_u_m_b_e_r [_N_B_O_O_P_T(_1_0)], _a_n_d _c_a_r_e_f_u_l_l_y _c_o_n_s_i_d_e_r _s_t_e_p _4 _b_e_l_o_w.
_R_o_u_t_i_n_e _F_E_A_O_I_N _s_h_o_u_l_d _f_e_t_c_h _i_n_f_o_r_m_a_t_i_o_n _a_b_o_u_t _t_h_e _e_l_e_c_t_r_o_n_i_c
_w_a_v_e_f_u_n_c_t_i_o_n _f_r_o_m _y_o_u_r _E_S_S _p_a_c_k_a_g_e _a_n_d _l_o_a_d _i_t _i_n_t_o _t_h_e _N_B_O
_C_O_M_M_O_N _b_l_o_c_k_s _a_n_d _F_I_L_E_4_8 _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e. _T_h_i_s _r_e_q_u_i_r_e_s
_i_n_t_i_m_a_t_e _k_n_o_w_l_e_d_g_e _o_f _w_h_e_r_e _t_h_e_s_e _i_t_e_m_s _a_r_e _s_t_o_r_e_d _i_n _t_h_e
_E_S_S _p_r_o_g_r_a_m, _s_o _t_h_e _F_E_A_O_I_N _e_x_a_m_p_l_e_s _o_f _t_h_e _d_i_s_t_r_i_b_u_t_i_o_n _m_a_y
_p_r_o_v_i_d_e _l_i_t_t_l_e _d_i_r_e_c_t _g_u_i_d_a_n_c_e. _S_e_e _S_e_c_t_i_o_n_s _C._3, _C._4 _f_o_r
_d_e_s_c_r_i_p_t_i_o_n _o_f _t_h_e _N_B_O _C_O_M_M_O_N _b_l_o_c_k_s _a_n_d _f_i_l_e _r_e_c_o_r_d_s _w_h_i_c_h
_m_u_s_t _b_e _i_n_i_t_i_a_l_i_z_e_d _b_y _t_h_i_s _r_o_u_t_i_n_e.
_N_o_t_e _t_h_a_t _t_h_e _N_B_O _a_n_a_l_y_s_i_s _w_i_l_l _p_e_r_f_o_r_m _p_r_o_p_e_r_l_y _w_i_t_h_o_u_t _t_h_e
_i_n_f_o_r_m_a_t_i_o_n _s_t_o_r_e_d _o_n _l_o_g_i_c_a_l _r_e_c_o_r_d_s _2, _5, _9, _3_0, _3_1, _4_0,
_4_1, _a_n_d _5_0-_5_2 _o_f _t_h_e _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e. _I_f _i_n_f_o_r_m_a_t_i_o_n _i_s
_n_o_t _p_r_o_v_i_d_e_d _o_n _t_h_e_s_e _r_e_c_o_r_d_s, _t_h_e _N_B_O _p_r_o_g_r_a_m _w_i_l_l _s_i_m_p_l_y
_s_h_u_t _o_f_f (_w_i_t_h _w_a_r_n_i_n_g_s) _a_n_y _r_e_q_u_e_s_t_e_d _k_e_y_w_o_r_d _o_p_t_i_o_n_s _w_h_i_c_h
_a_r_e _t_h_e_r_e_b_y _i_n_c_o_m_p_a_t_i_b_l_e. _I_n _a_d_d_i_t_i_o_n, _t_h_e _o_v_e_r_l_a_p _m_a_t_r_i_x
_o_f _r_e_c_o_r_d _1_0 _n_e_e_d _n_o_t _b_e _p_r_o_v_i_d_e_d _i_f _t_h_e _i_n_p_u_t _b_a_s_i_s _s_e_t _i_s
_o_r_t_h_o_g_o_n_a_l, _a_n_d _t_h_e _e_n_e_r_g_i_e_s _o_f _r_e_c_o_r_d _8 _a_r_e _n_o_t _r_e_q_u_i_r_e_d _i_f
_t_h_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s _i_s _n_o_t _i_m_p_l_e_m_e_n_t_e_d _f_o_r _y_o_u_r _E_S_S
July 11, 1995
- 136 -
_p_a_c_k_a_g_e.
_C_r_e_a_t_i_n_g _r_o_u_t_i_n_e _D_E_L_S_C_F _w_i_l_l _r_e_q_u_i_r_e _i_n_t_i_m_a_t_e _k_n_o_w_l_e_d_g_e _o_f
_t_h_e _S_C_F _r_o_u_t_i_n_e_s _i_n _t_h_e _p_a_r_e_n_t _E_S_S _p_r_o_g_r_a_m; _a_g_a_i_n, _v_e_r_s_i_o_n_s
_o_f _D_E_L_S_C_F _p_r_o_v_i_d_e_d _w_i_t_h _t_h_i_s _d_i_s_t_r_i_b_u_t_i_o_n _m_a_y _o_n_l_y _b_e _o_f
_m_i_n_i_m_a_l _a_s_s_i_s_t_a_n_c_e. _A_s _d_e_s_c_r_i_b_e_d _i_n _S_e_c_t_i_o_n _C._1_1, _S_R _D_E_L_S_C_F
_i_s _r_e_s_p_o_n_s_i_b_l_e _f_o_r _p_r_o_v_i_d_i_n_g _a _m_o_d_i_f_i_e_d _A_O _d_e_n_s_i_t_y _m_a_t_r_i_x _t_o
_a_n _S_C_F _e_n_e_r_g_y _e_v_a_l_u_a_t_o_r (_o_n_e _p_a_s_s _t_h_r_o_u_g_h_t _t_h_e _S_C_F _r_o_u_t_i_n_e_s)
_a_n_d _r_e_t_u_r_n_i_n_g _t_h_i_s _n_e_w _e_n_e_r_g_y _t_o _t_h_e _N_B_O _d_e_l_e_t_i_o_n _r_o_u_t_i_n_e_s
_v_i_a _t_h_e _F_I_L_E_4_8 _d_i_r_e_c_t _a_c_c_e_s_s _f_i_l_e. _I_f _y_o_u _d_o _n_o_t _i_n_t_e_n_d _t_o
_e_m_p_l_o_y _t_h_e _N_B_O _e_n_e_r_g_e_t_i_c _a_n_a_l_y_s_i_s, _y_o_u _n_e_e_d _n_o_t _p_r_o_v_i_d_e _t_h_i_s
_r_o_u_t_i_n_e _t_o _t_h_e _N_B_O _p_r_o_g_r_a_m. [_N_o_t_e _t_h_a_t _t_h_e _2_n_d-_o_r_d_e_r _p_e_r_-
_t_u_r_b_a_t_i_o_n _t_h_e_o_r_y _e_n_e_r_g_y _a_n_a_l_y_s_i_s _w_i_l_l _b_e _c_a_r_r_i_e_d _o_u_t (_p_r_o_-
_v_i_d_e_d _t_h_e _F_o_c_k _m_a_t_r_i_x _i_s _a_v_a_i_l_a_b_l_e) _e_v_e_n _i_f _y_o_u _d_o _n_o_t
_i_n_c_l_u_d_e _t_h_e _N_B_O_E_A_N _a_n_d _D_E_L_S_C_F _e_n_e_r_g_y _a_n_a_l_y_s_i_s _r_o_u_t_i_n_e_s.]
_I_n _a_d_d_i_t_i_o_n _t_o _t_h_e _e_x_p_l_i_c_i_t_l_y _s_y_s_t_e_m-_d_e_p_e_n_d_e_n_t _s_u_b_r_o_u_t_i_n_e_s
_R_U_N_N_B_O, _F_E_A_O_I_N, _a_n_d _D_E_L_S_C_F, _t_h_e_r_e _a_r_e _a _f_e_w _r_o_u_t_i_n_e_s _w_i_t_h_i_n
_t_h_e _N_B_O _p_r_o_g_r_a_m _w_h_i_c_h _c_a_n _b_e _c_o_n_s_i_d_e_r_e_d #_I_q_u_a_s_i#_N-_s_y_s_t_e_m
_d_e_p_e_n_d_e_n_t, _a_n_d _m_i_g_h_t, _t_h_e_r_e_f_o_r_e, _r_e_q_u_i_r_e _m_o_d_i_f_i_c_a_t_i_o_n.
_T_h_e_s_e _a_r_e _S_R _N_B_O_S_E_T (_S_e_c_t_i_o_n _C._5._2) _a_n_d _t_h_e `_I_N_P' _r_o_u_t_i_n_e_s
_N_B_O_I_N_P, _C_O_R_I_N_P, _C_H_S_I_N_P, _a_n_d _D_E_L_I_N_P (_S_e_c_t_i_o_n _C._9):
_S_R _N_B_O_S_E_T _a_s_s_i_g_n_s _t_h_e _l_o_g_i_c_a_l _f_i_l_e _n_u_m_b_e_r_s (_L_F_N_s) _3_1-_4_9 _t_o
_b_e _u_s_e_d _b_y _t_h_e _N_B_O _p_r_o_g_r_a_m. _A_s _m_e_n_t_i_o_n_e_d _a_b_o_v_e, _i_f _t_h_e_s_e
_a_r_e _i_n _c_o_n_f_l_i_c_t _w_i_t_h _t_h_e _f_i_l_e_s _e_m_p_l_o_y_e_d _b_y _t_h_e _p_a_r_e_n_t _E_S_S
_p_r_o_g_r_a_m, _t_h_e _c_o_n_f_l_i_c_t_i_n_g _L_F_N_s _w_i_l_l _h_a_v_e _t_o _b_e _r_e_a_s_s_i_g_n_e_d _i_n
_t_h_i_s _s_u_b_r_o_u_t_i_n_e.
_T_h_e `_I_N_P' _r_o_u_t_i_n_e_s _m_a_y _h_a_v_e _t_o _b_e _m_o_d_i_f_i_e_d _a_c_c_o_r_d_i_n_g _t_o _t_h_e
_m_a_n_n_e_r _i_n _w_h_i_c_h _t_h_e _i_n_p_u_t _f_i_l_e _o_f _t_h_e _p_a_r_e_n_t _p_r_o_g_r_a_m _s_h_o_u_l_d
_b_e _p_r_o_c_e_s_s_e_d _b_y _t_h_e _N_B_O _p_r_o_g_r_a_m. _M_o_r_e _s_p_e_c_i_f_i_c_a_l_l_y, _t_h_e_s_e
_r_o_u_t_i_n_e_s _e_i_t_h_e_r _r_e_w_i_n_d _t_h_e _i_n_p_u_t _f_i_l_e _b_e_f_o_r_e _s_e_a_r_c_h_i_n_g _f_o_r
_t_h_e_i_r _a_s_s_o_c_i_a_t_e_d _k_e_y_l_i_s_t _i_d_e_n_t_i_f_i_e_r, _o_r _t_h_e_y _s_i_m_p_l_y _b_e_g_i_n
_s_e_a_r_c_h_i_n_g _t_h_e _i_n_p_u_t _f_i_l_e _s_e_q_u_e_n_t_i_a_l_l_y _a_t _t_h_e _p_o_i_n_t _w_h_e_r_e _t_h_e
_p_a_r_e_n_t _p_r_o_g_r_a_m _l_e_f_t _o_f_f, _d_e_p_e_n_d_i_n_g _o_n _t_h_e _v_e_r_s_i_o_n _n_u_m_b_e_r
_s_p_e_c_i_f_i_e_d _i_n _N_B_O_O_P_T(_1_0). _B_e _s_u_r_e _t_h_i_s _p_a_r_a_m_e_t_e_r _i_s _c_o_n_-
_s_i_s_t_e_n_t _w_i_t_h _t_h_e _w_a_y _y_o_u _w_i_s_h _t_o _m_o_d_i_f_y _t_h_e _E_S_S _i_n_p_u_t _f_i_l_e
_f_o_r _N_B_O _i_n_p_u_t.
_0_0_1_1_1_1_1_1_1_1_0_0// _0_1_1_1_0_0_0_0_1_1_1_0// _0_1_1_0_0_0_0_0_0_1_1_0// _1_1_0_0_0_0_0_0_0_0_1_1//
_1_1_0_0_0_0_0_0_0_0_1_1// _1_1_0_0_0_0_0_0_0_0_1_1// _1_1_0_0_0_0_0_0_0_0_1_1// _0_1_1_0_0_0_0_0_0_1_1_0//
_0_1_1_1_0_0_0_0_1_1_1_0// _0_0_1_1_1_1_1_1_1_1_0_0// _0_0_0_0_1_1_1_1_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0//
_0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0//
_0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0//
_0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0//
_0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0// _0_0_0_0_0_0_0_0_0_0_0_0>>
#_H_S_e_c_t_i_o_n _D: _A_P_P_E_N_D_I_X#_N
#_B_D._1 _I_N_T_R_O_D_U_C_T_I_O_N#_N
July 11, 1995
- 137 -
_0 _T_h_i_s _A_p_p_e_n_d_i_x _c_o_n_t_a_i_n_s _s_y_s_t_e_m-_d_e_p_e_n_d_e_n_t _i_n_f_o_r_m_a_t_i_o_n _a_b_o_u_t
_N_B_O _i_n_p_u_t _a_n_d _s_o_u_r_c_e _c_o_d_e _f_o_r _t_h_e _E_S_S (_e_l_e_c_t_r_o_n_i_c _s_t_r_u_c_t_u_r_e
_s_y_s_t_e_m) _p_a_c_k_a_g_e_s _s_u_p_p_o_r_t_e_d _b_y _t_h_i_s _d_i_s_t_r_i_b_u_t_i_o_n. _W_e _a_s_s_u_m_e
_t_h_a_t _t_h_e _u_s_e_r _h_a_s _b_a_s_i_c _f_a_m_i_l_i_a_r_i_t_y _w_i_t_h _t_h_e _E_S_S _p_r_o_g_r_a_m _o_f
_i_n_t_e_r_e_s_t.
_0 _T_h_e _A_p_p_e_n_d_i_x _i_s _o_r_g_a_n_i_z_e_d _a_c_c_o_r_d_i_n_g _t_o _t_h_e _E_S_S _p_a_c_k_a_g_e_s
_s_u_p_p_o_r_t_e_d, _w_h_i_c_h _a_r_e _d_e_s_c_r_i_b_e_d _i_n _S_e_c_t_i_o_n_s _D._2-_D._7, _a_s _s_h_o_w_n
_b_e_l_o_w:
_0 _E_a_c_h _E_S_S _s_e_c_t_i_o_n _c_o_n_t_a_i_n_s _i_n_f_o_r_m_a_t_i_o_n _o_n:
_S_a_m_p_l_e _i_n_p_u_t _f_i_l_e _f_o_r _R_H_F/_3-_2_1_G _m_e_t_h_y_l_a_m_i_n_e
_N_B_O _p_r_o_g_r_a_m _i_n_s_t_a_l_l_a_t_i_o_n
_C_o_m_m_u_n_i_c_a_t_i_o_n _b_e_t_w_e_e_n _t_h_e _N_B_O _d_r_i_v_e_r_s _a_n_d _t_h_e _E_S_S _p_r_o_g_r_a_m
_0 _F_o_r _m_o_s_t _u_s_e_r_s, _o_n_l_y _t_h_e _f_i_r_s_t _s_e_c_t_i_o_n(_s) _o_n _s_a_m_p_l_e _i_n_p_u_t
_f_i_l_e _w_i_l_l _b_e _r_e_q_u_i_r_e_d _r_e_a_d_i_n_g. _F_o_r _t_h_e _p_r_o_g_r_a_m_m_e_r _r_e_s_p_o_n_s_i_-
_b_l_e _f_o_r _a_t_t_a_c_h_i_n_g _t_h_e _N_B_O _p_r_o_g_r_a_m _t_o _a_n _E_S_S _p_a_c_k_a_g_e, _t_h_e
_f_i_n_a_l _s_e_c_t_i_o_n _o_n _N_B_O _d_r_i_v_e_r_s _w_i_l_l _b_e _i_m_p_o_r_t_a_n_t _o_n_l_y _i_f _t_h_e
_a_v_a_i_l_a_b_l_e _E_S_S _v_e_r_s_i_o_n _d_i_f_f_e_r_s _s_i_g_n_i_f_i_c_a_n_t_l_y _f_r_o_m _t_h_a_t
_a_s_s_u_m_e_d _i_n _t_h_e _i_n_s_t_a_l_l_a_t_i_o_n _i_n_s_t_r_u_c_t_i_o_n_s.
_0 _I_n _t_h_e _A_p_p_e_n_d_i_x _w_e _u_s_e ``_S_R'' _a_n_d ``_F_N'' _t_o _d_e_n_o_t_e _s_u_b_r_o_u_-
_t_i_n_e_s _a_n_d _f_u_n_c_t_i_o_n_s, _r_e_s_p_e_c_t_i_v_e_l_y.
#_B_D._2 _G_A_U_S_S_I_A_N _8_8 _V_E_R_S_I_O_N#_N
#_I_D._2._1 _G_A_U_S_S_I_A_N _8_8 _s_a_m_p_l_e _i_n_p_u_t#_N
_0 _A _s_a_m_p_l_e _G_A_U_S_S_I_A_N _8_8 _i_n_p_u_t _f_i_l_e _t_o _r_e_c_r_e_a_t_e _t_h_e _d_e_f_a_u_l_t
_m_e_t_h_y_l_a_m_i_n_e (_R_H_F/_3-_2_1_G _a_t _P_o_p_l_e-_G_o_r_d_o_n _i_d_e_a_l_i_z_e_d _g_e_o_m_e_t_r_y)
_o_u_t_p_u_t _d_i_s_p_l_a_y_e_d _i_n _S_e_c_t_i_o_n _A._3 _i_s _s_h_o_w_n _b_e_l_o_w:
# _R_H_F/_3-_2_1_G
_M_e_t_h_y_l_a_m_i_n_e..._R_H_F/_3-_2_1_G//_P_o_p_l_e-_G_o_r_d_o_n _s_t_a_n_d_a_r_d _g_e_o_m_e_t_r_y
_0 _1
_C
_N _1 _C_N
_H _1 _C_H _2 _t_e_t
_H _1 _C_H _2 _t_e_t _3 _1_2_0. _0
_H _1 _C_H _2 _t_e_t _3 _2_4_0. _0
_H _2 _N_H _1 _t_e_t _3 _6_0. _0
_H _2 _N_H _1 _t_e_t _3 _3_0_0. _0
_C_N _1._4_7
_C_H _1._0_9
_N_H _1._0_1
_t_e_t _1_0_9._4_7_1_2
July 11, 1995
- 138 -
$_N_B_O $_E_N_D
#_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 -
77777777777777777777777777777777 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 -
7777777777777777777777 #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 -
77777777777777777777777777#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#u7arr 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 -
77777777777777777777777777777777777777777 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 -
777777777777777777777777777777777777777777777#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 -
7777777777777777777777777777777777777777777777777777#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 -
777777777777777777777777777777777777777777777777777770 #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 -
777777777777777#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 -
777777777777777777777777777777777777777777777777777#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 -
77777777777777777777777777777777777777777777777770 #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 -
77777777777777#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 -
7777777777 $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 -
777777777777777#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 -
77777777777777777777777777777777777777777777777777in 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 -
77777777777777777777777777777777777777777777777 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 -
777777777777777 $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 -
777777777777777#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 -
77777777777777777777777777777777777777777777777777777in 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 -
77777777777777777777777777777777777777770 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 -
7777777777777777777777777777777777777#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 -
7The 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 -
7777777777#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 -
7777777777777777777777777777777777777777777777in 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
L8mlaut owdin, P.-O.,A1
L8mlaut 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
L8mlaut 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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