#HNBO 3.0 Program Manual#N #N(#INatural Bond Orbital / Natural Population Analysis / Natural Localized Molecular Orbital Programs#N) E. D. Glendening, A. E. Reed, agger J. E. Carpenter, dagger and F. Weinhold #ITheoretical Chemistry Institute and Department of Chemis- try, University of Wisconsin, Madison, Wisconsin 53706#N 92717.#N 0 The various natural localized sets can be considered to result from a sequence of transformations of the in- put atomic orbital basis set { _______________ agger #C#RNote, however, that some electronic structure packages do not make provision for calculating the spin density matrices for some types of open-shell wavefunc- tions (e.g., MCSCF wavefunctions calculated by the GUGA formalism in the GAMESS system), so that NBO analysis cannot be applied in these cases.#O dagger #C#RIf the wavefunction is not calculated in an atom-centered basis set, it would be necessary to first compute a wavefunction for each isolated atom of the molecule (in the actual basis set and geometry of the molecular calculation), then select the most highly oc- cupied natural orbitals of each atomic wavefunction to compose a final set of linearly independent atom- centered basis functions of the required dimensionali- ty. Since atom-centered basis functions are the nearly universal choice for molecular calculations, the current _________________________ July 11, 1995 - 2 - NBO program makes no provision for this step.#O Guide, Section C. +0 +lf 0>> +0 +lf 0//' |<<3________________________ -dwid +0 ipen //+0 +dht ipen //+dhlfwid +0 ipen >> input basis arr NAOs arr NHOs arr NBOs arr NLMOs _________________________ Each natural localized set forms a complete orthonormal set of one-electron functions for expanding the delo- calized molecular orbitals (MOs) or forming matrix representations of one-electron operators. The overlap of associated ``pre-orthogonal'' NAOs (PNAOs), lacking only the interatomic orthogonalization step of the NAO procedure, can be used to estimate the strength of or- bital interactions in the usual way. 0 The optimal condensation of occupancy in the natural localized orbitals leads to partitioning into high- and low-occupancy orbital types (reduction in dimensionali- ty of the orbitals having significant occupancy), as reflected in the orbital labelling. The small set of most highly-occupied NAOs, having a close correspon- dence with the effective minimal basis set of semi- empirical quantum chemistry, is referred to as the ``natural minimal basis'' (NMB) set. The NMB (core + valence) functions are distinguished from the weakly occupied ``Rydberg'' (extra-valence-shell) functions that complete the span of the NAO space, but typically make little contribution to molecular properties. Similarly in the NBO space, the highly occupied NBOs of the natural Lewis structure can be distinguished from the ``non-Lewis'' antibond and Rydberg orbitals that complete the span of the NBO space. Each pair of valence hybrids , in the NHO basis give rise to a bond (b ) and antibond (ab ) in the NBO basis, b = ab = the former a Lewis (L) and the latter a non-Lewis (NL) orbital. The antibonds (valence shell non-Lewis orbi- tals) typically play the primary role in departures (delocalization) from the idealized Lewis structure. 0 The NBO program also makes extensive provision for energetic analysis of NBO interactions, based on the availability of a 1-electron effective energy operator (Fock matrix) for the system. Estimates of energy ef- fects are based on second-order perturbation theory, or on the effect of deleting certain orbitals or matrix elements and recalculating the total energy. NBO ener- gy analysis is dependent on the specific ESS to which the NBO program is attached, as described in the Appen- July 11, 1995 - 3 - F x y t 0.0001 0.5 .05 dpx dpy 0 1 ipen //+radius +0 0// F x ym t 0.0001 0.5 .05 dpx dpy 0 1 ipen // +0 +dht ipen //+diam -dht 0//+0 +dht ipen //-radius +0 0// F x ym t 0.0001 -0.5 -0.05 dpx dpy 0 1 ipen // +radius -dhlfht 0//'ext _________________________ dix. 0 The program is provided in a core set of NBO routines that can be attached to an electronic structure system of the user's choice. In addition, specific `driver' routines are provided that facilitate the attachment to popular #Iab initio#N and semi-empirical packages (GAUSSIAN-8X, GAMESS, HONDO, AMPAC, etc.). These ver- sions are described in individual Appendices. #IA.1.2 #IStructure of the NBO Program#N 0 The overall logical structure of the NBO program and its attachment to an electronic structure system (ESS) are illustrated in the block diagram, Fig. 1. This figure illustrates how the ESS and its scratch files (in the upper part of the diagram) communicate through the interface routines RUNNBO, FEAOIN, and DELSCF with the main NBO modules and associated direct access file (in the lower part). 0 The main NBO program is represented by modules la- belled ``NBO'' and ``NBOEAN.'' These refer to the con- struction of NBOs (including natural population analysis, construction of NAOs, NLMOs, etc.) and to NBO energy analysis, respectively. Each module consists of subroutines and functions that perform the required operations. These two modules communicate with the direct-access disk file NBODAF (LFN 48, labelled ``FILE48'' elsewhere in this manual) that is created and maintained by the NBO routines. Details of the NBO and NBOEAN modules, common blocks, and direct- access file are described in the Programmer's Guide, Section C. 0 The NBO program blocks communicate with the attached ESS through three system-dependent `driver' subroutines (RUNNBO, FEAOIN, DELSCF). The purpose of these drivers is to load needed information about the wavefunction and various matrices into the FILE48 direct access file and NBO common blocks. Although the ESS is usually thought of as `driving' the NBO program, from the point of view of the NBO program the ESS is merely a `device' that provides initial input (e.g., a density matrix and label information) or other feedback (a calculated en- ergy value) upon request. Each such ESS device there- fore requires special drivers to make this feedback July 11, 1995 - 4 - ' 2//+0 +lf 0//'file' 2>> #BFigure 1:#N Schematic diagram depicting flow of informa- tion between the electronic structure system (ESS) and the NBO program, and the commun#|ication lines connecting these programs _________________________ possible. Versions of the driver subroutines are in- cluded for several popular packages. The driver rou- tines are described in more detail in the Programmer's agger #RPresent address: Bayer AG, Abteilung AV-IM-AM, 5090 Leverkusen, Bayerwerk, Federal Republic of Ger- many. dagger #RPresent address: Department of Chemistry, University of California-Irvine, Irvine, California #HTable of Contents#N #HPREFACE: HOW TO USE THIS MANUAL#N 0 The NBO manual is divided into three major sections: 0 Section A (``General Introduction and Installation'') contains general introductory and `one-time' informa- tion for the novice user: what the program does, pro- gram structure and relationship to driver electronic structure package, initial installation, `quick start' sample input data, and a brief tutorial on sample out- put. 0 Section B (``NBO User's Guide'') is for the inter- mediate user who has an installed program and general familiarity with the standard (default) options of the NBO program. This section documents the list of #Ikeywords#N that can be used to alter the standard NBO job options, with examples of the resulting output. This section is mandatory for users who wish to use the July 11, 1995 - 5 - to the ESS scratch file (called the ``dictionary file,'' ``read-write file,'' etc., in various systems) and the NBO direct access file (NBODAF). Heavier box borders mark the ESS-specific driver routines (RUNNBO, FEAOIN, _________________________ program to its full potential, to `turn off' or `turn on' various NBO options for their specialized applica- tions. 0 Section C (``NBO Programmer's Guide'') is for accom- plished programmers who are interested in program logic and the detailed layout of the source code. This sec- tion describes the relationship of the source code sub- programs to the published algorithms for NAO, NBO, and NLMO determination, providing documentation at the lev- el of individual common blocks, functions, and subrou- tines. This in turn serves as a bridge to the `micro- documentation' included as comment statements within the source code. Section C also provides guidelines for constructing `driver' routines to attach the NBO programs to new electronic structure packages. #HSection A: GENERAL INTRODUCTION AND INSTALLATION#N #BA.1 INTRODUCTION TO THE NBO PROGRAM#N #IA.1.1 #IWhat Does the NBO Program Do?#N 0 The NBO program performs the analysis of a many- electron molecular wavefunction in terms of localized electron-pair `bonding' units. The program carries out the determination of natural atomic orbitals (NAOs), natural hybrid orbitals (NHOs), natural bond orbitals (NBOs), and natural localized molecular orbitals (NLMOs), and uses these to perform natural population analysis (NPA), NBO energetic analysis, and other tasks pertaining to localized analysis of wavefunction pro- perties. The NBO method makes use of only the first- order reduced density matrix of the wavefunction, and hence is applicable to wavefunctions of general mathematical form; in the open-shell case, the analysis is performed in terms of ``different NBOs for different spins,'' based on distinct density matrices for lpha and g r This section provides a brief introduction to NBO algorithms and nomenclature. 0 NBO analysis is based on a method for optimally transforming a given wavefunction into localized form, corresponding to the one-center (``lone pair'') and two-center (``bond'') elements of the chemist's Lewis structure picture. The NBOs are obtained as local block eigenfunctions of the one-electron density ma- July 11, 1995 - 6 - DELSCF) that directly interface the ESS program. The heavy dashed lines denote calls from the NBO program `backward' to the ESS program for information needed to carry out its tasks. Otherwise, the sequential flow of program control is generally from top to bottom and from left to right in the diagram. #IA.1.3 #IInput and Output#N 0 From the user's point of view, the #_input#/ to the NBO program attached to an ESS program consists simply of one or more keywords (an NBO #Ikeylist#N) included in the ESS input file. In effect, the NBO program reads these keywords to set various job options, then interrogates the ESS program through the DELSCF and FEAOIN drivers for additional information concerning the wavefunction. The general form of NBO keylists and the specific functions associated with each keyword are detailed in the User's Guide, Section B. The method of including NBO keylists in the input file for each ESS is detailed in the specific Appendix for the ESS. 0 The following information is passed from the ESS to the NBO program (transparent to the user): The one-electron density matrix #BD#N (or density matrices in the open-shell case) in the chosen atomic orbital (AO) basis set; The AO overlap matrix #BS#N, and label information identifying the symmetry (angular momentum type) and location (number of the atom to which affixed) for each AO; Atomic number (nuclear charge) of each atom. Certain additional information is written on the FILE48 direct access file and may be used in response to specific job options, such as the AO Fock matrix #BF#N, if energy analysis is requested; the AO dipole matrix #BM#N, if dipole moment analysis is requested; or information concerning the mathematical form of the AOs (orbital exponents, contraction coefficients, etc.), if orbital _________________________ trix, and are hence ``natural'' in the sense of L mlaut owdin, having optimal convergence properties for describing the electron density. The set of high- occupancy NBOs, each taken doubly occupied, is said to represent the ``natural Lewis structure'' of the molecule. Delocalization effects appear as weak depar- tures from this idealized localized picture. July 11, 1995 - 7 - plotting information is requested to be saved as input for a contour plotting program. 0 The principal #_output#/ from the NBO program con- sists of the tables and summaries describing the results of NBO analysis, included in the ESS output file. Sample NBO output is described in Section A.2.4 below. If requested, the NBO program may also write out transformation matrices or other data to disk files. The NBO program also creates or updates two files, the direct-access file (FILE48) and the `archive' file (FILE47) that can be used to repeat NBO analysis with different options, without running the ESS program to recalculate the wavefunction. Necessary details of these files are given in Section B.7 and the Programmer's Guide, Section C. #IA.1.4 #IGeneral Capabilities and Restrictions#N 0 Principal capabilities of the NBO program are: Natural population, natural bond orbital, and natural localized molecular orbital analysis of SCF, MCSCF, CI, and M0t oller-Plesset wavefunctions (main subroutine: NBO); For RHF closed-shell and UHF wavefunctions only, ener- getic analysis of the wavefunction in terms of the interactions (Fock matrix elements) between NBOs (main subroutine: NBOEAN); Localized analysis of molecular dipole moment in terms of NLMO and NBO bond moments and their interactions (main subroutine: DIPANL). 0 A highly transportable subset of standard FORTRAN 77 is employed, with no special compiler extensions of any vendor, and all variable names of six characters or less. Common abbreviations used in naming subprograms, variables, and keywords are: = overlap matrix = density matrix (or D) = Fock matrix = dipole matrix (or DXYZ, or DX, DY, DZ) = Natural Population Analysis = Natural Atomic Orbital = Natural Bond Orbital = Natural Localized Molecular Orbital = pre-orthogonal NAO (i.e., omit interatomic orthogonali- zation) hsp 0 Most of the NBO storage is allocated dynamically, to conform to the minimum required for the molecular sys- tem under study. However, certain NBO common blocks of fixed dimensionality are used for integer storage. These are currently dimensioned to accomodate up to 99 July 11, 1995 - 8 - atoms and 500 basis functions. Section C.3 describes how these restrictions can be altered. The program is not set up to handle complex wavefunctions, but can treat any real RHF, ROHF, UHF, MCSCF (including GVB), CI, or M0t oller-Plesset-type wavefunction (i.e., any form of wavefunction for which the requisite density matrices are available) for ground or excited states of general open- or closed-shell molecules. Effective core poten- tials (``pseudo#|potentials'') can be handled, includ- ing complete neglect of core electrons as assumed in semi-empirical treatments. The atomic orbital basis functions (up to #If#N orbitals in angular symmetry) may be of general Slater-type, contracted Gaussian- type, or other general composition, including the ``effective'' ortho#|normal valence-shell AOs of semi- empirical treatments. AO basis functions are assumed to be normalized, but in general non-orthogonal. #IA.1.5 #IReferences and Relationship to Previous Versions#N 0 This program (``version 3.0'') is an extension of previous versions of the NBO method incorporated in the semi-empirical program #IBONDO#N [F. Weinhold, #IQuan- tum Chemistry Program Exchange No. 408#N (1980); ``ver- sion 1.0''] and in a GAUSSIAN-82 implementation [A. E. Reed and F. Weinhold, #IQCPE Bull. #B5#N, 141 (1985); ``version 2.0''], and should be considered to supplant those versions. Version 3.0 also supplants the various specific versions (``the GAMESS version,'' ``the AMPAC version,'' etc.) that have been informally created and distributed to individual users outside the QCPE frame- work. Principal contributors to the development of the NBO methods and programs (1975-1990) are Principal references to the development and applica- tions of NAO/NBO/NLMO methods are: J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc. #B102#N, 7211-7218 (1980). A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B78#N, 4066-4073 (1983); A. E. Reed, R. B. Weinstock, and F. Weinhold, #IJ. Chem. Phys. #B83#N, 735-746 (1985). A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B83#N, July 11, 1995 - 9 - 1736-1740 (1985). J. E. Carpenter and F. Weinhold, #IJ. Molec. Struct. (Theochem) #B169#N, 41-62 (1988); J. E. Carpenter, #IPh. D. Thesis#N, University of Wisconsin, Madison, 1987. A. E. Reed, L. A. Curtiss, and F. Weinhold, #IChem. Rev. #B88#N, 899-926 (1988); F. Weinhold and J. E. Car- penter, in, R. Naaman and Z. Vager (eds.), ``The Struc- ture of Small Molecules and Ions,'' (Plenum, New York, 1988), pp. 227-236. 0 The principal enhancements of version 3.0 include: #IGeneralized Program Interface.#N Overall program organization (Fig. 1) has been modified to standardize communication with the main ESS program. This insures that all special ESS ``versions'' of the NBO program now have consistent options and capabilities (as long as the option is meaningful in the context of the ESS), and enables the program to be offered in a greater number of specialized ESS versions than were previously available. #INAO/NPA Summary Table.#N New tables give improved display of NAOs and natural populations, including the ``natural electron configuration'' of each atom (i.e., the occupancy and type of NAOs describing the atomic electron configuration of each atom). The new NAO sum- mary tables (Section A.3.2) include an SCF atomic orbi- tal energy (if available), a conventional atomic orbi- tal label (1#Is#N, 2#Is#N, 2#Ip#N, etc., in accordance with the labelling in isolated atoms), and a shell designation (Cor = core, Val = valence, or Ryd = Ryd- berg) to aid characterization of the NAO. #INBO Summary Table.#N A new NBO summary table (Section A.3.6) has been provided to summarize the energetics and delocalization patterns of the principal NBOs. This succinctly combines the most important information from the full NBO table, diagonal NBO Fock matrix ele- ments, and 2nd-order energy analysis. #IBond Bending Analysis.#N The program includes a new analysis of hydrid directionality and bond ``bending'' (keyword BEND, Section A.3.4). #IDipole Moment Analysis.#N The program includes new optional provision (keyword DIPOLE, Section B.6.3) for analysis of the molecular dipole moment in terms of July 11, 1995 - 10 - localized NLMOs and NBOs. #IPrint options.#N The program offers new structured printing options (Section B.2.4) that give greater con- venience and flexibility in controlling printed output, with improved provision for printing matrices or basis transformations involving general NAO, NHO, NBO, NLMO or pre-orthogonal (PNAO, PNHO, PNBO, PNLMO) basis sets. #IOrbital Contour Info.#N The program makes optional provision (keyword PLOT, Section B.2.5) for writing out files that can be used by an orbital plotting program (available separately through QCPE) to draw contour diagrams of the NBOs or other natural localized orbi- tals. #IEffective Core Potentials.#N The program now handles effective core potentials (pseudo#|potentials), or the complete neglect of core levels characteristic of semi-empirical wavefunctions (Section B.6.12). The program also includes three changes to correct problems of the previous version (which may have affected a small number of users): #IUnpolarized Cores.#N NAOs identified as ``core'' orbitals are now auto#|matically carried over as unhy- bridized 1-center core NBOs (Section B.3). This has virtually no effect on the form or occupancy of a core NBO, but averts the (rare) problem of unphysical mixing between core and valence lone pairs when the occupan- cies are `accidentally' degenerate (usually, both very close to 2.000...) within the numerical machine preci- sion. A warning message is printed when the core occu- pancy is less than 1.9990, indicating a possible ``core polarization'' effect of physical significance. #IExcited State Antibond Labels.#N The program now directly investigates the nodal structure of an NBO (by examining the overlap matrix in the PNHO basis) before assigning it a label as a ``bond'' (unstarred) or ``antibond'' (starred) NBO. In previous versions, these labels were assigned on the basis of the presumed higher occupancy of the in-phase bond combination, which was generally true for ground states, but not for excited states. The program now prints a warning mes- sage whenever it encounters the ``anomalous'' situation of an out-of-phase antibond NBO having higher occupancy than the corresponding in-phase bond NBO, indicative of an excited-state configuration. [WARNING: the overlap test cannot be applied to semi-empirical methods with orthogonal AOs (e.g., AMPAC), so antibond labels for these methods are assigned, as in previous versions, on July 11, 1995 - 11 - the basis of occupancy.] #IAlternative Resonance Structures.#N The program now institutes a search for alternative Lewis (`resonance') structures when two or more structures may be competi- tive, and returns the structure of lowest non-Lewis occupancy. This corrects a possible dependence on atomic numbering in cases of strong delocalization. Despite these changes and extensions, version 3.0 has been designed to be upward compatible with v. 2.0, as nearly as possible. Previous users of NBO 2.0 should find that their jobs run similarly (i.e., most keywords continue to function as in previous versions). Thus, experienced NBO users should find little difficulty in adapting to, and experimenting with, the new capabili- ties of the program. #BA.2 INSTALLING THE NBO PROGRAM#N 0 The NBO programs and manual are provided on a distri- bution tape. The tape contains three files: the TechSet code of this manual (file NBO.MAN), a file con- taining the core NBO source routines and supporting driver routines (file NBO.SRC), and the Fortran ``ena- bler'' program (file ENABLE.FOR). 0 In overview, the installation procedure involves the following steps (the details of each step being depen- dent on your operating system): #IEnabling the NBO routines.#N Copy the contents of the distribution tape onto your system. Using your system Fortran 77 compiler, compile and link the ena- bler program to create the ENABLE.EXE executable; for example, the VMS commands to create ENABLE.EXE are #T FOR ENABLE LINK ENABLE #NNow, run the ENABLE program (e.g., type ``RUN ENABLE'' in a VMS system), and answer the prompt #T NBO program version to enable? #Nby selecting from the available offerings. Each ESS package is associated with a 3-letter identifier (``G88'' for GAUSSIAN-88, ``GMS'' for GAMESS, ``AMP'' for AMPAC, etc.). The ENABLE program will create a file #IXXX#NNBO.FOR (where `#IXXX#N' is the identifier) that incorporates the appropriate drivers for your ESS. July 11, 1995 - 12 - #ICompiling the NBO routines.#N Using your system For- tran 77 compiler, compile the #IXXX#NNBO.FOR file to an object code file (say, #IXXX#NNBO.OBJ). [Compiler errors (if any) should be fixed before proceeding. Please notify the authors if you encounter undue diffi- culties in this step.] #IModifying the ESS routines.#N In general, the ESS source Fortran code must be modified to call the NBO routines near the point where the ESS performs Mulliken Population Analysis or evaluates properties of the final wavefunction. The modification generally con- sists of inserting a single statement (viz., ``CALL RUNNBO'') in one subroutine of your ESS system. See the appropriate Appendix of this Manual for detailed information on exactly how to modify the ESS code for your chosen system. #IRebuilding the integrated ESS/NBO program.#N Re- compile your modified ESS programs and link the result- ing object file (say, ESS.OBJ) with the #IXXX#NNBO.OBJ file to form the final ESS.EXE executable. In general, this step will closely follow the initial installation procedure for your ESS, with the exception that the #IXXX#NNBO.OBJ file must be included in the link state- ment (or deposited in one of the libraries accessed by the linker, etc.). Note that installation of the NBO programs into your ESS system in no way affects the way your system processes standard input files. The only change involves enabling the reading of NBO keylists (if detected in your input file), performance of the tasks requested in the keylist, and return of control to the parent ESS program in the state in which the NBO call was encountered. 0 If you are interfacing the NBO programs to a new ESS package (not represented in the driver routines pro- vided with this distribution), see Section C for gui- dance on how to create drivers for your ESS to provide the necessary information. Alternatively, see Section B.7 for a description of the input file to GENNBO, the stand-alone version of the NBO program. 0 The TechSet-coded version of this manual, NBO.MAN, can be printed on an HP LaserJet printer (`F' car- tridge) with the TECHSET technical typesetting program [ACS Software, American Chemical Society, Marketing Communications Dept., 1155 Sixteenth Street, N.W., Washington, D.C. 20036]. #BA.3 TUTORIAL EXAMPLE FOR METHYLAMINE#N July 11, 1995 - 13 - #IA.3.1 Running the Example#N 0 This section provides an introductory `quick start' tutorial on running a simple NBO job and interpreting the output. The example chosen is that of methylamine (CH#d3#uNH#d2#u) in Pople-Gordon idealized geometry, treated at the #Iab initio#N RHF/3-21G level. This simple split-valence basis set consists of 28 AOs (nine each on C and N, two on each H), extended by 13 AOs beyond the minimal basis level. 0 Input files to run this job (or its nearest equivalent) with each ESS are given in the Appendix. (The output shown below was created with the GAMESS system.) In most cases, you can modify the standard ESS input file to produce NBO output by simply includ- ing the line #T $NBO $END #Nat the end of the file. This is an `empty' NBO keyl- ist, specifying that NBO analysis should be carried out at the #Idefault#N level. 0 The default NBO output produced by this example is shown below, just as it appears in your output file. The start of the NBO section is marked by a standard header and storage info: ******************************************************************************* N A T U R A L A T O M I C O R B I T A L A N D N A T U R A L B O N D O R B I T A L A N A L Y S I S ******************************************************************************* Job title: Methylamine...RHF/3-21G//Pople-Gordon stan- dard geometry Storage needed: 2505 in NPA, 2569 in NBO ( 750000 available) #T @seg #NNote that all NBO output is formatted to a maximum 80-character width for convenient display on a computer terminal. The NBO heading echoes any requested key- words (none for the present default case) and shows an estimate of the memory requirements (in double preci- sion words) for the separate steps of the NBO process, compared to the total allocated memory available through your ESS process. Increase the memory allo- cated to your ESS process if the estimated NBO requests exceed the available storage. #IA.3.2 Natural July 11, 1995 - 14 - Population Analysis#N #N0 The next four NBO output segments summarize the results of natural population analysis (NPA). The first segment is the main NAO table, as shown below: NATURAL POPULATIONS: Natural atomic orbital occupan- cies NAO Atom # lang Type(AO) Occupancy Energy ---------- ----------------------------------------------- 1 C 1 s Cor( 1s) 1.99900 -11.04184 2 C 1 s Val( 2s) 1.09038 -0.28186 3 C 1 s Ryd( 3s) 0.00068 1.95506 4 C 1 px Val( 2p) 0.89085 -0.01645 5 C 1 px Ryd( 3p) 0.00137 0.93125 6 C 1 py Val( 2p) 1.21211 -0.07191 7 C 1 py Ryd( 3p) 0.00068 1.03027 8 C 1 pz Val( 2p) 1.24514 -0.08862 9 C 1 pz Ryd( 3p) 0.00057 1.01801 10 N 2 s Cor( 1s) 1.99953 -15.25950 11 N 2 s Val( 2s) 1.42608 -0.71700 12 N 2 s Ryd( 3s) 0.00016 2.75771 13 N 2 px Val( 2p) 1.28262 -0.18042 14 N 2 px Ryd( 3p) 0.00109 1.57018 15 N 2 py Val( 2p) 1.83295 -0.33858 16 N 2 py Ryd( 3p) 0.00190 1.48447 17 N 2 pz Val( 2p) 1.35214 -0.19175 18 N 2 pz Ryd( 3p) 0.00069 1.59492 19 H 3 s Val( 1s) 0.81453 0.13283 20 H 3 s Ryd( 2s) 0.00177 0.95067 21 H 4 s Val( 1s) 0.78192 0.15354 22 H 4 s Ryd( 2s) 0.00096 0.94521 23 H 5 s Val( 1s) 0.78192 0.15354 24 H 5 s Ryd( 2s) 0.00096 0.94521 25 H 6 s Val( 1s) 0.63879 0.20572 26 H 6 s Ryd( 2s) 0.00122 0.99883 27 H 7 s Val( 1s) 0.63879 0.20572 28 H 7 s Ryd( 2s) 0.00122 0.99883 #T @seg #NFor each of the 28 NAO functions, this table lists the atom to which NAO is attached (in the numbering scheme of the ESS program), the angular July 11, 1995 - 15 - momentum type `lang' (#Is#N, #Ip#dx#u#N, etc., in the coor- dinate system of the ESS program), the orbital type (whether core, valence, or Rydberg, and a conventional hydrogenic-type label), the orbital occupancy (number of electrons, or `natural popu- lation' of the orbital), and the orbital energy (in the favored units of the ESS program, in this case atomic units: 1 a.u. = 627.5 kcal/mol). [For example, NAO 4 (the highest energy C orbital of the NMB set) is the valence shell 2#Ip#N#dx#u orbital on carbon, occupied by 0.8909 electrons, whereas NAO 5 is a Rydberg 3#Ip#N#dx#u orbital with only 0.0014 electrons.] Note that the occu- pancies of the Rydberg (Ryd) NAOs are typically much lower than those of the core (Cor) plus valence (Val) NAOs of the natural minimum basis set, reflecting the dominant role of the NMB orbi- tals in describing molecular properties. 0 The principal quantum numbers for the NAO labels (1#Is#N, 2#Is#N, 3#Is#N, etc.) are assigned on the basis of the energy order if a Fock matrix is available, or on the basis of occupancy otherwise. A message is printed warning of a `population inversion' if the occupancy and energy ordering do not coincide. Summary of Natural Population Analysis: Natural Population Natural --------- -------------------------------------- Atom # Charge Core Valence Rydberg Total ---------- ------------------------------------------------------------- C 1 -0.44079 1.99900 4.43848 0.00331 6.44079 N 2 -0.89715 1.99953 5.89378 0.00384 7.89715 H 3 0.18370 0.00000 0.81453 0.00177 0.81630 H 4 0.21713 0.00000 0.78192 0.00096 0.78287 H 5 0.21713 0.00000 0.78192 0.00096 0.78287 H 6 0.35999 0.00000 0.63879 0.00122 0.64001 H 7 0.35999 0.00000 0.63879 0.00122 0.64001 ======================================================================= * Total * 0.00000 3.99853 13.98820 0.01328 18.00000 July 11, 1995 - 16 - #NThe next segment is an atomic summary showing the natural atomic charges (nuclear charge minus summed natural popula- tions of NAOs on the atom) and total core, valence, and Ryd- berg populations on each atom: #T @seg #NThis table succinctly describes the molecular charge distribution in terms of NPA charges. [For example, the carbon atom of methylamine is assigned a net NPA charge of minus 0.441 at this level; note also the slightly less positive charge on H(3) than on the other two methyl hydrogens: +0.184 vs. +0.217.] Natural Population -------- ------------------------------------------------ Core 3.99853 ( 99.9632% of 4) Valence 13.98820 ( 99.9157% of 14) Natural Minimal Basis 17.98672 ( 99.9262% of 18) Natural Rydberg Basis 0.01328 ( 0.0738% of 18) --- ----------------------------------------------------- #NNext follows a summary of the NMB and NRB populations for the composite system, summed over atoms: #T @seg #NThis exhibits the high percentage contribution (typically, > 99%) of the NMB set to the molecular charge distribution. [In the present case, for example, the 13 Rydberg orbitals of the NRB set contribute only 0.07% of the electron den- sity, whereas the 15 NMB functions account for 99.93% of the total.] #NFinally, the natural populations are summarized as an effective valence electron configuration (``natural electron configuration'') for each atom: Atom # Natural Electron Configuration --------- - ------------------------------------------------------------------ C 1 [core]2s( 1.09)2p( 3.35) N 2 [core]2s( 1.43)2p( 4.47) H 3 1s( 0.81) H 4 1s( 0.78) H 5 1s( 0.78) H 6 1s( 0.64) H 7 1s( 0.64) #T @seg July 11, 1995 - 17 - #NAlthough the occupancies of the atomic orbitals are non-integer in the molecular environment, the effective atomic configurations can be related to idealized atomic states in `promoted' configura- tions. [For example, the carbon atom in the above table is most nearly described by an idealized 1s#u2#d2s#u1#d2p#u3#d electron configuration.] #IA.3.3 Natural Bond Orbital Analysis#N #N0 The next segments of the output summarize the results of NBO analysis. The first segment reports on details of the search for an NBO natural Lewis structure: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 17.95048 0.04952 2 6 0 1 0 0 0.02 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals #T @seg #NNormally, there is but one cycle of the NBO search (cf. the ``RESONANCE'' keyword, Section B.6.6). The table sum- marizes a variety of information for each cycle: the occu- pancy thresh#|old for a `good' pair in the NBO search; the total populations of Lewis and non-Lewis NBOs; the number of core (CR), 2-center bond (BD), 3-center bond (3C), and lone pair (LP) NBOs in the natural Lewis structure; the number of low-occupancy Lewis (L) and `high-occupancy' (> 0.1e) non- Lewis (NL) orbitals; and the maximum deviation (`Dev') of any formal bond order from a nominal estimate (NAO Wiberg bond index) for the structure. [If the latter exceeds 0.1, additional NBO searches are initiated (indicated by the parenthesized number under `Cycle') for alternative Lewis structures.] The Lewis structure is accepted if all orbi- tals of the formal Lewis structure exceed the occupancy thresh#|old (default, 1.90 electrons). 0 #NNext follows a more detailed breakdown of the Lewis and non-Lewis occupancies into core, valence, and Rydberg shell contributions: WARNING: 1 low occupancy (<1.9990e) core orbital found on July 11, 1995 - 18 - C 1 -------------------------------------------------------- Core 3.99853 ( 99.963% of 4) Valence Lewis 13.95195 ( 99.657% of 14) ================== ============================ Total Lewis 17.95048 ( 99.725% of 18) ----------------------------------------------------- Valence non-Lewis 0.03977 ( 0.221% of 18) Rydberg non-Lewis 0.00975 ( 0.054% of 18) ================== ============================ Total non-Lewis 0.04952 ( 0.275% of 18) ----- --------------------------------------------------- #T @seg #NThis shows the general quality of the natural Lewis struc- ture description in terms of the percentage of the total electron density (e.g., in the above case, about 99.7%). The table also exhibits the relatively important role of the valence non-Lewis orbitals (i.e., the six valence antibonds, NBOs 23-28) relative to the extra-valence orbitals (the 13 Rydberg NBOs 10-22) in the slight departures from a local- ized Lewis structure model. (In this case, the table also includes a warning about a carbon core orbital with slightly less than double occupancy.) (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (1.99858) BD ( 1) C 1- N 2 ( 40.07%) 0.6330* C 1 s( 21.71%)p 3.61( 78.29%) -0.0003 -0.4653 -0.0238 -0.8808 -0.0291 -0.0786 -0.0110 0.0000 0.0000 ( 59.93%) 0.7742* N 2 s( 30.88%)p 2.24( 69.12%) -0.0001 -0.5557 0.0011 0.8302 0.0004 0.0443 -0.0098 0.0000 0.0000 2. (1.99860) BD ( 1) C 1- H 3 ( 59.71%) 0.7727* C 1 s( 25.78%)p 2.88( 74.22%) -0.0002 -0.5077 0.0069 0.1928 0.0098 0.8396 -0.0046 0.0000 0.0000 ( 40.29%) 0.6347* H 3 s(100.00%) -1.0000 -0.0030 July 11, 1995 - 19 - 3. (1.99399) BD ( 1) C 1- H 4 ( 61.02%) 0.7812* C 1 s( 26.28%)p 2.80( 73.72%) 0.0001 0.5127 -0.0038 -0.3046 -0.0015 0.3800 -0.0017 0.7070 -0.0103 ( 38.98%) 0.6243* H 4 s(100.00%) 1.0000 0.0008 4. (1.99399) BD ( 1) C 1- H 5 ( 61.02%) 0.7812* C 1 s( 26.28%)p 2.80( 73.72%) 0.0001 0.5127 -0.0038 -0.3046 -0.0015 0.3800 -0.0017 -0.7070 0.0103 ( 38.98%) 0.6243* H 5 s(100.00%) 1.0000 0.0008 5. (1.99442) BD ( 1) N 2- H 6 ( 68.12%) 0.8253* N 2 s( 25.62%)p 2.90( 74.38%) 0.0000 0.5062 0.0005 0.3571 0.0171 -0.3405 0.0069 -0.7070 -0.0093 ( 31.88%) 0.5646* H 6 s(100.00%) 1.0000 0.0020 6. (1.99442) BD ( 1) N 2- H 7 ( 68.12%) 0.8253* N 2 s( 25.62%)p 2.90( 74.38%) 0.0000 0.5062 0.0005 0.3571 0.0171 -0.3405 0.0069 0.7070 0.0093 ( 31.88%) 0.5646* H 7 s(100.00%) 1.0000 0.0020 7. (1.99900) CR ( 1) C 1 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0003 0.0000 -0.0002 0.0000 0.0001 0.0000 0.0000 0.0000 8. (1.99953) CR ( 1) N 2 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0001 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 9. (1.97795) LP ( 1) N 2 s( 17.85%)p 4.60( 82.15%) 0.0000 0.4225 0.0002 0.2360 -0.0027 0.8749 -0.0162 0.0000 0.0000 July 11, 1995 - 20 - 10. (0.00105) RY*( 1) C 1 s( 1.57%)p62.84( 98.43%) 0.0000 -0.0095 0.1248 -0.0305 0.7302 -0.0046 0.6710 0.0000 0.0000 11. (0.00034) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0146 0.9999 12. (0.00022) RY*( 3) C 1 s( 56.51%)p 0.77( 43.49%) 0.0000 -0.0023 0.7517 -0.0237 0.3710 -0.0094 -0.5447 0.0000 0.0000 13. (0.00002) RY*( 4) C 1 s( 41.87%)p 1.39( 58.13%) 14. (0.00116) RY*( 1) N 2 s( 1.50%)p65.53( 98.50%) 0.0000 -0.0062 0.1224 0.0063 0.0371 0.0197 0.9915 0.0000 0.0000 15. (0.00044) RY*( 2) N 2 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0132 0.9999 16. (0.00038) RY*( 3) N 2 s( 33.38%)p 2.00( 66.62%) 0.0000 0.0133 0.5776 0.0087 -0.8150 -0.0121 -0.0405 0.0000 0.0000 17. (0.00002) RY*( 4) N 2 s( 65.14%)p 0.54( 34.86%) 18. (0.00178) RY*( 1) H 3 s(100.00%) -0.0030 1.0000 19. (0.00096) RY*( 1) H 4 s(100.00%) -0.0008 1.0000 20. (0.00096) RY*( 1) H 5 s(100.00%) -0.0008 1.0000 21. (0.00122) RY*( 1) H 6 s(100.00%) -0.0020 1.0000 22. (0.00122) RY*( 1) H 7 s(100.00%) -0.0020 1.0000 23. (0.00016) BD*( 1) C 1- N 2 ( 59.93%) 0.7742* C 1 s( 21.71%)p 3.61( 78.29%) -0.0003 -0.4653 July 11, 1995 - 21 - -0.0238 -0.8808 -0.0291 -0.0786 -0.0110 0.0000 0.0000 ( 40.07%) -0.6330* N 2 s( 30.88%)p 2.24( 69.12%) -0.0001 -0.5557 0.0011 0.8302 0.0004 0.0443 -0.0098 0.0000 0.0000 24. (0.01569) BD*( 1) C 1- H 3 ( 40.29%) 0.6347* C 1 s( 25.78%)p 2.88( 74.22%) 0.0002 0.5077 -0.0069 -0.1928 -0.0098 -0.8396 0.0046 0.0000 0.0000 ( 59.71%) -0.7727* H 3 s(100.00%) 1.0000 0.0030 25. (0.00769) BD*( 1) C 1- H 4 ( 38.98%) 0.6243* C 1 s( 26.28%)p 2.80( 73.72%) -0.0001 -0.5127 0.0038 0.3046 0.0015 -0.3800 0.0017 -0.7070 0.0103 ( 61.02%) -0.7812* H 4 s(100.00%) -1.0000 -0.0008 26. (0.00769) BD*( 1) C 1- H 5 ( 38.98%) 0.6243* C 1 s( 26.28%)p 2.80( 73.72%) -0.0001 -0.5127 0.0038 0.3046 0.0015 -0.3800 0.0017 0.7070 -0.0103 ( 61.02%) -0.7812* H 5 s(100.00%) -1.0000 -0.0008 27. (0.00426) BD*( 1) N 2- H 6 ( 31.88%) 0.5646* N 2 s( 25.62%)p 2.90( 74.38%) 0.0000 -0.5062 -0.0005 -0.3571 -0.0171 0.3405 -0.0069 0.7070 0.0093 ( 68.12%) -0.8253* H 6 s(100.00%) -1.0000 -0.0020 28. (0.00426) BD*( 1) N 2- H 7 ( 31.88%) 0.5646* N 2 s( 25.62%)p 2.90( 74.38%) 0.0000 -0.5062 -0.0005 -0.3571 -0.0171 0.3405 -0.0069 -0.7070 -0.0093 ( 68.12%) -0.8253* H 7 s(100.00%) July 11, 1995 - 22 - -1.0000 -0.0020 #NNext follows the main listing of NBOs, displaying the form and occupancy of the complete set of NBOs that span the input AO space: #T @seg #NFor each NBO (1-28), the first line of printout shows the occupancy (between 0 and 2.0000 electrons) and unique label of the NBO. This label gives the type (``BD'' for 2-center bond, ``CR'' for 1-center core pair, ``LP'' for 1-center valence lone pair, ``RY*'' for 1-center Rydberg, and ``BD*'' for 2-center antibond, the unstarred and starred labels corresponding to Lewis and non-Lewis NBOs, respectively), a serial number (1, 2,... if there is a single, double,... bond between the pair of atoms), and the atom(s) to which the NBO is affixed. [For example, the first NBO in the sam- ple output is the 2-center bond (with 1.99858 electrons) between carbon (atom 1) and nitrogen (atom 2), the gma #dCN#u bond.] The next lines summarize the natural atomic hybrids #Ih#N#dA#u of which the NBO is composed, giving the percentage (100|#Ic#N#dA#u|#u2#d) of the NBO on each hybrid (in parentheses), the polarization coefficient #Ic#N#dA#u, the atom label, and a hybrid label showing the #Isp#N#u #d composition (percentage #Is#N-character, #Ip#N-character, etc.) of each #Ih#N#dA#u. [For example, the gma #dCN#u NBO is formed from an #Isp#N#u3.61#d hybrid (78.3% #Ip#N- character) on carbon interacting with an #Isp#N#u2.24#d hybrid (69.1% #Ip#N-character) on nitrogen, gma #dCN#u = 0.633(#Isp#N#u3.61#d)#dC#u + 0.774(#Isp#N#u2.24#d)#dN#u corresponding roughly to the qualitative concept of interacting #Isp#N#u3#d hybrids (75% #Ip#N-character) and the higher electronegativity (larger polarization coeffi- cient) of N.] Below each NHO label is the set of coeffi- cients that specify how the NHO is written explicitly as a linear combination of NAOs on the atom. The order of NAO coefficients follows the numbering of the NAO tables. [For example, in the first NBO entry, the carbon hybrid #Ih#N#dC#u of the gma #dCN#u bond has largest coefficients for the 2#und#d and 4#uth#d NAOs, corresponding to the approximate description #Ih#N#dC#u ~= minus 0.4653(2#Is#N)#dC#u minus 0.8808(2#Ip#N#dx#u)#dC#u in terms of the valence NAOs of the carbon atom.] In the CH#d3#uNH#d2#u example, the NBO search finds the C-N bond July 11, 1995 - 23 - (NBO 1), three C-H bonds (NBOs 2, 3, 4), two N-H bonds (NBOs 5, 6), N lone pair (NBO 9), and C and N core pairs (NBOs 7, 8) of the expected Lewis structure. NBOs 10-28 represent the residual non-Lewis NBOs of low occupancy. In this example, it is also interesting to note the slight asymmetry of the three gma #dCH#u NBOs, and the slightly higher occupancy (0.01569 #Ivs.#N 0.0077 electrons) in the gma *#<#dC#d1#uH#d3#u#u antibond (NBO 24) lying #Itrans#N to the nitrogen lone pair. #IA.3.4 NHO Directional Analysis#N 0 The next segment of output summarizes the angular proper- ties of the natural hybrid orbitals: NHO Directionality and "Bond Bending" (deviations from line of nuclear centers) [Thresholds for printing: angular deviation > 1.0 degree] hybrid p-character > 25.0% orbital occupancy > 0.10e Line of Centers Hybrid 1 Hybrid 2 --------------- ------------------- ------------------ NBO Theta Phi Theta Phi Dev Theta Phi Dev =============================================================================== 1. BD ( 1) C 1- N 2 90.0 5.4 -- -- -- 90.0 182.4 3.0 3. BD ( 1) C 1- H 4 35.3 130.7 34.9 129.0 1.0 -- -- -- 4. BD ( 1) C 1- H 5 144.7 130.7 145.1 129.0 1.0 -- -- -- 5. BD ( 1) N 2- H 6 144.7 310.7 145.0 318.3 4.4 -- -- -- 6. BD ( 1) N 2- H 7 35.3 310.7 35.0 318.3 4.4 -- -- -- 9. LP ( 1) N 2 -- -- 90.0 74.8 -- -- -- -- #T @seg #NThe `direction' of a hybrid is specified in terms of the polar (heta ) and azimuthal (hi ) angles (in the ESS coordinate system) of the vector describing its #Ip#N-component. The hybrid direction is compared with the direction of the line of centers between the two nuclei to determine the `bending' of the bond, expressed as the deviation angle (``Dev,'' in degrees) July 11, 1995 - 24 - between these two directions. For example, in the CH#d3#uNH#d2#u case shown above, the nitrogen NHO of the gma #dCN#u bond (NBO 1) is bent away from the line of C-N centers by 3.0 egree , whereas the carbon NHO is approximately aligned with the C-N axis (within the 1.0 egree threshold for print- ing). The N-H bonds (NBOs 5, 6) are bent even further (4.4 egree ). The information in this table is often useful in anticipating the direction of geometry changes resulting from geometry optimization (viz., likely reduced pyramidali- zation of the -NH#d2#u group to relieve the nitrogen bond `kinks' found in the tetrahedral Pople-Gordon geometry). #IA.3.5 Perturbation Theory Energy Analysis#N 0 The next segment summarizes the second-order perturbative estimates of `donor-acceptor' (bond-antibond) interactions in the NBO basis: Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis Threshold for printing: 0.50 kcal/mol E(2) E(j)-E(i) F(i,j) Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u. =============================================================================== within unit 1 2. BD ( 1) C 1- H 3 / 14. RY*( 1) N 2 0.84 2.18 0.038 3. BD ( 1) C 1- H 4 / 26. BD*( 1) C 1- H 5 0.52 1.39 0.024 3. BD ( 1) C 1- H 4 / 27. BD*( 1) N 2- H 6 3.03 1.37 0.057 4. BD ( 1) C 1- H 5 / 25. BD*( 1) C 1- H 4 0.52 1.39 0.024 4. BD ( 1) C 1- H 5 / 28. BD*( 1) N 2- H 7 3.03 1.37 0.057 5. BD ( 1) N 2- H 6 / 10. RY*( 1) C 1 0.56 1.78 0.028 5. BD ( 1) N 2- H 6 / 25. BD*( 1) C 1- H 4 2.85 1.51 0.059 6. BD ( 1) N 2- H 7 / 10. RY*( 1) C 1 0.56 1.78 0.028 6. BD ( 1) N 2- H 7 / 26. BD*( 1) C 1- H 5 2.85 1.51 0.059 7. CR ( 1) C 1 / 16. RY*( 3) N 2 0.61 13.11 0.080 7. CR ( 1) C 1 / 18. RY*( 1) H 3 1.40 11.99 0.116 7. CR ( 1) C 1 / 19. RY*( 1) H 4 1.55 11.99 0.122 July 11, 1995 - 25 - 7. CR ( 1) C 1 / 20. RY*( 1) H 5 1.55 11.99 0.122 8. CR ( 1) N 2 / 10. RY*( 1) C 1 1.51 16.23 0.140 8. CR ( 1) N 2 / 12. RY*( 3) C 1 0.84 16.77 0.106 8. CR ( 1) N 2 / 21. RY*( 1) H 6 0.61 16.26 0.089 8. CR ( 1) N 2 / 22. RY*( 1) H 7 0.61 16.26 0.089 9. LP ( 1) N 2 / 24. BD*( 1) C 1- H 3 8.13 1.13 0.086 9. LP ( 1) N 2 / 25. BD*( 1) C 1- H 4 1.46 1.14 0.037 9. LP ( 1) N 2 / 26. BD*( 1) C 1- H 5 1.46 1.14 0.037 #T @seg #NThis is carried out by examining all possible interactions between `filled' (donor) Lewis-type NBOs and `empty' (accep- tor) non-Lewis NBOs, and estimating their energetic impor- tance by 2nd-order perturbation theory. Since these interactions lead to loss of occupancy from the localized NBOs of the idealized Lewis structure into the empty non- Lewis orbitals (and thus, to departures from the idealized Lewis structure description), they are referred to as `delo- calization' corrections to the zeroth-order natural Lewis structure. For each donor NBO (#Ii#N) and acceptor NBO (#Ij#N), the stabilization energy E(2) associated with delo- calization (``2e-stabilization'') #Ii arr j#N is estimated as E(2) = Delta E#dij#u = q#di#u quo <> where #Iq#N#di#u is the donor orbital occupancy, \psilon #di#u, \psilon #dj#u are diagonal elements (orbital ener- gies) and F(i,j) is the off-diagonal NBO Fock matrix ele- ment. [In the example above, the #In#N#dN#u arr gma *#<#dCH#u interaction between the nitrogen lone pair (NBO 8) and the antiperiplanar C#d1#u-H#d3#u antibond (NBO 24) is seen to give the strongest stabilization, 8.13 kcal/mol.] As the heading indicates, entries are included in this table only when the interaction energy exceeds a default threshold of 0.5 kcal/mol. #IA.3.6 NBO Summary#N 0 Next appears a condensed summary of the principal NBOs, showing the occupancy, orbital energy, and the qualitative pattern of delocalization interactions associated with each: Natural Bond Orbitals (Summary): Princi- pal Delocalizations July 11, 1995 - 26 - NBO Occupancy Energy (geminal,vicinal,remote) =============================================================================== Molecular unit 1 (CH5N) 1. BD ( 1) C 1- N 2 1.99858 -0.89908 2. BD ( 1) C 1- H 3 1.99860 -0.69181 14(v) 3. BD ( 1) C 1- H 4 1.99399 -0.68892 27(v),26(g) 4. BD ( 1) C 1- H 5 1.99399 -0.68892 28(v),25(g) 5. BD ( 1) N 2- H 6 1.99442 -0.80951 25(v),10(v) 6. BD ( 1) N 2- H 7 1.99442 -0.80951 26(v),10(v) 7. CR ( 1) C 1 1.99900 -11.04131 19(v),20(v),18(v),16(v) 8. CR ( 1) N 2 1.99953 -15.25927 10(v),12(v),21(v),22(v) 9. LP ( 1) N 2 1.97795 -0.44592 24(v),25(v),26(v) 10. RY*( 1) C 1 0.00105 0.97105 11. RY*( 2) C 1 0.00034 1.02120 12. RY*( 3) C 1 0.00022 1.51414 13. RY*( 4) C 1 0.00002 1.42223 14. RY*( 1) N 2 0.00116 1.48790 15. RY*( 2) N 2 0.00044 1.59323 16. RY*( 3) N 2 0.00038 2.06475 17. RY*( 4) N 2 0.00002 2.25932 18. RY*( 1) H 3 0.00178 0.94860 19. RY*( 1) H 4 0.00096 0.94464 20. RY*( 1) H 5 0.00096 0.94464 21. RY*( 1) H 6 0.00122 0.99735 22. RY*( 1) H 7 0.00122 0.99735 23. BD*( 1) C 1- N 2 0.00016 0.57000 24. BD*( 1) C 1- H 3 0.01569 0.68735 25. BD*( 1) C 1- H 4 0.00769 0.69640 26. BD*( 1) C 1- H 5 0.00769 0.69640 27. BD*( 1) N 2- H 6 0.00426 0.68086 28. BD*( 1) N 2- H 7 0.00426 0.68086 ------------------------------- Total Lewis 17.95048 ( 99.7249%) Valence non-Lewis 0.03977 ( 0.2209%) Rydberg non-Lewis 0.00975 ( 0.0542%) ------------------------------- Total unit 1 18.00000 (100.0000%) Charge unit 1 0.00000 #T @seg #NThis table allows one to quickly identify the principal delocalizing acceptor orbitals associated with each donor NBO, and their topological relationship to this NBO, i.e., whether attached to the same atom (geminal, ``g''), to an July 11, 1995 - 27 - adjacent bonded atom (vicinal, ``v''), or to a more remote (``r'') site. These acceptor NBOs will generally correspond to the principal `delocalization tails' of the NLMO associated with the parent donor NBO. [For example, in the table above, the nitrogen lone pair (NBO 9) is seen to be the lowest- occupancy (1.97795 electrons) and highest-energy (minus 0.44592 a.u.) Lewis NBO, and to be primarily delocalized into antibonds 24, 25, 26 (the vicinal gma *#<#dCH#u NBOs). The summary at the bottom of the table shows that the Lewis NBOs 1-9 describe about 99.7% of the total electron density, with the remaining non-Lewis density found primarily in the valence-shell antibonds (particularly, NBO 24).] #HSection B: NBO USER'S GUIDE#N #BB.1 INTRODUCTION TO THE NBO USER'S GUIDE AND NBO KEYLISTS#N 0 Section B constitutes the general user's guide to the NBO program. It assumes that the user has an installed elec- tronic structure system (ESS) with attached NBO program, a general idea of what the NBO method is about, and some acquaintance with standard NBO terminology and output data. If you are completely inexperienced in these areas, read Section A (General Introduction and Installation) for the necessary background to this Section. 0 The User's Guide describes how to use the NBO program by modifying your input file to the ESS program to get some NBO output. The modification consists of adding a list of #Ikeywords#N in a prescribed #Ikeylist#N format. Four dis- tinct keylist ($KEY) types are recognized ($NBO, $CORE, $CHOOSE, and $DEL), and these will be described in turn in Sections B.2-B.5. Some of the details of inserting NBO keylists into the input file depend on the details of your ESS method, and are described in the appropriate Appendix for the ESS. However, the general form of NBO keylists and the meaning and function of each keyword are identical for all versions (insofar as the option is meaningful for the ESS), and are described herein. 0 The four keylist types have common rules of syntax: Keyl- ist delimiters are identified by a ``$'' prefix. Each keyl- ist begins with the parent keylist name (e.g., ``$NBO''), followed by any number of keywords, and ended with the word ``$END''; for example, #T July 11, 1995 - 28 - $NBO keyword1 keyword2 . . . $END !comment #N(The allowed keyword entries for each type of keylist are described in Sections B.2-B.5.) The keylist is ``free for- mat,'' with keywords separated by commas or any number of spaces. An NBO option is activated by simply including its keyword in the appropriate keylist. The order of keywords in the principal $NBO keylist does not matter, but multiple keylists must be given in the order (1) $NBO, (2) $CORE, (3) $CHOOSE, (4) $DEL of presentation in Sections B.2-B.5. Key- words may be typed in upper or lower case, and will be echoed near the top of the NBO output. A $KEY list can be continued to any number of lines, but all the entries of a $KEY list must appear in a distinct set of lines, starting with the $KEY name on the first line and ending with the closing $END on the last line (i.e., no two $KEY lists should share parts of the same line). As the above example indicates, any line in the keylist input may terminate with an exclamation point (!) followed by `comment' of your choice; the ``!'' is considered to terminate the line, and the trailing `comment' is ignored by the program. #BB.2 THE $NBO KEYLIST#N #IB.2.1 Overview of $NBO keywords#N 0 The $NBO keylist is the principal means of specifying NBO job options and controlling output, and must precede any other keylist ($CORE, $CHOOSE, or $DEL) in your input file. The allowed keywords that can appear in a $NBO keylist are grouped as follows: #IJob Control Keywords:#N #IJob Threshold Keywords:#N #IMa- trix Output Keywords:#N #IOther Output Control Keywords:#N #IPrint Level Control:#N PRINT=n Keywords are first listed and described according to these formal groupings in Sections B.2.2-B.2.6. Section B.6 illustrates the effect of commonly used $NBO keywords (as well as other $KEY lists) on the successive stages of NAO/NBO/NLMO transformation and subsequent energy or dipole analysis, with sample output for these keyword options. 0 Some keywords of the $NBO keylist require (or allow) numerical values or other parameters to specify their exact function. In this case, the numerical value or parameter must immediately follow the keyword after an equal sign (=) or any number of blank spaces. Examples: #T E2PERT=2.5 LFNPR 16 NBOMO=W25 #N(The equal sign is recommended, and will be used in the remaining examples.) July 11, 1995 - 29 - [0 Although the general user's interaction with the NBO pro- grams is usually through the documented keywords of Sections B.2.2-B.2.6, some additional `semi-documented' keywords are listed in Section B.2.7 which may be of interest to the spe- cialist.] #IB.2.2 Job Control Keywords#N 0 The keywords in this group activate or deactivate basic tasks to be performed by the NBO programs, or change the way the NBO search is conducted. Each keyword is described in terms of the option it activates (together with an indica- tion of where the option is useful): #IOPTION DESCRIPTION#N Request Natural Population Analysis and printing of NPA sum- mary tables (Section A.3.2). This keyword also activates calculation of NAOs, except for semi-empirical ESS methods. Request calculation of NBOs and printing of the main NBO table (Section A.3.3). Request printing of the NBO summary table (Section A.3.6). This combines elements of the NBO table and 2nd-order per- turbation theory analysis table (see below) in a convenient form for recognizing the principal delocalization patterns. Request search for highly delocalized structures (Section B.6.6). The NBO search normally aborts when one or more Lewis NBOs has less than the default occupancy threshold of 1.90 electrons for a `good' electron pair. When the RESO- NANCE keyword is activated, this threshold is successively lowered in 0.10 decrements to 1.50, and the NBO search repeated to find the best Lewis structure within each occu- pancy threshold. The program returns with the best overall Lewis structure (lowest total non-Lewis occupancy) found in these searches. (Useful for benzene and other highly delo- calized molecules.) Request that no bonds (2-center NBOs) are to be formed in the NBO procedure (Section B.6.7). The resulting NBOs will then simply be 1-center atomic hybrids. (Useful for highly ionic species.) Request search for 3-center bonds (Section B.6.8). The nor- mal default is to search for only 1- and 2-center NBOs. (Useful for diborane and other electron-deficient `bridged' species.) Skip the computation of NBOs, i.e., only determine NAOs and perform natural population analysis. (Useful when only NPA is desired.) Compute and print out the summary table of Natural Localized Molecular Orbitals (Section B.6.2). NLMOs are similar to July 11, 1995 - 30 - Boys or Edmiston-Ruedenberg LMOs, but more efficiently calcu- lated. (Useful for `semi-localized' description of an SCF or correlated wavefunction.) Activated automatically by all keywords that pertain to NLMOs (e.g., AONLMO, SPNLMO, DIPOLE). Note that the SKIPBO keyword has higher precedence than other keywords in this list, so that keywords with which it is implicitly in conflict (e.g., NBO, 3CBOND, NLMO) will be ignored if SKIPBO is included in the $NBO keylist. #IB.2.3 Job Threshold Keywords#N 0 The keywords in this group also activate new tasks to be performed by the NBO program, but these keywords may be modified by one or more parameters (thresholds) that control the precise action to be taken. (In each case the keywords may also be used without parameters, accepting the default values [in brackets].) #IOPTION DESCRIPTION#N Request the NHO Directional Analysis table (Section A.3.4). The three parameters [and default values] have the following significance: = threshold angular deviation for printing = threshold percentage #Ip#N-character for printing = threshold NBO occupancy for printing #NParameter values may be separated by a space or a comma. Example:#T BEND=2,10,1.9 #NThis example specifies that the bond-bending table should only include entries for angular deviations of at least 2 egree (ang), hybrids of at least 10% #Ip#N-character (pct), and NBOs of occupancy at least 1.9 electrons (occ). Request the Perturbation Theory Energy Analysis table (Sec- tion A.3.5), where = threshold energy (in kcal/mol) for printing Entries will be printed for NBO donor-acceptor interaction energies that exceed the `eval' threshold. Example:#T E2PERT=5.0 #NThis example would print only interactions of at least 5 kcal/mol (i.e., only the single entry for the 8.13 kcal/mol #In#N#dN#u arr gma *#<#dCH#u interaction in the output of Section A.3.5). July 11, 1995 - 31 - Request the Molecular Dipole Moment Analysis table (Section B.6.3), where = threshold dipole moment (Debye) for printing The program will carry out a decomposition of the total molecular dipole moment in terms of localized NLMO and NBO contributions, including all terms whose contribution (in vector norm) exceeds the `dval' threshold. Example:#T DIPOLE=0.1 #NThis example would print out dipole contributions of all NBOs (and their delocalization interactions) of magnitude ge 0.1hsp D. #NBoth the BEND and E2PERT keywords are activated by default at the standard PRINT level option (see Section B.2.6); to get an example of dipole moment analysis, include the keyl- ist #T $NBO DIPOLE $END #Nin your input file. Note that the DIPOLE keyword leads to an analysis in terms of both NBOs and NLMOs, so that the NLMO keyword (Section B.2.2) is automatically activated in this case. #IB.2.4 Matrix Output Keywords#N 0 The keywords in this group activate the printing of vari- ous matrices to the output file, or their writing to (or reading from) external disk files. The large number of key- words in this group provide great flexibility in printing out the details of the successive transformations, eps1 eps2 or the matrices of various operators in the natural local- ized basis sets. This ordered sequence of transformations forms the basis for naming the keywords. #_Keyword Names#/ 0 The keyword for printing the matrix for a particular basis transformation, IN arr OUT, is constructed from the corresponding acronymns for the two sets in the generic form ``INOUT''. For example, the transformation AO arr NBO is keyed as ``AONBO'', while that from NBOs to NLMOs is correspondingly ``NBONLMO''. The transformations are always specified in the ordered sequence shown above (i.e., ``AONBO'' is allowed, but ``NBOAO'' is an unrecognized `backward' keyword). Keywords are recognized for #Iall possible#N transformations from the input AOs to other sets July 11, 1995 - 32 - (NAO, NHO, NBO, NLMO, MO, or the pre-orthogonal PNAO, PNHO, PNBO, PNLMO sets) in the overall sequence leading to canonical MOs, i.e., AONAO AONHO AONBO AONLMO AOMO AOPNAO AOPNHO AOPNBO AOPNLMO and from each of the orthonormal natural localized sets to sets lying to the right in the sequence, i.e., NAONHO NAONBO NAONLMO NAOMO NHONBO NHONLMO NHOMO NBONLMO NBOMO NLMOMO The matrix T#dIN,OUT#u for a specified IN arr OUT transform has rows labelled by the IN set and columns labelled by the OUT set. 0 One can also print out the matrix representations of the Fock matrix (F), density matrix (DM), or dipole moment matrix (DI) in the input AO set or any of the natural local- ized sets (NAO, NHO, NBO, or NLMO). The corresponding key- word is constructed by combining the abbreviation (M) for the operator with that for the set (SET) in the generic form ``MSET''. For example, to print the Fock matrix (F) in the NBO set, use the keyword ``FNBO'', or to print the dipole matrix in the NLMO basis, use ``DINLMO''. (For the dipole matrix keywords, all three vector components will be printed.) One can also print out elements of the overlap matrix (S) in the input AO basis or any of the `pre- orthogonal' sets (PNAO, PNHO, PNBO, or PNLMO), using, e.g., ``SPNAO'' for the overlap matrix in the PNAO basis. The complete set of allowed keywords for operator matrices is: FAO FNAO FNHO FNBO FNLMO DMAO DMNAO DMNHO DMNBO DMNLMO DIAO DINAO DINHO DINBO DINLMO SAO SPNAO SPNHO SPNBO SPNLMO Other desired transformations can be readily obtained from the keyword transformations by matrix multiplication. #_Keyword Parameters#/ 0 Each generic matrix keyword (``MATKEY'') can include a July 11, 1995 - 33 - parameter that specifies the output operation to be performed on the matrix. The allowed MATKEY parameters are of two types (three for AONAO, NAONBO; see below): (print out the matrix in the standard output file, 'c' columns) (write out the matrix to disk file #In#N) #NThe first (P[c]) parameter is used to control output to the standard output file. When the MATKEY keyword is inserted in the $NBO keylist with no parameters, the matrix is by default printed (in its entirety) in the standard out- put file. Thus, ``MATKEY=P'' would be equivalent to ``MAT- KEY'', with no parameters. The complete `P[c]' form of the print parameter serves to truncate the printed matrix output to a specified number of columns [c]. For example, to print out only the first 16 columns of a matrix, use the form #T MATKEY=P16 (print 16 columns) #NFor certain matrices, one can also restrict printing to only the valence (VAL) or Lewis (LEW) columns with modified `[c]' specifiers. For the transformations to MOs, use the form #T MATKEY=PVAL (print core + valence MO columns only) #Nwhere ``MATKEY'' is AOMO, NAOMO, NHOMO, NBOMO, or NLMOMO (only). This will print out only the occupied MOs and the lowest few unoccupied MOs, e.g., the six lowest virtual MOs of the methylamine example (Section A.3), though not neces- sarily those with pre#|dominant valence character. Simi- larly, for the transformations to NBOs or NLMOs, use the form #T MATKEY=PLEW (print Lewis orbital columns only) #Nwhere ``MATKEY'' is AONBO, NHONBO, NAONBO, AONLMO, NAONLMO, NHONLMO, NBONLMO (or AOMO, NAOMO, NHOMO, NBOMO, NLMOMO). This prints out the Lewis NBOs or occupied MOs only, e.g., only the nine occupied NBOs or MOs of the methy- lamine example. Judicious use of these print parameters keeps printed output within reasonable bounds in calcula- tions with large basis sets. #NThe second type of MATKEY parameter (W[n]) is used to write the matrix (in its entirety) to a specified disk file [n]. By default, each keyword transformation matrix is associated with a particular logical file number (LFN) in the range 31-49, as shown in the table below: July 11, 1995 - 34 - #NWhen the ``MATKEY=Wn'' keyword is inserted in the $NBO keylist with no `n' specifier, the matrix is by default written out (in its entirety) to this LFN. Thus, ``MATKEY=W'' is equivalent to ``MATKEY=Wn'' if ``n'' is the default LFN for that keyword. Use the ``Wn'' parameter to direct output to any non-default LFN disk file. For exam- ple, the keyword #T AONBO=W22 #Nwould write out the AO arr NBO transformation to LFN = 22 (rather than the default LFN = 37). 0 The format of the printed output under the print `P' parameter differs from that written to an external file under the `W' parameter. The `P' output (intended for a human reader) includes an identifying label for each row, and gives the numerical entries to somewhat lesser precision (F8.4 format) than the corresponding `W' output (F15.9 for- mat), which is usually intended as input to another program. Use the ``MATKEY=W6'' keyword to route the more precise `W' form of the matrix to the standard output file, LFN 6. 0 For the AONAO, NAONBO matrices (only), one can also include a read parameter (R), #T AONAO=Rn NAONBO=Rn #Nwhich causes the matrix to be input to the program from LFN #In#N. This parameter has the effect of `freezing' orbitals to a set prescribed in the input file (thus bypass- ing the NBO optimization of these orbitals for the molecular system). For example, the keyword ``NAONBO=R44'' would have the effect of freezing the NAO arr NBO transformation coef- ficients to the form specified in LFN 44 (perhaps written with the ``NAONBO=W44'' keyword in a previous calculation on isolated molecules, and now to be used in a calculation on a molecular complex). Similarly, the keyword ``AONAO=R45'' could be used to force the analysis of an excited state to be carried out in terms of the NAOs of the ground state (previously written out with the ``AONAO=W45'' keyword). #IB.2.5 Other Output Control Keywords#N 0 The keywords in this group also help to control the I/O produced by a specified set of job options, and thus supple- ment the keywords of the previous section. However, the keywords of this section `steer' the flow of information that is routinely produced by the NBO program (or can be passed through from the ESS program) without materially affecting the actual jobs performed by the NBO program. The options associated with each keyword are tabulated below: #IOPTION DESCRIPTION#N July 11, 1995 - 35 - Set the logical file number (LFN) for NBO program output. The default LFN is #In#N = 6, the usual LFN for output from the ESS program. This option can be used to steer the NBO section of the job output to a desired file. Example:#T LFNPR=25 (re-direct NBO output to LFN 25) #N Request additional details of the NBO search. This option (primarily for programming and debugging purposes) records details of the NBO loops over atoms and atom pairs, enroute to the final NBOs. Request print-out of the NAO-Wiberg Bond Index array and related valency indices (Section B.6.5). The elements of this array are the sums of squares of off-diagonal density matrix elements between pairs of atoms in the NAO basis, and are the NAO counterpart of the Wiberg bond index [K. Wiberg, Tetrahedron #B24#N, 1083-1096 (1968)]. (This bond index is routinely used to `screen' atom pairs for possible bonding in the NBO search, but the values are not printed unless the BNDIDX keyword is activated.) Request writing of information concerning the AO basis set (geometrical positions, orbital exponents, contraction coef- ficients, etc.) to an external file, LFN 31. This is a por- tion of the information needed by the ORB#|PLOT orbital con- tour plotting programs (cf. ``PLOT'' keyword below.) 1. Request writing of #Iall#N files required by orbital contour plotting programs ORB#|PLOT. This activates the AOINFO keyword, as well as all the necessary matrix output keywords (AONBO=W37, etc.) that could be required for ORBPLOT. Request writing the FILE47 `archive' file to external disk file LFN = #In#N (or, if ``=n'' is not present, to the default LFN = 47). This file can serve as the input file to run the GENNBO program in stand-alone mode, to repeat the NBO analysis (possibly with new job options) without repeat- ing the calculation of the wavefunction (Section B.7). Request writing the NBO direct access file (DAF) to external disk file LFN = #In#N (or, if ``=n'' is not present, to the default LFN =48). #IB.2.6 Print Level Keywords#N 0 The keyword ``PRINT=n'' (#In#N = 0-4) can be used to give convenient, flexible control of all NBO output in terms of a specified print level #In#N. This keyword activates groups of keywords in a heirarchical manner, and thus incrementally increases the volume of output, ranging from #Ino#N NBO out- put (PRINT=0) to a considerable volume of detail (PRINT=4). The keywords associated with each print level are tabulated below [default value, PRINT=2]: July 11, 1995 - 36 - For each print level #In#N, the NBO output will include items activated by the listed keywords, as well as all items from lower print levels. 0 When additional keywords are included with a ``PRINT=n'' keyword in the $NBO keylist, the NBO output includes the additional keyword items as well as those implied by the print level. This can be used to tailor the NBO output to virtually any selection of output items. For example, the keylist #T $NBO PRINT=2 NLMO FNBO=P NAOMO=P11 $END #Nwould add to the standard methylamine output file of Sec- tion A.3 an NLMO summary table, the Fock matrix in the NBO basis, and the transformation coefficients for the first 11 molecular orbitals in terms of NAOs. Similarly, to produce the NPA listing only, one could use #T $NBO PRINT=1 SKIPBO $END #Nor #T $NBO PRINT=0 NPA $END #N[There is actually a slight difference between the two examples: The NBOs are determined by default (once the $NBO keylist is encountered), even if all output is suppressed with PRINT=0; in the first example, the keyword SKIPBO bypasses NBO determination, whereas in the second example the NBOs are still determined `in background.'] #IB.2.7 Semi-Documented Additional Keywords#N 0 Some additional keywords are listed below that may of use to specialists or program developers: #IOPTION DESCRIPTION#N Set the threshold of orbital occupancy desired for bond orbital selection. If this is not included, the default occupancy [1.90] will be used (or values decreasing from 1.90 to 1.50 by 0.10 steps, if the RESONANCE keyword is included). Set the projection threshold [default 0.20] to determine if a `new' hybrid orbital has too high overlap with hybrids previously found. Print total gross Mulliken populations by atom. Print gross Mulliken populations, by orbital and atom. Revises PAO to PNAO transformation matrix by post- multiplying by #BT#N#dRyd#u and #BT#N#dred#u [see the NPA July 11, 1995 - 37 - paper: A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. #B83#N, 735-746 (1985)]. Input or output of pure AO (PAO) to pre-NAO (PNAO) transfor- mation. The PAOs are AOs of pure angular momentum symmetry (rather than cartesian gaussians). This keyword can be used with read (`R'), write (`W', default LFN 43) or print (`P') parameters. Print out the bond-order matrix (Fock-Dirac density matrix) in the basis set of input AOs. This keyword can be used with write (`W', default LFN 49) or print (`P') parameters. #BB.3 THE $CORE LIST#N 0 In the Lewis structure picture, the inner `core' electron pairs are pictured as occupying orbitals having essentially isolated atomic orbital character. In NBO parlance, these core orbitals correspond to 1-center unhybridized NAOs of near-maximum occupancy, which are isolated on each center before the main NBO search begins for localized valence electron pairs. A warning message is printed if the occu- pancy of a presumed closed-shell core NBO falls below 1.9990 electrons (or 0.9990 in the open-shell case), indicative of a possible core-valence mixing effect of physical signifi- cance. 0 [In previous versions of the NBO program, core orbitals having the expected pure atomic character are found in essentially all cases, except where an `accidental' degen- eracy in occupancy of core and valence lone pairs leads to undesirable core-valence mixing; the present version expli- citly isolates core pairs as unhybridized NAOs prior to the main NBO search to prevent this unphysical effect.] 0 The NBO program contains a table giving the nominal number of core orbitals to be isolated on each type of atom (e.g., 1#Is#N for first-row atoms Li-Ne, 1#Is#N, 2#Is#N, 2#Ip#N for second-row atoms Na-Ar, etc.). At times, however, it is interesting to examine the effect of allowing core orbitals to mix into the bonding hybrids, or to hybridize (polarize) among themselves. This can be accomplished by including a $CORE keylist to specify the number of core orbitals to be isolated on each atomic center, thus modifying the nominal core table. Unlike other NBO keylists, the $CORE list includes only integers (rather than keywords) to specify the core modifications, but the rules are otherwise similar to those for other keylists. The $CORE list (if included) must follow the $NBO keylist and precede the $CHOOSE or $DEL keylists. 0 The format of the $CORE modification list is: July 11, 1995 - 38 - The keyword ``$CORE'' Pairs of integers, one pair for each center. The first integer indicates the atomic center (in the numbering of the main ESS) and the second is the number of core orbitals to be isolated on that atom. Note that atomic centers not included in the CORE list are assigned default cores. The keyword ``$END'', to indicate the end of core input. The entire list may also be condensed to a single line, but the word ``$CORE'' must occur as the first word of the line and ``$END'' as the last word; that is, the core modifica- tion keylist cannot continue on a line that contains other keylist information. 0 The core orbitals are isolated by occupancy, the most occupied NAOs being first selected, and full subshells are isolated at a time. Thus, for example, to select the five orbitals of the #In#N = 1 and #In#N = 2 shells as core orbi- tals, it would make no difference to select ``3'' or ``4'' (instead of ``5''), since all three of these choices would specify a core containing a 1#Is#N, 2#Is#N, and all three 2#Ip#N orbitals. The $CORE modification list is read only once, and applies to both lpha and p n-shell calcula- tion. An example, appropriate for Ni(1)-C(2)-O(3) with the indi- cated numbering of atoms, is shown below: #T $CORE 1 5 $END #NThis would direct the NBO program to isolate only 5 core orbitals on Nickel (atom 1), rather than the nominal 9 core orbitals. In other words, only 1#Is#N, 2#Is#N, and 2#Ip#N orbitals will be considered as core orbitals in the search for NBOs of NiCO, allowing the 3#Is#N and 3#Ip#N orbitals to mix with valence NAOs in bond formation. Since the carbon and oxygen atoms were not included in the modification list, the nominal set of core orbitals (1#Is#N only) is isolated on each of these atoms. [The alternative example #T $CORE 1 0 2 0 3 0 $END #N(no cores) would allow all NAOs to be included in the NBO search; this would be equivalent to the default treatment in the earlier version of the program (see Section A.1.5).] #BB.4 THE $CHOOSE KEYLIST (DIRECTED NBO SEARCH)#N 0 A $CHOOSE keylist requests that the NBO search be directed July 11, 1995 - 39 - to find a particular Lewis structure (`resonance structure') chosen by the user. (This is useful for testing the accu- racy of alternative resonance structure representations of the wavefunction, relative to the optimal Lewis structure returned in a free NBO search.) In the $CHOOSE list, a resonance structure is specified by indicating where lone pairs and bonds (including multiple bonds) are to be found in the molecule. In some cases, the user may wish to specify only the location of bonds, letting the NBO algo- rithm seek the best location for lone pairs, but it is usu- ally safest to completely specify the resonance structure, both lone pairs and bonds. 0 The format of the $CHOOSE list is: The keyword ``$CHOOSE'' The keyword ``ALPHA'' (only for open-shell wavefunction) If one-center (`lone') NBOs are to be searched for, type the keyword ``LONE'' followed by a list of pairs of numbers, the first number of each pair being the atomic center and the second the number of valence lone pairs on that atom. Ter- minate the list with ``END''. (Note that only the occupied #Ivalence#N lone pairs should be entered, since the number of core orbitals on each center is presumed known.) If two-center (`bond') NBOs are to be searched for, type the keyword ``BOND'', followed by the list of bond specifiers, and terminated by ``END''. Each bond specifier is one of the letters single bond double bond triple bond quadruple bond followed by the two atomic centers of the bond (e.g., ``D 9 16'' for a double bond between atoms 9 and 16). If three-center NBOs are to be searched for, type the key- word ``3CBOND'', followed by the list of 3-c bond specif- iers, and terminated by ``END''. Each 3-c bond specifier is again one of the letters ``S'' (single), ``D'' (double), ``T'' (triple), or ``Q'' (quadruple), followed by three integers for the three atomic centers (e.g., ``S 4 8 10'' for a single three-center bond 4-8-10). (Note that the 3CBOND keyword of the $NBO keylist is implicitly activated if 3-c bonds are included in a $CHOOSE list.) The word ``END'' to signal the end of the lpha spin list. The keyword ``BETA'' (for open-shell wavefunctions) The input for m format as above. The overall $CHOOSE list should always end with the ``$END'' keyword. July 11, 1995 - 40 - Two examples will serve to illustrate the $CHOOSE format (each is rather artificial, inasmuch as the specified $CHOOSE structure corresponds to the `normal' structure that would be found by the NBO program): The closed-shell H-bonded complex FH ots CO, with atom numbering F(1)-H(2) ots C(3)-O(4), might be specified as #T $CHOOSE LONE 1 3 3 1 4 1 END BOND S 1 2 T 3 4 END $END #NThis would direct the NBO program to search for three lone pairs on atom F(1), one lone pair on atom C(3), one lone pair on atom O(4), one bond between F(1)-H(2), and three bonds between C(3)-O(4). The open-shell FH ots O#d2#u complex, with atom numbering F(1)-H(2)#+...#-O(3)-O(4), and with the unpaired electrons on O#d2#u being of lpha spin, might be specified as #T $CHOOSE ALPHA LONE 1 3 3 3 4 3 END BOND S 1 2 S 3 4 END END BETA LONE 1 3 3 1 4 1 END BOND S 1 2 T 3 4 END END $END #NNote that this example incorporates the idea of ``dif- ferent Lewis structures for different spins,'' with a dis- tinct pattern of localized 1-c (`lone') and 2-c (`bond') functions for lpha and . 0 As with other keylists, the $CHOOSE keylist can be condensed to a smaller number of lines, as long as no line is shared with another keylist. The order of keywords within the $CHOOSE keylist should be as shown above (i.e., ALPHA before BETA, LONE before BOND, etc.), but the order of entries within a LONE or BOND list is immaterial. A $CORE keylist (if present) must precede the $CHOOSE list. #BB.5 THE $DEL KEYLIST (NBO ENERGETIC ANALYSIS)#N July 11, 1995 - 41 - #IB.5.1 Introduction to NBO Energetic Analysis#N 0 The fourth and final type of keylist is a `deletions' ($DEL) keylist, to activate NBO energetic analysis. This analysis is performed by (1) deleting specified elements (or blocks of elements) from the NBO Fock matrix, (2) diagonal- izing this new Fock matrix to obtain a new density matrix, and (3) passing this density matrix to the SCF routines for a single pass through the SCF energy evaluator. The differ- ence between this `deletion' energy and the original SCF energy provides a useful measure of the energy contribution of the deleted terms. Since a Fock matrix is required, the energetic analysis is performed for RHF and UHF wavefunc- tions only. 0 Input for the NBO energetic analysis is through the $DEL keylist, which specifies the deletions to be performed. Multiple analyses (deletions) can be performed during a sin- gle job, with each deletion included in the overall $DEL keylist. The nine distinct types of deletions input are described in Section B.5.2 below. 0 The deletions keylist begins with the ``$DEL'' keyword. For the analysis of UHF wavefunctions, the deletions for the lpha and b separately specified (see Section B.5.3). Otherwise, the input for closed shells RHF and UHF is ident- ical. The input is free format and the input for a single deletion can be spread over as many lines as desired. The desired deletions should be listed one after the other. After the last deletion, the word ``$END'' signals the end of the keylist. |<<__________________________ #BWARNING#N If symmetry is used, one must be careful to only do dele- tions that will preserve the symmetry of the electronic wavefunction!! If this is not done, the energy of the dele- tion will be incorrect because the assumption is made in evaluating the energy that the original symmetry still exists, and the variational principle may be violated. (For example, if symmetry is used for ethane, is is permissible to do a ``NOSTAR'' deletion, but not the deletion of a sin- gle C-H antibond.) The remedy is not to use symmetry in the SCF calculation. 0 In describing the deletion types, use is made of the terms ``molecular unit'' and ``chemical fragment.'' The NBO pro- gram looks at the chemical bonding pattern produced by the bonding NBOs and identifies the groups of atoms that are linked together in distinct ``molecular units'' (usually July 11, 1995 - 42 - synonymous with ``molecules'' in the chemical sense). The first atom that is not in molecular unit 1 will be in molecular unit 2, and so forth. For example, if the list of atoms is C(1), H(2), F(3), O(4), and bonding NBOs are found between C(1)- O(4) and H(2)-F(3), then molecular unit 1 will be CO and molecular unit 2 will be HF. A ``chemical fragment'' is taken to be any subset of the atoms, usually (but not neces- sarily) in the same molecular unit, and usually (but not necessarily) connected by bond NBOs. Typically, a chemical fragment might be specified to be a single atom, the four atoms of a methyl group, or any other `radical' of a molecu- lar unit, identified by giving the atom numbers of which the fragment consists. #IB.5.2 The Nine Deletion Types#N 0 The keywords and format to specify each of the nine allowed deletion types are described below: #_(1) Deletion of entire orbitals.#/ This is called for by typing ``DELETE'', then the number of orbitals to be deleted, then the keyword ``ORBITAL'' (or ``ORBITALS''), then the list of the orbitals to be deleted. Example: #TDELETE 3 ORBITALS 15 18 29 #N[See also deletion types (4) and (7) for deleting sets of orbitals.] |<<__________________________ #BWARNING#N The ``single-pass'' method of evaluating deletion energies is appropriate only for deletions of #Ilow#N-occupancy (non-Lewis) orbitals, for which the loss of self-consistency in the Coulomb and exchange potentials (due to redistribu- tion of the electron density of deleted orbitals) is small compared to the net energy change of deletion. It is funda- mentally erroneous to delete #Ihigh#N-occupancy (Lewis) orbitals by this procedure. #_(2) Deletion of specific Fock matrix elements.#/ This is called for by typing ``DELETE'', then the number of elements to be deleted, then the keyword ``ELEMENT'' (or ``ELEMENTS''), then the list of the elements to be deleted (each as a pair of integers). Example: #TDELETE 3 ELEMENTS 1 15 3 19 23 2 July 11, 1995 - 43 - #NThis example would result in the zeroing of the following Fock matrix elements: (1,15), (15,1), (3,19), (19,3), (23,2), (2,23). [See also deletion types (3), (5), (6), (8), (9) for deleting sets of elements.] #_(3) Deletion of off-diagonal blocks of the Fock matrix.#/ Each block is specified by two sets of orbitals, and all Fock matrix elements in common between these two sets are set to zero. This is called for by typing ``ZERO'', then the number of off-diagonal blocks to be zeroed, and then, for each block, the following: (1) the dimensions of the block, separated by the word ``BY'' (e.g., ``6 BY 3'' if the first set has 6 orbitals and the second set has 3 orbitals); (2) the list of orbitals in the first set; (3) the list of orbitals in the second set. An example is shown below: #T ZERO 2 BLOCKS 2 BY 5 3 4 9 10 11 14 19 3 BY 2 1 2 7 20 24 #NThis will set the following Fock matrix elements to zero: (3,9), (3,10), (3,11), (3,14), (3,19), (9,3), (10,3), (11,3), (14,3), (19,3), (4,9), (4,10), (4,11), (4,14), (4,19), (9,4), (10,4), (11,4), (14,4), (19,4), (1,20), (1,24), (2,20), (2,24), (7,20), (7,24) (20,1), (24,1), (20,2), (24,2), (20,7), (24,7) [Usually, in studying the total delocalization from one molecular unit to another, it is much easier to use deletion type (8) below. Similarly, in studying the total delocali- zation from one chemical fragment to another, it is easier to use deletion type (9).] #_(4) Deletion of all Rydberg and antibond orbitals.#/ The Rydberg and antibond orbitals are the non-Lewis NBO orbitals that have stars in their labels (RY*, BD*) in the NBO analysis output. To delete all these orbitals, simply enter ``NOSTAR''. The result of this deletion is the energy of the idealized NBO natural Lewis structure, with all Lewis NBOs doubly occupied. (Unlike other deletions, in which July 11, 1995 - 44 - there is a slight loss of variational self-consistency due to the redistributed occupancy of the deleted orbitals, the result of a ``NOSTAR'' deletion corresponds rigorously to the vari- ational expectation value of the determinant of doubly occu- pied Lewis NBOs). #_(5) Deletion of all vicinal delocalizations.#/ To delete all Fock matrix elements between Lewis NBOs and the vicinal non-Lewis NBOs, simply enter ``NOVIC''. #_(6) Deletion of all geminal delocalizations.#/ To delete all Fock matrix elements between Lewis NBOs and the geminal non-Lewis NBOs, simply enter ``NOGEM''. #_(7) Deletion of all starred (antibond/Rydberg) orbitals on a particular molecular unit.#/ This is called for by typing ``DESTAR'', then the number of molecular units to be de#|starred, then the keyword ``UNIT'' (or ``UNITS''), then the list of units. Example: #TDESTAR 2 UNITS 3 4 #N #_(8) Zeroing all delocalization from one molecular unit to another.#/ This is called for by typing ``ZERO'', then the number of delocalizations to zero, then the keyword ``DELOCALIZATION'' (can be abbreviated to ``DELOC''), and then, for each delo- calization, the word ``FROM'', the number of the donor unit, the word ``TO'', and the number of the acceptor unit. Example: #TZERO 2 DELOC FROM 1 TO 2 FROM 2 TO 1 #NThe above example would zero #Iall#N intermolecular delo- calizations between units 1 and 2 (i.e., both 1 arr 2 and 2 arr 1). The effect is to remove all Fock matrix elements between high-occupancy (core/lone pair/bond) NBOs of the donor unit to the low-occupancy (antibond/Rydberg) NBOs of the acceptor unit. The donor and acceptor units may be the same. #_(9) Zeroing all delocalization from one chemical fragment to another.#/ This is called for by typing ``ZERO'', then the number of July 11, 1995 - 45 - inter-fragment delocalizations to be zeroed, then the words ``ATOM BLOCKS'', and then, for each delocalization, the following: (1) the number of atoms in the two fragments, separated by the word ``BY'' (e.g., ``6 BY 3'' if the first fragment has 6 atoms and the second has 3 atoms); (2) the list of atoms in the first fragment; (3) the list of atoms in the second fragment. For example, to zero all delocalizations between the frag- ments defined by atoms (1,2) and by atoms (3,4,5), the $DEL entries would be #T ZERO 2 ATOM BLOCKS 2 BY 3 1 2 3 4 5 3 BY 2 3 4 5 1 2 #NIn this example, the first block removes the (1,2) arr (3,4,5) delocalizations, while the second removes the (3,4,5) arr (1,2) delocalizations. 0 For additional examples of $DEL input, see Section B.6.10. #IB.5.3 Input for UHF Analysis#N 0 Deletions of the alpha and beta Fock matrices can be done independently. The deletions are input as above (Section B.5.2) for RHF closed shell, but they must be specified separately for alpha and beta in the UHF case. 0 The deletion to be done on the alpha Fock matrix must be preceded by the keyword ``ALPHA'', and the deletion of the beta Fock matrix must be preceded by the keyword ``BETA''. (Actually, only the first letter ``A'' or ``B'' is searched for by the program.) The ALPHA deletion must precede the BETA deletion. The BETA deletion may be the same as the ALPHA deletion, or different. 0 NOTE: The types of the lpha NBOs often differ from those of the d tions lists are generally required. For example, O#d2#u (triplet) has one bond in the lpha system and three in the t m, if the unpaired electrons are in the lpha sys- tem. 0 Here are three examples to illustrate UHF open-shell dele- tions: Example 1: July 11, 1995 - 46 - #T ALPHA ZERO 1 DELOC FROM 1 TO 2 BETA NOSTAR #NExample 2: #T ALPHA ZERO 1 DELOC FROM 1 TO 2 BETA ZERO 0 DELOC #NExample 3: #T ALPHA DELETE 0 ORBITALS BETA DELETE 1 ORBITAL 8 #NIf no deletion is done, this must be specified using zero (0) with one of the deletion input formats, as shown in Examples 2,3 above. #BB.6 NBO KEYLIST ILLUSTRATIONS#N #IB.6.1 Introduction#N 0 This section illustrates the output produced by several important keyword options of the NBO keylists ($NBO, $CHOOSE, $DEL, $CORE lists), supplementing the illustrations of Section A.3. Excerpts are provided rather than full out- put, since, e.g., NPA analysis is unaffected by keywords that modify the NBO search. Keywords of general applicabil- ity are illustrated with the methylamine example (RHF/3-21G, Pople-Gordon geometry) of Section A.3, which should be con- sulted for further information. More specialized keywords (RESONANCE, 3CBOND, etc.) are illustrated with prototype molecules (benzene, diborane, etc.) chosen for the keyword. 0 Sections B.6.2-B.6.8 illustrate representative examples from the $NBO keyword groups, including NLMO, DIPOLE, BNDIDX, RESONANCE, NOBOND, 3CBOND, and matrix output key- words. Section B.6.9 and B.6.10 similarly illustrate the use of the $CHOOSE and $DEL keylists. Section B.6.11 illus- trates the output for open-shell UHF cases, emphasizing features associated with the ``different Lewis structures for different spins'' representation of lpha and S ction B.6.12 shows the effect of using effective core potentials for Cu#d2#u, also illustrating aspects of the inclusion of #Id#N functions. #IB.6.2 NLMO Keyword#N 0 When the NLMO keyword is activated, the program computes the NLMOs and prints out three tables summarizing their form. For the RHF/3-21G methylamine example (cf. Section A.3), the principal NLMO table is shown below: NATURAL LOCALIZED MOLECULAR ORBITAL (NLMO) ANALYSIS: Maximum off-diagonal element of DM in NLMO basis: 0.00000 Hybridization/Polarization Analysis of NLMOs in NAO Basis: July 11, 1995 - 47 - NLMO/Occupancy/Percent from Parent NBO/ Atomic Hybrid Contributions ---------- --------------------------------------------------------------------- 1. (2.00000) 99.9290% BD ( 1) C 1- N 2 40.039% C 1 s( 21.54%)p 3.64( 78.46%) 59.891% N 2 s( 30.98%)p 2.23( 69.02%) 0.015% H 3 s(100.00%) 0.021% H 6 s(100.00%) 0.021% H 7 s(100.00%) 2. (2.00000) 99.9301% BD ( 1) C 1- H 3 59.675% C 1 s( 25.44%)p 2.93( 74.56%) 0.040% N 2 s( 1.99%)p49.22( 98.01%) 40.258% H 3 s(100.00%) 3. (2.00000) 99.6996% BD ( 1) C 1- H 4 60.848% C 1 s( 25.25%)p 2.96( 74.75%) 0.093% N 2 s( 13.08%)p 6.65( 86.92%) 0.014% H 3 s(100.00%) 38.861% H 4 s(100.00%) 0.017% H 5 s(100.00%) 0.158% H 6 s(100.00%) 4. (2.00000) 99.6996% BD ( 1) C 1- H 5 60.848% C 1 s( 25.25%)p 2.96( 74.75%) 0.093% N 2 s( 13.08%)p 6.65( 86.92%) 0.014% H 3 s(100.00%) 0.017% H 4 s(100.00%) 38.861% H 5 s(100.00%) 0.158% H 7 s(100.00%) 5. (2.00000) 99.7206% BD ( 1) N 2- H 6 0.113% C 1 s( 5.15%)p18.41( 94.85%) 67.929% N 2 s( 25.82%)p 2.87( 74.18%) 0.137% H 4 s(100.00%) 0.014% H 5 s(100.00%) 31.793% H 6 s(100.00%) 6. (2.00000) 99.7206% BD ( 1) N 2- H 7 0.113% C 1 s( 5.15%)p18.41( 94.85%) 67.929% N 2 s( 25.82%)p 2.87( 74.18%) 0.014% H 4 s(100.00%) 0.137% H 5 s(100.00%) 31.793% H 7 s(100.00%) 7. (2.00000) 99.9499% CR ( 1) C 1 99.951% C 1 s(100.00%)p 0.00( 0.00%) July 11, 1995 - 48 - 0.013% H 3 s(100.00%) 0.013% H 4 s(100.00%) 0.013% H 5 s(100.00%) 8. (2.00000) 99.9763% CR ( 1) N 2 0.010% C 1 s( 22.30%)p 3.48( 77.70%) 99.980% N 2 s(100.00%)p 0.00( 0.00%) 9. (2.00000) 98.8972% LP ( 1) N 2 0.440% C 1 s( 1.05%)p94.15( 98.95%) 98.897% N 2 s( 17.85%)p 4.60( 82.15%) 0.489% H 3 s(100.00%) 0.085% H 4 s(100.00%) 0.085% H 5 s(100.00%) #T @seg #NFor each of the nine occuplied NLMOs, the table shows first the NLMO occupancy (necessarily 2.0000 at SCF level, as in the present example), the percentage of the total NLMO composition represented by this parent NBO (usually > 99%), and the label of the `parent' NBO. Below this, there fol- lows an NAO decomposition of the NLMO, showing the percen- tage of the NLMO on each atom and the hybrid composition ratios (effective #Isp#N#u #d character and percentage #Is- #N and #Ip#N-character) of the NAOs. For example, NLMO 9 is the most delocalized NLMO of the table, having only about a 98.9% contribution from the localized N(2) parent lone pair NBO, with `delocalization tails' composed primarily of con- tributions (~0.4% each) from C(1) and H(3), and smaller con- tributions (~0.09%) from H(4) and H(5). This corresponds to what might have been anticipated from the NBO summary table (Section A.3.6) or perturbation theory energy analysis table (Section A.3.5), which showed that the N(2) lone pair, NBO 9, is principally delocalized onto NBO 24, the vicinal C(1)-H(3) antibond [with lesser delocalizations onto NBOs 25, 26, the C(1)-H(4) and C(1)-H(5) antibonds]. #IB.6.3 DIPOLE Keyword#N 0 The DIPOLE keyword activates the NBO/NLMO analysis of the molecular dipole moment, as shown below for the example of RHF/3-21G methylamine (cf. Section A.3): Dipole moment analysis: [Print threshold: Net dipole > 0.02 Debye] NLMO bond dipole NBO bond dipole July 11, 1995 - 49 - ------------------------- ------------------------ Orbital x y z Total x y z Total =============================================================================== 1. BD ( 1) C 1- N 2 -0.76 -0.08 0.00 0.76 -0.76 -0.09 0.00 0.77 2. BD ( 1) C 1- H 3 0.49 1.90 0.00 1.96 0.50 1.90 0.00 1.97 deloc 14: 0.03 -0.01 0.00 0.03 deloc 25: -0.01 0.00 0.02 0.02 deloc 26: -0.01 0.00 -0.02 0.02 3. BD ( 1) C 1- H 4 0.67 -0.77 -1.50 1.81 0.71 -0.79 -1.50 1.84 deloc 27: -0.05 0.00 0.00 0.05 deloc 26: -0.02 0.03 -0.03 0.04 deloc 24: -0.01 -0.02 0.00 0.02 4. BD ( 1) C 1- H 5 0.67 -0.77 1.50 1.81 0.71 -0.79 1.50 1.84 deloc 28: -0.05 0.00 0.00 0.05 deloc 25: -0.02 0.03 0.03 0.04 deloc 24: -0.01 -0.02 0.00 0.02 5. BD ( 1) N 2- H 6 -0.45 0.44 0.86 1.06 -0.50 0.44 0.89 1.11 deloc 25: 0.06 -0.01 -0.02 0.06 6. BD ( 1) N 2- H 7 -0.45 0.44 -0.86 1.06 -0.50 0.44 -0.89 1.11 deloc 26: 0.06 -0.01 0.02 0.06 7. CR ( 1) C 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8. CR ( 1) N 2 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00 9. LP ( 1) N 2 -0.63 -2.85 0.00 2.91 -0.88 -2.93 0.00 3.06 deloc 24: 0.16 0.09 0.00 0.18 July 11, 1995 - 50 - deloc 25: 0.03 0.01 0.01 0.03 deloc 26: 0.03 0.01 -0.01 0.03 deloc 10: 0.02 -0.02 0.00 0.03 ---------- ------------------------------------------ Net dipole moment -0.45 -1.67 0.00 1.73 -0.71 -1.82 0.00 1.95 Delocalization correction 0.27 0.14 0.00 0.30 ---------- ------------------------------------------ Total dipole moment -0.45 -1.67 0.00 1.73 -0.45 -1.67 0.00 1.73 #T @seg #NThe bottom line of the table shows the individual (x,y,z) vector components (minus 0.45,minus 1.67,0.00) and length (1.73 D) of the total molecular dipole moment, in the coor- dinate system of the ESS program. This is decomposed in the main body of the table into the individual contributions of ``NLMO bond dipoles'' (which strictly add to give the net molecule dipole at the SCF level) and ``NBO bond dipoles'' (which must be added with their off-diagonal `deloc' contri- butions to give the net molecular moment). Each NLMO or NBO bond dipole vector t mu #dAB #u is evaluated as mab = mabe + mabn where mabe = 2#Ie#N a t r#Nar b t is the electronic dipole expectation value for an electron pair in the b NLMO or NBO, and mabn is the nuclear contribution of compensating unit positive charges at the positions of nuclei A and B (or both on A for a 1-center NBO). The `deloc' contributions below each NBO bond dipole show the off-diagonal corrections to an additive bond dipole approximation (i.e., the correc- tions to localized NBO bond dipoles to get the NLMO bond dipoles) to account for the delocalization from parent NBO #Ii#N onto other (primarily, non-Lewis) NBOs #Ij#N; in terms of the expansion of an NLMO in the set { } of NBOs, nlmo = this correction is (for each electron, lpha or ) .LM+10 + s <> where the primes on the summation denote omission of terms #Ik#N equal to #Ii#N or #Ij#N. For example, in the above table the largest individual contribution to t mu is from the nitrogen lone pair, table entry 9, which has an NLMO dipole of 2.91 Debye or NBO dipole of 3.06. The latter July 11, 1995 - 51 - has also the largest off-diagonal delocalization correction in the table, a 0.18 D correction due to the #In#N#dN#u arr gma *#<#dCH#u delocalization into the vicinal C(1)-H(3) antibond, NBO 24. 0 For a post-SCF (correlated) calculation, the dipole table would also include an additional line for the correction due to non-additivity of the NLMO bond dipoles. For an ionic species, there would also be an additional line for the ``residual nuclear charge'' contribution; here, one must be aware that the dipole moment is calculated with respect to the origin of the cartesian coordinate system chosen by the ESS program (since the dipole moment is origin-dependent in this case). 0 Note that the amount of detail in the dipole table can be altered by using the ``DIPOLE=thr'' form of the keyword to alter the threshold dipole (`thr') for printing [default: 0.02 D]. #IB.6.4 Matrix Output Keywords#N 0 Two simple examples will be given to illustrate the for- matting of output for operators or basis set transformation matrices using the matrix output keywords of Section B.2.4. For the RHF/3-21G methylamine example of Section A.3, the keyword ``FNHO'' would cause the Fock matrix in the NHO basis to be printed out. Shown below is a reproduction of the first eight columns (out of 28) of this output: NHO Fock matrix: NHO 1 2 3 4 5 6 7 8 ---------- ------- ------- ------- ------- ------- --- ---- ------- ------- 1. C1 ( N2 ) -0.0208 -0.7203 -0.0571 -0.0665 0.0438 0.0672 0.0438 0.0672 2. N2 ( C1 ) -0.7203 -0.3083 -0.0773 -0.0627 0.0835 0.0646 0.0835 0.0646 3. C1 ( H3 ) -0.0571 -0.0773 -0.1394 -0.6758 0.0638 0.0746 0.0638 0.0746 4. H3 ( C1 ) -0.0665 -0.0627 -0.6758 0.1349 0.0740 0.0672 0.0740 0.0672 5. C1 ( H4 ) 0.0438 0.0835 0.0638 0.0740 -0.1466 -0.6761 -0.0548 -0.0759 6. H4 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.6761 0.1541 -0.0759 -0.0697 7. C1 ( H5 ) 0.0438 0.0835 0.0638 0.0740 -0.0548 -0.0759 -0.1466 -0.6761 8. H5 ( C1 ) 0.0672 0.0646 0.0746 0.0672 -0.0759 -0.0697 -0.6761 0.1541 9. N2 ( H6 ) 0.0926 0.1499 0.0240 -0.0113 0.0912 -0.0078 -0.0349 0.0134 10. H6 ( N2 ) 0.1083 0.0826 -0.0010 0.0232 -0.0118 -0.0242 0.0017 -0.0224 July 11, 1995 - 52 - 11. N2 ( H7 ) 0.0926 0.1499 0.0240 -0.0113 -0.0349 0.0134 0.0912 -0.0078 12. H7 ( N2 ) 0.1083 0.0826 -0.0010 0.0232 0.0017 -0.0224 -0.0118 -0.0242 13. C1 (cr) 0.3962 0.4168 0.4400 0.3893 -0.4447 -0.3869 -0.4447 -0.3869 14. N2 (cr) 0.6147 0.7083 0.0039 0.0249 -0.0130 -0.0251 -0.0130 -0.0251 15. N2 (lp) 0.0762 0.0955 -0.1043 0.0254 -0.0386 0.0160 -0.0386 0.0160 16. C1 (ry*) -0.1320 0.0924 0.0705 -0.0815 0.0022 -0.0037 0.0022 -0.0037 17. C1 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0719 -0.0910 -0.0719 0.0910 18. C1 (ry*) -0.1023 0.0764 -0.0643 0.0795 -0.0074 0.0105 -0.0074 0.0105 19. C1 (ry*) 0.0266 -0.0213 0.0019 -0.0057 0.0667 -0.0788 0.0667 -0.0788 20. N2 (ry*) 0.0151 -0.0177 -0.0351 -0.0172 -0.0179 -0.0146 -0.0179 -0.0146 21. N2 (ry*) 0.0000 0.0000 0.0000 0.0000 -0.0158 -0.0249 0.0158 0.0249 22. N2 (ry*) 0.1799 -0.1440 -0.0064 0.0295 0.0038 -0.0289 0.0038 -0.0289 23. N2 (ry*) 0.0183 -0.0136 -0.0051 0.0213 0.0032 -0.0095 0.0032 -0.0095 24. H3 (ry*) 0.0253 -0.0038 0.2834 -0.3497 -0.0248 0.0047 -0.0248 0.0047 25. H4 (ry*) 0.0223 -0.0071 0.0211 -0.0068 -0.2789 0.3553 -0.0227 0.0069 26. H5 (ry*) 0.0223 -0.0071 0.0211 -0.0068 -0.0227 0.0069 -0.2789 0.3553 27. H6 (ry*) 0.0124 0.0172 -0.0067 0.0219 -0.0080 0.0097 0.0057 -0.0222 28. H7 (ry*) 0.0124 0.0172 -0.0067 0.0219 0.0057 -0.0222 -0.0080 0.0097 #T @seg #N 0 The NHO labels on each row identify the atom to which the NHO belongs, and (in parentheses) the atom toward which the hybrid is pointed, if a bond hybrid, or a 1-center label (cr, lp, lp*, or ry*), if a non-bonded hybrid. Thus, ``C 1 (N 2)'' (NHO 1) is the bonding hybrid on C(1) directed toward N(2), ``N 2(lp)'' (NBO 15) is a non-bonded (lone pair) hybrid on N(2), etc. This label allows one to find the precise form of the NHO in the main listing of NBOs. The FNHO matrix shows, for example, that the (1,2) Fock matrix element between the directly interacting NHOs forming the C-N bond NBO is -0.7203 a.u., whereas the (1,9) matrix July 11, 1995 - 53 - element, between the C(1) hybrid pointing toward N(2) and the N(2) hybrid pointing toward H(6), is 0.0926 a.u. 0 As a second example, the keyword ``NBOMO=PVAL'' would print out the core + valence columns of the NBO arr MO transformation, as reproduced below: MOs in the NBO basis: NBO 1 2 3 4 5 6 7 8 ---------- ------- ------- ------- ------- ------- --- ---- ------- ------- 1. C1 - N2 -0.0661 -0.0574 0.6288 -0.1243 0.0000 -0.3239 0.6816 0.0000 2. C1 - H3 -0.0018 -0.0578 0.2061 -0.4716 0.0000 0.7747 0.1386 0.0000 3. C1 - H4 0.0023 0.0579 -0.1836 0.4908 0.3813 0.2304 0.3921 0.5940 4. C1 - H5 0.0023 0.0579 -0.1836 0.4908 -0.3813 0.2304 0.3921 -0.5940 5. N2 - H6 0.0570 0.0000 -0.4742 -0.3567 -0.5937 -0.1954 0.3035 0.3814 6. N2 - H7 0.0570 0.0000 -0.4742 -0.3567 0.5937 -0.1954 0.3035 -0.3814 7. C1 (cr) -0.0021 0.9931 0.0692 -0.0920 0.0000 0.0006 0.0019 0.0000 8. N2 (cr) 0.9935 -0.0019 0.1048 0.0348 0.0000 -0.0131 0.0022 0.0000 9. N2 (lp) 0.0432 -0.0037 -0.1676 -0.1219 0.0000 0.3312 0.1525 0.0000 10. C1 (ry*) -0.0088 -0.0005 0.0114 0.0089 0.0000 -0.0016 -0.0086 0.0000 11. C1 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0109 0.0000 0.0000 -0.0070 12. C1 (ry*) -0.0063 0.0001 -0.0050 -0.0035 0.0000 -0.0030 0.0026 0.0000 13. C1 (ry*) 0.0020 -0.0002 -0.0003 -0.0003 0.0000 -0.0009 0.0002 0.0000 14. N2 (ry*) -0.0041 -0.0003 -0.0006 0.0016 0.0000 0.0192 0.0107 0.0000 15. N2 (ry*) 0.0000 0.0000 0.0000 0.0000 0.0080 0.0000 0.0000 0.0124 16. N2 (ry*) 0.0035 -0.0060 -0.0039 0.0102 0.0000 -0.0023 0.0040 0.0000 17. N2 (ry*) -0.0018 0.0023 -0.0007 0.0013 0.0000 -0.0007 0.0005 0.0000 18. H3 (ry*) -0.0008 -0.0094 -0.0103 0.0146 0.0000 0.0017 -0.0021 0.0000 19. H4 (ry*) -0.0008 -0.0100 -0.0061 0.0119 0.0062 0.0004 -0.0054 -0.0098 20. H5 (ry*) -0.0008 -0.0100 -0.0061 0.0119 -0.0062 0.0004 -0.0054 0.0098 21. H6 (ry*) -0.0052 -0.0013 -0.0147 -0.0018 -0.0027 July 11, 1995 - 54 - -0.0016 -0.0097 -0.0159 22. H7 (ry*) -0.0052 -0.0013 -0.0147 -0.0018 0.0027 -0.0016 -0.0097 0.0159 23. C1 - N2 * -0.0019 -0.0035 -0.0026 0.0025 0.0000 0.0043 0.0049 0.0000 24. C1 - H3 * -0.0013 -0.0024 0.0059 -0.0018 0.0000 -0.0349 -0.0139 0.0000 25. C1 - H4 * 0.0009 0.0028 -0.0138 0.0033 -0.0408 -0.0188 0.0061 0.0148 26. C1 - H5 * 0.0009 0.0028 -0.0138 0.0033 0.0408 -0.0188 0.0061 -0.0148 27. N2 - H6 * -0.0010 0.0051 -0.0047 0.0182 0.0179 0.0122 0.0154 0.0322 28. N2 - H7 * -0.0010 0.0051 -0.0047 0.0182 -0.0179 0.0122 0.0154 -0.0322 NBO 9 10 11 12 13 14 15 ---------- ------- ------- ------- ------- ------- --- ---- ------- 1. C1 - N2 0.1062 -0.0143 0.0006 0.0000 0.0049 0.0000 -0.0061 2. C1 - H3 -0.3343 -0.0044 0.0015 0.0000 0.0007 0.0000 -0.0080 3. C1 - H4 -0.1186 -0.0186 0.0103 0.0258 -0.0048 -0.0272 -0.0104 4. C1 - H5 -0.1186 -0.0186 0.0103 -0.0258 -0.0048 0.0272 -0.0104 5. N2 - H6 -0.1167 -0.0024 -0.0145 -0.0293 -0.0162 -0.0253 0.0040 6. N2 - H7 -0.1167 -0.0024 -0.0145 0.0293 -0.0162 0.0253 0.0040 7. C1 (cr) 0.0037 -0.0134 -0.0082 0.0000 0.0008 0.0000 -0.0008 8. N2 (cr) -0.0189 -0.0055 0.0030 0.0000 -0.0026 0.0000 0.0035 9. N2 (lp) 0.9007 -0.0144 0.0055 0.0000 0.0925 0.0000 0.0130 10. C1 (ry*) -0.0128 -0.0993 0.0553 0.0000 0.0536 0.0000 0.3301 11. C1 (ry*) 0.0000 0.0000 0.0000 0.0836 0.0000 0.1845 0.0000 12. C1 (ry*) -0.0039 -0.0612 0.0748 0.0000 -0.1160 0.0000 0.1213 13. C1 (ry*) -0.0018 0.0936 0.0192 0.0000 0.1022 0.0000 -0.1516 14. N2 (ry*) -0.0086 -0.0232 0.0071 0.0000 -0.0461 0.0000 -0.0178 15. N2 (ry*) 0.0000 0.0000 0.0000 0.0176 0.0000 -0.0856 0.0000 16. N2 (ry*) 0.0006 0.0395 -0.0836 0.0000 0.0221 0.0000 -0.1565 17. N2 (ry*) 0.0003 0.0614 -0.0222 0.0000 0.0114 July 11, 1995 - 55 - 0.0000 0.0584 18. H3 (ry*) -0.0218 -0.2483 -0.2232 0.0000 0.4827 0.0000 0.0001 19. H4 (ry*) 0.0060 -0.1973 -0.3224 -0.3372 -0.2069 -0.2151 -0.0483 20. H5 (ry*) 0.0060 -0.1973 -0.3224 0.3372 -0.2069 0.2151 -0.0483 21. H6 (ry*) 0.0027 -0.2869 0.2132 0.2297 -0.0372 -0.3543 -0.1737 22. H7 (ry*) 0.0027 -0.2869 0.2132 -0.2297 -0.0372 0.3543 -0.1737 23. C1 - N2 * -0.0031 -0.2357 0.2598 0.0000 -0.1096 0.0000 0.8051 24. C1 - H3 * -0.0799 -0.3214 -0.2654 0.0000 0.6687 0.0000 0.1133 25. C1 - H4 * -0.0369 0.2559 0.3890 0.4699 0.2968 0.3193 -0.0477 26. C1 - H5 * -0.0369 0.2559 0.3890 -0.4699 0.2968 -0.3193 -0.0477 27. N2 - H6 * -0.0031 0.4339 -0.3112 -0.3280 0.0474 0.4519 0.2168 28. N2 - H7 * -0.0031 0.4339 -0.3112 0.3280 0.0474 -0.4519 0.2168 #T @seg #N 0 In this transformation matrix, rows correspond to NBOs and columns to MOs (in the ordering used elesewhere in the pro- gram), and each basis NBO is further identified with a row label. The print parameter ``PVAL'' specified that only 15 MOs (the number of core + valence orbitals) should be printed, corresponding to the nine occupied MOs 1-9 and the lowest six virtual MOs 10-15. The matrix allows one to see the composition of each canonical MO in terms of localized bond NBOs. For example, MOs 5 and 8 can be approximately described as hi #d5#u ~= minus 0.594n + 0.381c hi #d8#u ~= 0.381n + 0.594c whereas hi #d6#u is primarily the C-H(3) NBO and hi #d9#u the N lone pair NBO. #IB.6.5 BNDIDX Keyword#N 0 The BNDIDX keyword activates the printing of several types of `bond order' and valency indices, based on different assumptions and formulas, but all having some connection to the NAO/NBO/NLMO formalism. We illustrate these bond order July 11, 1995 - 56 - tables for the example of RHF/3-21G methylamine (Section A.3). 0 The first segment of BNDIDX output shows the Wiberg bond index (the sum of squares of off-diagonal density matrix elements between atoms), as formulated in terms of the NAO basis set: Wiberg bond index matrix in the NAO basis: Atom 1 2 3 4 5 6 7 ---- ------ ------ ------ ------ ------ ------ -- ---- 1. C 0.0000 0.9964 0.9472 0.9394 0.9394 0.0020 0.0020 2. N 0.9964 0.0000 0.0208 0.0052 0.0052 0.8611 0.8611 3. H 0.9472 0.0208 0.0000 0.0004 0.0004 0.0002 0.0002 4. H 0.9394 0.0052 0.0004 0.0000 0.0009 0.0079 0.0005 5. H 0.9394 0.0052 0.0004 0.0009 0.0000 0.0005 0.0079 6. H 0.0020 0.8611 0.0002 0.0079 0.0005 0.0000 0.0003 7. H 0.0020 0.8611 0.0002 0.0005 0.0079 0.0003 0.0000 Wiberg bond index, Totals by atom: Atom 1 ---- ------ 1. C 3.8265 2. N 2.7499 3. H 0.9691 4. H 0.9544 5. H 0.9544 6. H 0.8720 7. H 0.8720 #T @seg #N 0 This index is intrinsically a positive quantity, making no distinction between net bonding or antibonding character of the density matrix elements. 0 The next segment tabulates the ``overlap-weighted NAO bond order,'' as shown below: July 11, 1995 - 57 - Atom-atom overlap-weighted NAO bond order: Atom 1 2 3 4 5 6 7 ---- ------ ------ ------ ------ ------ ------ -- ---- 1. C 0.0000 0.7815 0.7614 0.7633 0.7633 -0.0103 -0.0103 2. N 0.7815 0.0000 -0.0225 -0.0097 -0.0097 0.6688 0.6688 3. H 0.7614 -0.0225 0.0000 -0.0039 -0.0039 -0.0019 -0.0019 4. H 0.7633 -0.0097 -0.0039 0.0000 0.0024 0.0038 -0.0032 5. H 0.7633 -0.0097 -0.0039 0.0024 0.0000 -0.0032 0.0038 6. H -0.0103 0.6688 -0.0019 0.0038 -0.0032 0.0000 -0.0069 7. H -0.0103 0.6688 -0.0019 -0.0032 0.0038 -0.0069 0.0000 Atom-atom overlap-weighted NAO bond order, Totals by atom: Atom 1 ---- ------ 1. C 3.0488 2. N 2.0772 3. H 0.7273 4. H 0.7527 5. H 0.7527 6. H 0.6503 7. H 0.6503 #T @seg #N 0 This index corresponds to a sum of off-diagonal NAO den- sity matrix elements between atoms, each multiplied by the corresponding PNAO overlap integral. 0 Another type of BNDIDX output appears if the NLMO keyword is included, summarizing a formal ``NLMO/NPA bond order'' that can be associated with each NLMO: Individual LMO bond orders greater than 0.002 in magnitude, with the overlap between the hybrids in the NLMO given: Atom I / Atom J / NLMO / Bond Order / Hybrid Overlap / 1 2 1 0.8007741 0.7314361 1 2 5 0.0022694 0.1796696 1 2 6 0.0022694 0.1796696 July 11, 1995 - 58 - 1 2 9 0.0088061 0.3053730 1 3 2 0.8051647 0.7862263 1 3 9 -0.0088061 -0.5762575 1 4 3 0.7772179 0.7874312 1 4 5 -0.0022694 -0.5396947 1 5 4 0.7772179 0.7874312 1 5 6 -0.0022694 -0.5396947 1 6 3 -0.0031652 -0.0920524 1 6 5 0.0022694 0.0852070 1 7 4 -0.0031652 -0.0920524 1 7 6 0.0022694 0.0852070 2 3 9 -0.0097841 -0.0930204 2 4 5 -0.0027437 -0.0701717 2 5 6 -0.0027437 -0.0701717 2 6 5 0.6358512 0.7286061 2 7 6 0.6358512 0.7286061 4 6 3 0.0031652 0.0429202 4 6 5 0.0027437 0.0399352 5 7 4 0.0031652 0.0429202 5 7 6 0.0027437 0.0399352 #T @seg #NThis NLMO bond order is calculated by the method described by A. E. Reed and P. v.R. Schleyer [#IInorg. Chem. #B27#N, 3969-3987 (1988); #IJ. Am. Chem. Soc.#N (to be published)], based on the shared occupancies and hybrid overlaps (last column) of NAOs composing the NLMO. In the above table, for example, NLMO 1 occurs only in the first line, contributing a bond of formal order 0.801 between C(1) and N(2), whereas NLMO 9 (the nitrogen lone pair) contributes a slight strengthening (+0.0088) of the C(1)-N(2) bond, a weakening (-0.0088) of the vicinal C(1)-H(3) bond, and a slight nega- tive bond order (-0.0098) between atoms N(2), H(3). 0 The NLMO bond order contributions are then summed for each atom pair to give the net NLMO/NPA bond orders shown below: Atom-Atom Net Linear NLMO/NPA Bond Orders: Atom 1 2 3 4 5 6 7 ---- ------ ------ ------ ------ ------ ------ -- ---- 1. C 0.0000 0.8174 0.7960 0.7732 0.7732 -0.0013 -0.0013 2. N 0.8174 0.0000 -0.0104 -0.0030 -0.0030 0.6337 0.6337 3. H 0.7960 -0.0104 0.0000 -0.0020 -0.0020 0.0001 0.0001 4. H 0.7732 -0.0030 -0.0020 0.0000 0.0020 0.0062 July 11, 1995 - 59 - 0.0000 5. H 0.7732 -0.0030 -0.0020 0.0020 0.0000 0.0000 0.0062 6. H -0.0013 0.6337 0.0001 0.0062 0.0000 0.0000 -0.0001 7. H -0.0013 0.6337 0.0001 0.0000 0.0062 -0.0001 0.0000 #T @seg #NFor example, the table attributes a formal bond order of 0.8174 to the C(1)-N(2) bond of methylamine, the highest bond order in this molecule. (The higher value for C(1)- H(3) than for the other two CH bonds reflects an unsatisfac- tory aspect of this method of assessing bond order.) 0 These bond indices are based on different assumptions, and each has certain advantages and disadvantages. #ICaveat emptor!#N #IB.6.6 RESONANCE Keyword: Benzene#N 0 When NBO analysis is performed on a wavefunction that can- not be satisfactorily localized [i.e., in which one or more NBOs of the natural Lewis structure fail to achieve the threshold occupancy (1.90) for a satisfactory `pair'], the NBO program aborts with a message indicating that the wavefunction is unsuitable for localized analysis. For example, when benzene (RHF/STO-3G level, idealized Pople- Gordon geometry) is treated by the NBO program in default mode, one obtains the output: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44 2(2) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44 ---------- ------------------------------------------------------------------- Only strongly delocalized resonance structures can be found. The default procedure is to abort the NBO search. #T @seg July 11, 1995 - 60 - 0 #NWhen the RESONANCE keyword is activated for this same example, one obtains a summary of NBO search cycles as shown below: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44 2(2) 1.90 38.87476 3.12524 6 12 0 3 3 3 0.44 3(1) 1.80 38.87476 3.12524 6 12 0 3 3 3 0.44 4(2) 1.80 38.87476 3.12524 6 12 0 3 3 3 0.44 5(1) 1.70 38.87476 3.12524 6 12 0 3 3 3 0.44 6(2) 1.70 38.87476 3.12524 6 12 0 3 3 3 0.44 7(1) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44 8(2) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44 9(1) 1.50 40.87476 1.12524 6 15 0 0 0 3 0.44 10(2) 1.50 40.87476 1.12524 6 15 0 0 0 3 0.44 11(1) 1.60 40.87476 1.12524 6 15 0 0 0 3 0.44 ---------- ------------------------------------------------------------------- Structure accepted: RESONANCE keyword permits strongly delo- calized structure #T @seg #N 0 As this table shows, the occupancy threshold was succes- sively lowered from 1.90 to 1.50 by 0.1e for each cycle, and the NBO search repeated. In this case, the `best' Lewis structure (lowest overall non-Lewis occupancy, 1.12524e) was found in cycle 7, with occupancy thresh#|old 1.60e. The NBO program therefore reset the thresh#|old to this value and calculated the set of NBOs corresponding to this `best' Lewis structure, as shown below: (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- July 11, 1995 - 61 - ----- --------------------------------------------------------------------- 1. (1.98940) BD ( 1) C 1- C 2 ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.8109 0.0097 0.0000 ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.8109 0.0097 0.0000 2. (1.98940) BD ( 1) C 1- C 6 ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.4138 -0.6974 0.0000 ( 50.00%) 0.7071* C 6 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.3971 0.7071 0.0000 3. (1.66667) BD ( 2) C 1- C 6 ( 50.00%) 0.7071* C 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) 0.7071* C 6 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 4. (1.98977) BD ( 1) C 1- H 7 ( 51.73%) 0.7193* C 1 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 0.4137 0.7166 0.0000 ( 48.27%) 0.6947* H 7 s(100.00%) 1.0000 5. (1.98940) BD ( 1) C 2- C 3 ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.4138 -0.6974 0.0000 ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.3971 0.7071 0.0000 6. (1.66667) BD ( 2) C 2- C 3 ( 50.00%) 0.7071* C 2 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) 0.7071* C 3 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 July 11, 1995 - 62 - 7. (1.98977) BD ( 1) C 2- H 8 ( 51.73%) 0.7193* C 2 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 -0.4137 0.7166 0.0000 ( 48.27%) 0.6947* H 8 s(100.00%) 1.0000 8. (1.98940) BD ( 1) C 3- C 4 ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.3971 -0.7071 0.0000 ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.4138 0.6974 0.0000 9. (1.98977) BD ( 1) C 3- H 9 ( 51.73%) 0.7193* C 3 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 -0.8275 0.0000 0.0000 ( 48.27%) 0.6947* H 9 s(100.00%) 1.0000 10. (1.66667) BD ( 2) C 4- C 5 ( 50.00%) 0.7071* C 4 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) 0.7071* C 5 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 11. (1.98940) BD ( 1) C 4- C 5 ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.8109 -0.0097 0.0000 ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.8109 -0.0097 0.0000 12. (1.98977) BD ( 1) C 4- H10 ( 51.73%) 0.7193* C 4 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 -0.4137 -0.7166 0.0000 ( 48.27%) 0.6947* H10 s(100.00%) 1.0000 13. (1.98940) BD ( 1) C 5- C 6 ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.4138 0.6974 0.0000 ( 50.00%) 0.7071* C 6 s( 34.23%)p 1.92( July 11, 1995 - 63 - 65.77%) 0.0000 0.5851 -0.3971 -0.7071 0.0000 14. (1.98977) BD ( 1) C 5- H11 ( 51.73%) 0.7193* C 5 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 0.4137 -0.7166 0.0000 ( 48.27%) 0.6947* H11 s(100.00%) 1.0000 15. (1.98977) BD ( 1) C 6- H12 ( 51.73%) 0.7193* C 6 s( 31.53%)p 2.17( 68.47%) 0.0000 0.5615 0.8275 0.0000 0.0000 ( 48.27%) 0.6947* H12 s(100.00%) 1.0000 16. (1.99995) CR ( 1) C 1 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 17. (1.99995) CR ( 1) C 2 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 18. (1.99995) CR ( 1) C 3 s(100.00%) 1.0000 0.0000 -0.0001 0.0000 0.0000 19. (1.99995) CR ( 1) C 4 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 20. (1.99995) CR ( 1) C 5 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 21. (1.99995) CR ( 1) C 6 s(100.00%) 1.0000 0.0000 0.0001 0.0000 0.0000 22. (0.01077) BD*( 1) C 1- C 2 ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.8109 0.0097 0.0000 ( 50.00%) -0.7071* C 2 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.8109 0.0097 0.0000 23. (0.01077) BD*( 1) C 1- C 6 ( 50.00%) 0.7071* C 1 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.4138 -0.6974 0.0000 ( 50.00%) -0.7071* C 6 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.3971 0.7071 0.0000 24. (0.33333) BD*( 2) C 1- C 6 July 11, 1995 - 64 - ( 50.00%) 0.7071* C 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) -0.7071* C 6 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 25. (0.01011) BD*( 1) C 1- H 7 ( 48.27%) 0.6947* C 1 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 -0.4137 -0.7166 0.0000 ( 51.73%) -0.7193* H 7 s(100.00%) -1.0000 26. (0.01077) BD*( 1) C 2- C 3 ( 50.00%) 0.7071* C 2 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.4138 -0.6974 0.0000 ( 50.00%) -0.7071* C 3 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.3971 0.7071 0.0000 27. (0.33333) BD*( 2) C 2- C 3 ( 50.00%) 0.7071* C 2 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) -0.7071* C 3 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 28. (0.01011) BD*( 1) C 2- H 8 ( 48.27%) 0.6947* C 2 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 0.4137 -0.7166 0.0000 ( 51.73%) -0.7193* H 8 s(100.00%) -1.0000 29. (0.01077) BD*( 1) C 3- C 4 ( 50.00%) 0.7071* C 3 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.3971 -0.7071 0.0000 ( 50.00%) -0.7071* C 4 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.4138 0.6974 0.0000 30. (0.01011) BD*( 1) C 3- H 9 ( 48.27%) 0.6947* C 3 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 0.8275 0.0000 0.0000 ( 51.73%) -0.7193* H 9 s(100.00%) July 11, 1995 - 65 - -1.0000 31. (0.33333) BD*( 2) C 4- C 5 ( 50.00%) 0.7071* C 4 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 ( 50.00%) -0.7071* C 5 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 1.0000 32. (0.01077) BD*( 1) C 4- C 5 ( 50.00%) 0.7071* C 4 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.8109 -0.0097 0.0000 ( 50.00%) -0.7071* C 5 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.8109 -0.0097 0.0000 33. (0.01011) BD*( 1) C 4- H10 ( 48.27%) 0.6947* C 4 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 0.4137 0.7166 0.0000 ( 51.73%) -0.7193* H10 s(100.00%) -1.0000 34. (0.01077) BD*( 1) C 5- C 6 ( 50.00%) 0.7071* C 5 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 0.4138 0.6974 0.0000 ( 50.00%) -0.7071* C 6 s( 34.23%)p 1.92( 65.77%) 0.0000 0.5851 -0.3971 -0.7071 0.0000 35. (0.01011) BD*( 1) C 5- H11 ( 48.27%) 0.6947* C 5 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 -0.4137 0.7166 0.0000 ( 51.73%) -0.7193* H11 s(100.00%) -1.0000 36. (0.01011) BD*( 1) C 6- H12 ( 48.27%) 0.6947* C 6 s( 31.53%)p 2.17( 68.47%) 0.0000 -0.5615 -0.8275 0.0000 0.0000 ( 51.73%) -0.7193* H12 s(100.00%) -1.0000 #T @seg July 11, 1995 - 66 - #N 0 As one can see from this table, the set of NBOs obtained by the program corresponds to one of the two equivalent Kekulcute e structures, with reasonably well localized gma #dCC#u and gma #dCH#u NBOs (1.98940 and 1.98977 electrons, respectively), but three severely depleted i #dCC#u bonds (1.66667e) and corresponding high occupancy i *#<#dCC#u antibonds (0.33333e). Other sections of the NBO output (not shown) will similarly exhibit the sharp distinc- tions between benzene and more `typical' non-aromatic com- pounds. |<<__________________________ #-#BWARNING#N#+ If you attempt to analyze an open-shell wavefunction with an ESS method that produces only the ``spinless'' (spin- averaged) density matrix, rather than the separate density matrices for lpha and h job will likely abort, as in the default benzene example. However, you should #Inot#N use the RESONANCE keyword to bypass this abort! NBO analysis of an open-shell spinless density matrix is a fundamental misuse of the program. #IB.6.7 NOBOND Keyword#N 0 The NOBOND keyword forces the NBO program to analyze the wavefunction in terms of 1-center functions only, thus forc- ing a description of the bonding in terms of atomic or ionic hybrids. The modifications of NBO output that result from activating this keyword can be illustrated for the HF molecule (RHF/3-21G//RHF/3-21G level). This molecule might be described in terms of a polar covalent H-F bond or in terms of ionic H#u+#dhsp F#uminus #d interactions. 0 The default NBO analysis of this example is shown below: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 9.99942 0.00058 1 1 0 3 0 0 0.00 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals -------------------------------------------------------- July 11, 1995 - 67 - Core 1.99994 ( 99.997% of 2) Valence Lewis 7.99948 ( 99.994% of 8) ================== ============================ Total Lewis 9.99942 ( 99.994% of 10) ----------------------------------------------------- Valence non-Lewis 0.00000 ( 0.000% of 10) Rydberg non-Lewis 0.00058 ( 0.006% of 10) ================== ============================ Total non-Lewis 0.00058 ( 0.006% of 10) ----- --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (2.00000) BD ( 1) F 1- H 2 ( 75.22%) 0.8673* F 1 s( 16.31%)p 5.13( 83.69%) 0.0000 0.4036 0.0158 0.0000 0.0000 0.0000 0.0000 0.9148 0.0001 ( 24.78%) 0.4978* H 2 s(100.00%) 1.0000 0.0000 2. (1.99994) CR ( 1) F 1 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3. (2.00000) LP ( 1) F 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 1.0000 -0.0013 0.0000 0.0000 0.0000 0.0000 4. (2.00000) LP ( 2) F 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 -0.0013 0.0000 0.0000 5. (1.99948) LP ( 3) F 1 s( 83.71%)p 0.19( 16.29%) 0.0000 0.9149 -0.0052 0.0000 0.0000 0.0000 0.0000 -0.4036 -0.0062 6. (0.00002) RY*( 1) F 1 s( 0.00%)p 1.00(100.00%) 7. (0.00000) RY*( 2) F 1 s( 0.00%)p 1.00(100.00%) 8. (0.00000) RY*( 3) F 1 s( 0.00%)p 1.00(100.00%) 9. (0.00000) RY*( 4) F 1 s( 99.97%)p 0.00( July 11, 1995 - 68 - 0.03%) 10. (0.00056) RY*( 1) H 2 s(100.00%) 0.0000 1.0000 11. (0.00000) BD*( 1) F 1- H 2 ( 24.78%) 0.4978* F 1 s( 16.31%)p 5.13( 83.69%) ( 75.22%) -0.8673* H 2 s(100.00%) #T @seg #N As the output shows, default NBO analysis leads to a polar covalent description of HF. The gma #dHF#u bond, NBO 1, is formed from a #Ip#N-rich (#Isp#N#u5.13#d) hybrid on F and the 1#Is#N AO on H, strongly polarized (about 75.22%) toward F. This provides a satisfactory Lewis structure, describing 99.994% of the total electron density. 0 When the NOBOND keyword is activated to bypass the search for 2-center bonds, the NBO output is modified as shown below: /NOBOND / : No two-center NBO search NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.00 9.50378 0.49622 1 0 0 4 0 1 0.75 ---------- ------------------------------------------------------------------- Structure accepted: Search for bonds prevented by NOBOND keyword -------------------------------------------------------- Core 1.99993 ( 99.997% of 2) Valence Lewis 7.50385 ( 93.798% of 8) ================== ============================ Total Lewis 9.50378 ( 95.038% of 10) ----------------------------------------------------- Valence non-Lewis 0.49564 ( 4.956% of 10) Rydberg non-Lewis 0.00058 ( 0.006% of 10) ================== ============================ Total non-Lewis 0.49622 ( 4.962% of 10) ----- July 11, 1995 - 69 - --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (1.99993) CR ( 1) F 1 s(100.00%)p 0.00( 0.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 2. (2.00000) LP ( 1) F 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 1.0000 -0.0013 0.0000 0.0000 0.0000 0.0000 3. (2.00000) LP ( 2) F 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 -0.0013 0.0000 0.0000 4. (1.99948) LP ( 3) F 1 s( 83.71%)p 0.19( 16.29%) 0.0000 0.9149 -0.0052 0.0000 0.0000 0.0000 0.0000 -0.4036 -0.0062 5. (1.50436) LP ( 4) F 1 s( 16.31%)p 5.13( 83.69%) -0.0001 0.4036 0.0158 0.0000 0.0000 0.0000 0.0000 0.9148 0.0001 6. (0.49564) LP*( 1) H 2 s(100.00%) 1.0000 0.0000 7. (0.00002) RY*( 1) F 1 s( 0.00%)p 1.00(100.00%) 8. (0.00000) RY*( 2) F 1 s( 0.00%)p 1.00(100.00%) 9. (0.00000) RY*( 3) F 1 s( 0.00%)p 1.00(100.00%) 10. (0.00000) RY*( 4) F 1 s( 99.97%)p 0.00( 0.03%) 11. (0.00056) RY*( 1) H 2 s(100.00%) 0.0000 1.0000 #T @seg #N 0 In this case, the NBO output indicates a rather poor Lewis July 11, 1995 - 70 - structure (4.962% non-Lewis density), with a severely depleted F#uminus #d lone pair (NBO 5, the #Isp#N#u5.13#d hybrid) and significant occupancy (about 0.496e) in the `empty' H#u+#d 1#Is#N orbital (NBO 6) of the cation. The NOBOND comparison would therefore indicate the superiority of a polar covalent description in this case. #IB.6.8 3CBOND Keyword: Diborane#N 0 When the default NBO analysis is applied to diborane or related electron-deficient compounds, there is a dramatic failure to represent the electronic distribution in terms of 1- and 2-center functions only. For example, for B#d2#uH#d6#u at the RHF/3-21G//RHF/3-21G level, the default NBO search (if the RESONANCE keyword is activated to allow NBO printout) returns a fractured set of 4 units (two BH#d2#u#u+#d and two H#uminus #d fragments), with about 2.13 electrons unaccounted for (~15% non-Lewis occupancy), symp- tomatic of general breakdown of the conventional Lewis structure representation. 0 However, when the NBO search is extended to 3-center bonds by activating the 3CBOND keyword, one obtains the NBO output shown below: /3CBOND / : Search for 3-center bonds NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 15.94335 0.05665 2 4 2 0 0 0 0.15 2(2) 1.90 15.94335 0.05665 2 4 2 0 0 0 0.15 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals WARNING: 1 low occupancy (<1.9990e) core orbital found on B 1 1 low occupancy (<1.9990e) core orbital found on B 2 -------------------------------------------------------- Core 3.99702 ( 99.925% of 4) Valence Lewis 11.94633 ( 99.553% of 12) ================== ============================ Total Lewis 15.94335 ( 99.646% of 16) July 11, 1995 - 71 - ----------------------------------------------------- Valence non-Lewis 0.04565 ( 0.285% of 16) Rydberg non-Lewis 0.01100 ( 0.069% of 16) ================== ============================ Total non-Lewis 0.05665 ( 0.354% of 16) ----- --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (1.98467) 3C ( 1) B 1- B 2- H 3 ( 26.43%) 0.5141* B 1 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 -0.7067 -0.0245 0.0000 0.0000 0.5657 -0.0007 ( 26.43%) 0.5141* B 2 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 -0.7067 -0.0245 0.0000 0.0000 -0.5657 0.0007 ( 47.14%) 0.6866* H 3 s(100.00%) 1.0000 0.0066 2. (1.98467) 3C ( 1) B 1- B 2- H 4 ( 26.43%) 0.5141* B 1 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 0.7067 0.0245 0.0000 0.0000 0.5657 -0.0007 ( 26.43%) 0.5141* B 2 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 0.7067 0.0245 0.0000 0.0000 -0.5657 0.0007 ( 47.14%) 0.6866* H 4 s(100.00%) 1.0000 0.0066 3. (1.99425) BD ( 1) B 1- H 6 ( 48.80%) 0.6985* B 1 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 0.7067 -0.0243 -0.4239 -0.0222 ( 51.20%) 0.7156* H 6 s(100.00%) 1.0000 0.0004 4. (1.99425) BD ( 1) B 1- H 7 ( 48.80%) 0.6985* B 1 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 July 11, 1995 - 72 - -0.0061 0.0000 0.0000 -0.7067 0.0243 -0.4239 -0.0222 ( 51.20%) 0.7156* H 7 s(100.00%) 1.0000 0.0004 5. (1.99425) BD ( 1) B 2- H 5 ( 48.80%) 0.6985* B 2 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 -0.7067 0.0243 0.4239 0.0222 ( 51.20%) 0.7156* H 5 s(100.00%) 1.0000 0.0004 6. (1.99425) BD ( 1) B 2- H 8 ( 48.80%) 0.6985* B 2 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 0.7067 -0.0243 0.4239 0.0222 ( 51.20%) 0.7156* H 8 s(100.00%) 1.0000 0.0004 7. (1.99851) CR ( 1) B 1 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0007 0.0000 8. (1.99851) CR ( 1) B 2 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0000 9. (0.00147) RY*( 1) B 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0344 0.9994 0.0000 0.0000 10. (0.00080) RY*( 2) B 1 s( 4.02%)p23.87( 95.98%) 0.0000 0.0245 0.1990 0.0000 0.0000 0.0000 0.0000 -0.0214 0.9795 11. (0.00002) RY*( 3) B 1 s( 96.01%)p 0.04( 3.99%) 12. (0.00000) RY*( 4) B 1 s( 0.00%)p 1.00(100.00%) 13. (0.00147) RY*( 1) B 2 s( 0.00%)p 1.00(100.00%) July 11, 1995 - 73 - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0344 0.9994 0.0000 0.0000 14. (0.00080) RY*( 2) B 2 s( 4.02%)p23.87( 95.98%) 0.0000 0.0245 0.1990 0.0000 0.0000 0.0000 0.0000 0.0214 -0.9795 15. (0.00002) RY*( 3) B 2 s( 96.01%)p 0.04( 3.99%) 16. (0.00000) RY*( 4) B 2 s( 0.00%)p 1.00(100.00%) 17. (0.00181) RY*( 1) H 3 s(100.00%) -0.0066 1.0000 18. (0.00181) RY*( 1) H 4 s(100.00%) -0.0066 1.0000 19. (0.00070) RY*( 1) H 5 s(100.00%) -0.0004 1.0000 20. (0.00070) RY*( 1) H 6 s(100.00%) -0.0004 1.0000 21. (0.00070) RY*( 1) H 7 s(100.00%) -0.0004 1.0000 22. (0.00070) RY*( 1) H 8 s(100.00%) -0.0004 1.0000 23. (0.01464) 3C*( 1) B 1- B 2- H 3 ( 23.57%) 0.4855* B 1 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 -0.7067 -0.0245 0.0000 0.0000 0.5657 -0.0007 ( 23.57%) -0.4855* B 2 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 0.7067 0.0245 0.0000 0.0000 0.5657 -0.0007 ( 52.86%) -0.7271* H 3 s(100.00%) 1.0000 0.0066 24. (0.00026) 3C*( 1) B 1- B 2- H 3 ( 50.00%) 0.7071* B 1 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 0.7067 0.0245 0.0000 0.0000 -0.5657 0.0007 ( 50.00%) -0.7071* B 2 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 0.7067 0.0245 0.0000 0.0000 0.5657 -0.0007 ( 0.00%) 0.0000* H 3 s( 0.00%) July 11, 1995 - 74 - 0.0000 0.0000 25. (0.01464) 3C*( 1) B 1- B 2- H 4 ( 23.57%) 0.4855* B 1 s( 18.00%)p 4.55( 82.00%) 0.0005 0.4241 0.0124 0.7067 0.0245 0.0000 0.0000 0.5657 -0.0007 ( 23.57%) -0.4855* B 2 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 -0.7067 -0.0245 0.0000 0.0000 0.5657 -0.0007 ( 52.86%) -0.7271* H 4 s(100.00%) 1.0000 0.0066 26. (0.00026) 3C*( 1) B 1- B 2- H 4 ( 50.00%) 0.7071* B 1 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 -0.7067 -0.0245 0.0000 0.0000 -0.5657 0.0007 ( 50.00%) -0.7071* B 2 s( 18.00%)p 4.55( 82.00%) -0.0005 -0.4241 -0.0124 -0.7067 -0.0245 0.0000 0.0000 0.5657 -0.0007 ( 0.00%) 0.0000* H 4 s( 0.00%) 0.0000 0.0000 27. (0.00396) BD*( 1) B 2- H 5 ( 51.20%) 0.7156* B 2 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 -0.7067 0.0243 0.4239 0.0222 ( 48.80%) -0.6985* H 5 s(100.00%) 1.0000 0.0004 28. (0.00396) BD*( 1) B 2- H 8 ( 51.20%) 0.7156* B 2 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 0.7067 -0.0243 0.4239 0.0222 ( 48.80%) -0.6985* H 8 s(100.00%) 1.0000 0.0004 29. (0.00396) BD*( 1) B 1- H 6 ( 51.20%) 0.7156* B 1 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 July 11, 1995 - 75 - 0.7067 -0.0243 -0.4239 -0.0222 ( 48.80%) -0.6985* H 6 s(100.00%) 1.0000 0.0004 30. (0.00396) BD*( 1) B 1- H 7 ( 51.20%) 0.7156* B 1 s( 31.98%)p 2.13( 68.02%) -0.0002 0.5655 -0.0061 0.0000 0.0000 -0.7067 0.0243 -0.4239 -0.0222 ( 48.80%) -0.6985* H 7 s(100.00%) 1.0000 0.0004 #T @seg #N 0 The resulting NBO Lewis structure has improved signifi- cantly [only 0.057e (0.35%) non-Lewis occupancy]. The structure includes the expected 3-center B-H-B bonds (NBOs 1, 2), each with reasonably high occupancy (1.9847e). Each 3-c bond is composed of #Ip#N-rich (#Isp#N#u4.55#d) boron hybrids and the hydrogen 1#Is#N NAO, with about 47.14% of the orbital density on the central hydrogen. Note that each 3-center bond NBO is associated with #Itwo#N 3-c antibond NBOs (viz., NBOs 23, 24 for the first 3-c bond, NBO 1), which contribute in distinct ways to delocalization interac- tions. Of course, the accuracy of #Iany#N molecular Lewis structure might be improved slightly by extending the NBO search to 3-center bonds (thus allowing greater variational flexibility to maximize occupancy), but this example illus- trates the kind of #Iqualitative#N improvement that indi- cates when 3-center bonds are needed in the zeroth-order picture of the bonding. 0 Note that the NBO 3-c label may frequently have the wrong `connectivity' (as in the present case, e.g., where ``B 1- B 2- H 3'' is written instead of the more reasonable ``B 1- H 3- B 2''). This is a consequence of the fact that the NBO algorithms have no inkling of the positions of the atoms in space, and thus of which label is more `reasonable.' #IB.6.9 NBO Directed Search ($CHOOSE Keylist)#N 0 To illustrate the $CHOOSE keylist for a directed NBO search, we again make use of the methylamine example (Sec- tion A.3). The vicinal #In#N#dN#u arr gma *#<#dCH#u delo- calization, to which attention has been repeatedly called in the examples, may be associated, in resonance theory terms, with the ``double-bond, no-bond'' resonance structure shown below: W10R'#-0hsp H#d4#u#+hsp '// D11R'H#d5#u'//BD3'N#d2#u#<#+#++#-#- July 11, 1995 - 76 - '//W5R'H#d6#u'//D4R'H#d7#u'>> nobond To investigate the suitability of this resonance structure for describing the methylamine wavefunction, we would specify the $CHOOSE keylist (Section B.4) as follows: #T $CHOOSE !double-bond, no-bond resonance LONE 3 1 END BOND S 1 4 S 1 5 D 1 2 S 2 6 S 2 7 END $END #NWhen this is included in the input file, the NBO program produces the output shown below: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 16.66741 1.33259 2 6 0 1 1 2 0.95 ---------- ------------------------------------------------------------------- Structure accepted: NBOs selected via the $CHOOSE keylist WARNING: 1 low occupancy (<1.9990e) core orbital found on C 1 -------------------------------------------------------- Core 3.99853 ( 99.963% of 4) Valence Lewis 12.66888 ( 90.492% of 14) ================== ============================ Total Lewis 16.66741 ( 92.597% of 18) ----------------------------------------------------- Valence non-Lewis 1.30491 ( 7.249% of 18) Rydberg non-Lewis 0.02768 ( 0.154% of 18) ================== ============================ Total non-Lewis 1.33259 ( 7.403% of 18) ----- --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (1.95945) BD ( 1) C 1- N 2 ( 7.66%) 0.2768* C 1 s( 0.63%)p99.99( 99.37%) -0.0001 -0.0770 July 11, 1995 - 77 - -0.0186 0.5107 -0.0551 0.8520 -0.0632 0.0000 0.0000 ( 92.34%) 0.9609* N 2 s( 19.31%)p 4.18( 80.69%) 0.0000 0.4395 -0.0001 -0.1175 -0.0067 0.8905 -0.0110 0.0000 0.0000 2. (1.93778) BD ( 2) C 1- N 2 ( 39.14%) 0.6256* C 1 s( 36.80%)p 1.72( 63.20%) -0.0004 -0.6055 -0.0371 -0.7047 -0.0632 0.3594 -0.0471 0.0000 0.0000 ( 60.86%) 0.7801* N 2 s( 19.33%)p 4.17( 80.67%) -0.0001 -0.4396 0.0011 0.8364 -0.0016 0.3271 -0.0137 0.0000 0.0000 3. (1.98365) BD ( 1) C 1- H 4 ( 61.02%) 0.7811* C 1 s( 31.10%)p 2.22( 68.90%) 0.0001 0.5577 0.0006 -0.3480 0.0095 0.2603 0.0094 0.7070 -0.0103 ( 38.98%) 0.6244* H 4 s(100.00%) 1.0000 0.0008 4. (1.98365) BD ( 1) C 1- H 5 ( 61.02%) 0.7811* C 1 s( 31.10%)p 2.22( 68.90%) 0.0001 0.5577 0.0006 -0.3480 0.0095 0.2603 0.0094 -0.7070 0.0103 ( 38.98%) 0.6244* H 5 s(100.00%) 1.0000 0.0008 5. (1.99491) BD ( 1) N 2- H 6 ( 68.46%) 0.8274* N 2 s( 30.67%)p 2.26( 69.33%) 0.0000 0.5538 0.0005 0.3785 0.0165 -0.2232 0.0044 -0.7070 -0.0093 ( 31.54%) 0.5616* H 6 s(100.00%) 1.0000 0.0031 6. (1.99491) BD ( 1) N 2- H 7 ( 68.46%) 0.8274* N 2 s( 30.67%)p 2.26( 69.33%) 0.0000 0.5538 July 11, 1995 - 78 - 0.0005 0.3785 0.0165 -0.2232 0.0044 0.7070 0.0093 ( 31.54%) 0.5616* H 7 s(100.00%) 1.0000 0.0031 7. (1.99900) CR ( 1) C 1 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0003 0.0000 -0.0001 0.0000 0.0002 0.0000 0.0000 0.0000 8. (1.99953) CR ( 1) N 2 s(100.00%)p 0.00( 0.00%) 1.0000 -0.0001 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 9. (0.81453) LP ( 1) H 3 s(100.00%) 1.0000 0.0000 10. (0.01893) RY*( 1) C 1 s( 10.61%)p 8.42( 89.39%) 0.0000 -0.0737 0.3173 -0.0090 0.7223 0.0971 0.6021 0.0000 0.0000 11. (0.00034) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0146 0.9999 12. (0.00025) RY*( 3) C 1 s( 57.37%)p 0.74( 42.63%) 0.0000 -0.0012 0.7575 -0.0176 0.1886 -0.0071 -0.6248 0.0000 0.0000 13. (0.00002) RY*( 4) C 1 s( 32.38%)p 2.09( 67.62%) 14. (0.00117) RY*( 1) N 2 s( 1.48%)p66.74( 98.52%) 0.0000 -0.0067 0.1213 0.0062 0.0380 0.0166 0.9917 0.0000 0.0000 15. (0.00044) RY*( 2) N 2 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0132 0.9999 16. (0.00038) RY*( 3) N 2 s( 33.41%)p 1.99( 66.59%) July 11, 1995 - 79 - 0.0000 0.0133 0.5779 0.0087 -0.8150 -0.0120 -0.0392 0.0000 0.0000 17. (0.00002) RY*( 4) N 2 s( 65.14%)p 0.54( 34.86%) 18. (0.00177) RY*( 1) H 3 s(100.00%) 0.0000 1.0000 19. (0.00096) RY*( 1) H 4 s(100.00%) -0.0008 1.0000 20. (0.00096) RY*( 1) H 5 s(100.00%) -0.0008 1.0000 21. (0.00122) RY*( 1) H 6 s(100.00%) -0.0031 1.0000 22. (0.00122) RY*( 1) H 7 s(100.00%) -0.0031 1.0000 23. (1.02290) BD*( 1) C 1- N 2 ( 92.34%) 0.9609* C 1 s( 0.63%)p99.99( 99.37%) -0.0001 -0.0770 -0.0186 0.5107 -0.0551 0.8520 -0.0632 0.0000 0.0000 ( 7.66%) -0.2768* N 2 s( 19.31%)p 4.18( 80.69%) 0.0000 0.4395 -0.0001 -0.1175 -0.0067 0.8905 -0.0110 0.0000 0.0000 24. (0.22583) BD*( 2) C 1- N 2 ( 60.86%) 0.7801* C 1 s( 36.80%)p 1.72( 63.20%) -0.0004 -0.6055 -0.0371 -0.7047 -0.0632 0.3594 -0.0471 0.0000 0.0000 ( 39.14%) -0.6256* N 2 s( 19.33%)p 4.17( 80.67%) -0.0001 -0.4396 0.0011 0.8364 -0.0016 0.3271 -0.0137 0.0000 0.0000 25. (0.01415) BD*( 1) C 1- H 4 ( 38.98%) 0.6244* C 1 s( 31.10%)p 2.22( 68.90%) -0.0001 -0.5577 -0.0006 0.3480 -0.0095 -0.2603 -0.0094 -0.7070 0.0103 ( 61.02%) -0.7811* H 4 s(100.00%) -1.0000 -0.0008 26. (0.01415) BD*( 1) C 1- H 5 ( 38.98%) 0.6244* C 1 s( 31.10%)p 2.22( 68.90%) -0.0001 -0.5577 July 11, 1995 - 80 - -0.0006 0.3480 -0.0095 -0.2603 -0.0094 0.7070 -0.0103 ( 61.02%) -0.7811* H 5 s(100.00%) -1.0000 -0.0008 27. (0.01394) BD*( 1) N 2- H 6 ( 31.54%) 0.5616* N 2 s( 30.67%)p 2.26( 69.33%) 0.0000 -0.5538 -0.0005 -0.3785 -0.0165 0.2232 -0.0044 0.7070 0.0093 ( 68.46%) -0.8274* H 6 s(100.00%) -1.0000 -0.0031 28. (0.01394) BD*( 1) N 2- H 7 ( 31.54%) 0.5616* N 2 s( 30.67%)p 2.26( 69.33%) 0.0000 -0.5538 -0.0005 -0.3785 -0.0165 0.2232 -0.0044 -0.7070 -0.0093 ( 68.46%) -0.8274* H 7 s(100.00%) -1.0000 -0.0031 #T @seg #N 0 One can see that the $CHOOSE resonance structure is signi- ficantly inferior to the principal resonance structure found by the default NBO search in Section A.3. About 1.333e, or 7.4% of the electron density, is found in non-Lewis NBOs of the $CHOOSE structure (compared to 0.05e, or 0.3%, for the principal structure). Particularly defective is the hydride `lone pair' (NBO 9), which has less than half the expected occupancy (0.81453e). The C-N i bond (NBO 1) is seen to be more than 92% polarized toward N, indicative of essential lone pair character. 0 Note that structural elements shared by the two resonance structures (e.g., the two N-H bonds, which are common to both structures) need not have identical forms, since each detail of the NBOs is optimized with respect to the overall structure. #IB.6.10 NBO Energetic Analysis ($DEL Keylist)#N 0 The NBO energetic analysis with deletions ($DEL keylist) will be illustrated with two simple examples for RHF/3-21G methylamine (Section A.3). 0 The first example is the ``NOSTAR'' option (type 4, Sec- tion B.5), requesting deletion of all non-Lewis orbitals, July 11, 1995 - 81 - and hence leading to the energy of the idealized natural Lewis structure. The $DEL keylist in this case is #T $DEL NOSTAR $END #NThis leads to the output shown below: NOSTAR: Delete all Rydberg/antibond NBOs Deletion of the following orbitals from the NBO Fock matrix: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Occupations of bond orbitals: Orbital No deletions This deletion Change ---------- -------------------------------------------------------------------- 1. BD ( 1) C 1- N 2 1.99858 2.00000 0.00142 2. BD ( 1) C 1- H 3 1.99860 2.00000 0.00140 3. BD ( 1) C 1- H 4 1.99399 2.00000 0.00601 4. BD ( 1) C 1- H 5 1.99399 2.00000 0.00601 5. BD ( 1) N 2- H 6 1.99442 2.00000 0.00558 6. BD ( 1) N 2- H 7 1.99442 2.00000 0.00558 7. CR ( 1) C 1 1.99900 2.00000 0.00100 8. CR ( 1) N 2 1.99953 2.00000 0.00047 9. LP ( 1) N 2 1.97795 2.00000 0.02205 10. RY*( 1) C 1 0.00105 0.00000 -0.00105 11. RY*( 2) C 1 0.00034 0.00000 -0.00034 12. RY*( 3) C 1 0.00022 0.00000 -0.00022 13. RY*( 4) C 1 0.00002 0.00000 -0.00002 14. RY*( 1) N 2 0.00116 0.00000 -0.00116 15. RY*( 2) N 2 0.00044 0.00000 -0.00044 16. RY*( 3) N 2 0.00038 0.00000 -0.00038 17. RY*( 4) N 2 0.00002 0.00000 -0.00002 18. RY*( 1) H 3 0.00178 0.00000 -0.00178 19. RY*( 1) H 4 0.00096 0.00000 July 11, 1995 - 82 - -0.00096 20. RY*( 1) H 5 0.00096 0.00000 -0.00096 21. RY*( 1) H 6 0.00122 0.00000 -0.00122 22. RY*( 1) H 7 0.00122 0.00000 -0.00122 23. BD*( 1) C 1- N 2 0.00016 0.00000 -0.00016 24. BD*( 1) C 1- H 3 0.01569 0.00000 -0.01569 25. BD*( 1) C 1- H 4 0.00769 0.00000 -0.00769 26. BD*( 1) C 1- H 5 0.00769 0.00000 -0.00769 27. BD*( 1) N 2- H 6 0.00426 0.00000 -0.00426 28. BD*( 1) N 2- H 7 0.00426 0.00000 -0.00426 NEXT STEP: Evaluate the energy of the new density matrix that has been constructed from the deleted NBO Fock matrix by doing one SCF cycle. --------- --------------------------------------------------------------------- Energy of deletion : -94.618081014 Total SCF energy : -94.679444944 ------------------- Energy change : 0.061364 a.u., 38.506 kcal/mol #T @seg #N 0 In the output above, the NBO program first enumerates the 19 NBOs to be deleted by the ``NOSTAR'' request, then gives the complete list of NBOs with their occupancies before (``no deletions'') and after (``this deletion'') deletions, with the net change for each. For this NOSTAR deletion, each of the nine Lewis NBOs (1-9) necessarily gets 2.0000 electrons, and each of the non-Lewis NBOs (10-28) gets occu- pancy 0.0000. The program than reports the energy (minus 94.618081 a.u.) obtained from a single pass through the SCF evaluator with the modified density matrix. In this case, deletion of the 19 non-Lewis orbitals led to an energy change of only 0.061364 a.u. (38.5 kcal/mol), less than 0.07% of the total energy. 0 The next example is a more selective set of deletions between `chemical fragments' (type 9), selected by the $DEL July 11, 1995 - 83 - keylist input shown below: #T $DEL ZERO 2 ATOM BLOCKS 4 BY 3 1 3 4 5 2 6 7 3 BY 4 2 6 7 1 3 4 5 $END #NThis specifies removal of all delocalizing interactions from Lewis NBOs of the methyl fragment (atoms 1,3,4,5) into non-Lewis NBOs of the amine fragment (atoms 2,6,7), or vice versa. The NBO output for this example is shown below: Zero delocalization from NBOs localized on atoms: 1 3 4 5 to NBOs localized on atoms: 2 6 7 (NBOs in common to the two groups of atoms left out) Zero delocalization from NBOs localized on atoms: 2 6 7 to NBOs localized on atoms: 1 3 4 5 (NBOs in common to the two groups of atoms left out) Deletion of the NBO Fock matrix elements between orbitals: 2 3 4 7 and orbitals: 14 15 16 17 21 22 27 28 Deletion of the NBO Fock matrix elements between orbitals: 5 6 8 9 and orbitals: 10 11 12 13 18 19 20 24 25 26 Occupations of bond orbitals: Orbital No deletions This deletion Change ---------- -------------------------------------------------------------------- 1. BD ( 1) C 1- N 2 1.99858 1.99860 0.00002 2. BD ( 1) C 1- H 3 1.99860 1.99937 0.00077 3. BD ( 1) C 1- H 4 1.99399 1.99911 0.00512 4. BD ( 1) C 1- H 5 1.99399 1.99911 0.00512 5. BD ( 1) N 2- H 6 1.99442 1.99979 0.00537 6. BD ( 1) N 2- H 7 1.99442 1.99979 0.00537 7. CR ( 1) C 1 1.99900 1.99919 0.00019 8. CR ( 1) N 2 1.99953 1.99974 0.00021 9. LP ( 1) N 2 1.97795 1.99996 July 11, 1995 - 84 - 0.02201 10. RY*( 1) C 1 0.00105 0.00016 -0.00090 11. RY*( 2) C 1 0.00034 0.00000 -0.00033 12. RY*( 3) C 1 0.00022 0.00002 -0.00020 13. RY*( 4) C 1 0.00002 0.00002 0.00000 14. RY*( 1) N 2 0.00116 0.00004 -0.00112 15. RY*( 2) N 2 0.00044 0.00000 -0.00044 16. RY*( 3) N 2 0.00038 0.00003 -0.00035 17. RY*( 4) N 2 0.00002 0.00001 -0.00001 18. RY*( 1) H 3 0.00178 0.00088 -0.00090 19. RY*( 1) H 4 0.00096 0.00057 -0.00038 20. RY*( 1) H 5 0.00096 0.00057 -0.00038 21. RY*( 1) H 6 0.00122 0.00057 -0.00065 22. RY*( 1) H 7 0.00122 0.00057 -0.00065 23. BD*( 1) C 1- N 2 0.00016 0.00034 0.00018 24. BD*( 1) C 1- H 3 0.01569 0.00027 -0.01542 25. BD*( 1) C 1- H 4 0.00769 0.00055 -0.00714 26. BD*( 1) C 1- H 5 0.00769 0.00055 -0.00714 27. BD*( 1) N 2- H 6 0.00426 0.00009 -0.00417 28. BD*( 1) N 2- H 7 0.00426 0.00009 -0.00417 NEXT STEP: Evaluate the energy of the new density matrix that has been constructed from the deleted NBO Fock matrix by doing one SCF cycle. --------- --------------------------------------------------------------------- Energy of deletion : -94.635029232 Total SCF energy : -94.679444944 ------------------- Energy change : 0.044416 a.u., 27.871 kcal/mol #T July 11, 1995 - 85 - @seg #N 0 The output first lists the various orbitals and Fock matrix elements affected by this deletion, then the `before' and `after' occupancies and net changes for each NBO. In this case, one can see that the principal effect of the deletion was increased occupancy (+0.022) of the nitrogen lone pair, NBO 9, and depleted occupancy (minus 0.015) of the antiperiplanar gma *#<#dC#d1#uH#d3#u#u antibond, NBO 24, with somewhat lesser depletion (minus 0.007) of the other two C-H antibonds. The total energy change (loss of delo- calization energy) associated with this deletion was 27.9 kcal/mol. 0 To further pinpoint the source of this delocalization, one could do more selective deletions of individual orbitals or Fock matrix elements. For example, if one uses deletion type 2 (deletion of a single Fock matrix element, Section B.5.2) to delete the (9,24) element associated with the #In#N#dN#u arr gma *#<#dC#d1#uH#d3#u#u interaction, one finds a deletion energy of 7.06 kcal/mol associated with this interaction alone. [This value may be compared with the simple second-order perturbative estimate (8.13 kcal/mol) of the #In#N#dN#u arr gma *#<#dC#d1#uH#d3#u#u (9 arr 24) interaction that was noted in Section A.3.5.] #IB.6.11 Open-Shell UHF Output: Methyl Radical#N 0 Open-shell NBO output will be illustrated with the simple example of the planar methyl radical (CH#d3#u), treated at the UHF/6-31G* level (#IR#N#dCH#u = 1.0736hsp ngstrom ). In the open-shell case, one obtains two separate NPA and NBO listings, one for the lpha and one for the s t, corresponding to the ``different Lewis structures for dif- ferent spins'' description. A portion of the NBO output for the lpha spin manifold is reproduced below: NATURAL BOND ORBITAL ANALYSIS, alpha spin orbitals: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 0.90 4.99903 0.00097 1 3 0 1 0 0 0.00 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals -------------------------------------------------------- Core 0.99984 ( 99.984% of 1) July 11, 1995 - 86 - Valence Lewis 3.99919 ( 99.980% of 4) ================== ============================ Total Lewis 4.99903 ( 99.981% of 5) ----------------------------------------------------- Valence non-Lewis 0.00081 ( 0.016% of 5) Rydberg non-Lewis 0.00016 ( 0.003% of 5) ================== ============================ Total non-Lewis 0.00097 ( 0.019% of 5) ----- --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (0.99973) BD ( 1) C 1- H 2 ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%) 0.0000 0.5772 -0.0070 0.0000 -0.4076 -0.0110 0.7060 0.0191 0.0000 0.0000 -0.0338 0.0000 0.0000 -0.0195 -0.0090 ( 38.86%) 0.6233* H 2 s(100.00%) 1.0000 0.0080 2. (0.99973) BD ( 1) C 1- H 3 ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%) 0.0000 0.5772 -0.0070 0.0000 -0.4076 -0.0110 -0.7060 -0.0191 0.0000 0.0000 0.0338 0.0000 0.0000 -0.0195 -0.0090 ( 38.86%) 0.6233* H 3 s(100.00%) 1.0000 0.0080 3. (0.99973) BD ( 1) C 1- H 4 ( 61.14%) 0.7819* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%) 0.0000 0.5772 -0.0070 0.0000 0.8153 0.0221 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0391 -0.0090 ( 38.86%) 0.6233* H 4 s(100.00%) 1.0000 0.0080 4. (0.99984) CR ( 1) C 1 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 July 11, 1995 - 87 - 5. (1.00000) LP ( 1) C 1 s( 0.00%)p 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9978 -0.0668 0.0000 0.0000 0.0000 0.0000 0.0000 6. (0.00000) RY*( 1) C 1 s(100.00%)p 0.00( 0.00%)d 0.00( 0.00%) 7. (0.00000) RY*( 2) C 1 s(100.00%) 8. (0.00000) RY*( 3) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 9. (0.00000) RY*( 4) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 10. (0.00000) RY*( 5) C 1 s( 0.00%)p 1.00(100.00%) 11. (0.00000) RY*( 6) C 1 s( 0.00%)p 1.00( 0.23%)d99.99( 99.77%) 12. (0.00000) RY*( 7) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 13. (0.00000) RY*( 8) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 14. (0.00000) RY*( 9) C 1 s( 0.00%)p 1.00( 0.23%)d99.99( 99.77%) 15. (0.00000) RY*(10) C 1 s( 0.02%)p 0.00( 0.00%)d99.99( 99.98%) 16. (0.00005) RY*( 1) H 2 s(100.00%) 17. (0.00005) RY*( 1) H 3 s(100.00%) 18. (0.00005) RY*( 1) H 4 s(100.00%) 19. (0.00027) BD*( 1) C 1- H 2 ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%) 0.0000 -0.5772 0.0070 0.0000 0.4076 0.0110 -0.7060 -0.0191 0.0000 0.0000 0.0338 0.0000 0.0000 0.0195 0.0090 ( 61.14%) -0.7819* H 2 s(100.00%) -1.0000 -0.0080 20. (0.00027) BD*( 1) C 1- H 3 ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( 66.51%)d 0.00( 0.16%) 0.0000 -0.5772 0.0070 0.0000 0.4076 0.0110 0.7060 0.0191 0.0000 0.0000 -0.0338 0.0000 0.0000 0.0195 0.0090 ( 61.14%) -0.7819* H 3 s(100.00%) -1.0000 -0.0080 21. (0.00027) BD*( 1) C 1- H 4 ( 38.86%) 0.6233* C 1 s( 33.33%)p 2.00( July 11, 1995 - 88 - 66.51%)d 0.00( 0.16%) 0.0000 -0.5772 0.0070 0.0000 -0.8153 -0.0221 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0391 0.0090 ( 61.14%) -0.7819* H 4 s(100.00%) -1.0000 -0.0080 #T @seg #N 0 As can be seen in the output, the NBO spin-orbital occu- pancy threshold was set at 0.90 (rather than 1.90), and the occupancies of lpha Lewis spin-NBOs (1-5) are about 1.0000, but other aspects of the output are familiar. Note the slight admixture of #Id#N-character (0.16%) in the gma #dCH#u bond hybrids (NBOs 1-3), whereas the out-of-plane radical non-bonded orbital (NBO 5) has pure #Ip#N-character. 0 The NBO output for the z d') spin set then follows: NATURAL BOND ORBITAL ANALYSIS, beta spin orbitals: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 0.90 3.99981 0.00019 1 3 0 0 0 0 0.00 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals -------------------------------------------------------- Core 0.99985 ( 99.985% of 1) Valence Lewis 2.99996 ( 99.999% of 3) ================== ============================ Total Lewis 3.99981 ( 99.995% of 4) ----------------------------------------------------- Valence non-Lewis 0.00002 ( 0.000% of 4) Rydberg non-Lewis 0.00017 ( 0.004% of 4) ================== ============================ Total non-Lewis 0.00019 ( 0.005% of 4) ----- --------------------------------------------------- July 11, 1995 - 89 - (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (0.99999) BD ( 1) C 1- H 2 ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) 0.0000 0.5762 0.0080 0.0000 -0.4076 -0.0125 0.7059 0.0217 0.0000 0.0000 -0.0345 0.0000 0.0000 -0.0199 -0.0350 ( 44.20%) 0.6649* H 2 s(100.00%) 1.0000 -0.0069 2. (0.99999) BD ( 1) C 1- H 3 ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) 0.0000 0.5762 0.0080 0.0000 -0.4076 -0.0125 -0.7059 -0.0217 0.0000 0.0000 0.0345 0.0000 0.0000 -0.0199 -0.0350 ( 44.20%) 0.6649* H 3 s(100.00%) 1.0000 -0.0069 3. (0.99999) BD ( 1) C 1- H 4 ( 55.80%) 0.7470* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) 0.0000 0.5762 0.0080 0.0000 0.8151 0.0251 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0399 -0.0350 ( 44.20%) 0.6649* H 4 s(100.00%) 1.0000 -0.0069 4. (0.99985) CR ( 1) C 1 s(100.00%) 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5. (0.00002) LP*( 1) C 1 s( 10.35%)p 0.00( 0.00%)d 8.66( 89.65%) 6. (0.00000) RY*( 1) C 1 s( 98.99%)p 0.00( 0.00%)d 0.01( 1.01%) 7. (0.00000) RY*( 2) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 8. (0.00000) RY*( 3) C 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 9. (0.00000) RY*( 4) C 1 s( 0.00%)p 1.00(100.00%) 10. (0.00000) RY*( 5) C 1 s( 0.00%)p July 11, 1995 - 90 - 1.00(100.00%) 11. (0.00000) RY*( 6) C 1 s( 0.00%)p 1.00( 0.24%)d99.99( 99.76%) 12. (0.00000) RY*( 7) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 13. (0.00000) RY*( 8) C 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 14. (0.00000) RY*( 9) C 1 s( 0.00%)p 1.00( 0.24%)d99.99( 99.76%) 15. (0.00000) RY*(10) C 1 s( 91.02%)p 0.00( 0.00%)d 0.10( 8.98%) 16. (0.00006) RY*( 1) H 2 s(100.00%) 17. (0.00006) RY*( 1) H 3 s(100.00%) 18. (0.00006) RY*( 1) H 4 s(100.00%) 19. (0.00000) BD*( 1) C 1- H 2 ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) ( 55.80%) -0.7470* H 2 s(100.00%) 20. (0.00000) BD*( 1) C 1- H 3 ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) ( 55.80%) -0.7470* H 3 s(100.00%) 21. (0.00000) BD*( 1) C 1- H 4 ( 44.20%) 0.6649* C 1 s( 33.21%)p 2.00( 66.51%)d 0.01( 0.28%) ( 55.80%) -0.7470* H 4 s(100.00%) #T @seg #N 0 The principal difference to be seen is that the radical orbital (NBO 5) is essentially empty in this spin set, and the polarization of the gma #dCH#u bonds is somewhat altered (about 55.8% on the C atom in the s t set, #Ivs.#N 61.1% in the lpha set). [In other cases, the lpha and L wis structures might differ even in the number and location of 1-c (non-bonding) and 2-c (bond) structural elements.] Note that the overall quality of the open-shell natural Lewis structure description (> 99.9%) is comparable to that of ordinary closed-shell molecules, and the interpretation of the NBO output follows familiar lines. |<<__________________________ #-#BWARNING#N#+ You should not attempt to analyze an open-shell wavefunction with an ESS method that produces only the ``spinless'' (spin-averaged) density matrix, rather than the separate density matrices for lpha and h ir total populations are calculated correctly from the spinless density matrix, July 11, 1995 - 91 - NBOs and NLMOs are not. NBO analysis of an open-shell spinless density matrix is a fundamental misuse of the program. #IB.6.12 Effective Core Potential: Cu#d2#u Dimer#N 0 To illustrate some of the variations of NBO output associ- ated with use of effective core potentials (ECP) and inclu- sion of #Id#N orbitals, we use the example of the copper dimer Cu#d2#u (#IR#N = 2.2195hsp ngstrom ), treated at the RHF level with a Hay-Wadt ECP and valence DZ basis (RHF/LANL1DZ), carried out with the GAUSSIAN-88 system. (The wavefunction returned by GAUSSIAN-88 in this case corresponds to an excited state configuration of Cu#d2#u.) Since the NBO program communicates directly with the ESS program for details about the ECP, no special keywords are necessary. 0 Use of an ECP shows up most directly in the NPA portion of the output, shown below: NATURAL POPULATIONS: Natural atomic orbital occupancies NAO Atom # lang Type(AO) Occupancy Energy ----- ---------------------------------------------------- 1 Cu 1 s Val( 4s) 0.94240 -0.26321 2 Cu 1 s Ryd( 5s) 0.00019 0.92165 3 Cu 1 px Ryd( 4p) 0.99604 -0.06989 4 Cu 1 px Ryd( 5p) 0.00001 0.09916 5 Cu 1 py Ryd( 4p) 0.99604 -0.06989 6 Cu 1 py Ryd( 5p) 0.00001 0.09916 7 Cu 1 pz Ryd( 5p) 0.05481 1.09062 8 Cu 1 pz Ryd( 4p) 0.00062 0.52821 9 Cu 1 dxy Val( 3d) 0.00000 -0.36077 10 Cu 1 dxy Ryd( 4d) 0.00000 0.72280 11 Cu 1 dxz Val( 3d) 1.99997 -1.29316 12 Cu 1 dxz Ryd( 4d) 0.00398 0.75681 13 Cu 1 dyz Val( 3d) 1.99997 -1.29316 14 Cu 1 dyz Ryd( 4d) 0.00398 0.75681 15 Cu 1 dx2y2 Val( 3d) 1.99939 -1.38791 16 Cu 1 dx2y2 Ryd( 4d) 0.00061 0.67825 17 Cu 1 dz2 Val( 3d) 1.99890 -1.26114 18 Cu 1 dz2 Ryd( 4d) 0.00308 1.16392 19 Cu 2 s Val( 4s) 0.94240 -0.26321 20 Cu 2 s Ryd( 5s) 0.00019 0.92165 21 Cu 2 px Ryd( 4p) 0.99604 -0.06989 22 Cu 2 px Ryd( 5p) 0.00001 0.09916 23 Cu 2 py Ryd( 4p) 0.99604 -0.06989 24 Cu 2 py Ryd( 5p) 0.00001 0.09916 25 Cu 2 pz Ryd( 5p) 0.05481 1.09062 26 Cu 2 pz Ryd( 4p) 0.00062 0.52821 27 Cu 2 dxy Val( 3d) 0.00000 -0.36077 28 Cu 2 dxy Ryd( 4d) 0.00000 0.72280 29 Cu 2 dxz Val( 3d) 1.99997 -1.29316 30 Cu 2 dxz Ryd( 4d) 0.00398 0.75681 July 11, 1995 - 92 - 31 Cu 2 dyz Val( 3d) 1.99997 -1.29316 32 Cu 2 dyz Ryd( 4d) 0.00398 0.75681 33 Cu 2 dx2y2 Val( 3d) 1.99939 -1.38791 34 Cu 2 dx2y2 Ryd( 4d) 0.00061 0.67825 35 Cu 2 dz2 Val( 3d) 1.99890 -1.26114 36 Cu 2 dz2 Ryd( 4d) 0.00308 1.16392 [ 36 electrons found in the effective core potential] WARNING: Population inversion found on atom Cu 1 Population inversion found on atom Cu 2 Summary of Natural Population Analysis: Natural Population Natural --------- -------------------------------------- Atom # Charge Core Valence Rydberg Total ---------- ------------------------------------------------------------- Cu 1 0.00000 18.00000 8.94064 2.05936 29.00000 Cu 2 0.00000 18.00000 8.94064 2.05936 29.00000 ======================================================================= * Total * 0.00000 36.00000 17.88127 4.11873 58.00000 Natural Population -------- ------------------------------------------------ Effective Core 36.00000 Valence 17.88127 ( 81.2785% of 22) Natural Minimal Basis 53.88127 ( 92.8987% of 58) Natural Rydberg Basis 4.11873 ( 7.1013% of 58) --- ----------------------------------------------------- Atom # Natural Electron Configuration --------- - ------------------------------------------------------------------ Cu 1 [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05) Cu 2 [core]4s( 0.94)3d( 8.00)4p( 1.99)4d( 0.01)5p( 0.05) #T @seg #N 0 As noted below the first NPA table, 36 electrons were found in the ECP, so the labels for NAOs in the table begin with the designations 4#Is#N, July 11, 1995 - 93 - 5#Is#N, etc. of the presumed extra-core electrons. The ECP electrons are duly entered in the NPA tables (labelled as ``effective core'' in the NPA summary table) as part of the total Lewis occupancy, and are taken into proper account in assigning atomic charges. The NPA output in this case includes a ``population inversion'' message to warn that one or more NAO occupancies are not ordered in accor- dance with the energy order [e.g., the 3#Id#N#dxy#u orbital (NAO 9) is unoccupied in this excited configuration, although its energy lies below the occupied 4#Is#N, 4#Ip#N#dy#u, 4#Ip#N#dz#u levels.] 0 The main ECP effect in the NBO portion of the output is the omission of core NBOs, as illus- trated below: NATURAL BOND ORBITAL ANALYSIS: Occupancies Lewis Structure Low High Occ. ------------------- ----------------- occ occ Cycle Thresh. Lewis Non-Lewis CR BD 3C LP (L) (NL) Dev ============================================================================= 1(1) 1.90 57.99970 0.00030 0 3 0 8 0 0 0.00 ---------- ------------------------------------------------------------------- Structure accepted: No low occupancy Lewis orbitals -------------------------------------------------------- Effective Core 36.00000 Valence Lewis 21.99970 ( 99.999% of 22) ================== ============================ Total Lewis 57.99970 ( 99.999% of 58) ----------------------------------------------------- Valence non-Lewis 0.00000 ( 0.000% of 58) Rydberg non-Lewis 0.00030 ( 0.001% of 58) ================== ============================ Total non-Lewis 0.00030 ( 0.001% of 58) ----- --------------------------------------------------- (Occupancy) Bond orbital/ Coefficients/ Hybrids ----- ----- --------------------------------------------------------------------- 1. (2.00000) BD ( 1)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%) 0.9702 -0.0003 0.0000 0.0000 0.0000 July 11, 1995 - 94 - 0.0000 -0.2340 0.0245 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0225 0.0530 ( 50.00%) 0.7071*Cu 2 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%) 0.9702 -0.0003 0.0000 0.0000 0.0000 0.0000 0.2340 -0.0245 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0225 0.0530 2. (2.00000) BD ( 2)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) 0.0000 0.0000 0.9980 0.0029 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0035 -0.0630 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ( 50.00%) 0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) 0.0000 0.0000 0.9980 0.0029 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0035 0.0630 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3. (2.00000) BD ( 3)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) 0.0000 0.0000 0.0000 0.0000 0.9980 0.0029 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0035 -0.0630 0.0000 0.0000 0.0000 0.0000 ( 50.00%) 0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) 0.0000 0.0000 0.0000 0.0000 0.9980 0.0029 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 July 11, 1995 - 95 - 0.0035 0.0630 0.0000 0.0000 0.0000 0.0000 4. (2.00000) LP ( 1)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9998 -0.0175 0.0000 0.0000 5. (2.00000) LP ( 2)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0037 -0.0010 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0026 0.0000 0.0000 0.0000 0.0000 6. (2.00000) LP ( 3)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 0.0037 -0.0010 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0026 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 7. (1.99985) LP ( 4)Cu 1 s( 0.06%)p 0.02( 0.00%)d99.99( 99.94%) 0.0231 0.0070 0.0000 0.0000 0.0000 0.0000 -0.0030 -0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.9996 -0.0115 8. (2.00000) LP ( 1)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9998 -0.0175 0.0000 0.0000 July 11, 1995 - 96 - 9. (2.00000) LP ( 2)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 0.0000 0.0000 -0.0037 0.0010 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0026 0.0000 0.0000 0.0000 0.0000 10. (2.00000) LP ( 3)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 0.0000 0.0000 -0.0037 0.0010 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0026 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 11. (1.99985) LP ( 4)Cu 2 s( 0.06%)p 0.02( 0.00%)d99.99( 99.94%) 0.0231 0.0070 0.0000 0.0000 0.0000 0.0000 0.0030 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.9996 -0.0115 12. (0.00015) RY*( 1)Cu 1 s( 63.84%)p 0.51( 32.31%)d 0.06( 3.85%) -0.1106 0.7913 0.0000 0.0000 0.0000 0.0000 -0.4699 0.3199 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0064 -0.1962 13. (0.00000) RY*( 2)Cu 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 14. (0.00000) RY*( 3)Cu 1 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 15. (0.00000) RY*( 4)Cu 1 s( 31.12%)p 2.21( 68.87%)d 0.00( 0.00%) 16. (0.00000) RY*( 5)Cu 1 s( 7.79%)p11.84( 92.21%)d 0.00( 0.00%) 17. (0.00000) RY*( 6)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 18. (0.00000) RY*( 7)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 19. (0.00000) RY*( 8)Cu 1 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%) July 11, 1995 - 97 - 20. (0.00000) RY*( 9)Cu 1 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%) 21. (0.00000) RY*(10)Cu 1 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 22. (0.00000) RY*(11)Cu 1 s( 3.06%)p 0.35( 1.07%)d31.35( 95.87%) 23. (0.00015) RY*( 1)Cu 2 s( 63.84%)p 0.51( 32.31%)d 0.06( 3.85%) -0.1106 0.7913 0.0000 0.0000 0.0000 0.0000 0.4699 -0.3199 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0064 -0.1962 24. (0.00000) RY*( 2)Cu 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 25. (0.00000) RY*( 3)Cu 2 s( 0.00%)p 1.00(100.00%)d 0.00( 0.00%) 26. (0.00000) RY*( 4)Cu 2 s( 31.12%)p 2.21( 68.87%)d 0.00( 0.00%) 27. (0.00000) RY*( 5)Cu 2 s( 7.79%)p11.84( 92.21%)d 0.00( 0.00%) 28. (0.00000) RY*( 6)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 29. (0.00000) RY*( 7)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 30. (0.00000) RY*( 8)Cu 2 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%) 31. (0.00000) RY*( 9)Cu 2 s( 0.00%)p 1.00( 0.40%)d99.99( 99.60%) 32. (0.00000) RY*(10)Cu 2 s( 0.00%)p 0.00( 0.00%)d 1.00(100.00%) 33. (0.00000) RY*(11)Cu 2 s( 3.06%)p 0.35( 1.07%)d31.35( 95.87%) 34. (0.00000) BD*( 1)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%) ( 50.00%) -0.7071*Cu 2 s( 94.13%)p 0.06( 5.54%)d 0.00( 0.33%) 35. (0.00000) BD*( 2)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) ( 50.00%) -0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) 36. (0.00000) BD*( 3)Cu 1-Cu 2 ( 50.00%) 0.7071*Cu 1 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) ( 50.00%) -0.7071*Cu 2 s( 0.00%)p 1.00( 99.60%)d 0.00( 0.40%) July 11, 1995 - 98 - Natural Bond Orbitals (Summary): Princi- pal Delocalizations NBO Occupancy Energy (geminal,vicinal,remote) =============================================================================== Molecular unit 1 (Cu2) 1. BD ( 1)Cu 1-Cu 2 2.00000 -0.53276 2. BD ( 2)Cu 1-Cu 2 2.00000 -0.21503 3. BD ( 3)Cu 1-Cu 2 2.00000 -0.21503 4. LP ( 1)Cu 1 2.00000 -1.38854 5. LP ( 2)Cu 1 2.00000 -1.29317 6. LP ( 3)Cu 1 2.00000 -1.29317 7. LP ( 4)Cu 1 1.99985 -1.26133 8. LP ( 1)Cu 2 2.00000 -1.38854 9. LP ( 2)Cu 2 2.00000 -1.29317 10. LP ( 3)Cu 2 2.00000 -1.29317 11. LP ( 4)Cu 2 1.99985 -1.26133 12. RY*( 1)Cu 1 0.00015 0.70166 13. RY*( 2)Cu 1 0.00000 0.09932 14. RY*( 3)Cu 1 0.00000 0.09932 15. RY*( 4)Cu 1 0.00000 1.09217 16. RY*( 5)Cu 1 0.00000 0.44430 17. RY*( 6)Cu 1 0.00000 -0.36077 18. RY*( 7)Cu 1 0.00000 0.72280 19. RY*( 8)Cu 1 0.00000 0.75266 20. RY*( 9)Cu 1 0.00000 0.75266 21. RY*(10)Cu 1 0.00000 0.67888 22. RY*(11)Cu 1 0.00000 1.26372 23. RY*( 1)Cu 2 0.00015 0.70166 24. RY*( 2)Cu 2 0.00000 0.09932 25. RY*( 3)Cu 2 0.00000 0.09932 26. RY*( 4)Cu 2 0.00000 1.09217 27. RY*( 5)Cu 2 0.00000 0.44430 28. RY*( 6)Cu 2 0.00000 -0.36077 29. RY*( 7)Cu 2 0.00000 0.72280 30. RY*( 8)Cu 2 0.00000 0.75266 31. RY*( 9)Cu 2 0.00000 0.75266 32. RY*(10)Cu 2 0.00000 0.67888 33. RY*(11)Cu 2 0.00000 1.26372 34. BD*( 1)Cu 1-Cu 2 0.00000 0.41179 35. BD*( 2)Cu 1-Cu 2 0.00000 0.08327 36. BD*( 3)Cu 1-Cu 2 0.00000 0.08327 ------------------------------- Total Lewis 57.99970 ( 99.9995%) Valence non-Lewis 0.00000 ( 0.0000%) Rydberg non-Lewis 0.00030 ( 0.0005%) ------------------------------- Total unit 1 58.00000 (100.0000%) Charge unit 1 0.00000 #T July 11, 1995 - 99 - @seg #N 0 As the output shows, the NBO tables include reference to only 11 occupied NBOs, rather than the 29 that would appear in a full calculation. Semi-empirical methods that neglect core electrons (AMPAC, etc.) are handled similarly. 0 The output for the Cu#d2#u example also illustrates some aspects of the inclusion of #Id#N orbitals in the basis set. NBOs 4-7 and 8-11 represent the 3#Id#N#u8#d subshells on each atom, essentially of pure atomic #Id#N character (except for a small admixture of #Ip#N character in NBOs 7, 11). Both the gma #dCuCu#u bond (NBO 1) and the two i #dCuCu#u bonds (NBOs 2, 3) have very slight admixtures (< 0.4%) of #Id#N character. The remaining orbitals of predom- inant #Id#N character (NBOs 17-22 and 28-33) are of negligi- ble occupancy. Note that the abbreviated ``#Isp#u #dd#umu #d#N'' designations can lead to strange variations among hybrids of essentially similar character; thus, NBO 20 (#Ip#u1.0#dd#u99.9#d#N), NBO 21 (#Id#N#u1.0#d), and NBO 22 (#Is#u3.1#dp#u0.4#dd#u31.4#d#N) are all of nearly pure (> 95%) #Id#N character, the difference in labelling stemming from whether there is sufficient #Is#N or #Ip#N character (in numerical terms) to express the hybrid ratios in #Isp#u #dd#umu #d#N form. Consult the percentages of #Is#N-. #Ip#N-, and #Id#N-character whenever there is doubt about how to interpret a particular #Isp#u #dd#umu #d#N designa- tion. #BB.7 FILE47: INPUT FOR THE GENNBO STAND-ALONE NBO PROGRAM#N #IB.7.1 Introduction#N 0 The general NBO program, GENNBO, is a stand-alone program which is not directly attached to an ESS program. Rather, information about the wavefunction is provided to the core NBO routines by a sequential input file, FILE47, described in this section. 0 Some knowledge of FILE47 is useful even if your NBO pro- gram is attached to an ESS package. If requested (see the ARCHIVE option, Section B.2.5), the NBO program writes out FILE47 which summarizes all information pertaining to the computed electronic wavefunction. This file can be subse- quently used as input to the GENNBO program (reassigned as LFN 5) to repeat the analysis of this wavefunction; simply include the $NBO, $CORE, and $CHOOSE keylists in FILE47 and execute GENNBO. You need never recompute the wavefunction to vary its NBO analysis! In fact, generating the FILE47 input file is a useful way to archive a wavefunction for future use or reference. [Note: the GENNBO program can not perform the NBO energetic analysis ($DEL keylist) since this July 11, 1995 - 100 - would require access to the formatted one- and two-electron integrals of the parent ESS package.] 0 If you intend to use the NBO program in conjunction with an ESS package not supported in this distribution (i.e. for which no custom drivers are provided), you might consider attaching a routine to your ESS program which would write the proper form of FILE47 for input into the GENNBO program. Thus, a two-step process would be required to obtain the NBO analysis of a wavefunction: (i) the initial calculation of the wavefunction with the ESS package, writing FILE47; (ii) the NBO analysis using the GENNBO program with FILE47 as input. Alternatively, you may decide to attach the NBO pro- gram directly to your ESS package by writing your own driver routines. See the Programmer's Guide, Section C.13, for direction. 0 Section B.7.2 describes and illustrates the overall format of FILE47. Sections B.7.3-B.7.7 detail the entries of the keylists and datalists that compose this file. #IB.7.2 Format of the FILE47 Input File#N 0 The FILE47 input file is composed of a set of keylists and datalists, each list beginning with a ``$'' identifier (e.g. ``$BASIS'') and ending with ``$END'', #T $BASIS entries $END#N Individual lists are used to specify basis set information ($BASIS), density matrix elements ($DENSITY), and so forth. The order of the lists within FILE47 is immaterial. Entries within each datalist are generally free format, and may be continued on as many lines as desired. An exclamation point (!) on any line terminates input from the line, and may be followed by arbitrary comments. The $GENNBO keylist and the $COORD, $BASIS, $DENSITY, and $OVERLAP datalists are required, but the other datalists ($FOCK, $LCAOMO, $CON- TRACT, $DIPOLE) or the standard NBO keylists ($NBO, $CORE, $CHOOSE) are optional, depending on the requested applica- tion. If the $NBO keylist is not present in FILE47, the default NBO analysis is performed. 0 The entries of each keylist or datalist may be keywords, numerical matrix elements, or other parameters of prescribed form. A sample FILE47 input file (for the RHF/3-21G methyl#|amine example of Section A.3) is shown below: $GENNBO NATOMS=7 NBAS=28 UPPER BODM $END $NBO NAOMO=PVAL $END $COORD Methylamine...Pople-Gordon standard geometry...RHF/3-21G 6 6 -0.74464 -0.03926 0.00000 ! Carbon 7 7 0.71885 0.09893 0.00000 ! Nitrogen 1 1 -1.00976 -1.09653 0.00000 ! Hydrogen July 11, 1995 - 101 - 1 1 -1.15467 0.43814 0.88998 ! Hydrogen 1 1 -1.15467 0.43814 -0.88998 ! Hydrogen 1 1 1.09878 -0.34343 -0.82466 ! Hydrogen 1 1 1.09878 -0.34343 0.82466 ! Hydrogen $END $BASIS CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7 LABEL = 1,1,101,102,103,1,101,102,103,1,1,101,102,103,1,101,102,103, 1,1,1,1,1,1,1,1,1,1 $END $CONTRACT NSHELL = 16 NEXP = 21 NCOMP = 1, 4, 4, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 NPRIM = 3, 2, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 NPTR = 1, 4, 6, 7, 10, 12, 13, 15, 16, 18, 16, 18, 19, 21, 19, 21 EXP = 0.1722560E+03, 0.2591090E+02, 0.5533350E+01, 0.3664980E+01, 0.7705450E+00, 0.1958570E+00, 0.2427660E+03, 0.3648510E+02, 0.7814490E+01, 0.5425220E+01, 0.1149150E+01, 0.2832050E+00, 0.5447178E+01, 0.8245472E+00, 0.1831916E+00, 0.5447178E+01, 0.8245472E+00, 0.1831916E+00, 0.5447178E+01, 0.8245472E+00, 0.1831916E+00 CS = 0.2093132E+01, 0.2936751E+01, 0.1801737E+01, -0.7473843E+00, 0.7126610E+00, 0.2098285E+00, 0.2624092E+01, 0.3734359E+01, 0.2353454E+01, -0.1047101E+01, 0.9685501E+00, 0.2766851E+00, 0.3971513E+00, 0.5579200E+00, 0.1995672E+00, 0.3971513E+00, 0.5579200E+00, 0.1995672E+00, 0.3971513E+00, 0.5579200E+00, 0.1995672E+00 CP = 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.1709178E+01, 0.8856221E+00, 0.1857223E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.2808586E+01, 0.1456735E+01, 0.2944871E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 July 11, 1995 - 102 - $END $OVERLAP ! Overlap matrix elements in the AO basis 0.10000000E+01 0.19144744E+00 0.10000000E+01 . . . $END $DENSITY ! Bond-order matrix elements in the AO basis 0.20363224E+01 0.11085239E+00 0.10393086E+00 . . . $END $FOCK ! Fock matrix elements in the AO basis -0.11127777E+02 -0.28589754E+01 -0.89570272E+00 . . . $END $LCAOMO ! AO to MO transformation matrix -0.57428375E-03 -0.23835711E-02 0.17741799E-02 . . . $END $DIPOLE ! dipole matrix elements in the AO basis -0.14071733E+01 -0.26939974E+00 -0.14071733E+01 . . . $END #T @seg #N The nine lists of FILE47 are described in turn in the fol- lowing sections, making use of this example for illustra- tion. #IB.7.3 $GENNBO Keylist#N 0 The $GENNBO keylist (required) contains keywords essential to the proper execution of the NBO program. The following is the list of keywords recognized by this keylist: #IOPTION DESCRIPTION#N Instructs GENNBO to reuse an old NBO direct-access file, FILE48, rather than create a new FILE48 from the wavefunc- tion information contained in the FILE47 data#|lists. Therefore, if the REUSE keyword is specified, all data#|lists in FILE47 will be ignored, but the $NBO, $CORE, and $CHOOSE keylists will still be recognized. This keyword preempts all other keywords of the $GENNBO keylist. Number of atoms in the molecule (required). Number of basis functions (required). Designates an open shell wavefunction. GENNBO will subse- quently read in alpha and beta density, Fock, and MO coeffi- cient matrices. Indicates that the AO basis set is orthogonal (basis func- tions are always assumed normalized). If this keyword is specified, GENNBO will not read the $OVERLAP datalist. This keyword is incompatible with $NBO keywords for `pre- orthogonal' basis sets (SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, July 11, 1995 - 103 - AOPNHO, AOPNBO, AOPNLMO). Indicates that only the upper triangular portions of the overlap, density, Fock, and dipole matrices are listed in the their respective datalists. By default, GENNBO assumes that the full matrices are given. Indicates that the $DENSITY datalist contains the bond-order matrix (``Fock-Dirac density matrix'') rather than the den- sity matrix (i.e., matrix elements of the density operator). (In orthogonal AO basis sets, the bond-order matrix and den- sity matrix are identical, but in nonorthogonal basis sets they must be distinguished.) By default, GENNBO assumes this data#|list contains the density matrix elements. If ``BODM'' is included, the datalist elements are transformed with the AO overlap matrix to produce the true density matrix. Indicates that the atomic coordinates ($COORD) and the dipole integrals ($DIPOLE) are in atomic units, rather than the default angstroms. Indicates that the Fock matrix elements ($FOCK) have units of electron volts (eV), rather than the default atomic units (Hartrees). Instructs GENNBO to use the set of seven cubic #If#N-type functions rather than the ten Cartesian or seven pure #If#N functions (cf. Section B.7.5). The methylamine sample $GENNBO keylist specifies 7 atoms, 28 basis functions, upper triangular matrix input, and $DENSITY datalist containing the bond-order matrix. #IB.7.4 $COORD Datalist#N 0 The $COORD datalist (required, unless REUSE is specified in $GENNBO) contains the job title and information indicat- ing the identity and coordinates of each atom, including missing core electrons or effective core potentials. 0 The first line following the $COORD identifier is an arbi- trary job title, up to 80 characters. 0 Subsequent lines are used to specify the atomic number, the nuclear charge, and the (x,y,z) coordinates of each atom. [For example, atom 1 in the methylamine sample input is a carbon atom (atomic number 6) with nuclear charge 6 and coordinates x = minus 0.74464, y = minus 0.03926, z = 0.00000, in angstroms.] Coordinates are assumed to be in angstroms unless the BOHR keyword appears in the $GENNBO keylist, specifying atomic units. The atomic number and July 11, 1995 - 104 - nuclear charge are generally identical, but if core electrons are neglected (as in most semi-empirical treatments) or if effective core potentials (ECP) are employed, the nuclear charge will be less than the atomic number by the number of electrons neglected on that particular atom. Thus, for an AMPAC calculation, in which the two 1#Is#N core electron of a carbon atom are neglected, the line following the job title in the methylamine example would read #T 6 4 -0.74464 -0.03926 0.00000 ! Carbon#N where ``4'' is the effective (valence) nuclear charge of the atom. #IB.7.5 $BASIS Datalist#N 0 The $BASIS datalist (required, unless REUSE is specified in $GENNBO) provides essential information about the AO basis functions, specifying the atomic center and the angu- lar symmetry ( , x , y , z , etc.) of each AO. This information is contained in two arrays in this datalist called CENTER and LABEL. 0 The atomic center for each AO is specified by entering ``CENTER='' followed by the serial number of the atom for each AO, separated by commas or spaces. [For example, the entry #T CENTER = 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,6,6,7,7#N of the methylamine sample file indicates that the first 9 AOs (1-9) are centered on atom 1 (the carbon atom), the next nine AOs (10-18) on center 2, and so forth.] 0 The angular symmetry for each AO is specified by entering ``LABEL='' followed by a symmetry label for each AO, separated by commas or spaces. The NBO program handles #Is#N, #Ip#N, #Id#N, or #If#N (= 0-3) basis AOs, of either cartesian or pure angular symmetry types. The label for each AO is a 3-digit integer of the form + #Ik#N + #Im#N, where #Ik#N is 0 (cartesian) or 50 (pure), and #Im#N is a particular component of the symmetry (see table below). For #Is#N or #Ip#N AOs, the cartesian and pure sets are identi- cal, so each AO can be labelled in two distinct ways, but the six cartesian #Id#N functions can be transformed to the five pure #Id#N functions plus an additional #Is#N function, and the ten cartesian #If#N functions can be transformed to the seven pure #If#N functions plus three additional #Ip#N functions. Two distinct sets of pure #If#N functions are recognized, the ``standard'' [default] set and the ``cubic'' set, the latter being used whenever the ``CUBICF'' keyword is included in the $GENNBO keylist. July 11, 1995 - 105 - 0 The labels associated with each allowed AO function type are tabulated below, where #Ix, y, z#N refer to the speci- fied cartesian axis system: #_Pure #If#N ``cubic'' set:#/>> 351//#If#N(D1): x(5x#u2#dminus 3r#u2#d)>> 352//#If#N(D2): y(5y#u2#dminus 3r#u2#d)>> 353//#If#N(D3): z(5z#u2#dminus 3r#u2#d)>> 354//#If#N(B): xyz>> 355//#If#N(E1): x(z#u2#dminus y#u2#d)>> 356//#If#N(E2): y(z#u2#dminus x#u2#d)>> 357//#If#N(E3): z(x#u2#dminus y#u2#d)>> 356//#If#N(c3): x(x#u2#dminus 3y#u2#d)>> 357//#If#N(s3): y(3x#u2#dminus y#u2#d)>> [For example, in the methylamine sample input, the first nine entries of the LABEL array, #T LABEL = 1,1,101,102,103,1,101,102,103,. . .#N identify the first 9 AOs (of carbon) as being of , , x , y , z , , x , y , z type, respectively.] #IB.7.6 $CONTRACT Datalist#N 0 The $CONTRACT datalist (optional) contains additional information about the contraction coefficients and orbital exponents of AO basis functions. This information is not used in the NBO analysis of a wavefunction. However, if the AOINFO or PLOT keyword is specified in the $NBO keylist (See Section B.2.5), the GENNBO driver routines write out this information to an external file (LFN 31) in the proper for- mat for orbital plotting with the ORBPLOT program. Omit the $CONTRACT datalist if you do not intend to make orbital plots. 0 Two integers must be initially given: NSHELL (the number of shells of basis functions) and NEXP (the number of orbi- tal exponents). [In the methylamine example, there are 16 shells of basis functions and 27 orbital exponents.] These integers should precede the remainder of the basis set information of this datalist. 0 The number of components (basis functions) in each shell is specified in the NCOMP array. The sum of the components for each shell should equal the total number of basis func- tions. This list of components is a partitioning of the basis function centers and labels (in the $BASIS datalist) into shells. [For example, in the methylamine sample, the NCOMP array #T NCOMP = 1,4,4,. . .#N July 11, 1995 - 106 - indicates that the first three shells have a total of 9 (i.e. 1+4+4) basis functions. These are the 9 AOs (1-9) discussed previously in the $BASIS datalist.] 0 The NPRIM array gives the number of primitive gaussian functions of each shell. [For the methylamine example, the first three shells of the AO basis are contractions of #T NPRIM = 3,2,1,. . .#N three, two, and one primitives, respectively, corresponding to the conventional ``3-21G'' basis set designation.] 0 Pointers for each shell are listed in the NPTR array. These pointers specify the location of the orbital exponents (EXP) and contraction coefficients (CS, CP, CD, CF) for each shell. [In the sample input file, #T NPTR = 1,4,6,. . .#N the orbital exponents and contraction coefficients for the first three shells begin at elements 1, 4, and 6, respec- tively.] 0 EXP, CS, CP, CD, and CF are free format, real arrays con- taining the orbital exponents, and the s, p, d, and f con- traction coefficients of the AO basis set. NEXP elements should appear in each array, and the arrays of contraction coefficients need only appear if there are basis functions of that particular symmetry in the basis set. [For example, the 3-21G basis of the sample methylamine input only has #Is#N and #Ip#N basis functions. Therefore, the CD and CF arrays are not necessary.] 0 The information in the $CONTRACT datalist along with that in the $BASIS datalist is enough to completely determine the AO basis set. [For example, the second shell on the methy- lamine sample contains 4 basis functions (NCOMP). These are #Is#N, #Ip#N#dx#u, #Ip#N#dy#u, and #Ip#N#dz#u orbitals (LABEL), all centered on atom 1 (CENTER), and each basis function is a contraction of two primitive gaussians (NPRIM). From NPTR, EXP, CS, and CP, we find the explicit form of these functions: hi #ds#u(#Br#N) hsp = hsp + hi #dp#dx#u#u(#Br#N) = 1 + 2 hi #dp#dy#u#u(#Br#N) = 3 + 4 hi #dp#dz#u#u(#Br#N) = 5 + 6 July 11, 1995 - 107 - where #Br#N=(x,y,z) is measured in bohr units relative to the cartesian coordinates of atom 1.] #IB.7.7 Matrix Datalists#N 0 The remaining datalists ($OVERLAP, $DENSITY, $FOCK, $LCAOMO, $DIPOLE) specify various matrix elements possibly used by the NBO analysis. All entries in these datalists are free format, with entries separated by commas or spaces. Only the upper triangular portions of each symmetric matrix (overlap, density, Fock, dipole) should be provided if the UPPER keyword is specified in the $GENNBO keylist. The numbering of the matrix rows and columns must correspond to the ordering of the AOs in the $BASIS datalist. All three matrices of dipole integrals should appear in the $DIPOLE datalist, all #Ix#N integrals before #Iy#N before #Iz#N. 0 Of the matrix datalists, the $DENSITY datalist is always required, and the $OVERLAP data#|list is required for all non-orthogonal AO basis sets, but other data#|lists are optional (unless implicitly required by specified keyword options). Nevertheless, it is good practice to include as many of these datalists in FILE47 as possible for later use with keyword options which require them. The following table lists the $NBO keywords that require each datalist to be included in FILE47: #I$NBO Keywords Requiring the Datalist#N SAO, SPNAO, SPNHO, SPNBO, SPNLMO, AOPNAO, AOPNHO, AOPNBO, AOPNLMO E2PERT, FAO, FNAO, FNHO, FNBO, FNLMO AOMO, NAOMO, NHOMO, NBOMO, NLMOMO DIAO, DINAO, DINHO, DINBO, DINLMO, DIPOLE AOINFO, PLOT 0 For example, in the methylamine sample input, the keyword ``NAOMO=PVAL'' of the $NBO keylist requires that the $LCAOMO data#|list be present (in addition to the $OVERLAP, $DEN- SITY, and $FOCK data#|lists used for default PRINT=2 analysis), but the $DIPOLE data#|list might have been omit- ted in this case. Inclusion of the $LCAOMO data#|list (in addition to the $FOCK datalist) insures that degenerate MOs will be chosen in a prescribed way for decomposition in terms of other functions. July 11, 1995 - 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 |<<__________________________ #T |<<___ __ RUNNBO I II |<<___ __ |<<___ __ NBO NBOEAN |<<___ __ |<<___ __ |<<___ __ |<<___ __ (init.) NAODRV NBODRV NBODEL,DELETE, NBOSET (& simulation) NEWDM,RNKEIG, July 11, 1995 - 110 - JOBOPT SIMTRN NBODIM |<<___ __ |<<___ __ |<<___ __ |<<___ __ |<<___ __ |<<___ __ (prepare) NAO NAOANL NATHYB NLMO DIPANL SIMTRM (CHSDRV, MULANA CHOOSE) DFGORB |<<___ __ |<<___ __ |<<___ __ |<<___ __ (NAO formation) (NBO formation) LMOANL DIPELE LOADAV,ATDIAG, SRTNBO,XCITED,ANLYZE, SYMUNI DIPNUC SETBAS,NEWWTS, HTYPE,FRMHYB,HYBDIR, SYMORT WORTH,SCHMDT, HYBCMP,FNDMOL,NBOCLA, NEWRYD,RYDIAG, FNBOAN,NBOSUM,GETDEL, RYDSEL,REDIAG, BLDSTR,CORE,IWPRJ, REDBLK DEPLET,LOAD,PRJEXP, STASH,ORTHYB,FRMPRJ, ANGMNT,REPOL,FORMT, CYCLES #BC.3 LABELLED COMMON BLOCKS#N 0 The NBO programs contain eighteen labelled COMMON blocks to control information flow between subprograms (other than through explicit argument lists). Each COMMON block name begins with ``NB'' to minimize possible conflicts with a linked ESS program. The eighteen COMMON blocks can be divided into six `primary' and twelve `secondary' blocks, with regard to claim on the programmer's attention. The `primary' COMMON blocks 1-6 (/NBINFO/, /NBFLAG/, /NBOPT/, /NBAO/, /NBATOM/, and /NBIO/) contain variables that must be set by the ESS-specific driver routine FEAOIN, or by an equivalent interface pro- vided by the programmer. The remaining `secondary' blocks 7-18 are for internal communication only, and are ordinarily of lesser concern. The dimensions of COMMON block arrays are fixed by PARAMETER declarations of the form #T PARAMETER(MAXATM = 99,MAXBAS = 500) #Nwhere MAXATM and MAXBAS are, respectively, the maximum allowed numbers of atoms and basis functions. These program limits can therefore be simply altered. There is no diffi- culty in #Idecreasing#N either of these values, or in increasing MAXBAS (up to 999). However, the program cannot July 11, 1995 - 111 - readily adapt to MAXATM > 99, since this would result in format overflows in orbital labels throughout the output. All entries of a given COMMON block are generally of the same numeric type (INTEGER, LOGICAL, etc.), as specified below. The names (dummy), and meaning of variables in each primary COMMON block 1-6 are described briefly, with an asterisk (*) marking the items that must be passed from the external ESS program via driver routines: The INTEGER variables of this block store general informa- tion related to basis set dimensionality, spin manifold, number of atoms, and energy units: The LOGICAL variables of this block are set .TRUE. or .FALSE. depending on whether the ``condition'' (type of wavefunction, spin set, etc.) is satisfied: Note (Section B.6.11) that both lpha and d nsity matrices should be available if OPEN is set `.TRUE.' for the open- shell case. The INTEGER variables (flags) of this block are used for storing the keyword options selected by the user in the $NBO keylist. In many cases, a variable of the form IWOPT (``IW'' stands for ``I Want'') is set to one or zero (or to some Hollerith content; see below) depending on whether the ``requested option'' has been specified or not. The table also lists the keyword (if any) that requests the option: The keyword associated with each element I=1-54 of the JPRINT array is shown below (55-60 are not currently used): In general, if the flag is set to zero, its associated key- word option has not been specified. However, if an option is requested, its flag can be set to a variety of positive, negative, or Hollerith values, depending on the parameters specified with the keyword option. In particular, the option flags associated with the matrix output keywords, described in Section B.2.4, are set according to the follow- ing scheme: July 11, 1995 - 112 - The INTEGER arrays of this block store information on the atomic centers and angular symmetry of each AO: The INTEGER arrays of this block store information about the orbitals on each atomic center: The INTEGER variables of this block are the stored default logical file numbers for I/O operations. The table below identifies the value (default file assignment) and the con- tents of the file associated with each LFN (cf. Section B.2.4): The remaining `secondary' COMMON blocks 7-18 contain vari- ables that remain wholly within the system-independent code, and thus can be ignored with respect to interfacing to a new ESS. Blocks 7-13 involve communication with the Group I, II subprograms, whereas blocks 14-18 are wholly within the `support' routines of Groups III-VII. The INTEGER arrays of this block generally store information about the atomic, bond, and molecular units with which the NBOs or NAOs are associated. The meaning of all entries in COMMON/NBBAS/ #Ichanges#N between the NAO and NBO segments of the program, so this block functions virtually as `scratch storage,' and its entries must be approached with extreme caution! The following table indicates the meaning of COMMON/NBBAS/ entries during NBO segments (only!): The DOUBLE PRECISION variables of this block store the default values of various numerical thresh#|olds that can be set by the user: The INTEGER variables of this block store the number of orbitals associated with the ``LEW'' and ``VAL'' print parameters (Section B.2.4) and the 10 Hollerith fragments required to compose each of the 4 possible types of July 11, 1995 - 113 - localized orbital labels (AO, NAO, NHO, NBO): The INTEGER arrays of this block store information pertain- ing to the labelling of NAOs in the NPA output: The INTEGER scalars, vectors, and arrays of this block store information pertaining to ``molecular units'': The INTEGER variables of this block contain atom search lists to direct the search for NBOs and information pertain- ing to the `topology' (bond connectivity) of the molecule: The DOUBLE PRECISION variables of this block store informa- tion pertaining to the molecular dipole moment and charge distribution: The INTEGER variables of this block store general informa- tion related to the `card image' (line) being processed by the free-format input routines: The LOGICAL variables of this block store information related to the current line being read by the free-format input routines. In each case, the variable is set .TRUE. if the specified condition is met: The INTEGER variables of this block store information related to the NBO direct access file (FILE48). The PARAME- TER statement #T July 11, 1995 - 114 - PARAMETER (NBDAR = 100) #Nsets the maximum number of logical records accessible in FILE48: The INTEGER variables of this block provide scratch storage for writing to the NBO direct access file (FILE48). The PARAMETER statement #T PARAMETER (ISINGL = 2, LENGTH = 256) #Nsets the FILE48 physical record LENGTH to 256 longwords (1024 bytes): The LOGICAL variables of this block store information related to running the GENNBO program in stand-alone mode. In each case, the variable is set .TRUE. if the specified condition is met: #BC.4 DIRECT ACCESS FILE AND OTHER I/O#N 0 The principal I/O routines of Groups III-V are described in Sections C.7-C.9. The #Iinput#N to the NBO programs is primarily from the standard ESS input file (LFN 5), and the #Ioutput#N is primarily to the standard ESS output file (LFN 6). Other ``matrix output'' (read/write) I/O is by default assigned to LFNs 31-49 (see Table of Section B.2.4), or to a user-selectable LFN, based on keyword entries in the $NBO keylist. 0 The remaining two files that are routinely created or modified by the NBO programs are the FILE48 direct access file (LFN 48) and the FILE47 `archive' file (LFN 47, described in Section B.7). The latter file can also serve as the main input file (reassigned as LFN 5) when the NBO program is run in stand-alone GENNBO mode. 0 From the programmer's viewpoint, the most important infor- mation concerns the organization of the FILE48 direct access file. The records of this file are assigned as shown in the following table. The items marked with an asterisk (*) must be provided from the ESS program (e.g., through the FEAOIN driver), and hence are of particular importance to the pro- grammer: July 11, 1995 - 115 - [Cartesian coordinates (record 9) and dipole integrals (records 50-52) should be in angstrom units.] 0 The direct access file serves as a principal medium of communication between all segments of the NBO program. Input received from the ESS program (Section C.11) is immediately saved in the direct access file and subsequently fetched by other subprograms, using the fetch/save I/O rou- tines of Section C.7. Further information on the structure of the direct access file is specified in COMMON blocks 16, 17 of Section C.3. #BC.5 NAO/NBO/NLMO ROUTINES (GROUP I)#N #IC.5.1 SR NBO Master Subroutine#N 0 The subroutine of highest precedence in the core NBO pro- gram is SR NBO. This routine initially requests that the input file be searched for the $NBO keylist (See NBOINP, Section C.9). If found, SR NBO continues by calling three main clusters of programs, as shown below: |<<_________________________ |<<__________________________ |<<__________________________ |<<__________________________ #TV+30 SR NBO(CORE,MEMORY,NBOOPT)#N In addition, SR NBO creates a new NBO direct access file (DAF) each time it is called, and closes this file upon com- pletion (See NBOPEN and NBCLOS, Section C.9). 0 SR NBO is provided a memory vector, CORE, which is `MEMORY' double precision words in length. For modest-sized calculations (e.g. 10 heavy atoms with a double-zeta basis set), a vector of 50,000 words should be adequate. Although SR NBO performs an initial partitioning of this memory vec- tor, the majority of the dynamic memory allocation occurs in the NAO and NBO/NLMO formation routines, described in Sec- tions C.5.3 and C.5.4. 0 An array of job options, NBOOPT(10), is also passed to SR NBO. These job options identify the current version of the NBO program (i.e., the identity of the ESS calling program), control program input and execution, and determine several July 11, 1995 - 116 - of the default options of the NBO analysis, as summarized in the following table. [Entries marked with an asterisk (*) contain information pertaining to the identity or job options of the calling ESS program, and thus are of special concern to the programmer.] #IDESCRIPTION#N Do nothing (return control to calling program) Perform Natural Population Analysis (NPA) only Perform NPA/NBO/NLMO analyses, normal program run Perform NPA/NBO/NLMO analyses, don't read $NBO keylist Initiate energetic analysis, read one deletion from $DEL Complete energetic analysis, print the energy change SCF density MP first order density MP2 density MP3 density MP4 density CI one-particle density CI density QCI/CC den- sity Density correct to second order Perform the NBO/NLMO dipole analysis (force the DIPOLE key- word) Allow strongly delocalized Lewis structures (force the RESO- NANCE keyword) Spin-annihilated UHF (AUHF) wavefunction (unused) (unused) General version of the NBO program (GENNBO) AMPAC version GAMESS version HONDO version GAUSSIAN-8x version These options are read by job initialization routines (Sec- tion C.5.2) and stored in COMMON/NBOPT/, where they control events throughout the program. [Note that NBOOPT(2) is only used by the Gaussian versions.] #IC.5.2 Job Initialization Routines#N 0 The routines of this section initialize the default options and parameters, read and store the user's $NBO key- word options: This routine sets default option flags (COMMON/NBOPT/), default logical file numbers (COMMON/NBIO/), and default thresholds (COMMON/NBTHR/) for the NBO program. In addi- tion, SR NBOSET interprets the NBOOPT array, setting option flags appropriately. July 11, 1995 - 117 - This routine is primarily responsible for reading and set- ting option flags (COMMON/NBOPT/) according to the keywords specified in the $NBO keylist. It reads the $NBO keywords using the free format routines described in Section C.8, continuing until the word ``$END'' terminates the keylist. Options which are incompatible with the chosen wavefunction or program version are `shut off', and other options are `turned on' in accord with the requested print level ($NBO keyword PRINT). All keywords which are selected in the $NBO keylist are echoed in the output file. Determines the scratch memory requirements of the NBO pro- gram, as determined by the options selected in the $NBO keylist. Program execution halts if the memory requirements exceed the available memory. #IC.5.3 NAO Formation Routines#N 0 The principal task of this cluster of routines is to con- trol the formation of the NAOs from the input AO basis. In addition, these routines are responsible for the writing (to an external file) or printing (to the output file) of a variety of matrices in the AO, PNAO, and NAO basis sets, according to job options requested in the $NBO keylist. The first set of routines are called by SR NBO: This is the principal controller routine for non-orthogonal basis sets. The scratch vector A is partitioned within this routine according to the memory requirements of the NAO sub- programs. This routine `simulates' SR NAODRV in the case of a semi- empirical calculation, where the (orthonormal) basis AOs are the presumed effective valence shell atomic orbitals, and no NAO transformation is needed. Performs the transformation and analysis of the open-shell AO density matrix (alpha or beta spin) to the NAO basis. This routine employs the AO to NAO transformation, T, deter- mined by SR NAODRV: Simulates SR DMNAO for the open-shell semi-empirical case, when no transformation is required. Principal driver program for NBO formation; Section C.5.4. The next set of routines are called by the main NAO driver, July 11, 1995 - 118 - SR NAODRV. They include the principal subroutine, SR NAO, which generates the NAOs: Performs the similarity transformation S#ut#d*A*S leading to Mulliken populations, with S = overlap matrix, A = bond- order matrix. Evaluates Mulliken gross populations and performs Mayer- Mulliken bond-order analysis (requires bond order matrix). Performs the decomposition of `raw' cartesian #Id#N, #If#N, or #Ig#N AO sets to pure angular symmetry AOs (e.g., 6 cartesian #Id#N arr 5 pure #Id#N + 1 #Is#N); cf. Section B.7.5. This is the principal routine for formation of NAOs, follow- ing closely the algorithm described by A. E. Reed, R. B. Weinstock, and F. Weinhold, #IJ. Chem. Phys. #B83#N, 735-746 (1985). This is the principal routine for performing and printing out natural population analysis (NPA). The routine assigns orbital labels and energies and writes out the NPA, natural electron configuration (NEC), NAO-Wiberg bond index and overlap-weighted bond population tables. [Thresholds TEST, TEST2, ALLOW, ALLOW2 test for numerical conservation of an integer number of electrons.] Forms and outputs NCOL columns of the transformation matrix to MOs from a chosen localized set, specified by INDEX = 2 (NAO), 3 (NHO), 4 (NBO), or 5 (NLMO). Input matrix T is the transformation from AOs to the basis set specified by INDEX, and matrices TMO, C, and SCR are scratch arrays employed by this routine. #NThe remaining routines of this section are auxiliary sub- routines called by SR NAO to perform individual steps of the NAO algorithm: Averages the AO density matrix elements over the 2+ 1 com- ponents of for a particular atom, and loads the density matrix and overlap integrals for the orbitals of LISTAO into matrices A, B, respectively. Solves the generalized eigenvalue problem (A minus July 11, 1995 - 119 - EVAL*B)*C = 0 to diagonalize an atomic block. Selects the `occupied' NAOs to be included in the natural minimal basis set for a particular atom (up to Z = 105) and angular momentum symmetry type (L), and stores them in LSTOCC. Recomputes symmetry-averaged occupancy weights for PNAOs. This routine is only used in conjunction with the `PAOPNAO=R' keyword. This subroutine implements the occupancy-weighted symmetric orthogonalization (OWSO), a key feature of the NAO algo- rithm. [Note that BLK and BIGBLK share the same storage area, though they are dimensioned differently. The routine includes three numerical thresholds, WTTHR (10#uminus 3#d) for occupancy weight, DIAGTH (10#uminus 12#d) for Jacobi diagonalization, and DANGER (10#u3#d) for linear dependence difficulties.] Schmidt orthogonalization of column vectors of T. #NComputes new Rydberg NAOs after Schmidt orthogonalization of the Rydberg space to the NMB set. #NDiagonalizes an atomic Rydberg block and updates the PNAO transformation matrix. Partitions Rydbergs into `significantly occupied' (> WTTHR) and `negligibly occupied' (ts, assigning the latter to have equal (non-zero) occupancy weighting. This avoids numerical singularities associated with the OWSO occupancy weighting for orbitals of negligible occupancy, effectively replacing OWSO by ordinary L mlaut owdin-orthog#|onalization of these `residual' Rydbergs among themselves. [Threshold WTTHR (10#uminus 4#d) controls singularities of the inverse square-root weighting matrix.] Rediagonalizes the atomic density matrix blocks after sym- metry averaging. Finds the rediagonalization transformation for a specific atomic subblock of the density matrix. July 11, 1995 - 120 - #IC.5.4 NBO/NLMO Formation Routines#N 0 The master routine of this cluster is SRhsp hsp NBODRV(DM,T,A), which partitions the scratch storage vector (A) according to the memory requirements of the NBO forma- tion and analysis subprograms and controls the calculation of the transformation (T) from NAOs to NBOs using the NAO density matrix (DM). SR NBODRV calls either SR NATHYB (for the default NBO search) or SR CHSDRV (for the $CHOOSE directed NBO search) to form the NBOs. It also calls the NLMO formation routine (SR NLMO) and dipole analysis routine (SR DIPANL). According to job options selected in the $NBO keylist, SR NBODRV also transforms and outputs a variety of matrices in the PNHO, NHO, PNBO, NBO, PNLMO, and NLMO basis sets. [Note that the first NATOMS*NATOMS elements of the A vector store the Wiberg bond index elements determined in the NAO routines; these should not be destroyed until calcu- lation of NBOs is complete.] 0 The following routines are called by SR NBODRV: #NThis routine performs the basic NBO search, the central task of NBO analysis, closely following the description given by J. P. Foster and F. Weinhold, #IJ. Am. Chem. Soc. #B102#N, 7211-7218 (1980). The routine constructs the orthogonal matrix (T) for the NAO to NBO transformation from the input NAO density matrix (DM). The efficiency of the search procedure is enhanced by using the NAO-Wiberg bond index as a `GUIDE' to order the NBO search. [Beware the IBXM bond orbital permutation list (!), which reorders the LABEL array of COMMON/NBBAS/. The occupancy threshold, THRESH, determines whether an NBO is accepted during the search for bond orbitals (cf. SR CYCLES). Two numerical thresholds (PRJTHR, PRJINC) control possible linear dependencies: In the main loops over 1-c, 2-c (and 3-c) functions, each prospective NBO is checked for possible redundancy with previous NHOs by the PRJEXP (projection operator expectation value) test. The threshold PRJTHR for a `new' hybrid is initially set conservatively low (0.20), but will be auto-incremented by PRJINC (0.05) as needed to prevent linear dependency; any numerical singularity triggers IALARM and causes PRJTHR to be incremented and the entire NBO search repeated.] #NThis routine, the ``$CHOOSE driver,'' reads the $CHOOSE keylist, setting up the arrays NTOPO and I3CTR of COMMON/NBTOPO/ which will control the directed NBO search of SR CHOOSE. July 11, 1995 - 121 - #NThis routine is essentially similar to SR NATHYB, but the search loops are directed by the $CHOOSE specification. Reorders (dangerous!) the NBOs according to bond type and constituent atomic centers. NBOs are ordered BD (and 3C), CR, LP, LP*, RY*, BD* (and 3C*). Note that this step is not required for the proper execution of any of the NBO analysis or NLMO formation routines, but it leads to more readable output. Examines PNHO overlaps to determine whether NBOs were prop- erly labelled as `bonds' (unstarred, Lewis) or `antibonds' (starred, non-Lewis) in the NBO formation routines (SR NATHYB and SR CHOOSE). If incorrect nodal character is recognized in a bond or antibond (generally indicative of an excited state), a warning is printed and the orbital is relabelled. Note that this will probably mix the NBO order- ing set by SR SRTNBO. Prints out the principal table (Section A.3.3) of NBO analysis [using the IBXM ordering!], expressing each NHO in #Isp#u #d#N form. Analyzes input hybrid for polarization coefficient and per- centages of each angular momentum component (accepts up to #Ig#N orbitals). Forms the NAO to NHO transformation (THYB) and saves it on the DAF. Computes hybrid directionality and bond bending angles as determined from percentage #Ip#N-character for selected NBOs, and prints the BEND table (Section A.3.4). [Keyword- selectable thresh#|olds ATHR (angular deviation), PTHR (% #Ip#N-character), and ETHR (occupancy) control printing.] Finds direction and percentage #Ip#N-character of a given hybrid. Finds `molecular units' from NBO connectivity. Classifies NBOs according to donor/acceptor type, number of atomic centers, and parent molecular unit. July 11, 1995 - 122 - Performs the 2nd-order perturbation theory energy analysis of the NBO Fock matrix and prints the table (Section A.3.5). [Thresholds ETHR1 (intramolecular) and ETHR2 (intermolecu- lar) control printing.] Prepares and prints the NBO summary table (Section A.3.6). Assembles the delocalization list, LIST(NL), for the IBO#uth#d NBO. Only intramolecular and intermolecular delo- calizations which are stronger than THR1 and THR2 (in kcalhsp mol#uminus 1#d), respectively, are included in the list. Builds a character string containing delocalization informa- tion for the NBO summary table. This is the main routine for determination of the NLMOs, following closely the description given by A. E. Reed and F. Weinhold, #IJ. Chem. Phys. #B83#N, 1736-1740 (1985). [Numerical thresholds DIFFER (10#uminus 5#d), DONE (10#uminus 10#d), and EPS (10#uminus 11#d) control the modi- fied Jacobi diagonalizations.] #NPrints out details of the NAO arr NLMO transformation and the NAO/NLMO bond order table (Section B.6.2). Calculates and prints out the DIPOLE analysis table (Section B.6.3). Evaluates the #Ix,y,z#N (INDEX = 1,2,3) electronic dipole moment contributions, including delocalization contribu- tions, for each occupied NBO. Evaluates the nuclear contributions (DX, DY, DZ) to the molecular dipole moment. The following routines are called by SR NATHYB and SR CHOOSE in calculating the NBOs. Overall supervision of this set of routines is exercised by SR CYCLES. Other routines are associated with specific steps of the NBO algorithm: Performs the first step in the search for NBOs. This rou- tine identifies core orbitals and depletes the NAO density matrix of their contributions. July 11, 1995 - 123 - This function returns zero (no projection wanted) if still on the same atomic center, or one (projection operator should be formed) if this is a new center. `Depletes' density matrix of contribution from bond orbital (BORB), by subtracting its diagonal contribution from the spectral expansion of the density operator. This insures that the same electron pair will not be found twice in the NBO loops. Loads the appropriate atomic blocks of the density matrix into the local (2-c, 3-c) density matrix subblock (BLK), in preparation for diagonalization. Determines how much of a prospective bond orbital (BORB) is composed of hybrids already used. The projection operator onto the space of previously accepted hybrids is used to evaluate the expectation value of each hybrid component of BORB. Decomposes bond orbital (BORB) into constituent normalized hybrids and stores them in the hybrid array (Q). Performs symmetric (L mlaut owdin) orthogonalization on occu- pied atomic hybrids (PNHOs) to give final NHOs. [Threshold TOOSML (10#uminus 4#d) turns on the alarm (IALARM) to warn of numerical instabilities due to linear dependence.] Forms projection matrix to annihilate components of the occupied atomic hybrids on a given center. This routine augments the set of occupied atomic hybrids on a center with a sufficient number of Rydberg AOs (in order of occupancy) to complete the span of the basis set on that atom. Diagonalizes each 2x2 block of the density matrix in the basis of final NHOs to get the optimal polarization coeffi- cients for each NBO. Constructs the final NAO to NBO transformation matrix (T) from the final array of NHOs (Q) and polarization coeffi- cients (POL). July 11, 1995 - 124 - 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 - 125 - 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 - 126 - (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 - 127 - 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 - 128 - 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). July 11, 1995 - 129 - Writes the AO to NBO transformation, the NBO occupancies, and additional NBO info (NBOUNI, NBOTYP, LABEL, IBXM, and IATNO arrays) to an external disk file (LFN = minus IFLG). Similar to SR WRTNBO but for NLMOs. Note that the NLMO labels are identical to the NBO labels. Writes the atomic coordinates and AO basis set information to the `AOINFO' file LFN. The information contained in this file is identical to that of the $COORD, $BASIS, and $CON- TRACT datalists of the GENNBO input file (see Section B.7). For more information on the file format, see the subroutine source code. Writes the `ARCHIVE' file LFN (see Section B.7). General utility to write matrix A(MR,1) to an external file (LFN = minus IFLG) or print it to the output file (IFLG = number of columns to print, `FULL', `VAL', or `LEW'). TITLE is a CHARACTER*80 matrix label, and the rows of A are labelled according to the value of INDEX = 0 (atoms), 1 (AOs), 2 (NAOs), 3 (NHOs), 4 (NBOs), or 5 (NLMOs). This routine calls SR APRINT or SR AWRITE. Prints MCOL columns of matrix A to the output file. The format of the matrix is chosen according to the magnitude of the largest matrix element in A (cf. SR AOUT). Writes matrix A to external disk file LFN (cf. SR AOUT). Reads NC columns of the matrix A(MR,1) from the external file LFN. The job title in the external file is returned to the calling subroutine in the Hollerith array, JOB(20), and the LOGICAL variable ERROR is set to .TRUE. if an error occurred while reading. Prints the matrix A(MR,MC) to the standard output file. This routine is called only when the print formats of SR APRINT are unsuitable for matrix A. Interprets the Hollerith array STRING(LEN), storing the result in IFLG. The contents of STRING can be any of the read/write/print parameters such as `W38', `PVAL', `R43', etc., described in Section B.2.4, and the resulting value of IFLG is determined according to the discussion of July 11, 1995 - 130 - 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. July 11, 1995 - 131 - 2. Converts the Hollerith array IJ(LEN) into an integer IK. This is the inverse of SR IDIGIT. Converts a 2-digit integer N to two Hollerith characters NC1, NC2. Copies matrix A to matrix B. Stores the nominal ``core table,'' giving the number of core #Is#N, #Ip#N, #Id#N, #If#N orbitals for elements 1-105 (H to Lw, and elements 104, 105). This table controls the number of high-occupancy unhybridized NAOs that will be isolated and removed as core NBOs (taking account also of any effec- tive core potential). Decomposes a Hollerith variable I into its four individual Hollerith `bytes' IBYTE(4). Halts the execution of the NBO program if an unrecognizable keyword is found in the $NBO keylist. Converts the INTEGER variable KINT in the first ND elements of the Hollerith array IK(MAXD). This is the inverse of SR CONVIN. This Hollerith function determines whether the IBO arr JBO delocalization is vicinal (`v'), geminal (`g'), or remote (`r'), based on the derived NBO connectivity. 3. Diagonalizes a real symmetric matrix by the Jacobi rota- tions method. If ICONTR=0, a standard Jacobi diagonaliza- tion (unconstrained 2x2 rotations) is carried out. If ICONTR=1, the algorithm is prevented from mixing orbitals that are degenerate within `DIFFER' if the off-diagonal ele- ment connecting them is less than `DIFFER'. [Threshold DIFFER (10#uminus 5#d) controls degenerate mixing, DONE (10#uminus 13#d) is the maximum allowed off-diagonal ele- ment, and EPS (0.5x10#uminus 13#d) is a number between DONE and the machine pre#|cision.] This routine carries out a `limited' transformation of a matrix (T), using only the rows and columns specified by July 11, 1995 - 132 - vector M. The operations performed are T*A, A#ut#d*T*A, or A#ut#d*T according to the value of IOPT. Multiplies square matrices A*B (using scratch vector V) and stores result in A. Multiplies A#ut#d*B (using scratch vector V) and stores the result in B. The algorithm assumes that A*B is a symmetric, so about half the work is saved. [SR MATML2 is typically the second step in a similarity transform of B by A, where B (and thus A#ut#d*B*A) is symmetric.] Returns the (Hollerith) atomic symbol for atomic number IZ Normalizes the columns of A using the overlap matrix S. 4. Ranks the positive elements of integer LIST(N), lowest values first. [RANK and ARCRNK are integer vectors, with I = ARCRNK(N) if LIST(I) is the element of rank N.] Packs the upper-triangular portion of the symmetric matrix T(NBAS,NBAS) the first L2 elements of T. Orders the entries of vector EIG, highest values first. ARCRNK(I) is the old location of the I#uth#d highest value in EIG. On return, EIG(I) is the I#uth#d highest value. [Entries are not switched unless they differ by more than a DIFFER (5x10#uminus 8#d) threshold.] Performs the general similarity transform T#ut#d*A*T of A by T, using scratch vector V. Performs the `fast' similarity transform S#ut#d*A*S, assum- ing the result is symmetric. Transposes the matrix A: A arr A#ut#d. Unpacks an upper triangular matrix (vector of length L2) into a symmetric matrix T(NBAS,NBAS). July 11, 1995 - 133 - Specifies the nominal ``valence table,'' giving the number of valence AOs of each symmetry type for elements 1-105. Evaluates Euclidean length of vector X. This and the three following routines constitute the linear equations package for solving the system A*X = B for matrix X by the method of Gaussian elimination. Supports SR LINEQ. Supports SR LINEQ. Supports SR LINEQ. #BC.11 SYSTEM-DEPENDENT DRIVER ROUTINES (GROUP VII)#N 0 The routines of Group VII comprise the set of ESS- dependent driver routines which initiate the NBO and NBO energetic analyses and provide the NBO program with a variety of information about the electronic wavefunction. This section provides a brief, generic description of each of the driver routines. If you intend to write a set of routines for an ESS program not supported by this distribu- tion, refer to the driver source code for additional gui- dance. Also, see Section C.13 for helpful hints for attach- ing the NBO program to an ESS package. 0 The driver routines are grouped together at the end of the NBO source code. Since multiple versions of each driver are provided (one for each supported ESS package and GENNBO), all of the executable lines in these routines are `commented out' with an asterisk in the first column. In addition, every line of the drivers has an identifier `#IXXX#NDRV' in columns 73-78, where `#IXXX#N' is a 3-letter identifier for the associated ESS package. It is the responsibility of the program ENABLE to `uncomment' the appropriate lines of the code for the requested program version (see Section A.2). 0 The system-dependent driver routines are: Determines the logical file numbers for the input and output files (LFNIN and LFNPR) of the parent program, initializes the NBOOPT job option array Section C.5.1), and initiates the NBO analysis (SR NBO) and energetic analysis (SR NBOEAN). This routine is the only routine of the NBO pro- gram called directly by the parent ESS package. July 11, 1995 - 134 - Interrogates the scratch files and COMMON blocks of the parent program, providing the NBO program with required information of the electronic wavefunction via the NBO COM- MON blocks and FILE48 direct access file. (Note that for GENNBO, this routine directs the input of information from the GENNBO input file, FILE47.) The NBO COMMON blocks and FILE48 records which must be initialized by SR FEAOIN are discussed in Sections C.3, C.4. Additional information on the COMMON blocks and scratch files of the parent ESS pack- age is provided in the Appendices. Performs one of two tasks, depending of the value of NBOOPT(1). If NBOOPT(1) is set to 2, SR DELSCF provides the parent ESS program with the modified density matrix gen- erated by the NBO energetic analysis routines. The parent program will then compute the ``deletion energy'' for this modified wavefunction. If NBOOPT(1) is set to 3, SR DELSCF fetches the deletion energy from the parent program and writes it to the FILE48 direct access file. (The NBOOPT array is discussed in Section C.5.1). #BC.12 GENNBO AUXILIARY ROUTINES#N 0 An additional set of routines is provided for the GENNBO stand-alone program. These routines are called by the GENNBO driver routine FEAOIN and are responsible for reading the datalists of the GENNBO input file. Each of these rou- tines rewinds the input file before searching sequentially for its associated datalist. Thus, the order of datalists (as well as keylists) in the input file is immaterial. Each routine also checks that all required information in the datalist is given and stores this information on the FILE48 direct access file or in the NBO COMMON blocks. 0 Below we list each GENNBO auxiliary routine, indicating its associated datalist, but without furthur explanation: #BC.13 ATTACHING NBO TO A NEW ESS PROGRAM#N This section briefly outlines the steps to be considered when attaching the NBO program to a new ESS package that is not supported by this distribution. In general, you should try to identify the supported ESS package that is most similar to the ESS package you wish to use, and try to create driver routines modelled as closely as possible on those provided for the ESS. [In fact, exa- mining the source code for driver routines of #Iall#N sup- ported ESS packages is good preparation for writing your own drivers.] July 11, 1995 - 135 - Decide where in the parent ESS package you wish to perform the NBO analysis. This will necessarily be placed after the calculation of the wavefunction (and the associated density matrix), usually near the wavefunction analysis routines (e.g., the perennial ``Mulliken population analysis'' sec- tion) or wavefunction properties section of the code. If possible, restrict the modification of your ESS source code to insertion of a single ``CALL RUNNBO'' statement at some point where the information required for NBO analysis is known to be available. Check carefully for possible conflicts between the parent ESS program and the NBO program in (1) function or subrou- tine names, (2) COMMON block names, and (3) logical file assignments (LFNs) for I/O. NBO common block names all begin with /NB.../, and default LFN assignments are in the range 31-49. (Duplicate FN or SR names are detected by a linker.) Create new driver (interfacing) subroutines RUNNBO, FEAOIN, and DELSCF to perform the functions briefly described in Section C.11, using the drivers provided with this distribu- tion as templates insofar as possible. The following are a few helpful hints for each driver: The RUNNBO routine should be relatively straightforward to write, following an analogous example provided in this dis- tribution. Note that you can simply omit the calls to SR NBOEAN and SR DELSCF from RUNNBO if you do not plan to use the NBO energetic analysis (for example, because the DELSCF driver is unmanageable). If your parent program is quite different from any of those supported by this distribution, choose an alternate version number [NBOOPT(10)], and carefully consider step 4 below. Routine FEAOIN should fetch information about the electronic wavefunction from your ESS package and load it into the NBO COMMON blocks and FILE48 direct access file. This requires intimate knowledge of where these items are stored in the ESS program, so the FEAOIN examples of the distribution may provide little direct guidance. See Sections C.3, C.4 for description of the NBO COMMON blocks and file records which must be initialized by this routine. Note that the NBO analysis will perform properly without the information stored on logical records 2, 5, 9, 30, 31, 40, 41, and 50-52 of the direct access file. If information is not provided on these records, the NBO program will simply shut off (with warnings) any requested keyword options which are thereby incompatible. In addition, the overlap matrix of record 10 need not be provided if the input basis set is orthogonal, and the energies of record 8 are not required if the NBO energetic analysis is not implemented for your ESS July 11, 1995 - 136 - package. Creating routine DELSCF will require intimate knowledge of the SCF routines in the parent ESS program; again, versions of DELSCF provided with this distribution may only be of minimal assistance. As described in Section C.11, SR DELSCF is responsible for providing a modified AO density matrix to an SCF energy evaluator (one pass throught the SCF routines) and returning this new energy to the NBO deletion routines via the FILE48 direct access file. If you do not intend to employ the NBO energetic analysis, you need not provide this routine to the NBO program. [Note that the 2nd-order per- turbation theory energy analysis will be carried out (pro- vided the Fock matrix is available) even if you do not include the NBOEAN and DELSCF energy analysis routines.] In addition to the explicitly system-dependent subroutines RUNNBO, FEAOIN, and DELSCF, there are a few routines within the NBO program which can be considered #Iquasi#N-system dependent, and might, therefore, require modification. These are SR NBOSET (Section C.5.2) and the `INP' routines NBOINP, CORINP, CHSINP, and DELINP (Section C.9): SR NBOSET assigns the logical file numbers (LFNs) 31-49 to be used by the NBO program. As mentioned above, if these are in conflict with the files employed by the parent ESS program, the conflicting LFNs will have to be reassigned in this subroutine. The `INP' routines may have to be modified according to the manner in which the input file of the parent program should be processed by the NBO program. More specifically, these routines either rewind the input file before searching for their associated keylist identifier, or they simply begin searching the input file sequentially at the point where the parent program left off, depending on the version number specified in NBOOPT(10). Be sure this parameter is con- sistent with the way you wish to modify the ESS input file for NBO input. 001111111100// 011100001110// 011000000110// 110000000011// 110000000011// 110000000011// 110000000011// 011000000110// 011100001110// 001111111100// 000011110000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000// 000000000000>> #HSection D: APPENDIX#N #BD.1 INTRODUCTION#N July 11, 1995 - 137 - 0 This Appendix contains system-dependent information about NBO input and source code for the ESS (electronic structure system) packages supported by this distribution. We assume that the user has basic familiarity with the ESS program of interest. 0 The Appendix is organized according to the ESS packages supported, which are described in Sections D.2-D.7, as shown below: 0 Each ESS section contains information on: Sample input file for RHF/3-21G methylamine NBO program installation Communication between the NBO drivers and the ESS program 0 For most users, only the first section(s) on sample input file will be required reading. For the programmer responsi- ble for attaching the NBO program to an ESS package, the final section on NBO drivers will be important only if the available ESS version differs significantly from that assumed in the installation instructions. 0 In the Appendix we use ``SR'' and ``FN'' to denote subrou- tines and functions, respectively. #BD.2 GAUSSIAN 88 VERSION#N #ID.2.1 GAUSSIAN 88 sample input#N 0 A sample GAUSSIAN 88 input file to recreate the default methylamine (RHF/3-21G at Pople-Gordon idealized geometry) output displayed in Section A.3 is shown below: # RHF/3-21G Methylamine...RHF/3-21G//Pople-Gordon standard geometry 0 1 C N 1 CN H 1 CH 2 tet H 1 CH 2 tet 3 120. 0 H 1 CH 2 tet 3 240. 0 H 2 NH 1 tet 3 60. 0 H 2 NH 1 tet 3 300. 0 CN 1.47 CH 1.09 NH 1.01 tet 109.4712 July 11, 1995 - 138 - $NBO $END #T @seg 0 #NThe keylists of the NBO program should always appear at the bottom of the GAUSSIAN 88 input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL. NBO job options are selected by inserting their associated key- words (Section B.2) into the $NBO keylist. All NBO keywords are applicable to the electronic wavefunctions computed by the GAUSSIAN 88 programs. 0 If the NBO program encounters the end-of-file while searching for a keylist, the input file is rewound and the search for the keylist is continued. This is par- ticularly useful for jobs which call the NBO analysis several times. For example, an MP2 calculation with the GAUSSIAN 88 option DENSITY=ALL causes Link 601 to loop over three densities (SCF, Rho2, and MP2), and hence, the NBO analysis is called three times, once for each density. A single $NBO keylist (and $CORE and $CHOOSE keylists) will suffice as input for all three analyses. Alternatively, separate $NBO keylists, one for each density, could be inserted at the bottom of the GAUSSIAN 88 input file. - 138 - 0 The IOp parameters 40-43 of Link 601 exert additional control over the NBO program, as listed below: For example, to restrict the NBO output to the Natural Population analysis (NPA) only, set IOp(40) to minus 1 in all Link 601 entries of a GAUSSIAN 88 non-standard route, as shown below: #T 6/40=-1/1; #NBy default, the NBO analysis will be performed, read- ing keywords from the $NBO keylist [IOp(40)=0], on the density matrix for the current wavefunction. The DIPOLE and RESONANCE keywords are generally activated through the $NBO keylist rather than via the IOp param- eters. - 138 - #ID.2.2 NBO energetic analysis#N 0 Due to the overlay structure of the GAUSSIAN 88 pro- grams, a non-standard route must be employed to perform the NBO energetic analysis. The following table lists and describes the tasks of the GAUSSIAN 88 links in the order that they appear in the non-standard route: #IDESCRIPTION#N Perform the normal NBO analysis, storing information about the NBOs for the NBO energetic analysis on the FILE48 direct access file. Read the next deletion listed in the $DEL keylist. If there are no more deletions, move to the next link. Otherwise, compute the modified density matrix, store it on the read-write files, and skip the next link in the non-standard route. Finish GAUSSIAN 88 execution. Using the modified density matrix, compute the deletion energy by a single pass through the SCF energy evalua- tor. Store the deletion energy on the read-write files. Read the deletion energy from the read-write files and complete the energetic analysis. Step backwards, in the non-standard route, three links. 0 The following is a GAUSSIAN 88 input file that will generate, in addition to the default NBO output, the NLMO (Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of methylamine: # NONSTD 1//1; 2//2; 3/5=5,11=1,25=14,30=1/1,2,3,11,14; 4/7=1/1; 5//1; 6/7=2,8=2,9=2,10=2,19=1/1; 6/40=2/1(1); 99/5=1,9=1/99; 5/7=1,13=1/1; 6/40=3/1(-3); Methylamine...RHF/3-21G//Pople-Gordon standard geometry 0 1 C N 1 CN H 1 CH 2 tet H 1 CH 2 tet 3 120. 0 H 1 CH 2 tet 3 240. 0 H 2 NH 1 tet 3 60. 0 H 2 NH 1 tet 3 300. 0 CN 1.47 July 11, 1995 - 139 - CH 1.09 NH 1.01 tet 109.4712 $NBO NLMO DIPOLE $END $DEL NOSTAR ZERO 2 ATOM BLOCKS 4 BY 3 1 3 4 5 2 6 7 3 BY 4 2 6 7 1 3 4 5 $END #T @seg 0 #NNote that for the GAUSSIAN 88 version of the NBO pro- gram, each deletion in the $DEL keylist must begin on a new line of the input file (the first deletion can follow the ``$DEL'' keylist identifier, as shown above). The ``$END'' keylist terminator must also appear on its own line. - 139 - #ID.2.3 Geometry reoptimization with NBO deletions#N 0 The structural effects of electron delocalization can be examined by coupling the NBO energetic analysis to the Fletcher-Powell (numerical) geometry optimization routines of the GAUSSIAN 88 package. The following GAUSSIAN 88 input file will reoptimize selected internal coordinates of RHF/3-21G methylamine in the absence of its strong #In#N#dN#u arr gma #u*#d#d#> C C Run the NBO ener- getic analysis. C If(IOp(40).ge.2) then IDens = 0 ! SCF density for dele- tion runs IOp(41) = IDens Call RunNBO(Core,NGot,IOp,IContr) go to 999 endIf C C <<< End of first NBO insert >> C C Put density matrices first. C IPA = IEnd1 + 1 . . . - 140 - Call ElEner(IOut,ISelfE,SCFDen,ISCF,IROHF,NAE,NBE,NBasis, $ Core(IPA),Core(IV),MDV) C C <<< Beginning of second NBO insert >>> C C Run the NBO analysis. C If(IOp(40).ne.-2) then IOp(41) = IDens Call RunNBO(Core,NGot,IOp,IContr) endIf C C <<< End of second NBO insert >>> C else if(IDens1.eq.IDSt.and.IDens1.eq.IDEnd) then . . . Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT, $ Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip)) C C <<< Beginning of third NBO insert >>> C C The following line has been changed from "Call ChainX(0)" in C order to exit the NBO deletion loop after the deletions are done: C 999 Call ChainX(IContr) C C <<< End of third NBO insert >>> C Return End #T @seg 0 #NThe first NBO insert initiates the NBO energetic analysis of SCF wavefunctions. The second insert lies within a loop over densities, and thus, the NBO program is called once for each density matrix analyzed by this link. The third insert allows the NBO energetic analysis to exit from the loop in the non-standard route. The NBO program installation should continue as discussed in Section A.2. - 140 - #ID.2.5 NBO communication with GAUSSIAN 88#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following GAUSSIAN 88 routines, read-write files, and COMMON blocks: #_GAUSSIAN 88 routines:#/#T SR CharPn(IString) SR DENGET(IOut,IODens,IMeth,LenDen,GotIt,P) FN ILSW(IOPER,WHERE,WHAT) FN InToWP(Nints) FN ITqry(Ifile) SR TRead(IARN,X,M,N,MM,NN,K) SR TWrite(IARN,X,M,N,MM,NN,K) #N#_GAUSSIAN 88 read-write files:#/ #_GAUSSIAN 88 COMMON blocks:#/#T COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401), + ATMCHG(400),C(1200) COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5), + KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400) COMMON/B/EXX(6000),C1(6000),C2(6000),C3(6000),X(2000),Y(2000), + Z(2000),JAN(2000),SHELLA(2000),SHELLN(2000),SHELLT(2000), + SHELLC(2000),AOS(2000),AON(2000),NSHELL,MAXTYP INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON DIMENSION C4(2000),SHLADF(2000) EQUIVALENCE(C4(1),C3(2001)),(SHLADF(1),C3(4001)) #N #BD.3 GAUSSIAN 86 VERSION#N #ID.3.1 GAUSSIAN 86 sample input#N 0 See Section D.2.1. Note that the NBO IOp parameters of Link 601 are set to 40-43 (changed from 20-23 in previous distributions of the NBO program). #ID.3.2 NBO energetic analysis#N 0 See Section D.2.2. #ID.3.3 Geometry reoptimization with NBO deletions#N 0 See Section D.2.3. - 140 - #ID.3.4 NBO program installation#N 0 The NBO interfacing (driver) routines provided in this distribution were written for the Revision C version of GAUSSIAN 86, dated 30-APR-1986. Section D.3.5 lists the GAUSSIAN 86 dependent elements of the NBO driver routines that may need slight modification for other versions of the GAUSSIAN 86 programs. 0 Two modifications to SR MulDrv of Link 601 are required to run the NBO analysis: *Deck MulDrv Subroutine MulDrv(Core) . . . If(NGot.lt.IEnd1) Write(IOut,2002) IEnd1, NGot Len2 = (NGot-I2A+1)/NTT C C <<< Beginning of first NBO insert >>> C IF(IOp(40).GE.2.OR.IOp(41).NE.0) GO TO 999 C C <<< End of first NBO insert >>> C C Do population analysis. C CALL MULPOP(MaxAtm,IOP,IROHF,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS, . . . Call PrtPol(IOut,ISCF,IRotat,IRwDip,NAE,NBE,NBasis,NTT, $ Core(IExPol),Core(ICMO),Core(IT),Core(IEV),Core(IDip)) C C <<< Beginning of second NBO insert >>> C 999 Call GetSCM(-1,Core(1),NGot,3HNBO,0) Call RunNBO(Core,NGot,IOp,IContr) C C The follow- ing line has been changed from "999 Call ChainX(0)" in C order to exit the NBO deletion loop after deletions are com- plete. C Call ChainX(IContr) C C <<< End of second NBO insert >>> C Return End #T @seg - 140 - 0 #NThe first NBO insert allows Link 601 to by-pass the Mul- liken Population and electric moment analysis routines if the NBO energetic analysis is to be performed or if a corre- lated wavefunction is being analyzed. The second insert requests all available memory be allocated for the NBO pro- gram and initiates the NBO analysis. Note that the call to SR ChainX has been altered from the original code. The NBO program installation should continue as discussed in Section A.2. - 140 - #ID.3.5 NBO communication with GAUSSIAN 86#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following GAUSSIAN 86 routines, read-write files, and COMMON blocks: #_GAUSSIAN 86 routines:#/#T SR CharPn(IString) FN ILSW(IOPER,WHERE,WHAT) FN InToWP(Nints) FN ITqry(Ifile) SR TRead(IARN,X,M,N,MM,NN,K) SR TWrite(IARN,X,M,N,MM,NN,K) #N#_GAUSSIAN 86 read-write files:#/ #_GAUSSIAN 86 COMMON blocks:#/#T COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(401), + ATMCHG(400),C(1200) COMMON/LP2/NLP(1600),CLP(1600),ZLP(1600),KFIRST(400,5), + KLAST(400,5),LMAX(400),LPSKIP(400),NFroz(400) COMMON/B/EXX(1200),C1(1200),C2(1200),C3(1200),X(400),Y(400), + Z(400),JAN(400),SHELLA(400),SHELLN(400),SHELLT(400), + SHELLC(400),AOS(400),AON(400),NSHELL,MAXTYP INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON DIMENSION C4(400),SHLADF(400) EQUIVALENCE(C4(1),C3(401)),(SHLADF(1),C3(801)) #N #BD.4 GAUSSIAN 82 VERSION#N #ID.4.1 GAUSSIAN 82 sample input#N 0 See Section D.2.1. Note that the NBO IOp parameters of Link 601 are set to 40-43 (changed from 20-23 in previous distributions of the NBO program). #ID.4.2 NBO energetic analysis#N 0 See Section D.2.2. #ID.4.3 Geometry reoptimization with NBO deletions#N 0 See Section D.2.3. - 140 - #ID.4.4 NBO program installation#N 0 The NBO interfacing (driver) routines provided in this distribution were written for the Revision H version of GAUSSIAN 82, dated 28-NOV-1983. Section D.4.5 lists the GAUSSIAN 82 dependent elements of the NBO driver routines that may need slight modification for other versions of the GAUSSIAN 82 programs. 0 Two modifications to SR MulDrv of Link 601 are required to run the NBO analysis: *Deck MulDrv Subroutine MulDrv(Core) . . . IF(IPRINT.NE.0) $WRITE(IOUT,2001)I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,IEND C C <<< Beginning of first NBO insert >>> C C The fol- lowing line has been changed from "CALL GETSCM(IEND,...)", C in order to ask for all available memory. C CALL GETSCM(-1,CORE(1),JJJMEM,6HMULDRV,0) C IF(IOP(40).GE.2.OR.IOP(41).NE.0) GO TO 100 C C <<< End of first NBO insert >>> C C DO THE POPULATION ANALYSIS. CALL MULPOP(IOP,NATOMS,ICHARG,MULTIP,NAE,NBE,NBASIS,IAN,AtmChg, $ C,Core(I1),CORE(I2),CORE(I3),CORE(I4),CORE(I5), $ CORE(I6),CORE(I7),CORE(I8),CORE(I9),CORE(I10)) C C <<< Beginning of second NBO insert >>> C 100 CALL RUNNBO(CORE,JJJMEM,IOP,ICONTR) C C The fol- lowing line has been changed from "CALL CHAINX(0)" in C order to exit the NBO deletion loop after deletions are com- plete. C CALL CHAINX(ICONTR) C C <<< End of second NBO insert >>> C RETURN END #T @seg - 140 - 0 #NThe first NBO insert allows Link 601 to by-pass the Mul- liken Population analysis routines if the NBO energetic analysis is to be performed or if a correlated wavefunction is being analyzed. The second insert initiates the NBO analysis. Note that the calls to routines GETSCM and CHAINX have been altered from the original code. The NBO program installation should continue as discussed in Section A.2. - 140 - #ID.4.5 NBO communication with GAUSSIAN 82#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following GAUSSIAN 82 routines, read-write files, and COMMON blocks: #_GAUSSIAN 82 routines:#/#T SR CharPn(IString) FN ILSW(IOPER,WHERE,WHAT) FN InToWP(Nints) FN ITqry(Ifile) SR TRead(IARN,X,M,N,MM,NN,K) SR TWrite(IARN,X,M,N,MM,NN,K) #N#_GAUSSIAN 82 read-write files:#/ #_GAUSSIAN 82 COMMON blocks:#/#T COMMON/MOL/NATOM,ICHARG,MULTIP,NAE,NBE,NE,NBASIS,IAN(101), + ATMCHG(100),C(300) COMMON/LP2/NLP(400),CLP(400),ZLP(400),KFIRST(100,5), + KLAST(100,5),LMAX(100),LPSKIP(100),NFroz(100) COMMON/B/EXX(240),C1(240),C2(240),C3(240),X(80),Y(80), + Z(80),JAN(80),SHELLA(80),SHELLN(80),SHELLT(80), + SHELLC(80),AOS(80),AON(80),NSHELL,MAXTYP INTEGER SHELLA,SHELLN,SHELLT,SHELLC,SHLADF,AOS,AON DIMENSION C4(80),SHLADF(80) EQUIVALENCE(C4(1),C3(81)),(SHLADF(1),C3(161)) #N #BD.5 GAMESS VERSION#N #ID.5.1 GAMESS sample input#N 0 A sample GAMESS input file to recreate the default methy- lamine (RHF/3-21G at Pople-Gordon idealized geometry) output displayed in Section A.3 is shown below: $CONTRL SCFTYP=RHF RUNTYP=ENERGY $END $DATA Methylamine...RHF/3-21G//Pople-Gordon standard geometry CS 0 Carbon 6. -0.713673 -0.014253 0.000000 1 SV 3 N21 Nitrogen 7. 0.749817 0.123940 0.000000 1 SV 3 N21 Hydrogen 1. -0.978788 -1.071520 0.000000 1 SV 3 N21 July 11, 1995 - 141 - Hydrogen 1. -1.123702 0.463146 -0.889982 1 SV 3 N21 Hydrogen 1. 1.129752 -0.318420 0.824662 1 SV 3 N21 $END $GUESS GUESS=EXTGUESS $END $NBO $END #T @seg 0 #NNBO job options are selected by inserting their associ- ated keywords (Section B.2) into the $NBO keylist. All NBO keywords are applicable to the electronic wavefunctions com- puted by GAMESS. 0 The following is a modified GAMESS input file that will generate, in addition to the default NBO output, the NLMO (Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of methylamine: $CONTRL SCFTYP=RHF RUNTYP=ENERGY $END $DATA Methylamine...RHF/3-21G//Pople-Gordon standard geometry CS 0 Carbon 6. -0.713673 -0.014253 0.000000 1 SV 3 N21 Nitrogen 7. 0.749817 0.123940 0.000000 1 SV 3 N21 Hydrogen 1. -0.978788 -1.071520 0.000000 1 SV 3 N21 Hydrogen 1. -1.123702 0.463146 -0.889982 1 SV 3 N21 Hydrogen 1. 1.129752 -0.318420 0.824662 1 SV 3 N21 $END $GUESS GUESS=EXTGUESS $END $NBO NLMO DIPOLE $END $DEL NOSTAR July 11, 1995 - 142 - ZERO 2 ATOM BLOCKS 4 BY 3 1 3 4 5 2 6 7 3 BY 4 2 6 7 1 3 4 5 - 142 - $END #T @seg 0 #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted in any order within the GAMESS input file; the NBO program rewinds the input file each time it searches for a keylist. - 142 - #ID.5.2 NBO program installation#N 0 The NBO interfacing (driver) routines provided in this distribution were written for the GAMESS program dated 6- DEC-1989. Section D.5.3 lists the GAMESS dependent elements of the NBO driver routines that may need slight modification for other versions of the GAMESS program. 0 Only one command line is added to the GAMESS source code to run the NBO analysis. A call (``IF(RHO) CALL RUNNBO'') should be inserted at the end of the GAMESS properties pack- age (SR HFPROP in module PRPLIB), as shown below: C*MODULE PRPLIB *DECK HFPROP SUBROUTINE HFPROP(SCFTYP) . . . C C ----- SELECT DESIRED ELECTROSTATIC PROPERTIES ----- C CALL PRSELC(SCFTYP) C WRITE(IW,FMT='('' ...... END OF PROPERTY EVALUATION ......'')') CALL TIMIT(1) C C <<< BEGINNING OF NBO INSERT >>> C IF(RHO) CALL RUNNBO C C <<< END OF NBO INSERT >>> C RETURN END #T @seg 0 #NIf the density matrix is available (RHO = .TRUE.), the NBO analysis is performed each time the properties package is called within GAMESS. For example, the NBO analysis of the computed wavefunction will be performed for every single point calculation and for both the initial and final points of a geometry optimization. The NBO output will appear immediately after the Mulliken Population Analysis and the electric properties in the GAMESS output file. 0 The NBO program installation should continue as discussed - 142 - in Section A.2. #ID.5.3 NBO communication with GAMESS#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following GAMESS routines, records of the dictionary file, and COMMON blocks: #_GAMESS routines:#T#/ SR DAREAD(IDAF,IODA,V,LEN,NREC,NAV) FN ENUC(N,Z,C) ENTRY GOTFM(IPAR) SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK) SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK) SR SYMH(F,H,IA) FN TRACEP(A,B,N) SR VADD(A,I,B,J,C,K,N) ENTRY VALFM(IPAR) #_#NGAMESS dictionary file:#/ #_#NGAMESS COMMON blocks:#T#/ PARAMETER (MXGTOT=5000, MXSH=1000, MXATM=50) COMMON /ECP2 / CLP(400),ZLP(400),NLP(400),KFIRST(MXATM,6), + KLAST(MXATM,6),LMAX(MXATM),LPSKIP(MXATM), + IZCORE(MXATM) COMMON /FMCOM / CORE(1) COMMON /INFOA / NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(MXATM),C(3,MXATM) COMMON /INTFIL/ NINTMX,NHEX,NTUPL,PACK2E,INTG76 COMMON /IOFILE/ IR,IW,IP,IS,IPK,IDAF,NAV,IODA(99) COMMON /NSHEL / EX(MXGTOT),CS(MXGTOT),CP(MXGTOT),CD(MXGTOT), + KSTART(MXSH),KATOM(MXSH),KTYPE(MXSH),KNG(MXSH), + KLOC(MXSH),KMIN(MXSH),KMAX(MXSH),NSHELL COMMON /OUTPUT/ NPRINT,ITOL,ICUT,NORMF,NORMP,NOPK COMMON /RUNLAB/ TITLE(10),A(MXATM),B(MXATM),BFLAB(2047) COMMON /SCFOPT/ SCFTYP,BLKTYP,MAXIT,MCONV,NCONV,NPUNCH - 142 - COMMON /XYZPRP/ X(3) #BD.6 HONDO VERSION#N #ID.6.1 HONDO sample input#N 0 A sample HONDO input file to recreate the default methy- lamine (RHF/3-21G at Pople-Gordon idealized geometry) output displayed in Section A.3 is shown below: $CNTRL RUNFLG=0 $END $BASIS Methylamine...RHF/3-21G//Pople-Gordon standard geometry 0 0 15 1 N21 CS 0 Carbon 6. -0.713673 -0.014253 0.000000 Nitrogen 7. 0.749817 0.123940 0.000000 Hydrogen 1. -0.978788 -1.071520 0.000000 Hydrogen 1. -1.123702 0.463146 -0.889982 Hydrogen 1. 1.129752 - 0.318420 0.824662 $END $GUESS NGUESS=4 $END $INTGRL $END $WFN WFNFLG=0 $END $SCF NCO=9 $END $NBO $END #T @seg 0 #NNBO job options are selected by inserting their associ- ated keywords (Section B.2) into the $NBO keylist. All NBO keywords are applicable to the electronic wavefunctions com- puted by HONDO. 0 The following is a modified HONDO input file that will generate, in addition to the default NBO output, the NLMO (Section B.6.2), the dipole moment (Section B.6.3), and the NBO energetic (Section B.6.10) analyses of methylamine: $CNTRL RUNFLG=0 $END $BASIS Methylamine...RHF/3-21G//Pople-Gordon standard geometry 0 0 15 1 N21 CS 0 Carbon 6. -0.713673 -0.014253 0.000000 Nitrogen 7. 0.749817 0.123940 0.000000 Hydrogen 1. -0.978788 -1.071520 0.000000 Hydrogen 1. -1.123702 0.463146 -0.889982 Hydrogen 1. 1.129752 - 0.318420 0.824662 $END $GUESS NGUESS=4 $END July 11, 1995 - 143 - $INTGRL $END $WFN WFNFLG=0 $END $SCF NCO=9 $END $NBO NLMO DIPOLE $END $DEL NOSTAR ZERO 2 ATOM BLOCKS 4 BY 3 1 3 4 5 2 6 7 3 BY 4 2 6 7 1 3 4 5 - 143 - $END #T @seg 0 #NIn general, the $NBO, $CORE, $CHOOSE, and $DEL keylists can be inserted in any order within the HONDO input file; the NBO program rewinds the input file each time it searches for a keylist. - 143 - #ID.6.2 NBO program installation#N 0 The NBO interfacing (driver) routines provided in this distribution were written for HONDO 7.0, dated 18-JAN-1988. Section D.6.3 lists the HONDO dependent elements of the NBO driver routines that may need slight modification for other versions of the HONDO program. 0 Only one command line is added to the HONDO source code to run the NBO analysis. A call (``CALL RUNNBO'') should be inserted at the end of the HONDO properties package (SR PROPTY in module PRP), as shown below: SUBROUTINE PROPTY . . . C C ----- ELECTRON AND SPIN DENSITIES ----- C IF(NODEN.EQ.0) CALL ELDENS C C <<< BEGINNING OF NBO INSERT >>> C CALL RUNNBO C C <<< END OF NBO INSERT >>> C NCALL=0 IF(SOME) NCALL=1 CALL TIMIT(NCALL) RETURN . . . END #T @seg 0 #NThe NBO analysis is performed each time the properties package is called within HONDO. For example, the NBO analysis of the computed wavefunction will be performed (unless NOPROP=1 in the $CONTRL namelist) for every single point calculation, for each point on a scan of a potential energy surface, and for both the initial and final points of a geometry optimization. The NBO output will appear immedi- ately after the Mulliken Population Analysis and the elec- tric properties in the HONDO output file. 0 The NBO program installation should continue as discussed - 143 - in Section A.2. #ID.6.3 NBO communication with HONDO#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following HONDO routines, records of the dictionary file, and COMMON blocks: #_HONDO routines:#T#/ SR DAREAD(IDAF,IODA,IX,NX,IDAR) SR DIPAMS(BMASS,NCALL,NCODE,SOME) FN DOTTRI(A,B,N) FN ENUC(N,Z,C) SR HSTAR(D,F,XX,IX,NINTMX,IA,NOPK) SR HSTARU(DA,FA,DB,FB,XX,IX,XP,XK,IXPK,NINTMX,IA,NOPK) SR SYMFCK(F,H,IA) #_#NHONDO dictionary file:#/ #_#NHONDO COMMON blocks:#T#/ COMMON/IJPAIR/IA(1) COMMON/INFOA/NAT,ICH,MUL,NUM,NX,NE,NA,NB,ZAN(50),C(3,50) COMMON/INTFIL/NOPK,NOK,NOSQUR,NINTMX,NHEX,NTUPL,PACK2E COMMON/IOFILE/IR,IW,IP,IJK,IPK,IDAF,NAV,IODA(99) COMMON/MEMORY/MAXCOR,MAXLCM COMMON/MOLNUC/NUC(50) COMMON/NSHEL/EX(440),CS(440),CP(440),CD(440),CF(440),CG(440), + KSTART(120),KATOM(120),KTYPE(120),KNG(120), + KLOC(120),KMIN(120),KMAX(120),NSHELL COMMON/RUNLAB/TITLE(10),ANAM(50),BNAM(50),BFLAB(512) COMMON/SCFOPT/SCFTYP COMMON/SCM/CORE(1) COMMON/WFNOPT/WFNTYP #N #BD.7 AMPAC VERSION#N #ID.7.1 AMPAC sample input#N 0 A sample AMPAC input file that will create default methy- lamine (AM1 at Pople-Gordon idealized geometry) output simi- lar to the #Iab initio#N output displayed in Section A.3 is shown below: AM1 CH3NH2...AM1//Pople-Gordon standard geometry C 0.000000 0 0.000000 0 0.000000 0 0 0 0 N 1.470000 0 0.000000 0 0.000000 0 1 0 0 H 1.090000 0 109.471230 0 0.000000 0 1 2 0 H 1.090000 0 109.471230 0 120.000000 0 1 2 July 11, 1995 - 144 - 3 H 1.090000 0 109.471230 0 240.000000 0 1 2 3 H 1.010000 0 109.471230 0 60.000000 0 2 1 3 H 1.010000 0 109.471230 0 300.000000 0 2 1 3 $NBO $END #T @seg 0 #NThe keylists of the NBO program should always appear at the bottom of the AMPAC input file and should be ordered: $NBO, $CORE, $CHOOSE, $DEL. NBO job options are selected by inserting their associated keywords (Section B.2) into the $NBO keylist. 0 Due to the implicit orthogonality of the basis functions, the following NBO keywords are not applicable to the wavefunctions computed by AMPAC (or other semi-empirical packages): #T AOPNAO AOPNLMO NAONHO SPNAO AONAO DINAO NAONLMO SPNHO AOPNHO DMNAO NAOMO SPNBO AOPNBO FNAO SAO SPNLMO #NIn addition, the NBO keywords that require access to the AO dipole integrals (DIPOLE, DIAO, DINAO, DINHO, DINBO, DINLMO) are not applicable with AMPAC, since these integrals are unavailable to the NBO program. - 144 - 0 The following is a modified AMPAC input file that will generate, in addition to the default NBO output, the NLMO and the NBO energetic analyses of methylamine: AM1 CH3NH2...AM1//Pople-Gordon standard geometry C 0.000000 0 0.000000 0 0.000000 0 0 0 0 N 1.470000 0 0.000000 0 0.000000 0 1 0 0 H 1.090000 0 109.471230 0 0.000000 0 1 2 0 H 1.090000 0 109.471230 0 120.000000 0 1 2 3 H 1.090000 0 109.471230 0 240.000000 0 1 2 3 H 1.010000 0 109.471230 0 60.000000 0 2 1 3 H 1.010000 0 109.471230 0 300.000000 0 2 1 3 $NBO NLMO $END $DEL NOSTAR ZERO 2 ATOM BLOCKS 3 BY 4 1 3 4 5 2 6 7 4 BY 3 2 6 7 1 3 4 5 $END #T @seg - 144 - #ID.7.2 Sample NBO output for AMPAC wavefunctions#N 0 Since the AMPAC output differs in significant respects from the #Iab initio#N examples presented in Sections A,B, we present some excerpts from the NBO output and a brief discussion of the NBO analysis of the AM1 wavefunction for methylamine (Pople-Gordon idealized geometry). The numeri- cal values in these exerpts (summary tables) should be ade- quate for checking purposes. 0 The summary of the Natural Population Analysis (NPA) for methylamine is shown below: Summary of Natural Population Analysis: Natural Population Natural --------- -------------------------------------- Atom # Charge Core Valence Rydberg Total ---------- ------------------------------------------------------------- C 1 -0.13281 2.00000 4.13281 0.00000 6.13281 N 2 -0.34739 2.00000 5.34739 0.00000 7.34739 H 3 0.03346 0.00000 0.96654 0.00000 0.96654 H 4 0.08488 0.00000 0.91512 0.00000 0.91512 H 5 0.08488 0.00000 0.91512 0.00000 0.91512 H 6 0.13849 0.00000 0.86151 0.00000 0.86151 H 7 0.13849 0.00000 0.86151 0.00000 0.86151 ======================================================================= * Total * 0.00000 4.00000 14.00000 0.00000 18.00000 #T @seg 0 #NNote that the core electrons of all heavy atoms (neglected in the semi-empirical AMPAC procedure) are incor- porated into the NPA, along the lines of the treatment of effective core potentials (Section B.6.12). Note also that the numerical values of AM1 natural charges (and other quan- tities) differ significantly from those presented in Section A.3.2, reflecting a tendency toward somewhat reduced bond polarities in AM1 wavefunctions. July 11, 1995 - 145 - - 145 - The NBO summary table is shown below: Natural Bond Orbitals (Summary): Princi- pal Delocalizations NBO Occupancy Energy (geminal,vicinal,remote) =============================================================================== Molecular unit 1 (CH5N) 1. BD ( 1) C 1- N 2 1.99095 -20.60408 9(g),10(g),11(g),12(g),13(g) 2. BD ( 1) C 1- H 3 1.99184 -17.81012 8(g),10(g),11(g),9(g) 3. BD ( 1) C 1- H 4 1.98864 -17.75195 12(v),9(g),11(g),8(g) 4. BD ( 1) C 1- H 5 1.98864 -17.75195 13(v),9(g),10(g),8(g) 5. BD ( 1) N 2- H 6 1.98916 -19.74256 13(g),8(g),10(v) 6. BD ( 1) N 2- H 7 1.98916 -19.74256 12(g),8(g),11(v) 7. LP ( 1) N 2 1.98489 -15.52775 9(v) 8. BD*( 1) C 1- N 2 0.01048 4.75597 9. BD*( 1) C 1- H 3 0.02306 4.29359 10. BD*( 1) C 1- H 4 0.01070 4.57248 11. BD*( 1) C 1- H 5 0.01070 4.57248 12. BD*( 1) N 2- H 6 0.01090 5.27834 13. BD*( 1) N 2- H 7 0.01090 5.27834 ------------------------------- Total Lewis 17.92328 ( 99.5738%) Valence non-Lewis 0.07672 ( 0.4262%) Rydberg non-Lewis 0.00000 ( 0.0000%) ------------------------------- Total unit 1 18.00000 (100.0000%) Charge unit 1 0.00000 #T @seg 0 #NNote that in this case the orbital energies and other matrix elements of the Fock operator are printed in electron volts, the energy units of the AMPAC package. Note also that the physical pattern of delocalization effects differs significantly from that shown in Section A.3.6, the AM1 results portraying numerous strong #Igeminal#N interactions that are not present in the #Iab initio#N output. Other differences between the AM1 and #Iab initio#N wavefunctions will be evident throughout the NBO output. - 145 - July 11, 1995 - 146 - 0 Finally, we include the output segment showing the NBO energetic analysis of methylamine: NOSTAR: Delete all Rydberg/antibond NBOs Deletion of the following orbitals from the NBO Fock matrix: 8 9 10 11 12 13 Occupations of bond orbitals: Orbital No deletions This deletion Change ---------- -------------------------------------------------------------------- 1. BD ( 1) C 1- N 2 1.99095 2.00000 0.00905 2. BD ( 1) C 1- H 3 1.99184 2.00000 0.00816 3. BD ( 1) C 1- H 4 1.98864 2.00000 0.01136 4. BD ( 1) C 1- H 5 1.98864 2.00000 0.01136 5. BD ( 1) N 2- H 6 1.98916 2.00000 0.01084 6. BD ( 1) N 2- H 7 1.98916 2.00000 0.01084 7. LP ( 1) N 2 1.98489 2.00000 0.01511 8. BD*( 1) C 1- N 2 0.01048 0.00000 -0.01048 9. BD*( 1) C 1- H 3 0.02306 0.00000 -0.02306 10. BD*( 1) C 1- H 4 0.01070 0.00000 -0.01070 11. BD*( 1) C 1- H 5 0.01070 0.00000 -0.01070 12. BD*( 1) N 2- H 6 0.01090 0.00000 -0.01090 13. BD*( 1) N 2- H 7 0.01090 0.00000 -0.01090 NEXT STEP: Evaluate the energy of the new density matrix that has been constructed from the deleted NBO Fock matrix by doing one SCF cycle. --------- --------------------------------------------------------------------- Energy of deletion : 22.024 Total SCF energy : -5.051 ------------------- Energy change : 27.075 kcal/mol, 27.075 kcal/mol ---------- -------------------------------------------------------------------- #T @seg July 11, 1995 - 147 - 0 #NNote that the ``energy of deletion'' (22.0 kcal/mol), ``total SCF energy'' (-5.1 kcal/mol) and ``energy change'' (27.1 kcal/mol) are all given in terms of heats of forma- tion, the standard AM1 form of expressing molecular ener- gies. - 147 - #ID.7.3 NBO program installation#N 0 The NBO interfacing (driver) routines provided in this distribution were written for AMPAC, version 1.00. Section D.7.4 lists the AMPAC dependent elements of the NBO driver routines that may need slight modification for other ver- sions of the AMPAC program. 0 Only one command line is added to the AMPAC source code to run the NBO analysis. A command ``CALL RUNNBO'' should be inserted in the AMPAC properties package (SR WRITE in module WRITE), as shown below: SUBROUTINE WRITE(TIME0,FUNCT) . . . X=MECI(EIGS,C,CBETA,EIGB, NORBS,NMOS,NCIS, .TRUE.) ENDIF C C <<< BEGINNING OF NBO INSERT >>> C CALL RUNNBO C C <<< END OF NBO INSERT >>> C IF (INDEX(KEYWRD,'MULLIK') +INDEX(KEYWRD,'GRAPH') .NE. 0) THEN IF (INDEX(KEYWRD,'MULLIK') .NE. 0) THEN . . . #T @seg 0 #NThe NBO analysis is performed each time SR WRITE is called. For example, the NBO analysis of the computed wavefunction will be performed for every single point calcu- lation and at the end of geometry optimizations. The NBO output will appear immediately after the Mulliken Population Analysis in the AMPAC output file. 0 The NBO program installation should continue as discussed - 147 - in Section A.2. #ID.7.4 NBO communication with AMPAC#N 0 The NBO driver routines (RUNNBO, FEAOIN, DELSCF) access the following AMPAC routines and COMMON blocks: #_AMPAC routines:#T#/ SR GMETRY(GEO,COORD) SR HCORE(COORD,H,W,WJ,WK,ENUCLR) SR FOCK2(F,PTOT,P,W,WJ,WK,NUMAT,NFIRST,NMIDLE,NLAST) SR FOCK1(F,PTOT,PA,PB) FN HELECT(N,P,H,F) #_#NAMPAC COMMON blocks:#T#/ INCLUDE 'SIZES' COMMON /ATHEAT/ ATHEAT COMMON /DENSTY/ P(MPACK),PA(MPACK),PB(MPACK) COMMON /ENUCLR/ ENUCLR COMMON /FOKMAT/ F(MPACK),FB(MPACK) COMMON /GEOKST/ NATOM,LABELS(NUMATM),NA(NUMATM),NB(NUMATM), + NC(NUMATM) COMMON /GEOM / GEO(3,NUMATM) COMMON /HMATRX/ H(MPACK) COMMON /KEYWRD/ KEYWRD COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM), + NLAST(NUMATM),NORBS,NELECS,NALPHA,NBETA,NCLOSE, + NOPEN,NDUMY,FRACT COMMON /NATORB/ NATORB(107) COMMON /TITLES/ COMENT(10),TITLE(10) COMMON /VECTOR/ C(MORB2),EIGS(MAXORB),CBETA(MORB2),EIGB(MAXORB) COMMON /WMATRX/ WJ(N2ELEC),WK(N2ELEC) #N #N #HINDEX#N Acceptor orbital,A21 ACS Software,A11 AMPAC version,A2,A7,A8,B66,C17 Angular symmetry labels,A5,#IB68#N,C7 Antiperiplanar interaction,A19,A23,B50 Archive file (FILE47),A5, #IB62-71#N,C8,C14,C31,C36 Arrays IBXM,C9,C22,C23 JPRINT,C6 July 11, 1995 - 148 - NBOOPT,C16,#IC17#N,C18, C26,C30,C36,C39 Atom-centered basis functions,A1 Atomic charge,A14 Atomic orbitals,A1,A5,A6,B67-68 Contracted gaussian,A6,B69-70 Pure (PAO),#IB11#N,B67-68,C19,C30 Slater-type,A6 #Isee#N Atomic shell #Isee#N Core orbitals #Isee#N Pre-orthogonal orbitals Atomic shell Core,A7,A8,A13,A14,A16,C24 Rydberg,A2,A8,A13,A14,A16,C25 Valence,A8,A13,A14,A16 Atomic units,A13,B65,C4,C13 Attaching NBO to ESS program, A10-11,C36,C38-39 AUHF method #Isee#N Wavefunction type Azimuthal angle (hi ),A20,C33 Basis set #Isee#N Atomic orbitals Benzene (C#d6#uH#d6#u),B3,B32-36 Bond bending,A8,A20 #Isee#N Hybrid direction BONDO program,A7 Bond order,B29-31 Matrix,B11,B65,C19 Boys LMOs,B3 Brunck, T. K.,A7 Canonical MOs,B6,B27-28,B71,C20 Carpenter, J. E.,A7 Chemical fragment,#IB16#N,B19 $CHOOSE list #Isee#N Keylists Comments (!),B1,B63,C29 Comment statements,C1 COMMON blocks /NBAO/,C7 /NBATOM/,C7 /NBBAS/,C9,C22,C31,C30 /NBCRD1/,C11,C29 /NBCRD2/,C12,C29 /NBDAF/,C12,C27,C28 /NBDXYZ/,C11 /NBFLAG/,C5 /NBGEN/,C13,C30 /NBINFO/,C4 /NBIO/,C8,C18 /NBLBL/,C10,C32 July 11, 1995 - 149 - /NBMOL/,C10 /NBNAO/,C10 /NBONAV/,C12 /NBOPT/,C6-7,C18,C30 /NBTHR/,C9,C18 /NBTOPO/,C11,C22 Contour plotting program,A8,B9,B69 Contracted gaussian orbitals #Isee#N Atomic orbitals Copper dimer (Cu#d2#u),B56-61 $CORE list #Isee#N Keylists Core orbitals,A6,A7,A8,A16, B12-13,B56-61,B66,C24,C30,C33 Core polarization,A8,B12 Core table,B12,C33 DAF #Isee#N Direct access file Datalists,B63-64 $BASIS,#IB67-68#N,B71,C31,C37 $CONTRACT,#IB69-70#N,C31,C37 $COORD,B63,B65,#IB66#N,C31,C37 $DENSITY,B71 $DIPOLE,B65,B71,C37 $FOCK,B65,B71,C37 $LCAOMO,B71,C37 Matrix,B71 $OVERLAP,B65,B71,C37 #Id#N-orbitals,B53,B56,B61 Default output,A12,B10 Deletion types,B17-19 $DEL (deletions) list #Isee#N Keylists Delocalization,A1,A2,A21,B3,B32,B51 Delocalization tail,A22,B23 Density matrix,A1,A5,A6,B6-7,C13 #Isee#N Bond-order matrix #Isee#N Spin density matrices Depletion of density matrix,C24 Diborane (B#d2#uH#d6#u),B40-43 Dictionary file,A4 Different Lewis structures for different spin #Isee#N Open-shell calculation Dimension specification,C4 Dipole moment,A5,A6,A8,B5,B6-7, #IB24-25#N,B65,B71,C11,C15,C24 Direct access file (FILE48),A3,A4,A5, B9,B65,C12,#IC14-15#N,C16,C27, C28,C36-39 Directed NBO search #Isee#N Keylists, $CHOOSE Directional analysis July 11, 1995 - 150 - #Isee#N Hybrid direction Distribution tape,A10 Donor orbital,A21,A22 Double-bond, no-bond resonance,B44-47 Driver routines,A3 #Isee#N Subroutines RUNNBO, etc. Edmiston-Ruedenberg LMOs,B3 Effective core potential (ECP), A8,#IB56-61#N,B66 Electronic structure system (ESS),A3 Common blocks,A4 Connection to NBO program,A3,A4,A7, A10-11,B56,B62,C36,C38-39 Input file,A5,A11,A12 Output file,A5,A12 Scratch files,A4 #Isee#N AMPAC, GAUSSIAN-8X, #Ietc.#N ENABLE program,A10,C36 Energetic analysis,A3,A5,#IB16-19#N, C2,C26,C38,C39 #Isee#N Perturbation theory... Excited state,A6,A8,A15,B56,C23 #If#N-orbitals #Isee#N Angular symmetry labels #Isee#N Keyword CUBICF Fenske-Hall method #Isee#N MEDVL Fetch/Save routines,C15,C27 FILE48 #Isee#N Direct access file FILE47 #Isee#N Archive file Flow chart,A4,C3,C16 Fock matrix,A2,A5,A6,A8,A14,A21, B6,B16-20,B26,B48-51,B65,B71, C2,C23,C26,C39 Fortran 77,A6,A10 Foster, J.P.,C22 Free format,B1,C29 Freezing a transformation,B8 Functions EQUAL,C29 IHTYP,C34 IOINQR,C32 IWPRJ,C24 NAMEAT,C34 VECLEN,C35 GAMESS version,A1,A2,A7,A10,A12,C17 Gaussian elimination,C35 GAUSSIAN-8X version,A2,A7, A10,B56,C17 July 11, 1995 - 151 - Geminal interaction,A22,B18,C33 Generalized eigenvalue problem,C20 GENNBO input file #Isee#N Archive file GENNBO stand-alone program A10,B9,B62-71,C13,C36,C37,C38 Geometry,B66 Glendening, E. D.,A7 Groups of routines I (NAO/NBO/NLMO),C2,C16-25 II (energy analysis),C2,C26 III (direct access file),C2,C27-28 IV (free format input),C2,C29 V (other I/O),C2,C30-32 VI (general utility),C2,C33-35 VII (system-dependent),C2,C36 GUGA formalism,A1 GVB method #Isee#N Wavefunction type Hay-Wadt ECP,B56 HONDO version,A2,A10,C17,C27 Hybrid composition,A19,B23 Hybrid direction,A8,#IA20#N,B4,C23 Hydrogen fluoride (HF),B37-39 I/O routines #Isee#N Groups of routines INP routines,C30,C39 Input file,A5,B62,C14 Installation procedure,A10-11 Ionic hybrids,B37-39 Job control keywords,B2,B3 Job initialization routines,C16,C18 Job threshold keywords,B2,B4-5 Kekulcute e structure,B36 Keylist,A5,A11,A12,#IB1#N Keylists $CHOOSE,B1,B2,B12,#IB14-15#N,#IB44-47#N, B62,B63,B65,C6,C22,C30 $CORE,B1,B2,#IB12-B13#N, B62,B63,B65,C3,C6-7,C30 $DEL,B1,B2,B12,#IB16-20#N, #IB48-51#N,B62,C17,C26,C30 $GENNBO,#IB65#N,B66,C30 $NBO,B1,#IB2-11#N,B21-43,B62,B63, B65,B69,C6,C17,C18,C22,C30 Keyword names (matrix output),B6-7 Keyword parameters (matrix output),B7-8 Keywords AOINFO,B2,#IB9#N,B69,B71,C6,C31 AOMO,B2,B6,B71,C6 July 11, 1995 - 152 - AONAO,B2,B6,C6,C30-31 AONBO,B2,B6,C6,C31 AONHO,B2,B6,C6 AONLMO,B2,B3,B6,C6,C31 AOPNAO,B2,B6,B71,C6 AOPNBO,B2,B6,B71,C6 AOPNHO,B2,B6,B71,C6 AOPNLMO,B2,B6,B71,C6 ARCHIVE,B2,#IB9#N,#IB62-71#N,C6,C31 BEND,A8,#IA20#N,B2,#IB4#N,B5,B10,C6,C23 BNDIDX,B2,#IB9#N,B10,B21, #IB29-B31#N,C6 BOAO,B11,C6 BODM,#IB65#N,C6,C13 BOHR,#IB65#N,B66,,C13 CUBICF,#IB65#N,B68,C6 DESTAR,B18 DETAIL,B2,#IB9#N,C6 DIAO,B2,B7,B71,C6 DINAO,B2,B7,B71,C6 DINBO,B2,B7,B71,C6 DINHO,B2,B7,B71,C6 DINLMO,B2,B6,B7,B71,C6 DIPOLE,A8,B2,B3,#IB5#N,B10,B21, #IB24-25#N,B71,C6,C17,C24 DMAO,B2,B7,C6 DMNAO,B2,B7,C6 DMNBO,B2,B7,C6 DMNHO,B2,B7,C6 DMNLMO,B2,B7,C6 E2PERT,#IA21#N,B2,#IB4#N,B5,B10,B71,C6 EV,B65 FAO,B2,B7,B71,C6 FNAO,B2,B7,B71,C6 FNBO,B2,B6-8,B7,B71,C6 FNHO,B2,B7,#IB26#N,B71,C6 FNLMO,B2,B7,B71,C6 LFNPR,B2,#IB9#N,C8 Matrix output,B6-8,B26-28 MULAT,B11,C6 MULORB,B11 NAOMO,B2,B6-8,B71,C6 NAONBO,B6-8,C6 NAONHO,B6-8,C6 NAONLMO,B6-8,C6 NATOMS,B65 NBAS,B65 NBODAF,B2,B9 NBO,#IA16-19#N,B2,#IB3#N,B10,C6 NBOMO,B2,B6-8,#IB27-28#N,B71,C6 NBONLMO,B2,B6-8,C6 NBOSUM,#IA22-23#N,B2,#IB3#N,B10,C6,C23 NHOMO,B2,B6-8,B71,C6 NHONBO,B2,B6-8,C6 July 11, 1995 - 153 - NHONLMO,B2,B6-8,C6 NLMO,B2,#IB3#N,B5,B10,#IB22-23#N,C6 NLMOMO,B2,B6-8,B71,C6 NOBOND,B2,#IB3#N,B21,#IB37-39#N,C6 NOGEM,B18 NOSTAR,B18,#IB48-49#N NOVIC,B18 NPA,#IA13-15#N,B2,#IB3#N,B10,C6,C20 OPEN,B65 ORTHO,B65 PAOPNAO,B11,C6 PLOT,A8,B2,#IB9#N,B69,B71,C6 PRINT,B2,B5,#IB10#N,B71,C18,C6 PRJTHR,B11 RESONANCE,A16,B2,#IB3#N,B21, #IB32-36#N,C6,C17,C25 REUSE,#IB65#N,B66,B67,C13 RPNAO,B11,C6 SAO,B2,B7,B71,C6 SKIPBO,B2,#IB3#N,B10,C6 SPNAO,B2,B6-8,B7,B71,C6 SPNBO,B2,B7,B71,C6 SPNHO,B2,B7,B71,C6 SPNLMO,B2,B3,B7,B71,C6 3CBOND,B2,#IB3#N,B14,B21,#IB40-43#N,C6 THRESH,B11 UPPER,B65,B71,C13 ZERO,B19,#IB49-51#N Kinks #Isee#N Hybrid direction, Bond bending Labelled COMMON blocks,A3,A6,C4-13 #Isee#N COMMON blocks Lewis orbitals #Isee#N Natural bond orbitals Linear equations package,C35 Linear independence,A1,C22,C24 Logical file number (LFN),C8,C38,C39 L mlaut owdin, P.-O.,A1 L mlaut owdin orthogonalization,C21 Matrix multiplication,C34 Matrix output keywords, B2,#IB6-8#N,B9,#IB26-28#N,C7 Mayer-Mulliken bond-order,C19 MCSCF method #Isee#N Wavefunction type MEDVL version,A10 Memory allocation, A6,A12,C16,C18,C19,C22 Methylamine (CH#d3#uNH#d2#u), A12-23,B21-31,B44-51,B63-71 Methyl radical (CH#d3#u),B52-55 Molecular units,#IB16#N,B18,B19,C10,C23 July 11, 1995 - 154 - M0t oller-Plesset method #Isee#N Wavefunction type MOPAC version,A10 Mulliken population analysis, A10,B11,C19,C38 Multiple bonds,A19,B14,B44-47,B56-61 Naaman, R.,A7 NAO formation routines,C16,C19-21 Natural atomic orbital (NAO) Formation,A1,A7,C16,C19-21 Labels,A13-14,C10 Listing,A13,C10 Summary table,A7 #Isee#N Natural population analysis Natural bond orbital (NBO) Analysis,A1-2,A16-19 Formalism,A1-A2,A7 Labels,A8,A19,B27-28,B43,C9,C10,C32 Lewis,A2,A16,A19,A21,A23,B48-51,B17 Listing,#IA17-19#N,B2 Non-Lewis,A2,A16,A19, A21,A23,B17,B18,B48-51 Summary table,#IA22-23#N,C23 3-center,A16,#IB40-43#N #Isee#N Perturbation theory... #Isee#N NBO/NLMO formation routines Natural electron configuration (NEC), A7,#IA15#N,C20 Natural hybrid orbital (NHO) Directional analysis,A20 Formation,A1-2 Labels,B26,C10 Listing,A-19 #Isee#N Natural bond orbitals #Isee#N Hybrid direction Natural Lewis structure,A1-2,A16, A19,B3,B18,B48,B49 Energy,B18,B48 Natural localized molecular orbital (NLMO) Formation,A7,B3,C25 Listing,B3,#IB22-23#N Natural minimal basis (NMB) set,A2,A14 Natural population analysis (NPA), A3,A6,A7,#IA13-14#N,B3, B10,B21,B56-57,C20 Natural Rydberg basis (NRB) set,A2,A18 NBO direct access file #Isee#N Direct access file $NBO keylist #Isee#N Keylists NBO energetic analysis #Isee#N Energetic analysis #Isee#N Perturbation theory... July 11, 1995 - 155 - NBO.MAN file,A10,A11 NBO/NLMO formation routines, C16,C22-25 NBO program,Section C I/O,A5,A12,C27-32 Installation,A10-11 Organization,A3-4,C2-4 Restrictions,A6 #Isee#N Electronic structure system NBO.SRC file,A10,C1,C2 NBO summary table,#IA22-23#N,C23 NLMO/NPA bond order,B30-31 Non-Lewis orbitals #Isee#N Natural Bond Orbital Open-shell calculation, A1,A5,B14,B25,#IB52-55#N,B65,C5 #Isee#N Wavefunction type Orbital contour plotting program, A8,B9,B69 Orthogonalization,C20 L mlaut owdin (symmetric),C24 Occupancy-weighted (OWSO),C20,C21 Schmidt,C20 Output control keywords,B2,#IB9-10#N Output file,A8,A12,C1 Overlap matrix,A5,A6,A8,B6,B71,C38 singularities,C25 Overlap-weighted NAO bond order,B30 Perturbation theory energy analysis, A8,#IA21#N,B3,B4,C23,C39 Phi,A20,C33 PNAO, PNBO, PNHO, PNLMO #Isee#N Pre-orthogonal orbitals Polar angle (heta ),A20,C33 Polarization coefficients,A2,A19,C25 Pople-Gordon geometry,A12,A20,B21,B32 Population analysis #Isee#N Mulliken population analysis #Isee#N Natural population analysis Population inversion,A14,B57 Pre-orthogonal orbitals, A1-2,A6,A8,B6,B65,B71 Print parameters,B2,#IB7-8#N, B11,B27-28,C7,C10 Program groups,C2 #Isee#N Groups of routines Program limits Atoms,A6,C4 Basis functions,A6,C4 Program precedence,C2,C3 Pseudopotential #Isee#N Effective core potential July 11, 1995 - 156 - Pure AOs,B11 #Isee#N Atomic orbital QCPE,A7,A8 Read (R) parameter #Isee#N Print parameters Read-write file,A4 Reed, A. E.,A7,B11,B31,C19 References,A7 Remote interaction,A22,C33 Resonance structures,A9,B14-15,B32-33, B38,B39,B44-47,C11,C25 Rewind input file,C39 RHF method #Isee#N Wavefunction type Rives, A. B.,A7 ROHF method #Isee#N Wavefunction type Schleyer, P. v.R.,B31 2nd-order perturbation theory analysis #Isee#N Perturbation theory energy... Semi-documented keywords,B2,#IB11#N Similarity transformation,C19,C26,C34 Slater-type orbitals #Isee#N AO basis functions Spin #Isee#N Open-shell calculations Spin-annihilated UHF (AUHF) method #Isee#N Wavefunction type Spin density matrices,A1,B52-55,C5 Storage #Isee#N Memory allocation Subroutines,C2,C3 ANGLES,C33 ANLYZE,C23 AOUT,C31 APRINT,C31,C32 AREAD,C31 ATDIAG,C20 AUGMNT,C25 AWRITE,C31 BDFIND,C33 BLDSTR,C23 CHEM,C33 CHOOSE,C22,C23,C24 CHSDRV,C22 CHSINP,C30 CONSOL,C33 CONVIN,C33 CONVRT,C33 COPY,C33 CORE,C24 July 11, 1995 - 157 - CORINP,C30 CORTBL,C33 CYCLES,C22,C25 DEBYTE,C33 DELETE,C26 DELINP,C30 DELSCF,A3,A4,A5,C2,#IC36#N,C38,C39 DEPLET,C24 DFGORB,C19,C30 DIPANL,A6,C22,C24 DIPELE,C24 DIPNUC,C24 DMNAO,C19 DMSIM,C19 FACTOR,C35 FEAOIN,A3,A4,A5,C2,C6, C14,#IC36#N,C38,C39 FEAOMO,C27 FEAOM,C27 FEBAS,C27 FECOOR,C27 FEDNAO,C27 FEDRAW,C27 FEDXYZ,C27 FEE0,C27 FEFAO,C27 FEFNBO,C27 FEINFO,C27 FENBO,C27 Subroutines (#Icontinued#N) FENEWD,C27 FENLMO,C27 FEPNAO,C27 FEPPAO,C27 FESNAO,C27 FESRAW,C27 FETITL,C27 FETLMO,C27 FETNAB,C27 FETNAO,C27 FETNBO,C27 FETNHO,C27 FNBOAN,C23 FNDFLD,C29 FNDMOL,C23 FNDSOL,C35 FORMT,C25 FRMHYB,C23 FRMPRJ,C25 FRMTMO,C20 GENINP,C30 GETDEL,C23 HALT,C33 HFLD,C29 July 11, 1995 - 158 - HTYPE,C23 HYBCMP,C23 HYBDIR,C23 IDIGIT,C33 IFLD,C29 INTERP,C32 JACOBI,C25,C34 JOBOPT,C18,C29 LBLAO,C32 LBLNAO,C32 LBLNBO,C32 LBLNHO,C32 LIMTRN,C34 LINEQ,C33,C35 LMOANL,C24 LOADAV,C20 LOAD,C24 MATML2,C34 MATMLT,C34 MULANA,C19 NAOANL,C21 NAODRV,C2,C19 NAOSIM,C19 NAO,C19 NATHYB,C22,C23,C24 NBCLOS,C16,C28 NBINQR,C28 NBOCLA,C23 NBODEL,C26 NBODIM,C18 NBODRV,C2,C19,C22 NBOEAN,A3,A4,A6,C3,C26,C36,C39 NBOINP,C30 NBOPEN,C16,C27 NBOSET,C18,C39 NBO,A3,A4,C2,C16,C36 NBOSUM,C23 NBREAD,C28 NBWRIT,C28 NEWDM,C26 NEWRYD,C20 NEWWTS,C20 NLMO,C22,C24 NORMLZ,C34 ORDER,C34 ORTHYB,C24 OUTPUT,C32 PACK,C34 PRJEXP,C24 RANK,C34 RDCARD,C29 RDCORE,C30 RDPPNA,C30 RDTNAB,C31 July 11, 1995 - 159 - RDTNAO,C31 REDBLK,C21 REDIAG,C21 REPOL,C25 RFLD,C29 RNKEIG,C26 RUNNBO,A3,A4,#IC36#N,C38,C39 RYDIAG,C20 RYDSEL,C21 SETBAS,C20 SHMDT,C20 SIMLTR,C26 SIMTRM,C19 SIMTRN,C34 SIMTRS,C34 SRTNBO,C22 STASH,C24 STRTIN,C29 SUBST,C35 SVDNAO,C27 SVE0,C27 SVFNBO,C27 SVNBO,C27 SVNEWD,C27 SVNLMO,C27 SVPNAO,C27 SVPPAO,C27 SVSNAO,C27 SVTLMO,C27 Subroutines (#Icontinued#N) SVTNAB,C27 SVTNAO,C27 SVTNHO,C27 SYMORT,C25 SYMUNI,C25 TRANSP,C34 UNPACK,C35 VALTBL,C35 WRARC,C31 WRBAS,C31 WRMLMO,C31 WRPPNA,C30 WRTNAB,C31 WRTNAO,C30,C31 WRTNBO,C312 XCITED,C23 Symmetric orthogonalization,C24,C25 Symmetry,B16 System-dependent driver routines,C36 TechSet,A11,A20 Theta,A20,C33 3-center bonds #Isee#N Natural bond orbitals July 11, 1995 - 160 - Thresholds,C9 ALLOW2,C20 ALLOW,C20 ANG,B4 ATHR,C23 DANGER,C20,C25 DIAGTH,C20,C25 DIFFER,C24,C34,C34 DONE,C34 DVAL,B5,B25 EPS,C24,C34 ETHR1,C23 ETHR2,C23 ETHR,C23 EVAL,B4 OCC,B4 PCT,B4 PRJINC,C22 PRJTHR,B11,C22 PTHR,C23 TEST2,C20 TEST,C20 THRESH,C22 THR1,C23 THR2,C23 THRESH,B11,C25 TOOSML,C24 WORTH,C20 WTTHR,C20,C21 2e-stabilization,A21 UHF method #Isee#N Wavefunction type Upper triangular matrix, B65,B71,C13,C33,C34 Vager, Z.,A7 Valency index #Isee#N Bond order Versions, previous,#IA7#N,A9,B13 Vicinal interaction,A22-23,B18, B23,B25,B51,C33 Warnings,B16,B17,B36,B55 Wavefunction type AUHF,C5,C17 CI,A6,C5,C17 Complex,A6,C5 Correlated,B25 GVB,A6 MCSCF,A1,A6,C5 M0t oller-Plesset,A6,C17 RHF,A6,A12,B16,B56,C2 ROHF,A6,C5 July 11, 1995 - 161 - SCF,A6,B16,B25,C17 Semi-empirical,A7,A8,B66 UHF,A6,B16,B20,B52-55,C2,C5 Weinhold, F.,A7,B11,C19,C22 Weinstock, R. B.,A7,B11,C19 Wiberg bond index,A16,B9,B29,C20,C22 Write (W) parameter #Isee#N Print parameters July 11, 1995