NBO 7.0 Program Manual Natural Bond Orbital Analysis

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NBO 7.0 Program ManualNatural Bond OrbitalAnalysis Programscompiled and edited byFrank Weinhold and Eric D. GlendeningF. Weinhold: Theoretical Chemistry Institute and Department of Chemistry, University ofWisconsin, Madison, Wisconsin 53706E-mail: weinhold@chem.wisc.eduPhone: (608)262-0263E. D. Glendening: Department of Chemistry and Physics, Indiana State University, TerreHaute, Indiana 47809E-mail: glendening@indstate.eduPhone: (812)237-2235NBO7 Website: http://nbo7.chem.wisc.edu/(c) Copyright 1996-2021 Board of Regents of the University of Wisconsin System onbehalf of the Theoretical Chemistry Institute. All Rights Reserved.

Table of ContentsA.Table of ContentsPreface: HOW TO USE THIS MANUALTable 1: NBO Keyword/Keylist Quick SummaryGETTING A.3.2A.3.3A.3.4A.3.5A.3.6INTRODUCTION TO THE NBO 7.0 PROGRAMWhat Does the NBO Program Do?Input and OutputGeneral Capabilities and RestrictionsReferences and Relationship to Previous VersionsWhat's New in NBO 7.0?INSTALLING THE NBO PROGRAMTUTORIAL EXAMPLE FOR METHYLAMINERunning the ExampleNatural Population AnalysisNatural Bond Orbital AnalysisNHO Directional AnalysisPerturbation Theory Energy AnalysisNBO 5B.6.6B.6.7INTRODUCTION TO THE NBO USER'S GUIDE AND NBO B-23B-25B-29B-31B-31B-32B-34B-36B-39B-42B-46B.NBO USER'S GUIDETHE NBO KEYLISTOverview of NBO KeywordsJob Control KeywordsJob Threshold KeywordsMatrix Output KeywordsOther Output Control KeywordsPrint Level KeywordsSemi-Documented Additional KeywordsTHE CORE LISTTHE CHOOSE KEYLIST (DIRECTED NBO SEARCH)THE DEL KEYLIST (NBO ENERGETIC ANALYSIS)Introduction to NBO Energetic AnalysisThe Nine Deletion TypesInput for UHF AnalysisNBO ILLUSTRATIONSIntroductionNLMO KeywordDIPOLE KeywordMatrix Output KeywordsBNDIDX KeywordStrong Delocalization: BenzeneNOBOND Keyword: Hydrogen Fluoridei

.14.1B.14.2B.14.3B.15B.15.1B.15.2B.15.3Hypovalent Bonding: DiboraneNBO Directed Search ( CHOOSE Keylist)NBO Energetic Analysis ( DEL Keylist)Open-Shell UHF Output: Methyl RadicalEffective Core Potential: Cu2 DimerFILE47: INPUT FOR THE GenNBO STAND-ALONE NBO PROGRAMIntroductionFormat of FILE47 GENNBO Keylist COORD Keylist BASIS Datalist CONTRACT Datalist WF DatalistMatrix DatalistsNRT: NATURAL RESONANCE THEORY ANALYSISIntroduction: Single and Multi-Reference NRT AnalysisNRT Job Control KeywordsAuxiliary NRTSTR Keylist InputNRT IllustrationsNBBP: NATURAL BOND-BOND POLARIZABILITY INDICESIntroduction to NBBPNBBP Keyword Usage and Sample OutputSTERIC: NATURAL STERIC ANALYSISIntroduction to Natural Steric AnalysisSTERIC Keyword Usage and Sample OutputNEDA: NATURAL ENERGY DECOMPOSITION ANALYSISIntroduction to NEDAPerforming NEDASample NEDA InputSample NEDA OutputCHECKPOINTING OPTIONSIntroductionCheckpointing OptionsCheckpoint Permutation ListsExample: CAS/NBO and CI/NBO CalculationsCMO: CANONICAL MO ANALYSISIntroductionCMO Keyword Usage and Sample OutputNCS: NATURAL CHEMICAL SHIELDING ANALYSISIntroduction to Natural Chemical Shielding AnalysisNCS Keyword UsageNCS Sample OutputNJC: NATURAL J-COUPLING ANALYSISIntroduction to Natural J-Coupling AnalysisNJC Keyword Usage and Sample InputNJC Sample -155B-155B-161B-163

.33-CENTER, 4-ELECTRON HYPERBOND SEARCHIntroductionSample OutputNBCP: NATURAL BOND CRITICAL POINT ANALYSISIntroduction to Natural Bond Critical Point AnalysisNBCP Keyword UsageAdditional NBCP BP and NBCP PT Keyword OptionsNBCP Sample OutputNCE: NATURAL COULOMB ELECTROSTATICS ANALYSISIntroductionNCE Keyword Usage and Sample OutputNCU: NATURAL CLUSTER UNIT ANALYSISIntroduction to NCU AnalysisNCU Sample OutputPROP: GENERAL 1E PROPERTY ANALYSISMATRIX: GENERAL MATRIX OPERATOR ANDTRANSFORMATION OUTPUTSTRUCTURAL AND GRAPHICAL OUTPUT KEYWORDSEFFECTIVELY UNPAIRED ELECTRON DISTRIBUTIONNPEPA: NATURAL POLYELECTRON POPULATION ANALYSISIntroduction to NPEPANPEPA Keywords and the NPEPA KeylistSample Input and OutputRDM2: 2ND-ORDER REDUCED DENSITY MATRIX ELEMENTSIntroductionRDM2 Keyword and Sample OutputRNBO: RESONANCE NATURAL BOND ORBITALSIntroductionRNBO and PRNBO KeywordsRNBO -223

PREFACE: HOW TO USE THIS MANUALThe NBO7 Manual consists of two major divisions:Section A (“Getting Started”) contains introductory and one-time informationfor the novice user – what the program does, new program functionality,program installation, and a brief tutorial on sample output.Section B (“NBO User's Guide”) is for the experienced user who has aninstalled program and general familiarity with standard default NBO output.This section documents the many keywords that can be used to alter and extendstandard NBO job options, with examples of the resulting output. Section B ismandatory for users who wish to use the program to its full potential. Thissection describes keyword-controllable capabilities of the basic NBO modules(Sec. B.1-B.6) and GenNBO stand-alone program (Sec. B.7), as well as NBObased supplemental modules (Sec. B.8 et seq.).The NBO website http://nbo7.chem.wisc.edu/ provides additional tutorials,sample input and output for main program keywords, and explanatorybackground and bibliographic material to supplement this Manual.A quick-reference index to NBO keywords and keylists discussed in thismanual is presented in Table 1 below. The table lists default (in [brackets]) andoptional keywords, indicating whether additional parameters must be provided(Parms? Y yes; N no; opt. optional) with a brief summary of the keywordresult and the page number of the Manual for further reference.iv

Table 1: NBO Keyword/Keylist Quick SummaryKeywordParms? Keyword DescriptionPageMain ProgramOptions[BEND]opt.Hybrid directionality and “bond-bending”analysisA-25B-7CMOopt.Bonding character of canonical molecularorbitalsB-142DIPOLEopt.Dipole moment analysisB-8, 34[E2PERT]opt.2nd-order perturbative estimates of NBOinteractionsA-26B-7MATRIXYGeneral operator and transformation matrixB-192MEMORYYAllocate dynamic memoryB-6Natural bond-bond polarizability indicesB-103NBBPopt.NBCPNNatural bond critical point analysisB-170[NBO]opt.Natural bond orbital compositionsA-21B-5[NBOSUM]NNBO summary tableA-27B-5NCENNatural coulomb electrostatics analysisB-181NCSopt.Natural chemical shielding analysisB-147NCUopt.Natural cluster unit analysisB-185NJCopt.Natural J-coupling analysisB-155Natural localized molecular orbitalcompositionsB-5, 32NLMON[NPA]opt.Natural population analysisA-18B-5NPEPAopt.Natural poly-electron population analysisB-207NRTNNatural resonance theory analysisB-82PROPYGeneral 1e property analysisB-189v

RADICALNEffectively unpaired electron distributionB-199RDM2N2nd Order Reduced Density MatrixB-218RNBONResonance Natural Bond OrbitalB-222Natural steric analysisB-106Write AO basis information to LFN 31B-14Write ARCHIVE (FILE47) for stand-aloneGenNBO inputB-14,68NAO-Wiberg Bond Index and related valencyindicesB-14,39Fock-Dirac density matrix (“Bond ordermatrix”)B-16STERICopt.Control it cycles in NBO searchB-16DETAILNAdditional details of NBO searchB-16DISTNAtomic distance tableB-14FILEYSpecify filestem for PLOT files and other I/OB-14FIXDMNCorrect unphysical occupancies of input density B-17matrixMATRIXYPrint general matrix operator outputB-192MOLDENopt.Write geometry and orbitals in Molden formatB-197MOLUNITYUser-specified molecular unitsB-5MSPNBONMaximum Spin-Paired NBOs (spin-averageddensity matrix)B-5MULATNGross Mulliken populations, by atomB-16MULORBNGross Mulliken populations, by orbital andatomB-16NBOCMLopt.Write NLS in CML formatB-196NBODAFopt.Write NBO direct access file (DAF) to diskB-16NBOMOLopt.Write NLS in MDL formatB-196NOBONDN1-center atomic hybrids (no 2-c NBO search)B-46vi

NRTCHGYAlter maximum formal charge for candidateNRT structuresNRTCMLNWrite NRT resonance structures in CML format B-196NRTDTLNAdditional details of NRT searchB-88NRTE2YSpecify delocalization threshold for NRTsearchB-86NRTLSTYPrint leading NRTSTR structure specifications B-87NRTMOLopt.Write NRT resonance structures in MDLmolfile formatB-196NRTPARYAlter threshold for NRT parent structuresB-86PLOTNWrite files for orbital plottingB-14PRINTYHeirarchical print control of NBO outputB-15PRJTHRYAlter projection threshold for NHO searchB-16PROPYNBO/NLMO analysis of selected operatorsB-189RPNAONRevised pure AO (PAO) to PNAOtransformationB-16SKIPBONSkip NBO search (NPA only for PRINT 1)B-5Print eigenvectors of AO overlap matrixB-17Alter occupancy threshold for NBO searchB-16opt.Write XMol-formatted geometryB-197DIopt.Output dipole moment matrix (DIAO, DINAO,etc.)B-10DMopt.Output density matrix (DMAO, DMNAO, etc.)B-10Fopt.Output Fock matrix (FAO, FNAO, etc.)B-10Kopt.Output kinetic energy matrix (KAO, KNAO,etc.)B-10Sopt.Output overlap matrix (SAO, SPNAO, SPNBO, B-10SPNLMO)SVECTHRESHXMOLopt.YB-88Operator MatrixOutputvii

Vopt.Output 1-e (N-e attraction) potential matrix(VAO, VNAO, etc.)B-10AOPAOopt.Output AO to PAO transformationB-9AONAOopt.Output AO to NAO transformationB-9AOPNAOopt.Output AO to PNAO transformationB-9AONHOopt.Output AO to NHO transformationB-9AOPNHOopt.Output AO to PNHO transformationB-9AONBOopt.Output AO to NBO transformationB-9AOPNBOopt.Output AO to PNBO transformationB-9AONLMOopt.Output AO to NLMO transformationB-9AOPNLMOopt.Output AO to PNLMO transformationB-9AONOopt.Output AO to NO transformationB-9AOMOopt.Output AO to MO (LCAO-MO) transformationB-9PAOPNAOopt.Output PAO to PNAO transformationB-11,16NAONHOopt.Output NAO to NHO transformationB-9NAONBOopt.Output NAO to NBO transformationB-9NAONLMOopt.Output NAO to NLMO transformationB-9NAONOopt.Output NAO to NO transformationB-9NAOMOopt.Output NAO to MO transformationB-9NHONBOopt.Output NHO to NBO transformationB-9NHONLMOopt.Output NHO to NLMO transformationB-9NHONOopt.Output NHO to NO transformationB-9NHOMOopt.Output NHO to MO transformationB-9NBONLMOopt.Output NBO to NLMO transformationB-9NBONOopt.Output NBO to NO transformationB-9NBOMOopt.Output NBO to MO transformationB-9TransformationMatrix Outputviii

NLMONOopt.Output NLMO to NO transformationB-9NLMOMOopt.Output NLMO to MO transformationB-9NOMOopt.Output NO to MO transformationB-9AuxiliaryKeylists CHOOSEYSpecify alternative Lewis structure for NBOsearchB-20 COREYModify default NBO core tableB-18 DELYDelete selected NBOs, interactions, or blocks of B-23interactions NPEPAYSpecify user-selected configurationsB-207 NRTSTRYSpecify reference structures for NRT analysis(also NRTSTRA and NRTSTRB)B-89 BASISYAtomic centers and angular symmetries of AOsB-74 C10YDerivative MO coefficientsB-151 CONTRACTYContraction coefficients and orbital exponentsof AOsB-76 COORDYJob title, atoms, Cartesian coordinatesB-73 DENSITYYDensity matrix in AO basisB-69 DIPOLEYDipole matrix in AO basisB-69 FOCKYFock matrix in AO basisB-69 GENNBOYSpecify calculation model size, type and unitsB-71 H01YGIAO Hamiltonian first derivativesB-151 H11YGIAO Hamiltonian second derivativiesB-151 KINETICYKinetic energy matrix in AO basisB-69 LCAOMOYCanonical MOs in AO basisB-69 NUCLEARYNuclear-electron attraction matrix in AO basisB-69 OVERLAPYOverlap matrix in AO basisB-69Auxiliary FILE47Keylistsix

A.1 INTRODUCTION TO THE NBO 7.0 PROGRAMSection A: GETTING STARTEDA.1 INTRODUCTION TO THE NBO 7.0 PROGRAMA.1.1 What Does the NBO Program Do?The NBO program performs the analysis of a many-electron molecularwavefunction in terms of localized electron-pair bonding units. The programcarries out the determination of natural atomic orbitals (NAOs), natural hybridorbitals (NHOs), natural bond orbitals (NBOs), and natural localized molecularorbitals (NLMOs), and uses these to perform natural population analysis(NPA), NBO energetic (deletions) analysis, and other tasks pertaining tolocalized analysis of wavefunction properties, including natural resonancetheory (NRT) and natural chemical shielding (NCS) analysis. This sectionprovides a brief introduction to NBO algorithms and nomenclature.The NBO method makes use of only the first-order reduced density matrix ofthe wavefunction, and hence is applicable to wavefunctions of generalmathematical form. In the open-shell case, the analysis is performed in termsof “different NBOs for different spins,” based on distinct density matrices for αand β spin. [Note, however, that electronic structure packages may not providethe spin density matrices for certain types of open-shell wavefunctions (e.g.,MCSCF or CASSCF wavefunctions calculated by the GUGA formalism). Inthis case NBO analysis can only be applied in the “maximum spin-paired”(MSPNBO) formulation.]NBO analysis is based on a method for optimally transforming a givenwavefunction into localized form, corresponding to the one-center (“lone pair”)and two-center (“bond”) elements of the chemist's Lewis structure picture. TheNBOs are obtained as local block eigenfunctions of the density matrix, and arehence “natural” in the sense of Löwdin, having optimal convergence propertiesfor describing the electron density. The set of high-occupancy NBOs, eachtaken doubly occupied, is said to represent the “natural Lewis structure” (NLS)of the molecule. Delocalization effects appear as weak departures from thisidealized localized picture. (For transition metals, a normal-valent Lewis-likestructure conforms to a dodectet rule, rather than the normal octet rule formain-group elements.)The various natural localized sets can be considered to result from a sequenceof transformations of the input atomic orbital basis set {χi},input basis AOs NAOs NHOs NBOs NLMOsA-1

A.1 INTRODUCTION TO THE NBO 7.0 PROGRAM[Note that the restriction to starting AOs is not intrinsic. If the wavefunctionwere not calculated in an atom-centered basis, one could first computewavefunctions for the individual atoms (in the actual basis set and geometry ofthe molecular calculation) and select the most highly occupied natural orbitalsas the starting “atomic orbitals” for that atom. Indeed, NBOs have now beenobtained for a variety of systems in the framework of plane-wave and relatedgrid-type descriptions; see B. Dunnington and J. R. Schmidt, “Generalization ofNatural Bond Orbital Analysis to Periodic Systems: Applications to Solids andSurfaces via Plane-Wave Density Functional Theory,” J. Chem. Theor. Comp.8, 1902 (2012); L. P. Lee, D. J. Cole, M. C. Payne, and C.-K. Skylaris, “NaturalBond Orbital Analysis in Linear-Scaling Density Functional TheoryCalculations” calApplications . However, because atom-centered basis functions arethe nearly universal choice for molecular calculations, the NBO program makesno provision for this step.]Each natural localized set forms a complete orthonormal set of one-electronfunctions for expanding the delocalized molecular orbitals (MOs) or formingmatrix representations of one-electron operators. The overlap of associated“pre-orthogonal” NAOs (PNAOs), lacking only the interatomicorthogonalization step of the NAO procedure, can be used to estimate thestrength of orbital interactions in the usual way, based on Mulliken-typeapproximations.The optimal condensation of occupancy in the natural localized orbitals leads topartitioning into high- and low-occupancy orbital types (reduction indimensionality of the orbitals having significant occupancy), as reflected in theorbital labelling. The small set of most highly-occupied NAOs, having a closecorrespondence with the effective minimal basis set of semi-empirical quantumchemistry, 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 NAOspace, but typically make little contribution to molecular properties. Similarlyin the NBO space, the highly occupied NBOs of the natural Lewis structure(NLS) can be distinguished from the “non-Lewis” antibond and Rydbergorbitals that complete the span of the NBO space. Each pair of valence hybridshA, hB in the NHO basis give rise to a bond (σAB) and antibond (σ*AB) in theNBO basis,σAB cAhA cBhBσ*AB cBhA cAhBA-2

A.1 INTRODUCTION TO THE NBO 7.0 PROGRAMthe former a Lewis (L, occupied) and the latter a non-Lewis (NL, unoccupied)orbital. The antibonds (valence shell non-Lewis orbitals) typically play theprimary role in departures (delocalization) from the idealized Lewis structure.The NBO program also makes extensive provision for energetic analysis ofNBO interactions, based on the availability of a 1-electron effective energyoperator (Fock or Kohn-Sham matrix) for the system. [As noted above, theconstruction of NAOs and NBOs is wholly independent of any such energyoperator (or geometry) information.] Estimates of energy effects are based onsecond-order perturbation theory, or on the effect of deleting certain orbitals ormatrix elements and recalculating the total energy. NBO energetic analysis isdependent on the host electronic structure system (ESS) to which the NBOprogram is attached, as described in the Appendix. Analysis of a DFTcalculation is performed analogously to a Hartree-Fock calculation, but usesKohn-Sham orbitals that incorporate important effects of a correlated electronicdistribution that are displayed in details of the NAOs, NBOs, and theiroccupancies.The core features included in default NBO analysis output are described inSections B.1-B.6. However, many additional features can be requested byspecific keywords in general NBO .(keywords). END keylist input.These features include natural resonance theory (NRT keyword), natural stericanalysis (STERIC keyword), natural energy decomposition analysis (NEDAkeyword), natural bond critical point analysis (NBCP keyword), and manyothers, each described in separate sections of this Manual. NBO 7.0 nowincludes additional analysis options for natural polyelectron population analysis(NPEPA keyword), reduced 2nd-order density matrix and cumulant evaluations(RDM2 keyword), and resonance-averaged natural bond orbitals (RNBOkeyword). Keyword-requested options build on and extend the capabilities ofcore NBO analysis, and are described separately in Sections B.8 et seq.NBO 7.0 comes installed in a number of leading ESS packages, and one shouldfollow the instructions provided with the ESS on how to run NBO. However,the NBO 7.0 program can also be obtained as a binary or source codedistribution that, in principle, can be attached to any ESS of the user's choice.The download package for the NBO 7.0 binary distribution contains specificinterfacing routines or instructions to facilitate direct binary-to-binaryinteractivity with a number of popular ab initio packages (currently includingGaussian, GAMESS, Molpro, Orca).A-3

A.1 INTRODUCTION TO THE NBO 7.0 PROGRAMA.1.2 Input and OutputFrom the user's point of view, input to the NBO portion of an ESS/NBOprogram consists simply of one or more keywords enclosed in NBO keylists inthe ESS input file. The main NBO keylist (the NBO keylist) is of the form: NBO .(keywords). ENDSimple examples of such NBO keylists are NBOdipolenrt NBOfile myjob ENDarchiven

B.16 3-CENTER, 4-ELECTRON HYPERBOND SEARCH B-166 B.16.1 Introduction B-166 B.16.2 Sample Output B-168 B.17 NBCP: NATURAL BOND CRITICAL POINT ANALYSIS B-170 B.17.1 Introduction to Natural Bond Critical Point Analysis B-170 B.17.2 NBCP Keyword Usage B-173 B.17.3 Additional NBCP_BP and NBCP_PT Key

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