Essentials of Computational Chemistry Theories and Models Second Edition Christopher J. Cramer Department of Chemistry and Supercomputing Institute, University of Minnesota, USA Essentials of Computational Chemistry Second Edition Essentials of Computational Chemistry Theories and Models Second Edition Christopher J. Cramer Department of Chemistry and Supercomputing Institute, University of Minnesota, USA Copyright2004 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester, WestSussexPO198SQ,England Telephone(+44)1243779777 Email(forordersandcustomerserviceenquiries):[email protected] VisitourHomePageonwww.wileyeurope.comorwww.wiley.com AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedin anyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptunder thetermsoftheCopyright,DesignsandPatentsAct1988orunderthetermsofalicenceissuedbytheCopyright LicensingAgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermissioninwritingof thePublisher.RequeststothePublishershouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons Ltd,TheAtrium,SouthernGate,Chichester,WestSussexPO198SQ,England,oremailedto [email protected],orfaxedto(+44)1243770620. 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Includesbibliographicalreferencesandindex. ISBN0-470-09181-9(cloth:alk.paper)–ISBN0-470-09182-7(pbk. :alk.paper) 1. Chemistry,Physicalandtheoretical–Dataprocessing.2. Chemistry,Physicalandtheoretical–Mathematicalmodels. I.Title. QD455.3.E4C732004 541(cid:1).0285–dc22 2004015537 BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN0-470-09181-9(cased) ISBN0-470-09182-7(pbk) Typesetin10/12ptTimesbyLaserwordsPrivateLimited,Chennai,India PrintedandboundinGreatBritainbyAntonyRoweLtd,Chippenham,Wiltshire Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestry inwhichatleasttwotreesareplantedforeachoneusedforpaperproduction. For Katherine Contents Preface to the First Edition xv Preface to the Second Edition xix Acknowledgments xxi 1 What are Theory, Computation, and Modeling? 1 1.1 Definition of Terms 1 1.2 Quantum Mechanics 4 1.3 Computable Quantities 5 1.3.1 Structure 5 1.3.2 PotentialEnergySurfaces 6 1.3.3 ChemicalProperties 10 1.4 Cost and Efficiency 11 1.4.1 IntrinsicValue 11 1.4.2 HardwareandSoftware 12 1.4.3 Algorithms 14 1.5 Note on Units 15 Bibliography and Suggested AdditionalReading 15 References 16 2 Molecular Mechanics 17 2.1 History and Fundamental Assumptions 17 2.2 Potential Energy Functional Forms 19 2.2.1 BondStretching 19 2.2.2 ValenceAngleBending 21 2.2.3 Torsions 22 2.2.4 vanderWaalsInteractions 27 2.2.5 ElectrostaticInteractions 30 2.2.6 CrossTermsandAdditionalNon-bondedTerms 34 2.2.7 ParameterizationStrategies 36 2.3 Force-field Energies and Thermodynamics 39 2.4 Geometry Optimization 40 2.4.1 OptimizationAlgorithms 41 2.4.2 OptimizationAspectsSpecifictoForceFields 46 viii CONTENTS 2.5 Menagerie of Modern Force Fields 50 2.5.1 AvailableForceFields 50 2.5.2 Validation 59 2.6 Force Fields and Docking 62 2.7 Case Study: (2R∗,4S∗)-1-Hydroxy-2,4-dimethylhex-5-ene 64 Bibliographyand Suggested AdditionalReading 66 References 67 3 Simulations of Molecular Ensembles 69 3.1 RelationshipBetween MM Optima and Real Systems 69 3.2 Phase Space and Trajectories 70 3.2.1 PropertiesasEnsembleAverages 70 3.2.2 PropertiesasTimeAveragesofTrajectories 71 3.3 MolecularDynamics 72 3.3.1 HarmonicOscillatorTrajectories 72 3.3.2 Non-analyticalSystems 74 3.3.3 PracticalIssuesinPropagation 77 3.3.4 StochasticDynamics 79 3.4 MonteCarlo 80 3.4.1 ManipulationofPhase-spaceIntegrals 80 3.4.2 MetropolisSampling 81 3.5 Ensemble and Dynamical Property Examples 82 3.6 Key Details in Formalism 88 3.6.1 CutoffsandBoundaryConditions 88 3.6.2 Polarization 90 3.6.3 ControlofSystemVariables 91 3.6.4 SimulationConvergence 93 3.6.5 TheMultipleMinimaProblem 96 3.7 Force Field Performance in Simulations 98 3.8 Case Study: Silica Sodalite 99 Bibliographyand Suggested AdditionalReading 101 References 102 4 Foundations of Molecular Orbital Theory 105 4.1 QuantumMechanics and the Wave Function 105 4.2 The Hamiltonian Operator 106 4.2.1 GeneralFeatures 106 4.2.2 TheVariationalPrinciple 108 4.2.3 TheBorn–OppenheimerApproximation 110 4.3 Constructionof Trial Wave Functions 111 4.3.1 TheLCAOBasisSetApproach 111 4.3.2 TheSecularEquation 113 4.4 Hu¨ckel Theory 115 4.4.1 FundamentalPrinciples 115 4.4.2 ApplicationtotheAllylSystem 116 4.5 Many-electron Wave Functions 119 4.5.1 Hartree-productWaveFunctions 120 4.5.2 TheHartreeHamiltonian 121 4.5.3 ElectronSpinandAntisymmetry 122 4.5.4 SlaterDeterminants 124 4.5.5 TheHartree-FockSelf-consistentFieldMethod 126 Bibliographyand Suggested AdditionalReading 129 References 130 CONTENTS ix 5 Semiempirical Implementations of Molecular Orbital Theory 131 5.1 Semiempirical Philosophy 131 5.1.1 ChemicallyVirtuousApproximations 131 5.1.2 AnalyticDerivatives 133 5.2 Extended Hu¨ckel Theory 134 5.3 CNDO Formalism 136 5.4 INDO Formalism 139 5.4.1 INDOandINDO/S 139 5.4.2 MINDO/3andSINDO1 141 5.5 Basic NDDO Formalism 143 5.5.1 MNDO 143 5.5.2 AM1 145 5.5.3 PM3 146 5.6 General Performance Overview of Basic NDDO Models 147 5.6.1 Energetics 147 5.6.2 Geometries 150 5.6.3 ChargeDistributions 151 5.7 OngoingDevelopments in Semiempirical MO Theory 152 5.7.1 UseofSemiempiricalPropertiesinSAR 152 5.7.2 dOrbitalsinNDDOModels 153 5.7.3 SRPModels 155 5.7.4 LinearScaling 157 5.7.5 OtherChangesinFunctionalForm 157 5.8 Case Study: Asymmetric Alkylation of Benzaldehyde 159 Bibliography and Suggested AdditionalReading 162 References 163 6 Ab Initio Implementations of Hartree–Fock Molecular Orbital Theory 165 6.1 AbInitio Philosophy 165 6.2 Basis Sets 166 6.2.1 FunctionalForms 167 6.2.2 ContractedGaussianFunctions 168 6.2.3 Single-ζ,Multiple-ζ,andSplit-Valence 170 6.2.4 PolarizationFunctions 173 6.2.5 DiffuseFunctions 176 6.2.6 TheHFLimit 176 6.2.7 EffectiveCorePotentials 178 6.2.8 Sources 180 6.3 Key Technical and Practical Points of Hartree–Fock Theory 180 6.3.1 SCFConvergence 181 6.3.2 Symmetry 182 6.3.3 Open-shellSystems 188 6.3.4 EfficiencyofImplementationandUse 190 6.4 General Performance Overview of AbInitio HF Theory 192 6.4.1 Energetics 192 6.4.2 Geometries 196 6.4.3 ChargeDistributions 198 6.5 Case Study: Polymerization of 4-SubstitutedAromatic Enynes 199 Bibliography and Suggested AdditionalReading 201 References 201 x CONTENTS 7 Including Electron Correlation in Molecular Orbital Theory 203 7.1 Dynamical vs. Non-dynamical Electron Correlation 203 7.2 MulticonfigurationSelf-Consistent Field Theory 205 7.2.1 ConceptualBasis 205 7.2.2 ActiveSpaceSpecification 207 7.2.3 FullConfigurationInteraction 211 7.3 Configuration Interaction 211 7.3.1 Single-determinantReference 211 7.3.2 Multireference 216 7.4 Perturbation Theory 216 7.4.1 GeneralPrinciples 216 7.4.2 Single-reference 219 7.4.3 Multireference 223 7.4.4 First-orderPerturbationTheoryforSomeRelativisticEffects 223 7.5 Coupled-clusterTheory 224 7.6 Practical Issues in Application 227 7.6.1 BasisSetConvergence 227 7.6.2 SensitivitytoReferenceWaveFunction 230 7.6.3 Price/PerformanceSummary 235 7.7 Parameterized Methods 237 7.7.1 ScalingCorrelationEnergies 238 7.7.2 Extrapolation 239 7.7.3 MultilevelMethods 239 7.8 Case Study: EthylenedioneRadical Anion 244 Bibliographyand Suggested AdditionalReading 246 References 247 8 Density Functional Theory 249 8.1 Theoretical Motivation 249 8.1.1 Philosophy 249 8.1.2 EarlyApproximations 250 8.2 Rigorous Foundation 252 8.2.1 TheHohenberg–KohnExistenceTheorem 252 8.2.2 TheHohenberg–KohnVariationalTheorem 254 8.3 Kohn–ShamSelf-consistent Field Methodology 255 8.4 Exchange-correlation Functionals 257 8.4.1 LocalDensityApproximation 258 8.4.2 DensityGradientandKineticEnergyDensityCorrections 263 8.4.3 AdiabaticConnectionMethods 264 8.4.4 SemiempiricalDFT 268 8.5 Advantages and Disadvantages of DFT Compared to MO Theory 271 8.5.1 Densitiesvs.WaveFunctions 271 8.5.2 ComputationalEfficiency 273 8.5.3 LimitationsoftheKSFormalism 274 8.5.4 SystematicImprovability 278 8.5.5 Worst-caseScenarios 278 8.6 General Performance Overview of DFT 280 8.6.1 Energetics 280 8.6.2 Geometries 291 8.6.3 ChargeDistributions 294 8.7 Case Study: Transition-MetalCatalyzed Carbonylation of Methanol 299 Bibliographyand Suggested AdditionalReading 300 References 301