Quantum Chemistry and Dynamics of Excited States_ Methods and Applications-Wiley (2021)

2021·10.14 MB·english

by  Roland Lindh (editor)

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QuantumChemistryandDynamicsofExcitedStates
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Quantum Chemistry and Dynamics of Excited States
Methods and Applications
Edited by
Leticia González
InstituteofTheoreticalChemistry,FacultyofChemistry
UniversityofVienna
Austria
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Roland Lindh
DepartmentofChemistry–BMC
UppsalaUniversity
Sweden
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Thiseditionfirstpublished2021
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vii
Contents
ListofContributors xix
Preface xxiii
1 MotivationandBasicConcepts 1
SandraGómez,IgnacioFdez.Galván,RolandLindh,andLeticiaGonzález
1.1 MissionandMotivation 1
1.2 AtomicUnits 4
1.3 TheMolecularHamiltonian 5
1.4 DiracorBra-KetNotation 6
1.5 IndexDefinitions 7
(cid:2) 1.6 SecondQuantizationFormalism 7 (cid:2)
1.7 Born–OppenheimerApproximationandPotentialEnergySurfaces 9
1.8 AdiabaticVersusDiabaticRepresentations 10
1.9 ConicalIntersections 11
1.10 FurtherReading 12
1.11 Acknowledgments 12
PartI QuantumChemistry 13
2 Time-DependentDensityFunctionalTheory 15
MiquelHuix-Rotllant,NicolasFerré,andMarioBarbatti
2.1 Introduction 15
2.2 TDDFTFundamentals 16
2.2.1 TheRunge–GrossTheorems 16
2.2.2 TheTime-DependentKohn–ShamApproach 18
2.2.3 SolutionsofTime-DependentKohn–ShamEquations 19
2.2.3.1 Real-TimeTDDFT 19
2.2.3.2 Linear-ResponseTDDFT 20
2.3 Linear-ResponseTDDFTinAction 22
2.3.1 VerticalExcitationsandEnergySurfaces 22
2.3.1.1 VerticalExcitations:HowGoodareThey? 23
2.3.1.2 ReconstructedEnergySurfaces:HowGoodareThey? 25
2.3.2 ConicalIntersections 28
2.3.3 CouplingTermsandAuxiliaryWaveFunctions 30
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2.3.3.1 TheCasidaAnsatz 30
2.3.3.2 Time-DerivativeNon-AdiabaticCouplings 31
2.3.4 Non-AdiabaticDynamics 32
2.4 ExcitedStatesandDynamicswithTDDFTVariantsandBeyond 34
2.5 Conclusions 35
Acknowledgments 36
References 36
3 Multi-ConfigurationalDensityFunctionalTheory:Progressand
Challenges 47
ErikDonovanHedegård
3.1 Introduction 47
3.2 WaveFunctionTheory 50
3.3 Kohn–ShamDensityFunctionalTheory 50
3.3.1 DensityFunctionalApproximations 53
3.3.2 DensityFunctionalTheoryforExcitedStates 54
3.3.2.1 IssuesWithintheTime-DependentDensityFunctionalTheoryAnsatz 55
3.3.2.2 Self-InteractionError 55
3.3.2.3 Degeneracies,Near-DegeneraciesandtheSymmetryDilemma 56
3.4 Multi-ConfigurationalDensityFunctionalTheory 57
3.4.1 Semi-EmpiricalMulti-ConfigurationalDensityFunctionalTheory 57
3.4.2 Multi-ConfigurationalDensityFunctionalTheoryBasedtheOn-TopPairDensity 58
(cid:2) 3.4.2.1 DensityMatricesandtheOn-TopPairDensity 59 (cid:2)
3.4.2.2 EnergyFunctionalandExcitedStateswiththeOn-TopPairDensity 60
3.4.3 Multi-ConfigurationalDensityFunctionalTheoryBasedonRange-Separation 61
3.4.3.1 EnergyFunctionalandExcitedStatesinRange-SeparatedMethods 62
3.4.3.2 TheRange-SeparationParameterinExcitedStateCalculations 62
3.5 IllustrativeExamples 64
3.5.1 ExcitedStatesofOrganicMolecules 64
3.5.2 ExcitedStatesforaTransitionMetalComplex 65
3.6 Outlook 66
Acknowledgments 67
References 67
4 Equation-of-MotionCoupled-ClusterModels 77
MonikaMusiał
4.1 Introduction 77
4.2 TheoreticalBackground 79
4.2.1 Coupled-ClusterWaveFunction 79
4.2.2 TheEquation-of-MotionApproach 80
4.2.3 Similarity-TransformedHamiltonian 81
4.2.4 DavidsonDiagonalizationAlgorithm 82
4.3 ExcitedStates:EE-EOM-CC 84
4.3.1 EE-EOM-CCSDModel 84
4.3.2 EE-EOM-CCSDTModel 86
4.3.3 EE-EOM-CCResults 87
4.4 IonizedStates:IP-EOM-CC 89
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4.4.1 IP-EOM-CCSDModel 89
4.4.2 IP-EOM-CCSDTModel 89
4.4.3 IP-EOM-CCResults 90
4.5 Electron-AttachedStates:EA-EOM-CC 91
4.5.1 EA-EOM-CCSDModel 92
4.5.2 EA-EOM-CCSDTModel 92
4.5.3 EA-EOM-CCResults 92
4.6 Doubly-IonizedStates:DIP-EOM-CC 94
4.6.1 DIP-EOM-CCSDModel 95
4.6.2 DIP-EOM-CCSDTModel 95
4.6.3 DIP-EOM-CCResults 96
4.7 DoublyElectron-AttachedStates:DEA-EOM-CC 97
4.7.1 DEA-EOM-CCSDModel 98
4.7.2 DEA-EOM-CCSDTModel 98
4.7.3 DEA-EOM-CCResults 98
4.8 Size-ExtensivityIssueintheEOM-CCTheory 100
4.9 FinalRemarks 102
References 103
5 TheAlgebraic-DiagrammaticConstructionSchemeforthePolarization
Propagator 109
AndreasDreuw
(cid:2) 5.1 OriginalDerivationviaGreen’sFunctions 110 (cid:2)
5.2 TheIntermediateStateRepresentation 112
5.3 CalculationofExcitedStatePropertiesandAnalysis 114
5.3.1 ExcitedStateProperties 114
5.3.2 Excited-StateWaveFunctionandDensityAnalyses 116
5.4 PropertiesandLimitationsofADC 117
5.5 VariantsofEE-ADC 119
5.5.1 ExtendedADC(2) 119
5.5.2 UnrestrictedEE-ADCSchemes 120
5.5.3 Spin-FlipEE-ADCSchemes 121
5.5.4 Spin-Opposite-ScaledADCSchemes 122
5.5.5 Core-ValenceSeparated(CVS)EE-ADC 123
5.6 DescribingMolecularPhotochemistrywithADCMethods 125
5.6.1 PotentialEnergySurfaces 125
5.6.2 EnvironmentModelswithinADC 126
5.7 BriefSummaryandPerspective 126
Bibliography 127
6 FoundationofMulti-ConfigurationalQuantumChemistry 133
GiovanniLiManni,KaiGuther,DongxiaMa,andWernerDobrautz
6.1 ScalingProbleminFCI,CASandRASWaveFunctions 136
6.2 FactorizationandCouplingofSlaterDeterminants 138
6.2.1 SlaterCondonRules 140
6.3 ConfigurationStateFunctions 141
6.3.1 TheUnitaryGroupApproach(UGA) 142
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6.3.1.1 AnalogybetweenCSFsandSphericalHarmonics 143
6.3.1.2 Gel’fand-TsetlinBasis 143
6.3.1.3 PaldusandWeylTables 145
6.3.1.4 TheStep-Vector 148
6.3.2 TheGraphicalUnitaryGroupApproach(GUGA) 148
6.3.3 EvaluationofNon-VanishingHamiltonianMatrixElements 153
6.3.3.1 One-BodyCouplingCoefficients 154
6.3.3.2 Two-BodyMatrixElements 157
6.4 ConfigurationInteractionEigenvalueProblem 158
6.4.1 IterativeMethods 159
6.4.1.1 LanczosAlgorithm 159
6.4.1.2 DavidsonAlgorithm 160
6.4.2 Direct-CIAlgorithm 162
6.5 TheCASSCFMethod 165
6.5.1 TheMCSCFParameterization 167
6.5.2 TheMCSCFGradientandHessian 169
6.5.3 One-StepandTwo-StepProcedures 170
6.5.4 AugmentedHessianMethod 171
6.5.5 MatrixformoftheFirstandSecondDerivativesinMCSCF 171
6.5.6 QuadraticallyConvergingMethodwithOptimalConvergence 175
6.5.7 Orbital-CICouplingTerms 178
6.5.8 Super-CIfortheOrbitalOptimization 179
(cid:2) 6.5.9 RedundancyofActiveOrbitalRotations 181 (cid:2)
6.6 RestrictedandGeneralizedActiveSpaceWaveFunctions 182
6.6.1 GUGAAppliedtoCAS,RASandGASWaveFunctions 184
6.6.2 RedundanciesinGASSCFOrbitalRotations 186
6.6.3 MCSCFMolecularOrbitals 187
6.6.4 GASSCFAppliedtotheGd Molecule 188
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6.7 ExcitedStates 189
6.7.1 Multi-StateCISolver 190
6.7.2 State-SpecificandState-AveragedMCSCF 191
6.8 StochasticMulticonfigurationalApproaches 191
6.8.1 FCIQMCWorkingEquation 192
6.8.2 Multi-WaveFunctionApproachforExcitedStates 196
6.8.3 SamplingReducedDensityMatrices 196
Bibliography 198
7 TheDensityMatrixRenormalizationGroupforStrongCorrelationinGround
andExcitedStates 205
LeonFreitagandMarkusReiher
7.1 Introduction 205
7.2 DMRGTheory 207
7.2.1 RenormalizationGroupFormulation 207
7.2.2 MatrixProductStatesandMatrixProductOperators 210
7.2.3 MPS-MPOFormulationofDMRG 214
7.2.4 ConnectionbetweentheRenormalizationGroupandtheMPS-MPOFormulationof
DMRG 217
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7.2.5 DevelopmentstoEnhanceDMRGConvergenceandPerformance 218
7.3 DMRGandOrbitalEntanglement 218
7.4 DMRGinPractice 220
7.4.1 CalculatingExcitedStateswithDMRG 220
7.4.2 FactorsAffectingtheDMRGConvergenceandAccuracy 220
7.4.3 Post-DMRGMethodsforDynamicCorrelationandEnvironmentEffects 221
7.4.4 AnalyticalEnergyGradientsandNon-AdiabaticCouplingMatrixElements 222
7.4.5 TensorNetworkStates 224
7.5 ApplicationsinQuantumChemistry 225
7.6 Conclusions 230
Acknowledgment 231
References 231
8 Excited-StateCalculationswithQuantumMonteCarlo 247
JonasFeldtandClaudiaFilippi
8.1 Introduction 247
8.2 VariationalMonteCarlo 249
8.3 DiffusionMonteCarlo 252
8.4 WaveFunctionsandtheirOptimization 256
8.4.1 StochasticReconfigurationMethod 258
8.4.2 LinearMethod 259
8.5 ExcitedStates 261
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8.5.1 Energy-BasedMethods 261
8.5.2 Time-DependentLinear-ResponseVMC 263
8.5.3 Variance-BasedMethods 264
8.6 ApplicationstoExcitedStatesofMolecularSystems 265
8.7 AlternativestoDiffusionMonteCarlo 269
Bibliography 270
9 Multi-ReferenceConfigurationInteraction 277
FelixPlasserandHansLischka
9.1 Introduction 277
9.2 Basics 278
9.2.1 ConfigurationInteractionandtheVariationalPrinciple 278
9.2.2 TheSize-ExtensivityProblemofTruncatedCI 280
9.2.3 Multi-ReferenceConfigurationSpaces 282
9.2.4 Many-ElectronBasisFunctions:DeterminantsandCSFs 286
9.2.5 Workflow 287
9.3 TypesofMRCI 289
9.3.1 UncontractedandContractedMRCI 289
9.3.2 MRCIwithExtensivityCorrections 291
9.3.3 TypesofSelectionSchemes 293
9.3.4 ConstructionofOrbitals 293
9.4 PopularImplementations 294
9.5 Conclusions 295
References 295
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10 Multi-ConfigurationalReferencePerturbationTheorywithaCASSCF
ReferenceFunction 299
RolandLindhandIgnacioFdez.Galván
10.1 Rayleigh–SchrödingerPerturbationTheory 300
10.1.1 TheSingle-StateTheory 300
10.1.1.1 TheConventionalProjectionalDerivation 300
10.1.1.2 TheBi-VariationalApproach 304
10.1.2 ConvergencePropertiesandIntruderStates 308
10.1.2.1 RealandImaginaryShiftTechniques 310
10.2 Møller–PlessetPerturbationTheory 313
10.2.1 TheReferenceFunction 314
10.2.2 ThePartitioningoftheHamiltonian 315
10.2.3 TheFirst-OrderInteractingSpaceandSecond-OrderEnergyCorrection 316
10.3 State-SpecificMulti-ConfigurationalReferencePerturbationMethods 320
10.3.1 TheGenerationoftheReferenceHamiltonian 321
10.3.2 CAS-MP2Theory 322
10.3.3 CASPT2Theory 323
10.3.3.1 ThePartitioningoftheHamiltonian 324
10.3.3.2 TheFirst-OrderInteractingSpace 325
10.3.3.3 OtherActiveSpaceReferences 328
10.3.3.4 BenchmarkResults 329
10.3.3.5 IPEAShift 330
(cid:2) 10.3.4 MRMP2Theory 331 (cid:2)
10.3.4.1 ThePartitioningoftheHamiltonian 331
10.3.4.2 TheFirst-OrderInteractingSpace 332
10.3.5 NEVPT2Theory 333
10.3.5.1 ThePartitioningoftheHamiltonian 333
10.3.5.2 TheFirst-OrderInteractingSpace 335
10.3.6 PerformanceImprovements 336
10.4 Quasi-DegeneratePerturbationTheory 338
10.5 Multi-StateMulti-ConfigurationalReferencePerturbationMethods 341
10.5.1 Multi-StateCASPT2Theory 341
10.5.2 ExtendedMS-CASPT2Theory 342
10.6 SummaryandOutlook 343
Acknowledgments 345
References 345
Appendix 350
PartII NuclearDynamics 355
11 ExactQuantumDynamics(WavePackets)inReducedDimensionality 357
SebastianReiter,DanielKeefer,andReginadeVivie-Riedle
11.1 Introduction 357
11.2 FundamentalsofMolecularQuantumDynamics 358
11.2.1 WavePacketDynamics 358
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