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“Dolg-Driver” — 2015/1/17 — 12:36 — page i — #1
Computational Methods in Lanthanide
and Actinide Chemistry
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Computational
Methods in Lanthanide
and Actinide Chemistry
Edited by
MICHAEL DOLG
Institute for Theoretical Chemistry,
University of Cologne, Germany
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Thiseditionfirstpublished2015
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LibraryofCongressCataloging-in-PublicationData
Dolg,Michael,1958-
Computationalmethodsinlanthanideandactinidechemistry/MichaelDolg.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-68831-1(cloth)
1. Rareearthmetals. 2. Actinideelements. 3. Chemistry,Inorganic. I. Title.
QD172.R2D652015
546(cid:2).41–dc23
2014040220
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Setin10/12ptTimesLTStdbySPiPublisherServices,Pondicherry,India
1 2015
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Contents
Contributors xiii
Preface xvii
1 RelativisticConfigurationInteractionCalculationsforLanthanide
andActinideAnions 1
DonaldR.Beck,StevenM.O’MalleyandLinPan
1.1 Introduction 1
1.2 BoundRareEarthAnionStates 2
1.3 LanthanideandActinideAnionSurvey 3
1.3.1 PriorResultsandMotivationfortheSurvey 3
1.3.2 TechniquesforBasisSetConstructionandAnalysis 6
1.3.3 DiscussionofResults 9
1.4 ResonanceandPhotodetachmentCrossSectionofAnions 12
1.4.1 TheConfigurationInteractionintheContinuumFormalism 13
1.4.2 CalculationoftheFinalStateWavefunctions 15
2 StudyofActinidesbyRelativisticCoupledClusterMethods 23
EphraimEliavandUziKaldor
2.1 Introduction 23
2.2 Methodology 25
2.2.1 TheRelativisticHamiltonian 25
2.2.2 Fock-SpaceCoupledClusterApproach 25
2.2.3 TheIntermediateHamiltonianCCmethod 27
2.3 ApplicationstoActinides 30
2.3.1 ActiniumandItsHomologues:InterplayofRelativityand
Correlation 31
2.3.2 ThoriumandEka-thorium:DifferentLevelStructure 35
2.3.3 Rn-likeactinideions 39
2.3.4 Electronic Spectrum of Superheavy Elements Nobelium (Z=102)
andLawrencium(Z=103) 42
2.3.5 TheLevelsofU4+andU5+:DynamicCorrelationandBreit
Interaction 45
2.3.6 RelativisticCoupledClusterApproachtoActinideMolecules 48
2.4 SummaryandConclusion 49
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vi Contents
3 RelativisticAll-ElectronApproachestotheStudyoffElementChemistry 55
TrondSaueandLucasVisscher
3.1 Introduction 55
3.2 RelativisticHamiltonians 59
3.2.1 GeneralAspects 59
3.2.2 Four-ComponentHamiltonians 61
3.2.3 Two-ComponentHamiltonians 65
3.2.4 NumericalExample 69
3.3 ChoiceofBasisSets 71
3.4 ElectronicStructureMethods 73
3.4.1 CoupledClusterApproaches 75
3.4.2 Multi-ReferencePerturbationTheory 80
3.4.3 (Time-Dependent)DensityFunctionalTheory 82
3.5 ConclusionsandOutlook 83
4 Low-LyingExcitedStatesofLanthanideDiatomicsStudiedby
Four-ComponentRelativisticConfigurationInteractionMethods 89
HiroshiTatewaki,ShigeyoshiYamamotoandHirokoMoriyama
4.1 Introduction 89
4.2 MethodofCalculation 90
4.2.1 QuaternionSymmetry 90
4.2.2 BasisSetandHFR/DCMethod 91
4.2.3 GOSCIandRASCIMethods 91
4.3 GroundState 92
4.3.1 CeOGroundState 92
4.3.2 CeFGroundState 97
4.3.3 DiscussionofBondinginCeOandCeF 101
4.3.4 GdFGroundState 102
4.3.5 SummaryoftheChemicalBonds,ofCeO,CeF,GdF 104
4.4 ExcitedStates 106
4.4.1 CeOExcitedStates 106
4.4.2 CeFExcitedStates 108
4.4.3 GdFExcitedStates 108
4.5 Conclusion 116
5 TheComplete-Active-SpaceSelf-Consistent-FieldApproachandIts
ApplicationtoMolecularComplexesofthef-Elements 121
AndrewKerridge
5.1 Introduction 121
5.1.1 TreatmentofRelativisticEffects 123
5.1.2 BasisSets 123
5.2 IdentifyingandIncorporatingElectronCorrelation 124
5.2.1 TheHartreeProductWavefunction 124
5.2.2 SlaterDeterminantsandFermiCorrelation 124
5.2.3 CoulombCorrelation 126
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Contents vii
5.3 ConfigurationInteractionandtheMulticonfigurationalWavefunction 127
5.3.1 TheConfigurationInteractionApproach 127
5.3.2 CIandtheDissociationofH 128
2
5.3.3 StaticCorrelationandCrystalFieldSplitting 130
5.3.4 SizeInconsistencyandCoupledClusterTheory 131
5.3.5 ComputationalExpenseofCIandtheNeedforTruncation 132
5.4 CASSCFandRelatedApproaches 133
5.4.1 TheNaturalOrbitals 133
5.4.2 OptimisationoftheCASSCFWavefunction 133
5.4.3 VariantsandGeneralisationsofCASSCF 137
5.5 SelectionofActiveSpaces 138
5.5.1 ChemicalIntuitionandBjörn’sRules 138
5.5.2 NaturalOrbitalOccupations 139
5.5.3 RASProbing 139
5.6 DynamicalCorrelation 139
5.6.1 MultireferenceConfigurationInteraction 140
5.6.2 MultireferenceSecondOrderPerturbationTheory 140
5.7 Applications 141
5.7.1 BondinginActinideDimers 141
5.7.2 CovalentInteractionsintheU-OBondofUranyl 142
5.7.3 CovalencyandOxidationStateinf-ElementMetallocenes 143
5.8 ConcludingRemarks 144
6 RelativisticPseudopotentialsandTheirApplications 147
XiaoyanCaoandAnnaWeigand
6.1 Introduction 147
6.2 Valence-onlyModelHamiltonian 149
6.2.1 Pseudopotentials 150
6.2.2 Approximations 151
6.2.3 ChoiceoftheCore 153
6.3 PseudopotentialAdjustment 155
6.3.1 Energy-ConsistentPseudopotentials 155
6.3.2 Shape-ConsistentPseudopotentials 158
6.4 ValenceBasisSetsforPseudopotentials 161
6.5 SelectedApplications 162
6.5.1 DFTCalculatedM–X(M=Ln,An;X=O,S,I)BondLengths 163
6.5.2 Lanthanide(III)andActinide(III)Hydration 166
6.5.3 Lanthanide(III)andActinide(III)Separation 170
6.6 ConclusionsandOutlook 172
7 Error-BalancedSegmentedContractedGaussianBasisSets:
AConceptandItsExtensiontotheLanthanides 181
FlorianWeigend
7.1 Introduction 181
7.2 CoreandValenceShells:GeneralandSegmentedContractionScheme 182
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viii Contents
7.3 PolarizationFunctionsandErrorBalancing 185
7.4 ConsiderationsforLanthanides 187
8 GaussianBasisSetsforLanthanideandActinideElements:
StrategiesforTheirDevelopmentandUse 195
KirkA.PetersonandKennethG.Dyall
8.1 Introduction 195
8.2 BasisSetDesign 196
8.2.1 GeneralConsiderations 196
8.2.2 BasisSetsforthefBlock 197
8.3 OverviewofExistingBasisSetsforLanthanidesandActinideElements 204
8.3.1 All-ElectronTreatments 204
8.3.2 EffectiveCorePotentialTreatments 205
8.4 SystematicallyConvergentBasisSetsforthefBlock 206
8.4.1 All-Electron 207
8.4.2 Pseudopotential-Based 208
8.5 BasisSetConvergenceinMolecularCalculations 210
8.6 Conclusions 213
9 4f,5d,6s,andImpurity-TrappedExcitonStatesofLanthanidesinSolids 217
ZoilaBarandiaránandLuisSeijo
9.1 Introduction 217
9.2 Methods 220
9.2.1 Embedded-ClusterMethods 221
9.2.2 Combined Use of Periodic Boundary Condition Methods and
EmbeddedClusterMethods 227
9.2.3 AbsorptionandEmissionSpectra 227
9.3 Applications 228
9.3.1 BondLengths 228
9.3.2 EnergyGaps 231
9.3.3 Impurity-TrappedExcitons 232
9.3.4 Solid-State-LightingPhosphors 234
10 Judd-OfeltTheory—TheGolden(andtheOnlyOne)Theoretical
Tooloff-ElectronSpectroscopy 241
LidiaSmentek
10.1 Introduction 241
10.2 Non-relativisticApproach 245
10.2.1 StandardJudd-OfeltTheoryandItsOriginalFormulationof1962 248
10.2.2 ChallengesofabinitioCalculations 251
10.2.3 ProblemswiththeInterpretationofthef-Spectra 255
10.3 Third-OrderContributions 257
10.3.1 Third-OrderElectronCorrelationEffectiveOperators 259
10.4 RelativisticApproach 260
10.5 Parameterizationsofthef-Spectra 262
Description:The f-elements and their compounds often possess an unusually complex electronic structure, governed by the high number of electronic states arising from open f-shells as well as large relativistic and electron correlation effects. A correct theoretical description of these elements poses the highes
