Electronic Structure: Basic Theory and Practical Methods, 2nd Edition

791 Pages·2020·18.136 MB·English

by  Richard M. Martin

ELECTRONIC STRUCTURE
The study of the electronic structure of materials is at a momentous stage, with new
computational methods and advances in basic theory. Many properties of materials can
bedeterminedfromthefundamentalequations,andelectronicstructuretheoryisnowan
integralpartofresearchinphysics,chemistry,materialsscience,andotherfields.Thisbook
providesaunifiedexpositionofthetheoryandmethods,withemphasisonunderstanding
eachessentialcomponent.
New in the second edition are recent advances in density functional theory, an
introduction to Berry phases and topological insulators explained in terms of elementary
bandtheory,andmanynewexamplesofapplications.
Graduatestudentsandresearchscientistswillfindcarefulexplanationswithreferences
tooriginalpapers,pertinentreviews,andaccessiblebooks.Eachchapterincludesashort
list of the most relevant works and exercises that reveal salient points and challenge the
reader.
Richard M. Martin is Emeritus Professor of Physics at the University of Illinois
Urbana–ChampaignandAdjunctProfessorofAppliedPhysicsatStanfordUniversity.He
hasmadeimportantcontributionstomanyareasofmodernelectronicstructure,including
more than 200 papers, and is a coauthor of another major book in the field, Interacting
Electrons:TheoryandComputationalApproaches(CambridgeUniversityPress,2016).

Electronic Structure
Basic Theory and Practical Methods
RichardM.Martin
UniversityofIllinoisUrbana–Champaign
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Informationonthistitle:www.cambridge.org/9781108429900
DOI:10.1017/9781108555586
©RichardM.Martin2020
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Contents
Preface xix
Acknowledgments xxiv
ListofNotation xxvi
PartI OverviewandBackgroundTopics
1 Introduction 1
1.1 QuantumTheoryandtheOriginsofElectronicStructure 2
1.2 WhyIstheIndependent-ElectronPictureSoSuccessful? 3
1.3 EmergenceofQuantitativeCalculations 7
1.4 TheGreatestChallenge:ElectronInteractionandCorrelation 10
1.5 DensityFunctionalTheory 11
1.6 ElectronicStructureIsNowanEssentialPartofResearch 11
1.7 MaterialsbyDesign 12
1.8 TopologyofElectronicStructure 13
2 Overview 15
2.1 ElectronicStructureandthePropertiesofMatter 15
2.2 ElectronicGroundState:BondingandCharacteristicStructures 17
2.3 VolumeorPressureAstheMostFundamentalVariable 19
2.4 HowGoodIsDFTforCalculationofStructures? 21
2.5 PhaseTransitionsunderPressure 23
2.6 StructurePrediction:NitrogenSolidsandHydrogenSulfide
SuperconductorsatHighPressure 26
2.7 MagnetismandElectron–ElectronInteractions 31
2.8 Elasticity:Stress–StrainRelations 33
2.9 PhononsandDisplacivePhaseTransitions 35
2.10 ThermalProperties:Solids,Liquids,andPhaseDiagrams 38
2.11 SurfacesandInterfaces 44
2.12 Low-DimensionalMaterialsandvanderWaalsHeterostructures 47
2.13 Nanomaterials:BetweenMoleculesandCondensedMatter 48
2.14 ElectronicExcitations:BandsandBandgaps 50
viii Contents
2.15 ElectronicExcitationsandOpticalSpectra 54
2.16 TopologicalInsulators 57
2.17 TheContinuingChallenge:ElectronCorrelation 57
3 TheoreticalBackground 60
3.1 BasicEquationsforInteractingElectronsandNuclei 60
3.2 CoulombInteractioninCondensedMatter 64
3.3 ForceandStressTheorems 65
3.4 GeneralizedForceTheoremandCouplingConstantIntegration 67
3.5 StatisticalMechanicsandtheDensityMatrix 68
3.6 Independent-ElectronApproximations 69
3.7 ExchangeandCorrelation 74
Exercises 78
4 PeriodicSolidsandElectronBands 81
4.1 StructuresofCrystals:Lattice+Basis 81
4.2 ReciprocalLatticeandBrillouinZone 90
4.3 ExcitationsandtheBlochTheorem 94
4.4 Time-ReversalandInversionSymmetries 98
4.5 PointSymmetries 100
4.6 IntegrationovertheBrillouinZoneandSpecialPoints 101
4.7 DensityofStates 105
Exercises 106
5 UniformElectronGasandsp-BondedMetals 109
5.1 TheElectronGas 109
5.2 NoninteractingandHartree–FockApproximations 111
5.3 CorrelationHoleandEnergy 117
5.4 Bindinginsp-BondedMetals 121
5.5 ExcitationsandtheLindhardDielectricFunction 122
Exercises 126
PartII DensityFunctionalTheory
6 DensityFunctionalTheory:Foundations 129
6.1 Overview 129
6.2 Thomas–Fermi–DiracApproximation 130
6.3 TheHohenberg–KohnTheorems 131
6.4 ConstrainedSearchFormulationofDFT 135
6.5 ExtensionsofHohenberg–KohnTheorems 137
6.6 IntricaciesofExactDensityFunctionalTheory 139
6.7 DifficultiesinProceedingfromtheDensity 141
Exercises 143
Contents ix
7 TheKohn–ShamAuxiliarySystem 145
7.1 ReplacingOneProblemwithAnother 145
7.2 TheKohn–ShamVariationalEquations 148
7.3 SolutionoftheSelf-ConsistentCoupledKohn–ShamEquations 150
7.4 AchievingSelf-Consistency 157
7.5 ForceandStress 160
7.6 InterpretationoftheExchange–CorrelationPotentialV 161
xc
7.7 MeaningoftheEigenvalues 162
7.8 IntricaciesofExactKohn–ShamTheory 163
7.9 Time-DependentDensityFunctionalTheory 166
7.10 OtherGeneralizationsoftheKohn–ShamApproach 167
Exercises 168
8 FunctionalsforExchangeandCorrelationI 171
8.1 Overview 171
8.2 E andtheExchange–CorrelationHole 172
xc
8.3 Local(Spin)DensityApproximation(LSDA) 174
8.4 HowCantheLocalApproximationPossiblyWorkAsWellAsItDoes? 175
8.5 Generalized-GradientApproximations(GGAs) 179
8.6 LDAandGGAExpressionsforthePotentialVσ (r) 183
xc
8.7 AverageandWeightedDensityFormulations:ADAandWDA 185
8.8 FunctionalsFittedtoDatabases 185
Exercises 186
9 FunctionalsforExchangeandCorrelationII 188
9.1 BeyondtheLocalDensityandGeneralizedGradientApproximations 188
9.2 GeneralizedKohn–ShamandBandgaps 189
9.3 HybridFunctionalsandRangeSeparation 191
9.4 FunctionalsoftheKineticEnergyDensity:Meta-GGAs 195
9.5 OptimizedEffectivePotential 197
9.6 Localized-OrbitalApproaches:SICandDFT+U 199
9.7 FunctionalsDerivedfromResponseFunctions 203
9.8 NonlocalFunctionalsforvanderWaalsDispersionInteractions 205
9.9 ModifiedBecke–JohnsonFunctionalforV 209
xc
9.10 ComparisonofFunctionals 209
Exercises 213
PartIII ImportantPreliminariesonAtoms
10 ElectronicStructureofAtoms 215
10.1 One-ElectronRadialSchrödingerEquation 215
10.2 Independent-ParticleEquations:SphericalPotentials 217
10.3 Spin–OrbitInteraction 219
10.4 Open-ShellAtoms:NonsphericalPotentials 219