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1 The Basic Approach1

1．Quantum Mechanics1

A．Waves and Observables1

B．Atomic States4

2．Tight-Binding Theory and the Simplest Molecule11

A．Molecular Orbitals11

B．Extended Hückel Theory13

C．Electronic Structure of Li214

D．The Total Energy15

3．The Simplest Many-Atom System,a Metal16

A．Energy Bands18

B．Matching to Free-Electron Bands19

C．Cohesion20

4．Hybrid States and Semiconductors22

A．Needed Parameters22

B．The Nitrogen Molecule24

C．sp-Hybrids27

D．Semiconductors32

E．Overall Organization of Solid-State Systems33

5．Ionic Insulators36

A．Independent Ions36

B．Couplings and Perturbation Theory37

6．Simple Metals and Pseudopotentials39

A．Empty-Core Pseudopotentials39

B．Effective Interaction Between Ions41

C．Partly-Filled Bands43

7．Transition-Metal and f-Shell Systems43

A．Coupling of d-States44

B．The Coulomb Ud45

C．The Energy Bands and the Friedel Model45

D．Correlated States in f-Shell Metals46

E．Transition-Metal and f-Shell-Metal Compounds47

8．Surfaces and Other Bonding Types49

A．Surface Energies49

B．Other Systems51

2 Bonding in Tetrahedral Semiconductors53

1．The Crystal Structure and Notation53

2．Hybrids and Their Coupling57

A．sp3-Hybrids57

B．The Covalent Energy,V259

C．The Polar Energy,V361

D．The Metallic Energy,V163

E．The Overlap Repulsion.,V0(d)65

F．Total Energies and Coulomb Effects69

3．The Cohesive Energy70

A．The Bond Orbital Approximation and Matrices70

B．Metallization75

C．Homopolar Systems78

D．Polar Systems81

E．Coulomb Corrections82

4．The Dependence of Energy upon Volume84

A．Trends in Bond Lengths85

B．The Radial Force Constant86

C．The Grüneisen Constant89

5．Structural Stability and Moments93

A．The Second Moment94

B．The Dependence Upon Structure99

C．The Fourth Moment101

D．Structural Stability102

E．Angular Rigidity103

3 Elastic Properties of Semiconductors107

1．Elastic Constants and Bulk Modulus108

2．Shear Constants109

A．Twist Distortion111

B．Graphitic Distortion and Internal Displacements113

C．Interatomic Metallization and Effects of Polarity118

3．Vibrational Frequencies121

A．Acoustic Modes124

B．Optical Modes126

C．Effects of Polarity128

4．Interatomic-Interaction Models130

A．Traditional Models131

B．The Angular Force Puzzle132

C．A Solution for Carbyne134

D．Application to Tetrahedral Semiconductors139

4 The Dielectric Properties of Semiconductors142

1．Bond Dipoles and Effective Charges143

2．Electronic Susceptibilities146

A．The Linear Response146

B．The Effect of Metallization149

C．Higher-Order Susceptibilities152

D．Magnetic Susceptibility158

3．Internal Displacement Properties161

A．The Transverse Charge161

B．Optical Mode Splitting164

C．The Static Dielectric Constant165

D．The Piezoelectric Effect167

E．Elastooptic Effect170

F．Electrooptic Effect174

G．Dielectric Response in the Infrared176

5 Semiconductor Energy Bands179

1．Wavenumbers and Brillouin Zones.180

2．Bonding and Antibonding Bands183

A．Bands from the coupling V1184

B．Bands for polar crystals187

C．The effects of V1x188

3．Full Tight-Binding Bands188

A．sp3-bands188

B．A Peripheral s＊-State191

C．Fitting the Free-Electron Bands192

D．Obtaining Universal Parameters194

E．Application to Polar Systems196

F．The Band States197

G．Spin-Oribit Coupling199

4．More Accurate Bands203

5．Corrections to the Bands206

A．Coulomb Enhancement of the Gaps207

B．Polarons210

C．Wannier Functions213

6 Electronic Properties214

1．The Valence-Band Maximum.214

2．Optical Absorption217

A．Vertical Transitions217

B．The Optical Matrix Elements218

C．The Absorption Threshold221

D．Indirect Gaps224

E．The Optical Absorption Peaks225

3．Effective Masses226

A．Conduction-Band Mass at г227

B．Light-Hole Mass231

C．Heavy-Hole Mass232

D．Masses for Indirect Minima234

4．Dynamics of Band States235

A．The Dynamical Equations235

B．Limitations of the Theory236

C．The Dynamics of Holes237

5．The Form of the Hole Bands238

A．Heavy- and Light-Hole Bands238

B．Negative Gaps240

C．Spin-Orbit-Split Bands241

D．Density of States245

6．The Optical Absorption Rate248

A．The Matrix elements248

B．The Rate251

7 Effects of Lattice Distortions254

1．Deformation Potentials for Dilatations255

A．Nonorthogonality and Electrostatic Contributions256

B．Predicted Deformation Potentials257

C．Experimental Values259

2．Band Shifts Due to Shear Distortions261

A．The Effects of Nonorthogonality262

B．Indirect Gap Conduction Bands263

C．Valence Bands265

D．Shifts of the Spin-Orbit Split Bands267

3．The Electron-Phonon Interaction269

A．Interactions for Simple Systems271

B．Acoustic Modes and Conduction Electrons274

C．Electrostatic Contributions in Polar Crystals278

D．Interaction with Optical Modes279

E．Holes and Local Lattice Rotations280

F．Acoustic Modes and Holes283

a．Light Holes and Longitudinal Modes283

b．Light Holes and Shear Modes286

c．Heavy Holes and Light-Heavy Matrix Elements287

G．Electrostatic Potentials and Screening287

H．Electron Scattering by Acoustic Modes290

8 Impurities and Defects293

1．Semiconductor Alloys294

A．Enthalpies of Solution294

B．Lattice Distortions296

C．Doping and Energies of Substitution300

D．Alloy Energy Bands and Scattering304

2．Impurity States307

3．Vacancies and Interstitials313

A．The Ideal Vacancy314

B．Jahn-Teller Distortion314

C．The Tetrahedral and Shared-Site Interstitials317

D．The Role in Diffusion321

9 Bonding In Ionic Crystals324

1．The Independent-Ion Model326

A．Coulomb Effects and Closed-Shell Ions326

B．Crystal Structures and Electrostatic Energy328

C．The Band Gap332

D．The Cohesive Energy336

E．The Born Electrostatic Model339

F．Coulomb Enhancements of the Gap.341

2．Coupled Ions343

A．Covalent Corrections to the Energy344

B．The Energy Bands345

C．Special Points348

D．Volume-Dependent Properties in Second Order350

10 Elastic Properties of Ionic Crystals353

1．The Overlap Repulsion354

A．Based upon Local-Density Theory354

B．Fitting the Power-Law Form356

C．Second-Neighbor Repulsions358

2．Resonant Bonds358

3．Volume-Dependent Properties361

A．Equilibrium Spacing361

B．Cohesive Energy363

C．Bulk Modulus363

D．Grüneisen Constant365

4．Elastic Constants366

A．The Shear Constant,(c11-c12)/2367

B．The Shear Constant,c44,and the Chemical Grip368

C．Vibrational Frequencies369

5．Coulomb Contributions372

A．Volume-Dependent Properties374

B．Elastic Constants375

11 Dielectric Properties of Ionic Solids379

1．The Optical Dielectric Susceptibility379

A．The Alkali Halides382

B．Noble-Metal Halides384

C．Divalent Compounds384

D．Ten-Electron Compounds385

E．The Implication of the Errors387

F．Local-Field Effects387

G．Application to Other Ionic Solids389

2．Effective Ionic Charges389

A．The Static Effective Charge390

B．The Transverse Charge392

C．The Static Dielectric Constant396

12 Covalent Insulators,SiO2399

1．The Structure and Bonding Unit400

2．The Parameters402

3．Cohesive Energy406

A．Metallization408

B．Inter-atomic Metallization409

4．Radial Force Constant410

5．The Angle at Oxygen411

6．Elasticity and the Bonding Unit414

7．The Vibrational Frequencies417

8．The Refractive Index418

9．Effective Transverse Charge419

10．Energy Bands421

11．Summary of the SiO2 Study424

12．Other Covalent Insulators425

A．GeO2425

B．Oxyanions,Sulfates,etc.425

C．Thallium Arsenic Selenide429

D．Other Mixed Covalent-Ionic Solids430

E．A Complex Semiconductor,SiP2430

13 Simple Metals,Electronic Structure434

1．Crystal Structures435

2．Free-Electron States439

3．Tight-Binding Theory440

A．Cohesive Energy440

B．The Bulk Modulus443

4．Pseudopotentials444

A．Empty-Core Pseudopotentials446

B．Madelung and Total Free-Electron Energy449

C．Equilibrium Spacing and Bulk Modulus452

D．Higher-Order Terms454

5．Structure Factors and Form Factors455

6．Screening of Pseudopotentials456

A．Fermi-Thomas Theory457

B．Screened Form Factors459

C．The Real-Space Pseudopotential,w(r)461

D．More Accurate Screening462

7．Diffraction and Fermi Surfaces463

A．Motion in a Uniform Magnetic Field463

B．Construction of Fermi Surfaces468

C．Fermi-Surface Distortions471

D．Magnetic Breakdown473

8．Scattering by Defects474

9．Electron-Phonon Interaction476

A．The Structure Factor476

B．Electron Scattering479

14 Simpla Metals,Bonding Properties483

1．The Band-Structure Energy483

A．Vibrational Frequencies and the Kohn Effect486

B．Other Properties488

2．Interatomic Interactions489

A．The Effective Interaction489

B．The Total Energy491

C．Volume Dependence of the Total Energy492

3．Properties from Interatomic Interactions495

A．The Bulk Modulus496

B．Deviations from the Cauchy Relations497

C．Poisson's Ratio498

D．The Grüneisen Constant499

4．Calculation of Vibration Spectra500

5．Liquid Metals.504

A．Liquid Structure Factors504

B．Resistivity507

6．Pseudopotentials and Covalent Bonding508

A．Coupling Through the[100]2π/a States508

B．Polar Systems512

7．Alloys513

A．Heats of Solution514

a．Homovalent solutions.519

b．Heterovalent solutions.521

B．Alloy Formation Energies522

15 Transition Metals530

1．Transition-Metal Pseudopotentials532

A．Pseudopotentials and OPW's532

B．Atomic d-States534

C．Hybridization with d-States535

D．Contribution to the Pseudopotential538

2．Coupling Between d-States542

A．The dd-Coupling542

B．The Slater-Koster Tables544

C．Energy Bands545

D．Fermi Surfaces and Density of States550

3．The Atomic Sphere Approximation554

A．The Atomic Surface Method556

B．Values for rd558

C．Further Approximations559

4．The Friedel Model559

A．Band Width from the Second Moment560

B．Coulomb Shifts and Values for εd561

C．Hybridization Already Included563

D．The Total Energy565

E．The Cohesive Energy569

F．Volume-Dependent Properties571

G．Crystal Structure Determination576

H．Transition-Metal Alloys578

5．Interatomic Interactions and Elasticity582

A．The Effective Interaction582

B．Elastic Constants584

C．Multibody Forces584

6．Ferromagnetism586

A．The Exchange Energy587

B．The Ferromagnetic State588

16 f-Shell Metals593

1．Correlated States593

A．An Exact Solution594

B．The Unrestricted Hartree-Fock Approximation595

C．Self-Interactions597

D．Generalization to d-and f-Bands598

a．Local Moments in the UHF Approximation598

b．Generalizing the Exact Result599

2．Parameters for f-Shell Systems601

A．ff-Coupling602

B．General Formulae606

C．Coulomb Uf607

D．Spin-Orbit Coupling608

E．The sd-Electrons610

3．Electronic Structure of Rare Earths612

A．The f-Electrons612

B．The Cohesive Energy614

C．The Volume-Dependent Energy616

D．Interatomic Interactions617

E．Crystal Structure618

4．Electronic Structure of the Actinides618

A．The Cohesive Energy618

B．Volume-Dependent Properties619

C．Interatomic Interactions624

D．Crystal Strucutres624

5．Criterion for Local Moments625

A．Phase Shifts626

B．The Friedel Sum Rule628

C．Resonant States629

D．The Criterion631

6．Strongly Correlated Systemse637

A．The Electronic Structure of Americium637

B．Antiferromagnetism638

C．The Kondo Effect639

D．Heavy Fermion Systems640

17 Transition-Metal(AB)Compounds641

1．Parameters for Compounds642

2．The Monoxides,Nitrides and Carbides647

A．The Octet Compounds647

B．Other Oxides and Nitrides648

3．Quantitative Theory650

A．The Essential Electronic Structure650

B．Bands for the Compounds652

C．Covalent and Polar Energies656

D．The d-State Energy,εd659

E．The pd-Bonding Energy and Cohesion661

F．The Volume-Dependent Properties664

4．Correlated States668

A．Correlation Energy668

B．The Metal-Insulator Transition670

5．The Role of d-States in Semiconductors672

18 Other Transition and f-Shell Compounds679

1．Compounds of f-Shell Metals679

A．Rare-Earth Compounds680

B．Actinide Compounds682

2．The Dioxides688

A．TiO2,Rutile688

B．RuO2688

3．Trioxides,the Perovskites692

A．The Perovskite Structure693

B．The Electronic Structure695

C．Bonding Properties699

D．Madelung Energies701

E．The Electron-Phonon Interaction703

4．The Cuprates704

A．The Electronic Structure705

B．Peierls Instabilities and the Antiferromagnetic State708

C．Phonons,Paramagnons,and Excitons711

19 Surfaces and Interfaces714

1．Surface Energies714

A．Elemental Semiconductors715

B．Ionic Crystals and Polar Semiconductors.716

C．Metal Surfaces.716

D．Interaction Between Surfaces and Giant Magnetoresistance723

2．Photothresholds,Work Functions and Electron Affinities727

A．Corrections to the Tight-Binding Photothreshold727

B．Photothresholds in Semiconductors.728

C．Work Functions in Metals729

3．Reconstruction on Semiconductor Surfaces731

A．The Silicon(111)2×1 and General(110)Surfaces732

B．The Silicon(100)2×1733

C．Polar Surfaces734

D．The Silicon(111)7×7737

4．Interfaces738

A．Matching Wavefunctions at Heterojunctions739

B．Semiconductor Band Line-Ups741

C．Other Views743

D．Strain-Layer Superlattices745

E．Metal-Semiconductor Interfaces747

F．Adsorbed Atoms on Semiconductors749

20 Other Systems752

1．Non-Tetrahedral Covalent Solids752

A．Two Nearest Neighbors,S,Se and Te752

B．Multicenter Bonds754

C．Zn3P2757

D．Boron759

2．Inert-Gas Solids and Molecular Crystals761

A．Electronic Structure of Inert-Gas Solids761

B．Excitons763

C．Dielectric Polarizability764

D．Van-der-Waals Interaction765

E．Lennard-Jones Interaction767

F．Molecular Solids769

3．π-Bonded Systems770

A．Graphite770

a．Energy Bands770

b．The π-Bonding Energy772

B．Fullerenes773

C．The Heme Group775

4．Systems with Hydrogen779

A．H2780

B．Central Hydrides781

C．Hydrocarbons783

D．Shared-Hydrogen Bonding783

Author Index787

Subject Index807