1 The Basic Approach 1
1．Quantum Mechanics 1
A．Waves and Observables 1
B．Atomic States 4
2．Tight-Binding Theory and the Simplest Molecule 11
A．Molecular Orbitals 11
B．Extended Hückel Theory 13
C．Electronic Structure of Li2 14
D．The Total Energy 15
3．The Simplest Many-Atom System,a Metal 16
A．Energy Bands 18
B．Matching to Free-Electron Bands 19
C．Cohesion 20
4．Hybrid States and Semiconductors 22
A．Needed Parameters 22
B．The Nitrogen Molecule 24
C．sp-Hybrids 27
D．Semiconductors 32
E．Overall Organization of Solid-State Systems 33
5．Ionic Insulators 36
A．Independent Ions 36
B．Couplings and Perturbation Theory 37
6．Simple Metals and Pseudopotentials 39
A．Empty-Core Pseudopotentials 39
B．Effective Interaction Between Ions 41
C．Partly-Filled Bands 43
7．Transition-Metal and f-Shell Systems 43
A．Coupling of d-States 44
B．The Coulomb Ud 45
C．The Energy Bands and the Friedel Model 45
D．Correlated States in f-Shell Metals 46
E．Transition-Metal and f-Shell-Metal Compounds 47
8．Surfaces and Other Bonding Types 49
A．Surface Energies 49
B．Other Systems 51
2 Bonding in Tetrahedral Semiconductors 53
1．The Crystal Structure and Notation 53
2．Hybrids and Their Coupling 57
A．sp3-Hybrids 57
B．The Covalent Energy,V2 59
C．The Polar Energy,V3 61
D．The Metallic Energy,V1 63
E．The Overlap Repulsion.,V0(d) 65
F．Total Energies and Coulomb Effects 69
3．The Cohesive Energy 70
A．The Bond Orbital Approximation and Matrices 70
B．Metallization 75
C．Homopolar Systems 78
D．Polar Systems 81
E．Coulomb Corrections 82
4．The Dependence of Energy upon Volume 84
A．Trends in Bond Lengths 85
B．The Radial Force Constant 86
C．The Grüneisen Constant 89
5．Structural Stability and Moments 93
A．The Second Moment 94
B．The Dependence Upon Structure 99
C．The Fourth Moment 101
D．Structural Stability 102
E．Angular Rigidity 103
3 Elastic Properties of Semiconductors 107
1．Elastic Constants and Bulk Modulus 108
2．Shear Constants 109
A．Twist Distortion 111
B．Graphitic Distortion and Internal Displacements 113
C．Interatomic Metallization and Effects of Polarity 118
3．Vibrational Frequencies 121
A．Acoustic Modes 124
B．Optical Modes 126
C．Effects of Polarity 128
4．Interatomic-Interaction Models 130
A．Traditional Models 131
B．The Angular Force Puzzle 132
C．A Solution for Carbyne 134
D．Application to Tetrahedral Semiconductors 139
4 The Dielectric Properties of Semiconductors 142
1．Bond Dipoles and Effective Charges 143
2．Electronic Susceptibilities 146
A．The Linear Response 146
B．The Effect of Metallization 149
C．Higher-Order Susceptibilities 152
D．Magnetic Susceptibility 158
3．Internal Displacement Properties 161
A．The Transverse Charge 161
B．Optical Mode Splitting 164
C．The Static Dielectric Constant 165
D．The Piezoelectric Effect 167
E．Elastooptic Effect 170
F．Electrooptic Effect 174
G．Dielectric Response in the Infrared 176
5 Semiconductor Energy Bands 179
1．Wavenumbers and Brillouin Zones. 180
2．Bonding and Antibonding Bands 183
A．Bands from the coupling V1 184
B．Bands for polar crystals 187
C．The effects of V1x 188
3．Full Tight-Binding Bands 188
A．sp3-bands 188
B．A Peripheral s＊-State 191
C．Fitting the Free-Electron Bands 192
D．Obtaining Universal Parameters 194
E．Application to Polar Systems 196
F．The Band States 197
G．Spin-Oribit Coupling 199
4．More Accurate Bands 203
5．Corrections to the Bands 206
A．Coulomb Enhancement of the Gaps 207
B．Polarons 210
C．Wannier Functions 213
6 Electronic Properties 214
1．The Valence-Band Maximum. 214
2．Optical Absorption 217
A．Vertical Transitions 217
B．The Optical Matrix Elements 218
C．The Absorption Threshold 221
D．Indirect Gaps 224
E．The Optical Absorption Peaks 225
3．Effective Masses 226
A．Conduction-Band Mass at г 227
B．Light-Hole Mass 231
C．Heavy-Hole Mass 232
D．Masses for Indirect Minima 234
4．Dynamics of Band States 235
A．The Dynamical Equations 235
B．Limitations of the Theory 236
C．The Dynamics of Holes 237
5．The Form of the Hole Bands 238
A．Heavy- and Light-Hole Bands 238
B．Negative Gaps 240
C．Spin-Orbit-Split Bands 241
D．Density of States 245
6．The Optical Absorption Rate 248
A．The Matrix elements 248
B．The Rate 251
7 Effects of Lattice Distortions 254
1．Deformation Potentials for Dilatations 255
A．Nonorthogonality and Electrostatic Contributions 256
B．Predicted Deformation Potentials 257
C．Experimental Values 259
2．Band Shifts Due to Shear Distortions 261
A．The Effects of Nonorthogonality 262
B．Indirect Gap Conduction Bands 263
C．Valence Bands 265
D．Shifts of the Spin-Orbit Split Bands 267
3．The Electron-Phonon Interaction 269
A．Interactions for Simple Systems 271
B．Acoustic Modes and Conduction Electrons 274
C．Electrostatic Contributions in Polar Crystals 278
D．Interaction with Optical Modes 279
E．Holes and Local Lattice Rotations 280
F．Acoustic Modes and Holes 283
a．Light Holes and Longitudinal Modes 283
b．Light Holes and Shear Modes 286
c．Heavy Holes and Light-Heavy Matrix Elements 287
G．Electrostatic Potentials and Screening 287
H．Electron Scattering by Acoustic Modes 290
8 Impurities and Defects 293
1．Semiconductor Alloys 294
A．Enthalpies of Solution 294
B．Lattice Distortions 296
C．Doping and Energies of Substitution 300
D．Alloy Energy Bands and Scattering 304
2．Impurity States 307
3．Vacancies and Interstitials 313
A．The Ideal Vacancy 314
B．Jahn-Teller Distortion 314
C．The Tetrahedral and Shared-Site Interstitials 317
D．The Role in Diffusion 321
9 Bonding In Ionic Crystals 324
1．The Independent-Ion Model 326
A．Coulomb Effects and Closed-Shell Ions 326
B．Crystal Structures and Electrostatic Energy 328
C．The Band Gap 332
D．The Cohesive Energy 336
E．The Born Electrostatic Model 339
F．Coulomb Enhancements of the Gap. 341
2．Coupled Ions 343
A．Covalent Corrections to the Energy 344
B．The Energy Bands 345
C．Special Points 348
D．Volume-Dependent Properties in Second Order 350
10 Elastic Properties of Ionic Crystals 353
1．The Overlap Repulsion 354
A．Based upon Local-Density Theory 354
B．Fitting the Power-Law Form 356
C．Second-Neighbor Repulsions 358
2．Resonant Bonds 358
3．Volume-Dependent Properties 361
A．Equilibrium Spacing 361
B．Cohesive Energy 363
C．Bulk Modulus 363
D．Grüneisen Constant 365
4．Elastic Constants 366
A．The Shear Constant,(c11-c12)/2 367
B．The Shear Constant,c44,and the Chemical Grip 368
C．Vibrational Frequencies 369
5．Coulomb Contributions 372
A．Volume-Dependent Properties 374
B．Elastic Constants 375
11 Dielectric Properties of Ionic Solids 379
1．The Optical Dielectric Susceptibility 379
A．The Alkali Halides 382
B．Noble-Metal Halides 384
C．Divalent Compounds 384
D．Ten-Electron Compounds 385
E．The Implication of the Errors 387
F．Local-Field Effects 387
G．Application to Other Ionic Solids 389
2．Effective Ionic Charges 389
A．The Static Effective Charge 390
B．The Transverse Charge 392
C．The Static Dielectric Constant 396
12 Covalent Insulators,SiO2 399
1．The Structure and Bonding Unit 400
2．The Parameters 402
3．Cohesive Energy 406
A．Metallization 408
B．Inter-atomic Metallization 409
4．Radial Force Constant 410
5．The Angle at Oxygen 411
6．Elasticity and the Bonding Unit 414
7．The Vibrational Frequencies 417
8．The Refractive Index 418
9．Effective Transverse Charge 419
10．Energy Bands 421
11．Summary of the SiO2 Study 424
12．Other Covalent Insulators 425
A．GeO2 425
B．Oxyanions,Sulfates,etc. 425
C．Thallium Arsenic Selenide 429
D．Other Mixed Covalent-Ionic Solids 430
E．A Complex Semiconductor,SiP2 430
13 Simple Metals,Electronic Structure 434
1．Crystal Structures 435
2．Free-Electron States 439
3．Tight-Binding Theory 440
A．Cohesive Energy 440
B．The Bulk Modulus 443
4．Pseudopotentials 444
A．Empty-Core Pseudopotentials 446
B．Madelung and Total Free-Electron Energy 449
C．Equilibrium Spacing and Bulk Modulus 452
D．Higher-Order Terms 454
5．Structure Factors and Form Factors 455
6．Screening of Pseudopotentials 456
A．Fermi-Thomas Theory 457
B．Screened Form Factors 459
C．The Real-Space Pseudopotential,w(r) 461
D．More Accurate Screening 462
7．Diffraction and Fermi Surfaces 463
A．Motion in a Uniform Magnetic Field 463
B．Construction of Fermi Surfaces 468
C．Fermi-Surface Distortions 471
D．Magnetic Breakdown 473
8．Scattering by Defects 474
9．Electron-Phonon Interaction 476
A．The Structure Factor 476
B．Electron Scattering 479
14 Simpla Metals,Bonding Properties 483
1．The Band-Structure Energy 483
A．Vibrational Frequencies and the Kohn Effect 486
B．Other Properties 488
2．Interatomic Interactions 489
A．The Effective Interaction 489
B．The Total Energy 491
C．Volume Dependence of the Total Energy 492
3．Properties from Interatomic Interactions 495
A．The Bulk Modulus 496
B．Deviations from the Cauchy Relations 497
C．Poisson's Ratio 498
D．The Grüneisen Constant 499
4．Calculation of Vibration Spectra 500
5．Liquid Metals. 504
A．Liquid Structure Factors 504
B．Resistivity 507
6．Pseudopotentials and Covalent Bonding 508
A．Coupling Through the[100]2π/a States 508
B．Polar Systems 512
7．Alloys 513
A．Heats of Solution 514
a．Homovalent solutions. 519
b．Heterovalent solutions. 521
B．Alloy Formation Energies 522
15 Transition Metals 530
1．Transition-Metal Pseudopotentials 532
A．Pseudopotentials and OPW's 532
B．Atomic d-States 534
C．Hybridization with d-States 535
D．Contribution to the Pseudopotential 538
2．Coupling Between d-States 542
A．The dd-Coupling 542
B．The Slater-Koster Tables 544
C．Energy Bands 545
D．Fermi Surfaces and Density of States 550
3．The Atomic Sphere Approximation 554
A．The Atomic Surface Method 556
B．Values for rd 558
C．Further Approximations 559
4．The Friedel Model 559
A．Band Width from the Second Moment 560
B．Coulomb Shifts and Values for εd 561
C．Hybridization Already Included 563
D．The Total Energy 565
E．The Cohesive Energy 569
F．Volume-Dependent Properties 571
G．Crystal Structure Determination 576
H．Transition-Metal Alloys 578
5．Interatomic Interactions and Elasticity 582
A．The Effective Interaction 582
B．Elastic Constants 584
C．Multibody Forces 584
6．Ferromagnetism 586
A．The Exchange Energy 587
B．The Ferromagnetic State 588
16 f-Shell Metals 593
1．Correlated States 593
A．An Exact Solution 594
B．The Unrestricted Hartree-Fock Approximation 595
C．Self-Interactions 597
D．Generalization to d-and f-Bands 598
a．Local Moments in the UHF Approximation 598
b．Generalizing the Exact Result 599
2．Parameters for f-Shell Systems 601
A．ff-Coupling 602
B．General Formulae 606
C．Coulomb Uf 607
D．Spin-Orbit Coupling 608
E．The sd-Electrons 610
3．Electronic Structure of Rare Earths 612
A．The f-Electrons 612
B．The Cohesive Energy 614
C．The Volume-Dependent Energy 616
D．Interatomic Interactions 617
E．Crystal Structure 618
4．Electronic Structure of the Actinides 618
A．The Cohesive Energy 618
B．Volume-Dependent Properties 619
C．Interatomic Interactions 624
D．Crystal Strucutres 624
5．Criterion for Local Moments 625
A．Phase Shifts 626
B．The Friedel Sum Rule 628
C．Resonant States 629
D．The Criterion 631
6．Strongly Correlated Systemse 637
A．The Electronic Structure of Americium 637
B．Antiferromagnetism 638
C．The Kondo Effect 639
D．Heavy Fermion Systems 640
17 Transition-Metal(AB)Compounds 641
1．Parameters for Compounds 642
2．The Monoxides,Nitrides and Carbides 647
A．The Octet Compounds 647
B．Other Oxides and Nitrides 648
3．Quantitative Theory 650
A．The Essential Electronic Structure 650
B．Bands for the Compounds 652
C．Covalent and Polar Energies 656
D．The d-State Energy,εd 659
E．The pd-Bonding Energy and Cohesion 661
F．The Volume-Dependent Properties 664
4．Correlated States 668
A．Correlation Energy 668
B．The Metal-Insulator Transition 670
5．The Role of d-States in Semiconductors 672
18 Other Transition and f-Shell Compounds 679
1．Compounds of f-Shell Metals 679
A．Rare-Earth Compounds 680
B．Actinide Compounds 682
2．The Dioxides 688
A．TiO2,Rutile 688
B．RuO2 688
3．Trioxides,the Perovskites 692
A．The Perovskite Structure 693
B．The Electronic Structure 695
C．Bonding Properties 699
D．Madelung Energies 701
E．The Electron-Phonon Interaction 703
4．The Cuprates 704
A．The Electronic Structure 705
B．Peierls Instabilities and the Antiferromagnetic State 708
C．Phonons,Paramagnons,and Excitons 711
19 Surfaces and Interfaces 714
1．Surface Energies 714
A．Elemental Semiconductors 715
B．Ionic Crystals and Polar Semiconductors. 716
C．Metal Surfaces. 716
D．Interaction Between Surfaces and Giant Magnetoresistance 723
2．Photothresholds,Work Functions and Electron Affinities 727
A．Corrections to the Tight-Binding Photothreshold 727
B．Photothresholds in Semiconductors. 728
C．Work Functions in Metals 729
3．Reconstruction on Semiconductor Surfaces 731
A．The Silicon(111)2×1 and General(110)Surfaces 732
B．The Silicon(100)2×1 733
C．Polar Surfaces 734
D．The Silicon(111)7×7 737
4．Interfaces 738
A．Matching Wavefunctions at Heterojunctions 739
B．Semiconductor Band Line-Ups 741
C．Other Views 743
D．Strain-Layer Superlattices 745
E．Metal-Semiconductor Interfaces 747
F．Adsorbed Atoms on Semiconductors 749
20 Other Systems 752
1．Non-Tetrahedral Covalent Solids 752
A．Two Nearest Neighbors,S,Se and Te 752
B．Multicenter Bonds 754
C．Zn3P2 757
D．Boron 759
2．Inert-Gas Solids and Molecular Crystals 761
A．Electronic Structure of Inert-Gas Solids 761
B．Excitons 763
C．Dielectric Polarizability 764
D．Van-der-Waals Interaction 765
E．Lennard-Jones Interaction 767
F．Molecular Solids 769
3．π-Bonded Systems 770
A．Graphite 770
a．Energy Bands 770
b．The π-Bonding Energy 772
B．Fullerenes 773
C．The Heme Group 775
4．Systems with Hydrogen 779
A．H2 780
B．Central Hydrides 781
C．Hydrocarbons 783
D．Shared-Hydrogen Bonding 783
Author Index 787
Subject Index 807