DeutschesFachbuch.de : Quantum Chemistry of Solids The LCAO First Principles Treatment of Crystals Von Robert A. Evarestov

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Contents
Part TheoryI
1 Introduction 3
2 Space Groups and Crystalline Structures 7
2.1 Translation and Point Symmetry of Crystals 7
2.1.1 Symmetry of Molecules and Crystals: Similarities and Differences 7
2.1.2 Translation Symmetry of Crystals. Point Symmetry of Bravais Lattices. Crystal C...
2.2 Space Groups 16
2.2.1 Space Groups of Bravais Lattices. Symmorphic and Nonsymmorphic Space Groups 16
2.2.2 Three-periodic Space Groups 18
2.2.3 Site Symmetry in Crystals. Wyckoff Positions 22
2.3 Crystalline Structures 26
2.3.1 Crystal-structure Types. Structure Information for Computer Codes 26
2.3.2 Cubic Structures: Diamond, Rocksalt, Fluorite, Zincblende, Cesium Chloride, Cub...
2.3.3 Tetragonal Structures: Rutile, Anatase and La 2 CuO 434
2.3.4 Orthorhombic Structures: LaMnO 3 and YBa 2 Cu 30737
2.3.5 Hexagonal and Trigonal Structures: Graphite, Wurtzite, Corundum and ScMnO 342
3 Symmetry and Localization of Crystalline Orbitals 47
3.1 Translation and Space Symmetry of Crystalline Orbitals. Bloch Functions 47
3.1.1 Symmetry of Molecular and Crystalline Orbitals 47
3.1.2 Irreducible Representations of Translation Group. Brillouin Zone 51
3.1.3 Stars of Wavevectors. Little Groups. Full Representations of Space Groups 58
3.1.4 Small Representations of a Little Group. Projective Representations of Point Gr...
3.2 Site Symmetry and Induced Representations of Space Groups 66
3.2.1 Induced Representations of Point Groups. Localized Molecular Orbitals 66
3.2.2 Induced Representations of Space Groups in q-basis 71
3.2.3 Induced Representations of Space Groups in k-basis. Band Representations 73
3.2.4 Simple and Composite Induced Representations 76
3.2.5 Simple Induced Representations for Cubic Space Groups Oh, Ohand Oh 78
3.2.6 Symmetry of Atomic and Crystalline Orbitals in MgO, Si and SrZr 03 Crystals 83
3.3 Symmetry of Localized Crystalline Orbitals. Wannier Functions ....86
3.3.1 Symmetry of Localized Orbitals and Band Representations of Space Groups 86
3.3.2 Localization Criteria in Wannier-function Generation 90
3.3.3 Localized Orbitals for Valence Bands: LCAO approximation ..94
3.3.4 Variational Method of Localized Wannier-function Generation on the Base of Bloc...
4 Hartree-Fock LCAO Method for Periodic Systems 105
4.1 One-electron Approximation for Crystals 105
4.1.1 One-electron and One-determinant Approximations for Molecules and Crystals 105
4.1.2 Symmetry of the One-electron Approximation Hamiltonian ..109
4.1.3 Restricted and Unrestricted Hartree-Fock LCAO Methods for Molecules 111
4.1.4 Specific Features of the Hartree-Fock Method for a Cyclic Model of a Crystal 11...
4.1.5 Restricted Hartree-Fock LCAO Method for Crystals 119
4.1.6 Unrestricted and Restricted Open-shell Hartree-Fock Methods for Crystals 122
4.2 Special Points of Brillouin Zone 124
4.2.1 Supercells of Three-dimensional Bravais Lattices 124
4.2.2 Special Points of Brillouin-zone Generating 125
4.2.3 Modification of the Monkhorst-Pack Special-points Meshes ...128
4.3 Density Matrix of Crystals in the Hartree-Fock Method 132
4.3.1 Properites of the One-electron Density Matrix of a Crystal . . .132
4.3.2 The One-electron Density Matrix of the Crystal in the LCAO Approximation 137
4.3.3 Interpolation Procedure for Constructing an Approximate Density Matrix for Peri...
5 Electron Correlations in Molecules and Crystals 147
5.1 Electron Correlations in Molecules: Post-Hartree-Fock Methods 147
5.1.1 What is the Electron Correlation ?147
5.1.2 Configuration Interaction and Multi-configuration Self-consistent Field Methods...
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Index
AAdiabatic approximation 105
BBand representation 78
- SrZr 03 crystal 84
- MgO and Si crystals 84
Basic translation vectors 11
Basis sets in molecular calculations
- localized atomic-like orbitals
- Gaussian-basis notations 290
- Gaussian-type orbitals 285
- Slater-type orbitals 283, 285
- correlation-consistent basis 291
- minimal-basis set 287
- polarization functions 288
Basis sets in periodic calculations
- localized atomic-like orbitals 283
- Gaussian-type basis 294
basis set superposition error 297
- molecular-basis adaptation 291
- plane waves 281
Boundless crystal 10
Bravais lattice 11 2 D (plane) 460
base-centered 12
body-centered 12
- cubic 14
- face-centered 12
- hexagonal 14
- monoclinic 12
- orthorhombic 13
- parameters 12
- point symmetry 11
- primitive 12
- tetragonal 14
- triclinic 12, 14
- type 12
Brillouin zone
- special points 126
- Monkhorst-Pack 129
- cubic crystals 128
- modified Monkhorst-Pack 130
- supercell generation 127
- symmetry line 57
- symmetry point 57
Bulk crystals
- Compton profile
- Cu 2 0 383
band structure
- MgO, Ti 02 377
bulk moduli, elastic constants
- SrTiOs, BaTiOs, PbTiO, 3 402
bulk modulus
- Cu 2 0 399
- Ti 02 phases 401
- cohesive energy
- Ti 02 396
- corundum-like oxides 397
- cyclic cluster model
- AI 2 O 3 431
- density of states
- SrTiOs, SrZrOs 380
- projected density of states 379
- electron-density maps
- Cu 2 0 382
- electron-momentum density
- Cu 2 0 383
- magnetic structure
- LaMnOs 385, 388
- ScMn 03 391
- phonon symmetry
- Ti 02 405
- polymorphs
- SrZrOs 403
- structure parameters
- Sn 02 (110) 496
- Ti 02 396
- supercell model
- SrTiOOs 446
- total energy
- cohesive energy 394
- vibrational frequences
- Ti 02 407
- calculation 404
CChemical bonding in crystals
- Wannier functions for valence bands
crystalline oxides 358
- localized orbitals
- local electronic structure properties 363
- Wannier-type atomic functions
- PbTiOs 354
- SrTi 03 ,
BaTi 03 353
- local properties of electronic structure 351
- bulk crystal
- TiO,
Ti 02 ,
Ti 2 03 342, 344, 347
crystallographic valence
crystalline oxides 335
cyclic cluster
crystalline oxides 334, 335
Cu 4 03 ,
Pb 2 03 ,
Pb 3 04 339
- La 2 Cu 04 ,
La 2 Ni 04 341
- YBa 2 Cu 3 07 340
- density matrix
- LCAO 328
- natural orbitals 330, 332
- electron correlation
- molecular-crystalline approach 332
- Ti 2 03 349
- local properties of electronic structure
- atomic population 329
- bond order, covalency 329
- total atomic valency 330
- localized orbitals
- MgO 368
- SrZrOs 364, 368
- population analysis
- projection technique 369
- projection technique
- Si, SiC, GaAs, MgO, Ti 02 370
- SrTiOs, SrZr 03 372, 374
Computer programs for LCAO calculations 527
Conventional unit cell 15
Crystal structure
cubic
- zincblende 31
- antifluorite 31
cesium chloride 32
- diamond 29
- fluorite 31
- perovskite 33
- rocksalt 30
- database 27
- description 26
- hexagonal
- ScMn 03 45
- graphite 43
- wurtzite ZnS 45
- orthorhombic
- LaMnOs 38
- rhombohedral
- QA 1 2 0 3 , corundum 46
- tetragonal
- La 2 Cu 04 37
- YBa 2 Cu 3 07 41
- anatase 36
- rutile 35
- type 26
Crystal system
cubic 12
- hexagonal 12
- monoclinic 12
- orthorhombic 12
- rhombohedral 12
- syngony 11, 12
- tetragonal 12
- triclinic 12
Crystallographic point groups
- Schönflies notation 15
- international notation 15
DDensity matrix
- crystal 133
- LCAO approximation 137
- approximate 140
- properties 133, 135
- cyclic cluster
- properties 136
- molecule 107
Density-functional theory (molecules)
- Thomas-Fermi model 231
Density-functional theory(crystals)
- LCAO approximation 250
- HSE screened Coulomb hybrid functional 259
- HSE 03
hybrid functional 261
- Kohn-Sham equations 252
- linear-scaling method 253, 256
- screened Coulomb hybrid functional 262
- exchange-correlation functionals 264
- LDA+U method 275
- SIC-LSDA method 271
Density-functional theory (molecules)
- Hohenberg-Kohn theorems 232
- Kohn-Sham equations 234, 237
- generalized-gradient approximation
- GGA
- PBE functional 243
- exchange-correlation functionals 242
- local spin density approximation LSDA 239
- local density approximation LDA
- exchange-correlation functionals 239
- orbital-dependent exchange-correlation
- functionals 244
- hybrid functionals 246, 248
EEffective core potentials
- relativistic 314
- basis sets 318
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