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Martin R.M. — Electronic Structure: Basic Theory and Practical Methods

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Название: Electronic Structure: Basic Theory and Practical Methods

Автор: Martin R.M.

Аннотация:

The study of the electronic structure of materials is at a momentous stage, with the emergence of new computational methods and theoretical approaches. This volume provides an introduction to the field and describes its conceptual framework, the capabilities of present methods, limitations, and challenges for the future. Many properties of materials can now be determined directly from the fundamental equations of quantum mechanics, bringing new insights into critical problems in physics, chemistry, and materials science.

Язык:

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 2004

Количество страниц: 624

Добавлена в каталог: 01.07.2009

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Предметный указатель

$r_{s}$ , definition      100
$r_{s}$ , typical values      101
Adiabatic approximation      53 482—484
Angle resolved photoemission      see "Photoemission"
Anharmonicity      see "Lattice dynamics"
APW      see "Augmented plane wave method"
Arnoldi method      558
Atomic Sphere Approximation      199—201 333 360 362 532 533
Atomic units, Hartree      53 188 316
Atomic units, Rydberg      316
Augmented plane wave method      7 235 313—323
Band gaps, "band gap problem"      43 46
Band gaps, derivative discontinity in functional      143 145 149 265
Band gaps, fundamental gap definition      40
Band gaps, non-local functionals      44 166 303 304 416
Band gaps, semiconductors      44 265
Band structure, $BaTiO_{3}$       264
Band structure, $C_{60}$       38
Band structure, $MgB_{2}$       48
Band structure, $YBa_{2}Cu_{3}O_{7}$       354 364
Band structure, Al      327
Band structure, canonical fcc      336
Band structure, Cu      42
Band structure, Cu-Ni alloys      330
Band structure, ferromagnetic Ni      322
Band structure, free electrons in a fcc crystal      240
Band structure, GaAs      244 361
Band structure, Ge      7 43 361
Band structure, Ge (100) surface      303
Band structure, graphite      48
Band structure, Na      6 114
Band structure, nanotubes      270
Band structure, Os      360
Band structure, tight-binding, $CuO_{2}$ planes      283
Band structure, tight-binding, nanotubes      287
Band structure, tight-binding, Ni      285
Band structure, tight-binding, Si      284
Band structure, tight-binding, square lattice      280
Band structure, transition metal 3d series      321
Band theory, early history      4—8
Band theory, non-interacting excitations in crystals      85—89
Band theory, overview of methods      233—235
Bardeen, J.      7 9 105 256
Berry's phase, polarization      27 401 439—441
Berry's phase, spin waves      24 393 446
Bethe, H.      3—5 46
Bloch functions      87—89 246 399 418 565
Bloch functions, and Wannier functions      418—421
Bloch functions, Berry's phase and polarization      439—441
Bloch theorem      4 233 234 389 404
Bloch theorem, first proof      85—89
Bloch theorem, second proof      238—239
Bloch theorem, third proof      273—274
Bloch, E.      4 234 272
Bohr, N.      2 8
Bond order      460
Born — Oppenheimer approximation      see "Adiabatic approximation"
Bravais lattice      see "Translation symmetry"
Brillouin zone (BZ)      74 239
Brillouin zone (BZ) and Bragg scattering      88 239
Brillouin zone (BZ), definition      83
Brillouin zone (BZ), examples      84
Brillouin zone (BZ), irreducible (IBZ)      91
Broyden method      180 258 548—549
Broyden method, modified      181 182 549
Bulk modulus, atomic sphere approximation      533
Bulk modulus, definition      16
Bulk modulus, sp-bonded metals      113
Bulk modulus, transition metals      18
Callaway, J.      7
Canonical bands      333—338
Canonical bands, densities of states      337
Canonical bands, fcc lattice      336
Canonical bands, potential function      335
Car — Parrinello simulations      see "Quantum molecular dynamics"
Catalysis      31—32
Catalysis, Ziegler — Nata reaction      31
Chebyshev polynomials      542
Chebyshev polynomials, expansion of Fermi function      461
Chebyshev polynomials, expansion of time dependence      414
chemical potential      32 34 60 128 179 268
Clebsch — Gordan coefficients      192 541
Cluster, metal      409
Cluster, metals      36
Cluster, optical properties      see "Optical properties"
Cluster, semiconductor      36—37 409—411
Clusters      36—39 409—417
Cohesive energy transition metals      18
Conjugate gradient      see "Minimization methods"
Correlation      8 51 67—68
Correlation energy, definition      67
Correlation energy, Hedin — Lundquist      479
Correlation energy, homogeneous gas      108—112
Correlation energy, Perdew — Zunger fit to QMC energies      480
Correlation energy, quantum Monte Carlo      109
Correlation energy, self-consistent GW approximation      109
Correlation energy, Vosko — Wilkes — Nusiar fit to QMC energies      480
Correlation energy, Wigner interpolation formula      108 479
Coulomb Sums, Ewald method      255 500—504 509—511 516
Coulomb Sums, Madelung constant      112 503—504
CPA      see "Multiple scattering theory"
Crystal momentum, definition      88
Crystal structure basis      73 77—80
Crystal structure, $MgB_{2}$       78
Crystal structure, close-packed      80
Crystal structure, close-packed, cubic (fcc)      81
Crystal structure, close-packed, hexagonal (hcp)      81
Crystal structure, definition      73
Crystal structure, diamond      79
Crystal structure, graphene plane      77
Crystal structure, NaCl      78
Crystal structure, perovskite      79
Crystal structure, square $CuO_{2}$ plane      77
Crystal structure, ZnS      79
Crystal symmetry      73
Crystal symmetry, inversion      89
Crystal symmetry, point operations      91
Crystal symmetry, time reversal      89
Crystal symmetry, translations      see "Translation symmetry"
Davidson algorithm      548 559
defects      35—36
Defects, "negative U"      35 36
Defects, DX: Si in GaAs      35
Defects, extended      467
Defects, H in Si      35 36
Density functional perturbation theory      395—401
Density functional theory      119—185
Density functional theory, also      see "Functionals"
Density functional theory, constrained      161 199
Density functional theory, current functional      128 161
Density functional theory, Hohenberg — Kohn functional      124—125 131
Density functional theory, Hohenberg — Kohn theorems      120—126 133 137 147 436
Density functional theory, Kohn — Sham method      see "Kohn — Sham method"
Density functional theory, Levy — Lieb functional      125 126 134
Density functional theory, Mermin functional      127 130 133 147 178
Density matrix      60
Density matrix and O(N) methods      463—466
Density matrix, homogeneous gas, non-interacting electrons      103—104
Density matrix, idempotency      463
Density matrix, independent-particle      62
Density matrix, McWeeny purification      464
Density matrix, polynomial representation      461—462
Density matrix, spectral representation      462
Density of states, $MgB_{2}$       49
Density of states, canonical      337
Density of states, critical points      96
Density of states, critical points, line, square, cube      280 281 294
Density of states, critical points, one dimension      98
Density of states, critical points, three dimensions      98
Density of states, definition      96

Density of states, ferromagnetic Fe      293 353
Density of states, fullerenes      459
Density of states, graphene plane      459
Density of states, liquid C      381
Density of states, liquid Fe and Co      458
Density of states, maximum entropy method      459 461 551
Density of states, moments      458—459 550
Density of states, moments, definition      550
Density of states, phonon      see "Phonons"
Density of states, random vector sampling      461 550
Density of states, recursion method      457
Density-polarization functional theory      129 149 436
DFT      see "Density functional theory"
Dielectric function      492—498
Dielectric function, also      see "Optical properties"
Dielectric function, conductivity      494
Dielectric function, lattice contribution      496
Dielectric function, Lindhard      115 394 402 495
Dielectric function, longitudinal scalar function      495
Dielectric function, non-interacting particles      407
Dielectric function, transverse tensor function      496
Dirac equation      193—195
Dirac equation, scalar relativistic approximation      195
Dirac, P.      2 8 193
Drude, P.K.L.      3
Elastic constants      21 22 390
Elastic constants, non-linear      21
Elasticity      21
Electron, discovery of      1
Electron-phonon interaction      401—402
Electron-phonon interaction, $MgB_{2}$       48
Empirical pseudopotential method (EPM)      see "Pseudopotential methods"
Energy, density      519—527
Energy, exchange-correlation      65—68 138 152—171
Energy, total energy expressions      54—56 137 255—256 307—308 500—506
Enthalpy, definition      19
Ewald sum      see "Coulomb Sums"
Exchange      8 65—67
Exclusion principle      2
Fermi energy, chemical potential for electrons      36
Fermi energy, homogeneous gas, non-interacting electrons      102
Fermi surface      95 399 401
Fermi surface and density functional theory      131
Fermi surface and Kohn — Sham theory      146
Fermi surface, $MgB_{2}$       49
Fermi surface, calculation in Green's function approach      328
Fermi surface, definition      45
Fermi surface, homogeneous gas      102
Fermi surface, Luttinger theorem      102
Fermi surface, square lattice      280 281
Fermi, E.      2 7 120 205 206
Ferroelectricity      442 443
Feynman, R.P.      57 71 182 513
Flouquet theorem      88
Force theorem      56—59 182 291 373 377 466 511
Force theorem, alternative form      529—535
Force theorem, generalized      58 390 513 514 526
Force theorem, localized-orbital formulation      308—309
Force theorem, Pulay correction      183 308
Form factor      217 240
Free energy      60 122 128 178 381 392
Free energy, definition      19
Friedel oscillations      104 115 329
Fullerenes      37 38 459 465
Functionals, equations      476—478
Functionals, exact exchange (EXX)      44 162—165
Functionals, exchange-correlation      152—171 479—481
Functionals, hybrid      165
Gaunt coefficients      192 325 334 541
Gibbs free energy, definition      19
Grand potential      60 127 178 179 464 467
Grand potential, definition      32
GW calculations, Ge (100) surface bands      303
GW calculations, Ge bands      43
GW calculations, Si bands      304
GW method      43 109
Harris — Weinert — Foulkes functional      175—177
Hartree — Fock      302
Hartree — Fock, approximation      62—65
Hartree — Fock, equations      63
Hartree — Fock, equations, atoms      189—192
Hartree — Fock, Fermi surface singularity      105
Hartree — Fock, He and $H_{2}$       167—169
Hartree — Fock, homogeneous gas      104—107
Hartree, atomic units      53
Hartree, D.R.      5 161
Hartree, energy      56
Hartree, potential      61
Hartree, self-consistent method      61—62
Heisenberg, W.      2—4 8 22 513
Heitler — London orbitals      3
Helium atom, test of functionals      167
Hellmann — Feynman theorem      see "Force theorem"
Hellmann, H.      7 57 205
Herman, F.      7
Herring, W.C.      7 35 36 205 207—208 256 382
Hubbard model      161 171 422
Hund's rules      8
Hydrogen, atom, test of functionals      171
Hydrogen, bond      15 29
Hydrogen, metal at high pressure      243 463
Hydrogen, molecule, test of functionals      167 168
Insulators, Mott      136 162 282 303 355
Interfaces, band offset      34 266—267 360 507—508
Interfaces, band offset, Si/Ge      267
Janak theorem      144
KKR      see "Multiple scattering theory"
Kohn anomaly      115 451
Kohn — Sham method      152 135—185
Kohn — Sham method, equations, atoms      189—192
Kohn — Sham method, equations, general formulation      138—139 172—174
Kohn — Sham method, He and $H_{2}$       167—169
Kohn — Sham method, self-consistency      see "Self-consistency"
Kohn, W.      115 120 444 450
Koopmans' theorem      64
Kramers' theorem      89 90
Kramers, H.      90 494
Lanczos algorithm      455 456 458 473 550 557—558 569
LAPW      see "Linearized augmented plane wave method"
Lattice constant, transition metal series      18
Lattice dynamics and electronic structure      387—402
Lattice dynamics, anharmonicity      16 26 50 266 391
Lattice dynamics, dynamical matrix      389
Lattice dynamics, effective charges      27 265 389 393 399 442 443 448 496—497
Lattice dynamics, force constants      389
Lattice dynamics, phonons      see "Phonons"
Lattice dynamics, piezoelectricity      27 497
Lattice instability, ferroelectricity      26
Lattice instability, omega phase      391
LCAO      see "Localized orbital methods"
Lewis, G.N.      3
Linear-scaling methods      302 428 450—474
Linear-scaling methods, "Divide and Conquer"      460
Linear-scaling methods, density matrix      461—466
Linear-scaling methods, Green's functions      455—458 462
Linear-scaling methods, moments      458—459
Linear-scaling methods, non-orthogonal orbitals      468—469
Linear-scaling methods, recursion      456—460
Linear-scaling methods, Wannier functions      453 466—468
Linearization in augmented methods      345—350
Linearized augmented plane wave method      235 350—355
Linearized augmented plane wave method, full potential      364
Linearized muffin-tin orbital method      235 355—362
Linearized muffin-tin orbital method, beyond linear, NMTO      362
Linearized muffin-tin orbital method, full potential      364
Linearized muffin-tin orbital method, localized formulation      358
LMTO      see "Linearized muffin-tin orbital method"
localization      444—446
Localized orbital methods      234
Localized orbital methods, atom-centered orbitals      273—274

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