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Harrison W.A. — Elementary electronic structure
Harrison W.A. — Elementary electronic structure



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Название: Elementary electronic structure

Автор: Harrison W.A.

Аннотация:

This text presents an account of analytic electronic structure, to be distinguished from computational electronic structure. Both are based upon a one-electron approximation, local-density theory, and the determination of the quantum-mechanical electronic states. They both seek to predict the properties of the resulting solids, or molecules on the basis of these states.In the computational mode, the minimum number of approximations are used, and numerical solutions are sought. Here we seek instead to focus on the most important aspects of the solution, making what approximations are necessary in order to proceed analytically and obtain formulae for the properties. This reducing of the problem to basics is almost always less accurate that the computational solution, but has the advantage that it displays the dependence of any property on the parameters of the system. It gives us an understanding of the property in a sense that a numerical solution, or a direct measurement, cannot.


Язык: en

Рубрика: Физика/

Серия: Библиотека «Математическое просвещение»

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 819

Добавлена в каталог: 19.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ionic crystals, elastic constants      366ff
Ionic crystals, elastic constants, coulomb corrections      375ff
Ionic crystals, energy bands      345ff
Ionic crystals, energy gap      333ff
Ionic crystals, energy gap, enhancement      341ff
Ionic crystals, Gruneisen constant      351 365
Ionic crystals, independent-ion model      326ff
Ionic crystals, lattice spacing (bond length)      330 361ff
Ionic crystals, overlap repulsion      350 354ff
Ionic crystals, polarizable ions      380
Ionic crystals, second-neighbor interactions      358
Ionic crystals, static dielectric constant      395ff
Ionic crystals, structure      329
Ionic crystals, surfaces      50 716 736
Ionic crystals, vibrational modes      369ff
Ionicity      142 143
Ionization potentials      10 676
Ionization potentials, central hydrides      782
Ionization potentials, inert-gas atoms      762
Ions, from alchemy      35
Jahn — Teller distortion      314
jj coupling      610
Jones Zone      508
Kohn effect      487
Kondo effect      639
Koopmans’ theorem      327
Langevan term in magnetic susceptibility      159
Lanthenides      see “f-shell metals”
Lattice distance, semiconductors, insulators      see “Bond length”
Lattice distance, simple metals      see “Nearest-neighbor distance”
Lattice distance, transition metals      see “Atomic sphere radius”
Lattice distortions      see also “Impurities”
Lattice distortions in perovskites      702
Lattice vibrations      see “Vibrational frequencies”
Lattice wavenumbers      181
LDA      5 194 354ff
LEED      715
Lennard — Jones interaction      67 767ff
Lindhard dielectric function      462 485
Linear combination of atomic orbitals      11
Linear thermal expansion      see “Thermal expansion”
Liquids, silicon      35
Liquids, simple metal      504ff
Local density approximation      5 194 354ff
Local moments (magnetic)      47 598
Local moments (magnetic), rare earths      613ff
Local orbitals (Wannier functions)      213
Local pseudopotentials      445 533 540
Local-density theory      5 194 354ff
Local-field effects      152 387ff
Localization of electrons      see “Correlated states”
Lone pairs      401 782
Long-range forces      104
Long-range forces, metals      585
Long-range forces, semiconductors      131ff
Low Energy Election Diffraction      715
LS coupling      609
Lyddane — Sachs — Teller relation      165
Madelung energy, Born model of ionic crystals      339
Madelung energy, constant, table      331
Madelung energy, energy, ionic crystals      329ff
Madelung energy, liquids      506
Madelung energy, perovskite crystals      701ff
Madelung energy, potential      82
Madelung energy, shear-constant predictions      367 375
Madelung energy, simple metals      449ff
Madelung energy, surfaces      716
Madelung energy, vibrational frequencies, metals      487
Magnesium telluride      372
Magnetic breakdown      235 473
Magnetic deflection of electrons      463
Magnetic metals      586ff
Magnetic metals, rare earths      614
Magnetic susceptibility, ferromagnets      590
Magnetic susceptibility, semiconductors      158ff
Many-body theory      see “Correlation energy” and “Multi-atom forces”
Matching conditions, interfaces      739ff 741ff
Matching free-electron and tight-binding bands, metals      786pr
Matching free-electron and tight-binding bands, one dimension      19
Matching free-electron and tight-binding bands, semiconductors      191ff
Matrix elements, between d-states      542ff
Matrix elements, between f-states      602
Matrix elements, between p- and d-states      48 642ff 697
Matrix elements, between p- and f-states      642ff
Matrix elements, between p-states      23 24 646 655
Matrix elements, between s- and d-states      697
Matrix elements, between s- and p-states      22 23 24
Matrix elements, between s-states      22 23 24
Matrix elements, decomposition of      23 24 544ff
Matrix elements, distant neighbors      191
Matrix elements, from free-electron fit      19 192ff
Matrix elements, gradient, and of r      220
Matrix elements, mathematics of      73
Matrix elements, meaning      18
Matrix elements, optical electric fields      219 248
Matrix elements, phonons in simple metals      476ff
Matrix elements, size of neglected      52pr
Matrix elements, Slater — Koster tables with $V_{ll'm}$      544ff
Metal-induced gap states      744
Metal-insulator transition      670
Metallic energy, semiconductors, table      60
Metallicity      64
Metallicity, effective-mass effects      228
Metallicity, effects on bands      187 223
Metallization      64 75ff
Metallization, alloys, effects in      301
Metallization, bond length, effect on      85
Metallization, charge redistribution      106pr
Metallization, dielectric susceptibility, effect on      149ff
Metallization, force constant, effect on      87
Metallization, Griineisen constant, effect on      91
Metallization, interatomic      118ff
Metallization, interatomic, carbyne      141pr
Metallization, moments method      98
Metallization, silicon dioxide      407 411
Metallization, structure, effect on      100
Metals      see “Simple metals” and “Transition metals”
Metals, simple      434ff
Metals, simplest case      16 750pr 751pr
Metals, surfaces      50 716ff
MgS, two structures      35
Molecular orbitals      11ff
Molten solids      see “Liquids”
Moments method      93ff 578
Moments method, need for high moments      138
Muffin-tin potential      531
Muffin-tin potential, figure      536
Multi-atom forces      496 584 585 586
Multicenter bonds      754ff
NaCl      see “Ionic crystals”
NaCl, basic electronic structure      36
Nearest-neighbor distance, alloys, simple metals      523
Nearest-neighbor distance, empty-core radius from      493
Nearest-neighbor distance, prediction, simple metals      751pr
Nearest-neighbor distance, semiconductors      see “Bond length”
Nearest-neighbor distance, table, ionic crystals      330
Nearest-neighbor distance, table, metals      438
Nearest-neighbor distance, transition metals      see “Atomic sphere radius”
Negative energy gaps      239 240
Negative-U center      322 733
Nesting of Fermi surfaces      552
Neutrality levels in semiconductors      744
Neutrality of atoms in solids      69 70
Niobates      692
Nitrides, f-shell metals      680ff (see also “Ionic crystals” and “Transition-metals (compounds)”)
Nitrogen molecule      24ff
Noble gases      761ff
Noble-metal halides      see “Ionic crystals”
Noble-metal halides, susceptibility      384
Nonbonding bands      345 650 688
Nonorthogonality      see “Overlap interaction”
Nonorthogonality, electron-phonon interaction      256 262ff
Normalization      3
Normalization, of $sp^3$-hybrids      58
One-electron approximation      5
Operators      3
Optical absorption      248
Optical absorption, formulae      251
Optical absorption, spectrum      217ff 248ff
Optical absorption, threshold      253pr
Optical dielectric constant      see “Dielectric susceptibility”
Optical matrix elements      219 226ff 246ff.
Optical threshold, semiconductors      216ff 221
Optical vibrational modes      126ff
Optical vibrational modes, electron-phonon interaction      279
Optical vibrational modes, fluorite      378pr
Optical vibrational modes, ionic crystals      369ff
Optical vibrational modes, longitudinal-transverse splitting      165
Optical vibrational modes, silicon      141pr
Optical vibrational modes, table of frequencies, semiconductors      211
Orbital Correction Method      764 782
Orthogonality      4
Orthogonality, of $sp^3$-hybrids      58
Orthogonality, of many-electron states      598
Orthogonalized Plane Waves      445 532ff
Oscillatory interactions      see “Friedel oscillations”
Overlap interaction, Bechstedt from      67ff
Overlap interaction, d-states      568 569 582
Overlap interaction, effect on internal displacements      117
Overlap interaction, effect on photothresholds      728
Overlap interaction, f-states      604
Overlap interaction, general l      606
Overlap interaction, ionic crystals      350 354ff 360
Overlap interaction, metals      41
Overlap interaction, multicenter bonds      755ff
Overlap interaction, origin of      15
Overlap interaction, p- and d-states      663
Overlap interaction, semiconductors      65ff
Overlap interaction, variation $1/d^4$      16 66 117
Oxyanions      425ff 769
p-states      6 7 482pr
p-states, p-state radius      644
Packing fractions      481pr
Paramagnetic susceptibility, semiconductors      159 160
Paramagnons      712
pd-coupling      47 642ff
Peierls instability      708ff 733
Periodic boundary conditions      17 181
Periodic table      see “Solid-Stale Table”
Periodic table, origin of periodicity      40
Peripheral States      191
Peripheral States, effective mass effects      232
Perovskites      692ff
Perturbation theory, ionic compounds      343ff
Perturbation theory, metallization of bonds      75ff
Perturbation theory, second-order      37 38
Perturbation theory, simple metal pseudopotentials      456
Perturbation theory, time-dependent      38
Phase shifts      626ff
Phonons      269
Phonons, spectra      see “Vibrational frequencies”
Phosphates      425ff
Photothresholds      50
Photothresholds, metals      see “Work functions”
Photothresholds, semiconductors      727
Pi-bonded chain model      733
Pi-bonding, graphite      770ff
Pi-bonding, molecules      24
Pi-states      22 770ff
Piezoelectric effect      167ff 278 279 421
Planck’s constant      2
Plane waves      2
Plasma frequency, semiconductors      290
Poisson’s ratio, simple metals      498 499
Polar bonds, semiconductors      34
Polar energy      61ff
Polar energy, ionic crystals      359
Polar energy, perovskites      695
Polar energy, pseudopotentials, related to      512 513
Polar energy, semiconductors, table      60
Polar energy, silicon dioxide      405
Polar energy, transition-metal compounds      656
polar molecules      30
Polarity, effect on bands      187
Polarity, effect on lattice vibrations      128ff
Polarity, effect on masses      228
Polarity, semiconductors      62
Polarity, table for semiconductors      60
Polarizable ions      380 765
Polarons      210ff
Primitive cells      56 180
Primitive lattice wavenumbers      181
Primitive translations      180
Promotion energy, actinides      618
Promotion energy, rare earths      614
Promotion energy, semiconductors      70—73
Promotion energy, transition-metal oxides      648 649
Pseudopotentials      39 445ff 532ff
Pseudopotentials, covalent crystals      508
Pseudopotentials, empty-core      39 445ff
Pseudopotentials, empty-core radii, fit to equilibrium spacing      493 571 617
Pseudopotentials, empty-core radii, rare earths, table      617
Pseudopotentials, empty-core radii, simple metals, table      453
Pseudopotentials, empty-core radii, transition metals, table      539 574
Pseudopotentials, form factors      456
Pseudopotentials, illustrative figure      40
Pseudopotentials, local approximation      533
Pseudopotentials, OPW formulation      532
Pseudopotentials, overlap repulsion from      67
Pseudopotentials, phase shifts, relation to      629
Pseudopotentials, real-space plot      463
Pseudopotentials, screening      456ff
Pseudopotentials, simple metals      444ff
Pseudopotentials, transition-metal      532ff
Pseudowavefunction      39 40 532
Pynte structure      430
Quantization      5
quantization of angular momentum      5
quantum mechanics      1ff
Quasiparticles      434
Radial distribution function      504
Radial force constant      see “Force constant”
Radial Schroedinger equation      446 481 482
Radiationless recombination      321
Rare earths      see also “f-shell metals”
Rare earths, cohesion      614ff
Rare earths, compounds      680ff
Rare earths, electronic structure      612ff
Rare earths, empty-core pseudopotentials      617
Rare earths, volume-dependent energy      616
Reconstruction of semiconductor surfaces      50 715 731ff
Reduced mass      129 130 165 370 378
Refractive index      147 (see also “Dielectric susceptibility”)
Rehybridization      110 114
Relaxation rate      see “Scattering”
Relaxation, near impurities      297 298 322pr
Renormalized-atom approach      562
resistivity      see “Scattering”
Resonant bonds      51 347 772 773
Resonant response      175ff
Resonant states      629
Rigid-band model      554
Rigid-hybrid model      114ff
Rigid-hybrid model for optical-mode vibrations      141pr
Rock salt      see “Ionic crystals”
Rock salt, structure      329
Ruderman — Kittel interaction      613 638
Russel — Saunders coupling      609
Rutile      688
s-states      6 7
1 2 3 4
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