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Dreizler R.M., Gross E.K.U. Density Functional Theory: An Approach to the Quantum Many-Body Problem
Dreizler R.M., Gross E.K.U.  Density Functional Theory: An Approach to the Quantum Many-Body Problem









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: Density Functional Theory: An Approach to the Quantum Many-Body Problem

: Dreizler R.M., Gross E.K.U.

:

Quantum mechanics was still in swaddling clothes when Thomas, Fermi, Dirac and von Weizsacker initiated the line of thought from which this work derives. Its current vitality owes much to a result achieved by Hohenberg and Kohn (who supplies the foreword) in 1964. The monograph provides advanced graduate students and many-body physicists/chemists with careful review of the present state of a rich body of technique, the objective of which is to by-pass solution of the Schrodinger equation enroute to a fairly detailed description of the ground state properties of many body systems. Has the feel of a review article which outgrew the capacity of any journal (which, the authors inform us, was in fact its origin), and retains at least some of the attractive brevity of such a review, the whole done up in the familiar Springer style.


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: 18.02.2007

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$r_s$ definition      150
$X_a$ method      46
1/Z expansion      132ff 270
Airy function      92 94
Alpha parameter in $X_a$ theory      86 99 123 191
Anomalous density      see Density
Asymptotic expansion      81 95
Atomic electron affinities      see Electron affinity
Atomic groundstate energies      see Groundstate energy
Atomic ionisation potentials      see Ionisation potential
Auxiliary noninteracting system      44
Average-density approximation      189 230
Band gap      23 33 145ff
Band structure      271
BCS gap equation      74
BCS model      41 72
Bethe Goldstone equation      171
Bijectivity      5
Bloch density matrix      see Density matrix
Bloch equation      90
Bogoliubov de Gennes equations      72
Bogoliubov Valatin transformation      70
Bond lengths, molecular      see Equilibrium separation
Bonding energies, molecular      31 102 125 131 135 238ff
Born Oppenheimer approximation      31
Boson systems      39 109
Bounds, for excited states      33
Bounds, for kinetic exchange-correlation contribution      48
Bounds, for potential terms      19
Bounds, lower, for kinetic energy      18 105 110
Bounds, lower, for Weizsacker term      112
Bounds, upper, for kinetic energy      19 105
Breit interaction      245 260 264
Brown Ravenhall disease      246
canonical ensemble      48
Central field approximation      195
chemical potential      21 23 28 39 62 130 146 148
Classical turning point      see Turning point problem
Clusters      244
Commutator expansion      80
Compressibility      169
Compressibility sum rule      167ff
Compressibility sum rule, self-consistency condition      168 170
Compton profile      38 123
Conduction band      145
Configuration interaction      241
Constrained search method      13ff 27 32 34 37 38 65 247
Convexity      14 22 125
Correlation diagram, diatomic      137
Correlation energy functional, average density approximation      189
Correlation energy functional, for homogeneous electron gas      164
Correlation energy functional, for homogeneous relativistic electron gas      261
Correlation energy functional, gradient expansion of      214ff
Correlation energy functional, in terms of correlation hole      188
Correlation energy functional, Langreth Mehl approximation      225ff
Correlation energy functional, local density approximation for      176ff
Correlation energy functional, wave vector analysis of      196ff
Correlation energy functional, weighted-density approximation      190
Correlation energy functional,orrelation energy functional, local spin density approximation for      178ff
Correlation functions      151 173 274
Correlation hole      188
Coulomb hole      see Correlation hole
Counter term technique      259
Coupled cluster expansion      171
Coupling constant integration      69 144 161 174 183ff 202 207 222
Current density      see Four-current density
Cusp condition      108
Cut-off, momentum space      198 225
Cut-off, real space      119
Degenerate groundstates, density functional theory of      7ff 34 51ff
Density gradient expansion      see Gradient expansion
Density matrix functional theory      36
Density matrix, ensemble      58
Density matrix, Hartree Fock      89 117
Density matrix, Kohn Sham      11 76 120
Density matrix, one-particle, Bloch      90ff
Density matrix, one-particle, Dirac      11 17 47 51 75 92 107 273
Density matrix, one-particle, in momentum space      37
Density matrix, one-particle, of harmonic oscillator problem      93
Density matrix, one-particle, relativistic      257ff
Density matrix, spin      26
Density matrix, statistical      11 14
Density matrix, two-particle      39 120 173 273
Density moments      238
Density, anomalous      40 70
Density, atomic groundstate      126
Density, change      105 152
Density, electron hole      42
Density, ensemble      11 35 50 58
Density, fluctuation      151
Density, grand canonical      28
Density, groundstate      5ff
Density, Hartree Fock      95 103
Density, Kohn Sham      45 95
Density, magnetic moment      25 88 267
Density, momentum      37 123
Density, square root of      62
Density, transition state      58
Density-density response function      152ff 155 274
Derivative discontinuity, of chemical potential      23
Derivative discontinuity, of exchange-correlation energy      145ff
Derivative discontinuity, of groundstate energy      23ff
Derivative discontinuity, of noninteracting kinetic energy      87 110 137
Derivative discontinuity, relation to band gap      145ff
Diagrammatic expansion      139ff 204ff 258ff
Diagrams, exchange      163
Diagrams, ladder      167 171 210
Diagrams, ring      164
Diamagnetism      25
Diatomic systems      125 130 239ff
Dielectric response function      155 167
Dirac density matrix      see Density matrix
Dirac equation      245 252
Dirac Fock method      245
Discontinuity      see Derivative discontinuity
Dissociation energies, molecular      see Bonding energies
Dyson eigenvalues      148
Dyson equation, for effective interaction      139 154
Dyson equation, for one-particle Green's function      33 139 142 148 208 258
Dyson equation, for polarisation insertion      157
Electron affinity      23 146 230 236
Electron removal energies      46 194
Electronegativity      238
Ensemble, density      11 35
Ensemble, energy      36 58 60
Ensemble, finite temperature      28
Ensemble, Rayleigh Ritz principle for      34
Ensemble,grand canonical      28
entropy      28 121
Entropy maximisation      121
Equidensity orbitals      see Orbitals
Equilibrium separation, molecular      239 270
Exchange energy functional, Dirac form      see Kohn Sham form
Exchange energy functional, for homogeneous electron gas      163
Exchange energy functional, for homogeneous relativistic electron gas      257 261
Exchange energy functional, for metal surface      101 198ff
Exchange energy functional, Gaussian formula      122
Exchange energy functional, gradient correction      84 98 205 225
Exchange energy functional, in Hartree Fock limit      207
Exchange energy functional, in local density approximation      176ff
Exchange energy functional, in terms of exchange hole      117
Exchange energy functional, Kohn Sham form      76ff 120
Exchange energy functional, phase-space approach to      120ff
Exchange energy functional, Rade approximants for      115
Exchange energy functional, scaling behaviour      67
Exchange energy functional, Slater from      61
Exchange energy functional, wave vector analysis of      198 228
Exchange energy, atomic      98ff
Exchange energy, surface      101ff
Exchange hole      117ff 123 192 195 261
Exchange potential      67 86 145 188
Exchange-correlation energy functional, at finite temperatures      30
Exchange-correlation energy functional, for ensembles      59
Exchange-correlation energy functional, for superconducting systems      71
Exchange-correlation energy functional, gradient expansion of      202 214ff
Exchange-correlation energy functional, in terms of self-energy insertion      144
Exchange-correlation energy functional, Kohn Sham form      45 48 54 185 202ff 222
Exchange-correlation energy functional, relativistic      250ff
Exchange-correlation hole      174 183 185 192
Exchange-correlation potential      45 51 53 60 63 68 86 144 181ff 187
Excitation energy      57 60
Excited states, density functional theory of      32 57
Fermi energy      56 83 99
Fermi energy, local      79
Fermi hole      see Exchange hole
Fermi momentum      99 162
Fermi momentum, local      82
Fermi surface      73
Fermi surface, from Dyson equation      148
Fermi surface, from Kohn Sham equation      148
Fermi Amaldi correction      192
Ferromagnetic electron gas      172
Feynman propagator      see Green's function
Fluctuation dissipation theorem      152 202
Foldy Wouthuysen transformation      265
Four-current density      247 249ff 258
Four-point function      140ff 210ff 218
Four-potential      247
Fractional occupation of Kohn Sham orbitals      43 54ff 193
Fractional particle number      20ff
Friedel oscillations      204
Functional differentiability      11 50
Furry's theorem      249
Ginzburg Landau theory      39
Gordon decomposition of four-current operator      266
Gordon Kim method      103 244
Gradient expansion, convergence of      95ff 222
Gradient expansion, for metal surfaces      95
Gradient expansion, in terms of wave vector decomposition      222
Gradient expansion, local convergence      103
Gradient expansion, local truncation      103
Gradient expansion, of exchange-correlation energy      175 199ff
Gradient expansion, of Green's function      79 85 260
Gradient expansion, of Kohn Sham exchange energy      84 98 205ff
Gradient expansion, of noninteracting kinetic energy      30 83 95 204
Gradient expansion, of one-particle density matrix      78 91
Gradient expansion, of relativistic noninteracting kinetic energy      253ff
Gradient expansion, with local field correction      220
Grand canonical potential      28 41
Green's function, diagrammatic expansion of      139
Green's function, free-particle      139
Green's function, Hartee Fock one-particle      164
Green's function, Kohn Sham one-particle      143 222
Green's function, one-particle      33 139 151 205 208 274
Green's function, one-particle, relativistic      244 249ff 258 264
Green's function, two-particle      140 270
Groundstate energy functional, English Hohenberg Kohn functional      12
Groundstate energy functional, Hartree Fock limit      32
Groundstate energy functional, Hohenberg Kohn functional      6ff
Groundstate energy functional, Levy Lieb functional      14
Groundstate energy functional, Lieb Valone functional      14
Groundstate energy functional, Perdew Parr Levy Balduz functional      20
Groundstate energy functional, total energy functional      6 10 13 26 36 125 173
Groundstate energy, in Kohn Sham scheme      52 54 184
Groundstate energy, of atoms      131ff 230ff
Groundstate energy, of homogeneous electron gas      160 162ff
GW approximation      147
Hardness      24
Hartree Fock approximation      31 46 95 110 123 133 144 163 176 186 194 207
Hartree Fock plus correlation approach      195 229ff
Hartree Fock systems approach      230 236
Hartree Fock Bogoliubov theory      72
Hartree Fock Slater approximation      57 64 86 191
Hellmann Feynman theorem      68 161 184 230 239 244
High density limit      151
High density limit, of correlation energy      165
High density limit, of gradient correction to correlation energy      212 215 227
Hohenberg Kohn theorem      184 223
Hohenberg Kohn theorem, basic, nonrelativistic      4ff
Hohenberg Kohn theorem, for degenerate groundstates      7ff
Hohenberg Kohn theorem, for excited states      35ff
Hohenberg Kohn theorem, for finite temperature systems      29ff
Hohenberg Kohn theorem, for multicomponent systems      31
Hohenberg Kohn theorem, for noninteracting systems      44
Hohenberg Kohn theorem, for one-particle density matrix functional      37
Hohenberg Kohn theorem, for relativistic systems      246ff
Hohenberg Kohn theorem, for spinpolarised systems      26ff
Hohenberg Kohn theorem, for superconducting systems      42ff
Hohenberg Kohn theorem, in Hartree Fock limit      31ff
Hohenberg Kohn theorem, in momentum space      38
Hohenberg Kohn Mermin theory      see Hohenberg Kohn theorem for finite temperature
Homogeneity of functional      109
Homogeneous electron gas      99 105 150ff
Homogeneous relativistic electron gas      261ff
Hubbard model      147 149
Hypernetted chain approximation      171
Idempotency      47 114 118
Impurity problem      30
insulators      23 145 149
Interatomic potential      103
Irreducible polarisation insertion      see Polarisation insertion
Irreducible self-energy      see Self-energy
Irreducible vertex function      see Vertex function
Janak theorem      56
Jellium model      see Homogeneous electron gas
Kinetic energy functional, atomic      96ff
Kinetic energy functional, convergence of gradient expansion      95ff
Kinetic energy functional, exchange-correlation contribution      68 185
Kinetic energy functional, extensions of noninteracting      49ff
Kinetic energy functional, gradient correction      see Kinetic energy functional Kirzhnits
Kinetic energy functional, gradient corrections at finite temperature      30 84
Kinetic energy functional, Hartree Fock limit      109
Kinetic energy functional, Kirzhnits term      84ff 94 105ff 204
Kinetic energy functional, local behaviour of gradient corrections      85 95ff 107
Kinetic energy functional, local phase space form      120ff
Kinetic energy functional, noninteracting      17 44 45 49 64 76ff 85 91 110 173
Kinetic energy functional, noninteracting for ensembles      59
Kinetic energy functional, noninteracting Pade approximants      113
Kinetic energy functional, nonintracting higher order gradient corrections      83
Kinetic energy functional, on lattice      12
Kinetic energy functional, relativistic      254ff 269
Kinetic energy functional, scaling behaviour      65ff
Kinetic energy functional, surface      100
Kinetic energy functional, Thomas Fermi term      19 85 94 106 110 162 176
Kinetic energy functional, Weizsacker      17 64 84 94 105ff
Kinetic equation approach      170
Kirzhnits method      79ff 251ff
Kohn Sham band gap      145ff
Kohn Sham equations, for ensembles      58ff
Kohn Sham equations, for excited states      58ff
Kohn Sham equations, for nondegenerate groundstates      45ff 143
Kohn Sham equations, for relativistic systems      248ff 271
Kohn Sham equations, for spin-polarised systems      52ff
Kohn Sham equations, for superconductors      70ff
Kohn Sham equations, orbital-free representation of      77
Kohn Sham equations, self interaction corrected      193ff
Kohn Sham Green's function      see Green's function
Kohn Sham orbital energies      46 194ff 236ff
Kohn Sham potential      46 62 156 194
Koopmans' theorem      194
Lamb shift      230
Langreth Mehl functional      225ff
Laplace transform, inverse      77 80
Latter correction      192
Legendre transform functional      14 31
Lindhard function      106 156 202
Linear response theory      87 152ff 199 223
Liquids      131
Local density approximation      174 176ff 230 234 239 276
Local density approximation, relativistic      264ff
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