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| Eschrig H. — The Fundamentals of Density Functional Theory |
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| Предметный указатель |
 -spaces 62
 -approach 83
 118
 -additive 112
Absolutely summable 113
action 164 167 168
Adiabatic approximation 56
Adiabatic forces 55
Adiabaticity assumption 52
Affine-linear 75 100
Almost everywhere (a.e.) 62 113
Angular momentum density 186
Anticommutator 31
Aufbau principle 90
Banach space 110
Banach space, reflexive 119
Banach — Alaoglu theorem 119
Base of topology 107
Bispinor 173
Bohr radius 17
Bolzano — Weierstrass theorem 108
Borel set 111
Bose condensed field 172
Bound minimum 124
Bounded linear functional 118
Bounded linear operator 117
Canonical momentum density 166
Cauchy net 110
Cauchy sequence 110
Chain rule for functional derivatives 123
Charge conservation 161
chemical potential 68 93
Classical electron radius 168
Closed set 106
Closed-shell Hartree — Fock method 25
Commutator 30
Compact 108
Complete set 29
Complete set, of spin-orbitals 15
Complete set, of TV-particle states 23
Complete space 110
Compton wavelength 169
Conjugate function 102
Conjugate functional 120
continuous 110
Continuous linear operator 118
Convex 101 120
Convex hull 105 121
Coupling constant 16 51
Creation and annihilation operators 32
Creation and annihilation operators, bosonic 30
Creation and annihilation operators, fermionic 31
Current density functional F[J, Q] 181
Current density functional H[J] 182
Current density functional K[J] 183
Current density, paramagnetic 189
de Rham’s cohomology 164
Density functional by Hohenberg and Kohn 77
Density functional by Hohenberg and Kohn, of kinetic energy 79
Density functional by Levy and Lieb 84
Density functional by Lieb 129
Density functional for N-particle density matrices 88
Density functional H[n] 138
Density functional K[n] 140
Density matrix 86
Density matrix, reduced 35—47
Density operator 32 40
Density parameter  69
Dirac equation 172—174
Dirac operator 191
Dirac operator, squared 192
Dirac sea 191
Distance 108
Dual pair 120 121
d’Alembert operator 162
electromagnetic field 161
Electromagnetic potentials 161
Electron affinity 93
Electron liquid, homogeneous 68 144—148
Electronegativity 94
Ensemble state 86
Essential supremum (ess sup) 62
Exchange and correlation energy 47 149 189
Exchange and correlation field 187
Exchange and correlation hole 47—50
Exchange energy 26
Exchange energy, of the homogeneous electron liquid 146
Exchange hole 40 48
Exchange potential operator 27
Exchange term 20
F-derivative 122
Fenchel’s duality 126
Fermi energy 68
Fermi radius 23
Fermion gas, interaction-free 38
Fermion gas, interaction-free, homogeneous 22 37 40 48
Field operators 32
Fine structure constant 160 169
Finite from below 101
Fock operator 27 28
Fock space 29
Four-current density 163 173 183
Four-field tensor 163
Four-momentum 167
Four-potential 163
Four-velocity 167
Fractional orbital occupation numbers 86
Free Dirac field 174
Free minimum 124
Free photon field 170
Functional derivative 81 122—124
Fundamental form 162
Fundamental tensor 162
G-derivative 122
Gap correction 152
Gauge invariance 76 181 184
Generalized sequence 108
Gradient expansion 73
Groundstate 75
Groundstate energy 75 128 181
Groundstate energy, ensemble 86
Groundstate, degenerate 78
Groundstate, determinantal 79
Groundstate, ensemble 86
Groundstate, non-degenerate 78
Groundstate, of the quantum field 179
Groundstate, spin-polarized 95
Hahn — Banach theorem 103 121
Hamiltonian 13
Hamiltonian density 166
Hamiltonian density, of electromagnetic coupling 175
Hamiltonian, effective, of the inhomogeneous quantum field system 180
Hamiltonian, field quantized 33
Hamiltonian, for Coulomb systems 54
Hamiltonian, for Coulomb systems, total 55
Hamiltonian, in Heisenberg representation 24
Hamiltonian, in momentum representation 19
Hamiltonian, in natural units 17
Hamiltonian, in occupation number representation 32
Hamiltonian, in Schrodinger representation 16
Hamiltonian, of QED 177
Hamiltonian, of the free Dirac field 175
Hamiltonian, of the free photon field 171
Hamiltonian, of the homogeneous electron liquid 144
Hamiltonian, on the torus 57
| Hard potential barrier 76
Hartree energy 26 47
Hartree potential 27
Hartree unit 17
Hartree — Fock energy 26 28
Hartree — Fock orbitals 27
Hartree-Fock equations 27
Hausdorff property 106
Heisenberg picture 170
Heitler — London ansatz 50
Hellmann — Feynman theorem 52
Hilbert space 13 116
Hilbert space, N-particle, bosonic 16
Hilbert space, N-particle, fermionic 15
Hohenberg — Kohn variational principle 77 183
Holder’s Inequality 115
Hole state 33
Homo 28 94
Hyperplane 119
Hyperplane of support 121
Inf-sup problem 125
Inner point 106
Ionization potential 94
Janak’s theorem 89 93
Jump of the Kohn — Sham potential 141
kinetic energy 43 47
Kinetic energy functional 61
Kinetic energy, exchange and correlation contribution 52
Klein — Gordon equation 172
Kohn — Sham exchange and correlation energy 52
Kohn — Sham exchange and correlation hole 53 150
Kohn — Sham exchange and correlation potential 81 149 184
Kohn — Sham orbital 82
Kohn — Sham orbital energy 95 98
Kohn — Sham — Dirac equation 188
Kohn — Sham — Dirac equation, general 184 187
Koopmans’ theorem 28
Lagrange density 165
Lagrange function 126
Lagrange multiplier 124—126
Lagrange multiplier, abstract 126
Lebesgue integral 113
Lebesgue measure 111
Lebesgue space 115—117
Legendre transform 102 120
Limes 106
Limes, of a net 108
Local current density approximation 189
Local density approximation (LDA) 83 148—152
Locally convex space 109
Lorentz gauge 162 171
Lorentz transformation 164
Lower semicontinuous 101 120
LUMO 28 93
Magnetization density 186
Main theorem for extremal problems 119
Maxwell’s equations 161 163
mean field 27
Measurable function 112
Measurable set 112
Metric space 108
Minimum problem 119
Minkowski’s geometry 162
Minkowski’s inequality 115
Molecular field 27 28
N-representable density 84
n-representable potential 77
Natural orbitals 88
Natural units 17
Neighbourhood 106
Net 108
Norm 109
Normal order 171 178
Open set 106
Open-shell Hartree — Fock method 25
Orbital current density 185
Orbital relaxation energy 28
p-summable function 114
Pair correlation function 40
Pair density 38
Particle density 23 35
Particle number operator 30
Pauli — Hellmann — Feynman theorem 52
Perdew — Zunger interpolation of  148
Periodic boundary conditions 18
Poisson’s equation 65
Potential gauge constant 76
Pure state 35
Pure-state v-representable density 77
Quantum electrodynamics (QED) 160
Regular measure 112
Relativistic dispersion relation 167
Relativistic effects magnitude 160
Renormalization 34 171 179 183
Rest mass 167
Riesz — Fisher theorem 116
Saddle point 126
Scaled nuclear charges 54
Schrodinger picture 170
Schwarz’ inequality 116
Self-consistent field 28
Self-interaction 26 46 50 183 184
Seminorm 109
Side condition 124
simplex 87
Slater determinant 15
Sobolev’s inequality 129
Spin current density 186
Spin density 43
Spin magnetization density 43
Spin operator 14
Spin polarization 95—98
Spin polarization, degree of 44 146
Spin-density matrix 36 44
Spin-orbital 15
Spinor 14
Subdifferential 103 121
Subgradient 102 120
Tangent of support 103
Taylor expansion of a functional 123
Teller’s no-binding theorem 71
Thermodynamic limit 33 56—59 93
Thomas — Fermi energy 63
Thomas — Fermi energy, of the atom 67
Thomas — Fermi equation 64 153
Thomas — Fermi functional 61
Thomas — Fermi screening length 69
Thomas — Fermi —  Weizsacker theory 73
Thomas — Fermi — Dirac theory 72
Topological space 106
topology 106
Torus 18 56 130 131
Total charge 179
Trace 36
Transition state 94
Vacuum permeability po 161
Vacuum permittivity eo 161
Virial theorem 55
Virial theorem, of Thomas — Fermi theory 71
von Barth — Hedin interpolation function  147
Vorticity 189
Wavenumber space 18
Weak lower semicontinuous 120
Weak topology 119
Weak* topology 119
Young’s inequality 102
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