Energy Density Functional Theory of Many-Electron Systems

1. Energy density functional theory: historical and bibliographic sketch.- 1.1. The Thomas-Fermi theory and its sequels.- 1.2. One-electron equations.- 1.3. Bibliographic sketch Monographies and books.- 2. Many-electron wavefunctions, density matrices, reduced density matrices and variational principles.- 2.1. Pure states and emsembles in quantum mechanics.- 2.2. Reduced density matrices.- 2.3. Spin structure of wavefunctions and reduced density matrices.- 2.4. Variational principle in the Schrödinger picture of quantum chemistry.- 3. The one-electron density.- 3.1. The meaning of the one-electron density.- 3.2. The one-electron density and molecular structure.- 3.3. Charge distributions and atomic charges.- 3.4. Quantum mechanics of an atomic fragment.- 3.5. Molecular structure and its relation to topologic properties of one-electron densities.- 3.5.b. Catastrophe points and their relation to the change in molecular structure.- 4. An Introduction to density functional theory from the perspective of the independent-particle model and its corrections.- 4.0. Preamble.- 4.1. The Hartree-Fock variational approach.- 4.2. The exact level.- 4.3. The kinetic energy term.- 4.4. The N-representability problem for D2 and ?.- 5. The Thomas-Fermi energy density functional and its generalization.- 5.1. Formulation of the Thomas-Fermi model for atoms and ions.- 5.2. Leading quantum corrections to the Thomas-Fermi atom.- 5.3. Post Thomas-Fermi-Dirac-von Weizsaker developments in density functional theory.- 5.4. Molecular structure and molecular interactions from the perspective of the Thomas- Fermi theory and its extensions.- 6. Foundations of density functional theory.- 6.0. Preamble.- 6.1. Correspondence between ground-state one-electron densities and external potentials.- 6.2.v-representability of one-electron densities.- 6.3 N-representability of one-electron densities.- Problems.- 6.4. The second Hohenberg-Kohn theorem.- 6.5. Universal functionals for non-v-representable one-electron densities.- 6.6. Approximate method for the determination of universal functional.- 6.7. A universal functional of the reduced first-order density operator.- 7. A rigorous formulation of the variational principle in density functional theory.- 7.1. Introductory remarks.- 7.2. Explicit construction of the energy density functional.- 7.3 Reformulation of the Hohenberg-Kohn theorems.- 7.4. The spin-density functional formalism.- 7.5. Density functional theory for excited states.- 7.6 The non-adiabatic energy density functional theory.- 7.7. The concept of fractional occupation numbers in density functional theory.- 7.8. N-representability of experimentally determined densities.- 7.9. The inverse problem in density functional theory.- 8. The self-consistent field concept in density functional theory.- 8.1. Introductory comments.- 8.2. The Slater-Kohn-Sham ansatz. Self-consistent field version of exchange-only density functional theory.- 8.3. The inverse problem in the Slater-Kohn-Sham ansatz.- 8.4 The Kohn-Sham ansatz.- 9. Synopsis and future trends.- 9.1 Density functional theory: overview and interfaces.- Theory of nuclear structure.- 9.2 Concluding remarks.