Energy Density Functional Theory of Many-Electron Systems [Hardcover]

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.- Review articles.- International meetings.- 2. Many-electron wavefunctions, density matrices, reduced density matrices and variational principles.- 2.1. Pure states and emsembles in quantum mechanics.- 2.1.a. The measurement process in quantum mechanics.- 2.1.b. The Liouville formalism.- 2.1.c. Wavefunctions.- 2.l.d. The ATh-order density operator for a pure state.- 2.1.e. The ATh-order density matrix for a pure state.- 2.1.f. Representation of DiNin a continuons coordinate basis.- 2.1.g. The expectation value of an operator.- 2.1.h. The Nth-order density operator for mixed states or emsembles.- 2.1.i. Equivalence between Liouvilles and Schr?dingers equation for pure states.- 2.l.j. The case of mixed states or emsembles.- 2.l.k. The Liouvillian as a superoperator.- Problems.- 2.2. Reduced density matrices.- 2.2.a. Definition.- 2.2.b. The case of a single Slater determinant.- 2.2.c. The case of a linear combination of Slater determinants.- 2.2.d. Some properties of D1 and D2.- 2.2.e. Average values of operators.- Problems.- 2.3. Spin structure of wavefunctions and reduced density matrices.- Problems.- 2.4. Variational principle in the Schr?dinger picture of quantum chemistry.- 2.4.a. General formulation.- 2.4.b. The expectation value of the Hamiltonian.- 2.4.c. Introduction to point transformations: The virial theorem.- Problems.- 3. The one-electron density.- 3.1. The meaning of the one-electron density.- 3.1.a. The physical interpretation of ?(r) for N identical particles.- 3.1.b. The physical interpretation of ?(r) for N identical particles in the presence of M nuclei.- 3.1.c. The electronic and nuclear density for H2+.- 3.l.d. The evidence for atomic fragments.- 3.1.e. Other properties of the one-electron density.- Asymptotic behavior.- Cusp condition.- MultipolelÓ"