Hartree-Fock Model Calculation for Atoms and Crystals Plus Corrections to the Hartree-Fock Excitation Energies

Abstract

One is interested in being able to describe many body systems of electrons and nuclei and their response to external perturbations. The systems are of course atoms, molecules, solids and gases and liquids. In doing so, one generally divides this problem into three parts: the description of the electronic system; the description of the nuclear motion; and the interaction of the two systems. The non-relativistic Hamiltonian of the total system is

$$H=\sum\limits_{b}{\frac{{{P}_{b}}^{2}}{2{{M}_{b}}}}+{{e}^{2}}\sum\limits_{b<c}{\frac{{{Z}_{b}}{{Z}_{c}}}{\left| {{\overset{\to }{\mathop{R}}\,}_{b}}-{{\overset{\to }{\mathop{R}}\,}_{c}} \right|}}+\sum\limits_{i}{\frac{{{P}_{i}}^{2}}{2m}}+{{e}^{2}}\sum\limits_{i<j}{\frac{1}{\left| {{\overset{\to }{\mathop{r}}\,}_{i}}-\overset{\to }{\mathop{{{r}_{j}}}}\, \right|}}-{{e}^{2}}\sum\limits_{b,i}{\frac{{{Z}_{b}}}{\left| {{\overset{\to }{\mathop{r}}\,}_{i}}-{{\overset{\to }{\mathop{R}}\,}_{b}} \right|}}$$

(1.1)

.