THEORETICAL STUDIES OF THE X-ALPHA APPROXIMATION AND ITS APPLICATIONS (SCATTERING, CONFIGURATION, INTERACTION, IRON, COBALT-SULFUR, SULFUR).

摘要

A rigorous presentation of density functional theory is made, for which the X{dollar}alpha{dollar} approximation is derived a priori. In addition, the multiple scattering (MS) approximation is derived and a discussion of the practical considerations necessary for the implementation of the method is given. Three major applications of the X{dollar}alpha{dollar} and MS approximations are then presented. First, a study of the implementation of configuration interaction (CI) using MS-X{dollar}alpha{dollar} orbitals as basis functions is studied. Performing calculations on the atomic systems of magnesium and chromium and on the molecular system of ozone, it was found that X{dollar}alpha{dollar} and MS-X{dollar}alpha{dollar} wave functions are reasonable for the application of CI. However, the use of the charge partitioning technique for the evaluation of molecular integrals over the MS-X{dollar}alpha{dollar} orbital functions was found to be unsatisfactory for quantitative results. Qualitative results may be obtained with the charge partitioning technique if a further approximation is made. Second, the derivation and application of equations for solving the X{dollar}alpha{dollar} equations numerically in confocal elliptic coordinates for diatomic molecules is presented. The difference from previous approaches is that the core orbitals are treated separately as nucleus centered functions so that application to heavy metal dimers is more feasible. Calculations on the hydrogen and lithium dimers indicate that more work is required for useful accuracy in the transformations between core and valence type functions. Finally, two sets of MS-X{dollar}alpha{dollar} calculations are given. One set is on the iron dimer and the other is on a set of cobalt-sulfur clusters, each containing a core structure of octahedral symmetry Co{dollar}sb{lcub}8{rcub}{dollar}S{dollar}sb{lcub}14{rcub}{dollar}, which is similar to the unit structure in cobalt pentlandite.