A Tour of the Foundations of
Computational Chemistry and Material Science
Lecture 1: ab initio Methods



Central Field Assumption

A further assumption, which is done for practical reasons, is the central field assumption. This is done so that angular decomposition can be performed. So instead of solving a system of three dimensional integro-differential equations for the tex2html_wrap_inline987 one is solving a system of one dimensional differential equations.

The angular decomposition proceeds as follows;

  1. Non-relativistic case: L-S coupling scheme,

    equation134

  2. Relativistic case :

    equation144

    where tex2html_wrap_inline989 is a spherical spinor written as,

    equation160

    and,

    equation167.

This gives a set of radial equations for P(r).



Author: Dr. Warren Perger and Ken Flurchick