Reduction from Ŝ_z to Ŝ² eigenspace

Abstract

Calculation of matrix elements between determinants is much easier than between spin eigenfunctions. It should be possible to use this simplicity and perform a direct reduction of structure constants matrices from Ŝ _z to Ŝ²-adapted space. The disadvantages of using determinants instead of spin eigenfunctions are twofold: first, the number of many-electron functions needed in calculation is greater than neccessary. Second, it is not always clear which state was computed. One can reduce the number of functions needed in calculation retaining the simplicity of matrix element calculation by taking a simple combination of determinants, as it was done by Handy (1980), but still the number of functions is significantly larger than neccessary. The method described in this section is equally simple, leads to rigorous coupling coefficients of Ŝ² eigenfunctions, and may easily be extended to more complicated cases such as L̂² eigenfunctions.