One‐ and two‐particle fractional parentage for arbitrary point groups, configurations, and coupling schemes

Abstract

AbstractThe fractional parentage coefficients (CFPS) for arbitrary symmetry (including non‐simply reducible point groups), different coupling schemes, and several open shells are discussed with emphasis on the common features. The differences between the coupling schemes arise merely from a different interpretation of the relevant symmetry group. The formulation uses the particle‐number representation (so‐called second quantization), in which the CFPS appear as the reduced matrix elements of the creation or annihilation operators. This shows, that there is no principal difference in the fractional parentage scheme of one or several open shells. For the latter case the theory of adjective CFPS is worked out and applied to an example of octahedral symmetry.