Applications of a method for the analyses of many-electron wavefunctions

Abstract

We show how the method of successive partial orthogonalizations can be used to obtain approximate Hartree-Fock (HF) pair functions directly from the hydrogenic pair functions. The method is more practical than accurate but with the explicit Z-dependence of the bar -nuclei pair functions just eleven such pair functions are needed to obtain an approximate HF pair function by this method for any pair of orbitals in any first row atom. We use the same method of analysis to extract HF orbitals directly from suitable trial functions for the He-He system at several internuclear distances and and also for the auto-ionizing 2s^2 2p^2 states of helium. This approach avoids a separate variational calculation for the HF wave function and furthermore it provides approximate HF pair functions for these auto-ionizing states.