Angular part of trial wavefunction for solving helium Schr\"{o}dinger equation

Abstract

In this article, the form of basis set for solving helium Schr\"{o}dinger equation is reinvestigated in perspective of geometry. With the help of theorem proved by Gu $et~al.$, we construct a convenient variational basis set, which emphasizes the geometric characteristics of trial wavefuncions. The main advantage of this basis is that the angular part is complete for natural $L$ states with $L + 1$ terms and for unnatural $L$ states with $L$ terms, where $L$ is the total angular quantum number. Compared with basis sets which contain three Euler angles, this basis is very simple to use. More importantly, this basis is quite easy to be generalized to more particle systems.