Basis functions for electronic structure calculations on spheres

TL;DR

This paper introduces spherical Gaussian basis functions for electronic structure calculations on spheres, providing efficient integral computations and demonstrating superior performance over spherical harmonics for localized electrons.

Contribution

The paper presents a new spherical Gaussian basis and efficient algorithms for integrals, advancing electronic structure methods on spherical domains.

Findings

Spherical gaussians outperform spherical harmonics for localized electrons

General formulas for integrals on spheres of any dimension

Efficient computational algorithms using Cauchy-Schwarz bound

Abstract

We introduce a new basis function (the spherical gaussian) for electronic structure calculations on spheres of any dimension $D$. We find \alert{general} expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the $D = 2$ case, we show that spherical gaussians are more efficient than spherical harmonics when the electrons are strongly localized.