Ground state of two electrons on a sphere

TL;DR

This paper investigates the ground state of two electrons on a spherical surface using various electronic structure models, achieving near-exact solutions and analyzing different regimes and corrections.

Contribution

It provides a comprehensive comparison of electronic structure methods for this system, including near-exact solutions and asymptotic analysis for large radii.

Findings

Explicitly correlated treatments yield near-exact energies.

Møller-Plesset corrections improve accuracy.

Asymptotic solutions describe large-radius behavior.

Abstract

We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius $R$. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theory to explicitly correlated treatments, the last of which lead to near-exact wavefunctions and energies for any value of $R$. M{\o}ller-Plesset energy corrections (up to fifth-order) are also considered, as well as the asymptotic solution in the large-$R$ regime.