Ground state of two electrons on concentric spheres

TL;DR

This paper investigates the quantum states of two electrons on concentric spheres with different radii, analyzing various electronic structure models and their accuracy, and exploring electron correlation effects and Coulomb holes.

Contribution

It extends previous work to concentric spheres, compares multiple models, and provides insights into electron localization and correlation in this geometry.

Findings

Unrestricted Hartree-Fock over-localizes electrons.

Evidence of a long-range Coulomb hole in large-spheres regime.

Near-exact wave functions achieved through configuration interaction.

Abstract

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.