Large coupling-strength expansion of the M{\o}ller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms

TL;DR

This paper investigates the large coupling-strength limit of the adiabatic connection in density functional theory, deriving analytical solutions and variational expressions for key systems like the hydrogen atom, H2 molecule, and electron gas.

Contribution

It provides new analytical and variational expressions for the leading terms of the large coupling-strength expansion, extending understanding beyond paradigmatic cases.

Findings

Analytical solutions for the asymptotic behavior of the hydrogen atom.

Variationally optimal expressions for the large coupling-density functionals.

Extension of the analysis to H2 molecule and uniform electron gas.

Abstract

We study in detail the first three leading terms of the large coupling-strength limit of the adiabatic connection that has as weak-interaction expansion the M{\o}ller-Plesset perturbation theory. We first focus on the H atom, both in the spin-polarized and the spin-unpolarized case, reporting numerical and analytical results. In particular, we derive an asymptotic equation that turns out to have simple analytical solutions for certain channels. The asymptotic H atom solution for the spin-unpolarized case is then shown to be variationally optimal for the many-electron spin-restricted closed-shell case, providing expressions for the large coupling-strength density functionals up to the third leading order. We also analyze the H2 molecule and the uniform electron gas.