Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms

Abstract

We study in detail the first three leading terms of the strong-interaction limit of the adiabatic connection that has as weak-interaction expansion the Møller-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 strong-interaction limit density functionals up to the third leading order. We also analyze the H 2 molecule and the uniform electron gas.

Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms

“…We have confirmed this limiting behaviour by computing the RHF energy with a half-occupied orbital, also known as the "spin-unpolarised" atom with fractional spins. [44][45][46] As expected, this half-occupied RHF solution becomes degenerate with the two-electron RHF energy at small Z (Fig 1 : top panel).…”