Adiabatic connection at negative coupling strengths

TL;DR

This paper extends the adiabatic connection in density functional theory to negative coupling strengths, providing exact solutions for two-electron systems and a new interpolation method that accurately estimates correlation energies without virtual orbitals.

Contribution

It introduces a generalized adiabatic connection for negative coupling strengths and proposes an interpolation approach that improves correlation energy estimates in DFT.

Findings

Exact solutions for two-electron systems at negative coupling

Interpolation method yields accurate correlation energies

Analysis of near-degeneracy effects in Be series

Abstract

The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength $\alpha$ (with {\em attractive} electrons). In the extreme limit $\alpha\to-\infty$ a simple physical solution is presented and its implications for DFT (as well as its limitations) are discussed. For two-electron systems (a case in which the present solution can be calculated exactly), we find that an interpolation between the limit $\alpha\to-\infty$ and the opposite limit of infinitely strong repulsion ($\alpha\to+\infty$) yields a rather accurate estimate of the second-order correlation energy $E\cor\glt[\rho]$ for several different densities $\rho$, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near-degeneracy.