Adiabatic Connection for Strictly-Correlated Electrons

TL;DR

This paper introduces an alternative adiabatic connection framework based on strictly-correlated electrons, offering new insights into density functional theory and potential for improved functional development.

Contribution

It develops a novel adiabatic connection formula using a strictly-correlated electron reference, expanding the theoretical foundation of DFT beyond the Kohn-Sham approach.

Findings

Derived a decorrelation energy relating strictly-correlated and real systems

Applied the theory to uniform electron gas, Hooke's atom, and stretched hydrogen molecule

Provided an alternative perspective for understanding and constructing DFT functionals

Abstract

Modern density functional theory (DFT) calculations employ the Kohn-Sham (KS) system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc). The adiabatic connection formula gives an exact expression for Exc. We consider DFT calculations that instead employ a reference of strictly-correlated electrons. We define a "decorrelation energy" that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely the uniform electron gas, Hooke's atom, and the stretched hydrogen molecule. The adiabatic connection for strictly-correlated electrons provides an alternative perspective for understanding density functional theory and constructing approximate functionals.