Adiabatic Connection in the Low-Density Limit

TL;DR

This paper rigorously derives a key condition in density functional theory's adiabatic connection, proposes a parametric integrand form satisfying this condition, and demonstrates its accuracy for weakly-correlated two-electron systems.

Contribution

It provides a rigorous derivation of the vanishing lambda^(-1) term in the adiabatic connection expansion and introduces a new accurate parametric form for the integrand.

Findings

The lambda^(-1) term in the expansion vanishes as lambda approaches infinity.

The proposed integrand form accurately models weakly-correlated two-electron systems.

The derivation confirms a fundamental property of the adiabatic connection in DFT.

Abstract

In density functional theory (DFT), the exchange-correlation functional can be exactly expressed by the adiabatic connection integral. It has been noticed that as lambda goes to infinity, the lambda^(-1) term in the expansion of W(lambda) vanishes. We provide a simple but rigorous derivation to this exact condition in this work. We propose a simple parametric form for the integrand, satisfying this condition, and show that it is highly accurate for weakly-correlated two-electron systems.