Towards non-local density functionals by explicit modeling of the exchange-correlation hole in inhomogeneous systems

TL;DR

This paper introduces a new non-local density functional that models the exchange-correlation hole explicitly, aiming to improve accuracy in challenging situations like bond breaking by satisfying key physical constraints.

Contribution

The paper proposes a novel approach to develop a non-local density functional by explicitly modeling the exchange-correlation hole, satisfying several physical conditions that previous functionals do not.

Findings

Improved description of dissociating hydrogen molecule

Better binding curve compared to local density approximation

Functional satisfies key physical constraints

Abstract

We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these requirements. These demands are achieved by screening the exchange hole in such a way that the pair-correlation function is symmetric and satisfies the sum-rule. These two features immediately imply (1) and (2) while the explicit dependence of the exchange hole on the Kohn-Sham orbitals implies (3). Preliminary calculations show an improved physical description of the dissociating hydrogen molecule. Though the total energy is still far from perfect, the binding curve from our non-local density functional provides a significant improvement over the local density approximation.