Exchange energies with forces in density-functional theory

TL;DR

This paper introduces a novel force-based approach in density-functional theory that replaces traditional energy functionals with exact force expressions, offering a promising route for more efficient and potentially more accurate exchange-correlation approximations.

Contribution

It develops a force-based framework for exchange energies in DFT, including scalar and vector potentials, and demonstrates its advantages over traditional energy-based methods.

Findings

Force-based exchange potential compares well with optimized effective-potential results.

Method offers benefits in computational efficiency and non-locality.

Provides a new route for non-adiabatic approximations in time-dependent DFT.

Abstract

We propose exchanging the energy functionals in ground-state DFT with physically equivalent exact force expressions as a new promising route towards approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic-shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective-potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route towards numerically inexpensive non-local and (in the time-dependent case) non-adiabatic approximations.