Exchange energies with forces in density-functional theory
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.
Keywords
Cite
@article{arxiv.2203.16980,
title = {Exchange energies with forces in density-functional theory},
author = {Nicolas Tancogne-Dejean and Markus Penz and Andre Laestadius and Mihály A. Csirik and Michael Ruggenthaler and Angel Rubio},
journal= {arXiv preprint arXiv:2203.16980},
year = {2024}
}