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arXiv · 2203.16980

Exchange energies with forces in density-functional theory

Nicolas Tancogne-Dejean·Markus Penz·Andre Laestadius·Mihály A. Csirik·Michael Ruggenthaler·Angel Rubio
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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.

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Nicolas Tancogne-Dejean, Markus Penz, Andre Laestadius, Mihály A. Csirik, Michael Ruggenthaler, Angel Rubio. 2022-03-31. Exchange energies with forces in density-functional theory. https://doi.org/10.1063/5.0177346

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