Exchange energies with forces in density-functional theory
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arXiv
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| Format: | Preprint |
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2022
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| author | Tancogne-Dejean, Nicolas Penz, Markus Laestadius, Andre Csirik, Mihály A. Ruggenthaler, Michael Rubio, Angel |
| author_facet | Tancogne-Dejean, Nicolas Penz, Markus Laestadius, Andre Csirik, Mihály A. Ruggenthaler, Michael Rubio, Angel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16980 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exchange energies with forces in density-functional theory Tancogne-Dejean, Nicolas Penz, Markus Laestadius, Andre Csirik, Mihály A. Ruggenthaler, Michael Rubio, Angel Chemical Physics Other Condensed Matter Quantum Physics 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. |
| title | Exchange energies with forces in density-functional theory |
| topic | Chemical Physics Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2203.16980 |