Exchange-only virial relation from the adiabatic connection
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914979338256384 |
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| author | Laestadius, Andre Csirik, Mihály A. Penz, Markus Tancogne-Dejean, Nicolas Ruggenthaler, Michael Rubio, Angel Helgaker, Trygve |
| author_facet | Laestadius, Andre Csirik, Mihály A. Penz, Markus Tancogne-Dejean, Nicolas Ruggenthaler, Michael Rubio, Angel Helgaker, Trygve |
| contents | The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength $λ$ at $λ=0$. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on $v$-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit ($λ\searrow 0$) involving the exchange-correlation potential $v_\mathrm{xc}^λ$, which exists by assumption of $v$-representability. On the other hand, a local-exchange potential $v_\mathrm{x}$ is not warranted to exist as such a limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19144 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exchange-only virial relation from the adiabatic connection Laestadius, Andre Csirik, Mihály A. Penz, Markus Tancogne-Dejean, Nicolas Ruggenthaler, Michael Rubio, Angel Helgaker, Trygve Chemical Physics Mathematical Physics Quantum Physics The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength $λ$ at $λ=0$. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on $v$-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit ($λ\searrow 0$) involving the exchange-correlation potential $v_\mathrm{xc}^λ$, which exists by assumption of $v$-representability. On the other hand, a local-exchange potential $v_\mathrm{x}$ is not warranted to exist as such a limit. |
| title | Exchange-only virial relation from the adiabatic connection |
| topic | Chemical Physics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2310.19144 |