Improved Lieb-Oxford bound on the indirect and exchange energies
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910383417065472 |
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| author | Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
| author_facet | Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
| contents | The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12473 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Improved Lieb-Oxford bound on the indirect and exchange energies Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert Mathematical Physics Statistical Mechanics Chemical Physics The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy. |
| title | Improved Lieb-Oxford bound on the indirect and exchange energies |
| topic | Mathematical Physics Statistical Mechanics Chemical Physics |
| url | https://arxiv.org/abs/2203.12473 |