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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2303.14149 |
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| _version_ | 1866916658389450752 |
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| author | Corso, Thiago Carvalho |
| author_facet | Corso, Thiago Carvalho |
| contents | We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14149 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit Corso, Thiago Carvalho Mathematical Physics 81V74 (Primary) 35J05, 35P20 (Secondary) We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory. |
| title | Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit |
| topic | Mathematical Physics 81V74 (Primary) 35J05, 35P20 (Secondary) |
| url | https://arxiv.org/abs/2303.14149 |