Quantum chemistry for solids made simple on the Clifford torus
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908689530617856 |
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| author | Alrakik, Amer Bendazzoli, Gian Luigi Evangelisti, Stefano Berger, J. Arjan |
| author_facet | Alrakik, Amer Bendazzoli, Gian Luigi Evangelisti, Stefano Berger, J. Arjan |
| contents | We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction of a periodic gaussian basis set that is compatible with the topology of the Clifford torus. We illustrate our approach by calculating the ground-state energy of a periodic chain of hydrogen atoms within both Hartree-Fock and coupled cluster theory. We demonstrate that our approach yields the correct ground-state energy in the thermodynamic limit by comparing it to the ground-state energy of a ring of hydrogen atoms in the same limit. Since equivalent ring-like calculations for three-dimensional solids are impossible, our approach is an excellent alternative to perform quantum-chemistry calculations of solids. Our Clifford formalism can be seamlessly combined with current implementations of quantum-chemistry methods designed for atoms and molecules to make them applicable to solids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum chemistry for solids made simple on the Clifford torus Alrakik, Amer Bendazzoli, Gian Luigi Evangelisti, Stefano Berger, J. Arjan Quantum Physics Other Condensed Matter We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction of a periodic gaussian basis set that is compatible with the topology of the Clifford torus. We illustrate our approach by calculating the ground-state energy of a periodic chain of hydrogen atoms within both Hartree-Fock and coupled cluster theory. We demonstrate that our approach yields the correct ground-state energy in the thermodynamic limit by comparing it to the ground-state energy of a ring of hydrogen atoms in the same limit. Since equivalent ring-like calculations for three-dimensional solids are impossible, our approach is an excellent alternative to perform quantum-chemistry calculations of solids. Our Clifford formalism can be seamlessly combined with current implementations of quantum-chemistry methods designed for atoms and molecules to make them applicable to solids. |
| title | Quantum chemistry for solids made simple on the Clifford torus |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2508.03917 |