Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918324169867264 |
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| author | Majumder, Surya Widdowson, Daniel Elkin, Yury Anosova, Olga Cooper, Andrew I Day, Graeme M Kurlin, Vitaliy |
| author_facet | Majumder, Surya Widdowson, Daniel Elkin, Yury Anosova, Olga Cooper, Andrew I Day, Graeme M Kurlin, Vitaliy |
| contents | Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units. However, Z' discontinuously changes under almost any displacement of atoms, which can arbitrarily scale up a primitive cell. This discontinuity was recently resolved by a hierarchy of invariant descriptors that continuously change under all small perturbations.
We introduce a Continuous Invariant-based Asymmetry (CIA) to quantify (in physically meaningful Angstroms) the deviation of a periodic crystal from a higher symmetry form. Our experiments on several Crystal Structure Prediction datasets show that about a half of simulated crystals have high values of CIA, while all experimental structures in these datasets have CIA=0. On another hand, many crystals with high values Z' in the Cambridge Structural Database (CSD) turned out to be close to more symmetric forms with Z'<=1 due to low values of CIAs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry Majumder, Surya Widdowson, Daniel Elkin, Yury Anosova, Olga Cooper, Andrew I Day, Graeme M Kurlin, Vitaliy Metric Geometry Materials Science 68U05, 74E15, 51M15 Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units. However, Z' discontinuously changes under almost any displacement of atoms, which can arbitrarily scale up a primitive cell. This discontinuity was recently resolved by a hierarchy of invariant descriptors that continuously change under all small perturbations. We introduce a Continuous Invariant-based Asymmetry (CIA) to quantify (in physically meaningful Angstroms) the deviation of a periodic crystal from a higher symmetry form. Our experiments on several Crystal Structure Prediction datasets show that about a half of simulated crystals have high values of CIA, while all experimental structures in these datasets have CIA=0. On another hand, many crystals with high values Z' in the Cambridge Structural Database (CSD) turned out to be close to more symmetric forms with Z'<=1 due to low values of CIAs. |
| title | Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry |
| topic | Metric Geometry Materials Science 68U05, 74E15, 51M15 |
| url | https://arxiv.org/abs/2510.13746 |