AI3SD Video: The Crystal Isometry Principle
AI3SD Video: The Crystal Isometry Principle
The strongest and most practical equivalence of periodic crystals is rigid motion or isometry preserving all inter-atomic distances. The Crystal Isometry Principle (CRISP) says [1] that all real non-equivalent crystals should have non-isometric structures of atomic centres without chemical labels. If one atom is replaced by another one, distances to neighbouring atoms are inevitably perturbed, which can be detected by recent geometric invariants independent of any thresholds. More than 200 million pairwise comparisons of all periodic crystals with full geometric data from the Cambridge Structural Database (CSD) over two days on a modest desktop found five pairs of suspicious entries with different compositions but identical geometries [1, section 7]. For instance, all geometric parameters of HIFCAB and JEPLIA are identical to the last decimal place, but one atom of Cadmium is replaced by Manganese. With the help of the Cambridge Crystallographic Data Centre, all journals that published the underlying papers started investigations into data integrity. These experiments confirm that all periodic crystals (without restricting them to any chemical composition) live in a common Crystal Isometry Space (CRISP) parameterised by complete invariants. For example, diamond and graphite consisting of identical carbon atoms occupy in this CRISP space different positions given by unique geographic-style coordinates and a well-defined distance. In the same way, Mendeleev put all chemical elements (despite their obvious differences) into a single periodic table parameterised by two discrete coordinates: the period and group number. The new invariant coordinates extend Mendeleev’s table to the continuous space CRISP containing all existing and not yet discovered periodic crystals. [1] Widdowson, Mosca, Pulido, Kurlin, Cooper. Average Minimum Distances. MATCH Commun. Math. Comput. Chem. 87, 529-559 (2022), kurlin.org/projects/periodic-geometry-topology/AMD.pdf
Kurlin, Vitaliy
2dca60fb-2563-4ce1-a85a-0ab8cf00c54d
Frey, Jeremy G.
ba60c559-c4af-44f1-87e6-ce69819bf23f
Kanza, Samantha
b73bcf34-3ff8-4691-bd09-aa657dcff420
Niranjan, Mahesan
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
2 March 2022
Kurlin, Vitaliy
2dca60fb-2563-4ce1-a85a-0ab8cf00c54d
Frey, Jeremy G.
ba60c559-c4af-44f1-87e6-ce69819bf23f
Kanza, Samantha
b73bcf34-3ff8-4691-bd09-aa657dcff420
Niranjan, Mahesan
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
Kurlin, Vitaliy
(2022)
AI3SD Video: The Crystal Isometry Principle.
Frey, Jeremy G., Kanza, Samantha and Niranjan, Mahesan
(eds.)
AI4SD Network+ Conference, Chilworth Manor , Southampton, United Kingdom.
01 - 03 Mar 2022.
(doi:10.5258/SOTON/AI3SD0203).
Record type:
Conference or Workshop Item
(Other)
Abstract
The strongest and most practical equivalence of periodic crystals is rigid motion or isometry preserving all inter-atomic distances. The Crystal Isometry Principle (CRISP) says [1] that all real non-equivalent crystals should have non-isometric structures of atomic centres without chemical labels. If one atom is replaced by another one, distances to neighbouring atoms are inevitably perturbed, which can be detected by recent geometric invariants independent of any thresholds. More than 200 million pairwise comparisons of all periodic crystals with full geometric data from the Cambridge Structural Database (CSD) over two days on a modest desktop found five pairs of suspicious entries with different compositions but identical geometries [1, section 7]. For instance, all geometric parameters of HIFCAB and JEPLIA are identical to the last decimal place, but one atom of Cadmium is replaced by Manganese. With the help of the Cambridge Crystallographic Data Centre, all journals that published the underlying papers started investigations into data integrity. These experiments confirm that all periodic crystals (without restricting them to any chemical composition) live in a common Crystal Isometry Space (CRISP) parameterised by complete invariants. For example, diamond and graphite consisting of identical carbon atoms occupy in this CRISP space different positions given by unique geographic-style coordinates and a well-defined distance. In the same way, Mendeleev put all chemical elements (despite their obvious differences) into a single periodic table parameterised by two discrete coordinates: the period and group number. The new invariant coordinates extend Mendeleev’s table to the continuous space CRISP containing all existing and not yet discovered periodic crystals. [1] Widdowson, Mosca, Pulido, Kurlin, Cooper. Average Minimum Distances. MATCH Commun. Math. Comput. Chem. 87, 529-559 (2022), kurlin.org/projects/periodic-geometry-topology/AMD.pdf
Video
ai4sd_march_2022_day_2_VitaliyKurin
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Published date: 2 March 2022
Additional Information:
Dr Vitaliy Kurlin is a Reader working in the Materials Innovation Factory at Liverpool since 2016. He completed a PhD in Geometry and Topology at Moscow State University in 2003 and held a Marie Curie International Incoming Fellowship in 2005-2007. Since 2018 he leads the Liverpool team of four co-Is in the £3.5M EPSRC grant `Application-driven Topological Data Analysis’ with Oxford. Since 2021 he is the Royal Academy of Engineering industry fellow at the Cambridge Crystallographic Data Centre. His Data Science group includes more than 10 researchers developing the new area of Periodic Geometry for applications in Crystallography.
Venue - Dates:
AI4SD Network+ Conference, Chilworth Manor , Southampton, United Kingdom, 2022-03-01 - 2022-03-03
Identifiers
Local EPrints ID: 468630
URI: http://eprints.soton.ac.uk/id/eprint/468630
PURE UUID: 8ac3d9be-740d-4050-8d76-8ab719681543
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Date deposited: 19 Aug 2022 16:32
Last modified: 17 Mar 2024 03:51
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Author:
Vitaliy Kurlin
Editor:
Mahesan Niranjan
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