Average Minimum Distances of periodic point sets are fundamental invariants for mapping all periodic crystals.

Widdowson, Daniel ORCID: 0000-0002-5958-0703, Mosca, Marco ORCID: 0000-0002-1764-2814, Pulido, Angeles, Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 and Cooper, Andrew I (2022) Average Minimum Distances of periodic point sets are fundamental invariants for mapping all periodic crystals. MATCH Communications in Mathematical and in Computer Chemistry, 87 (3). pp. 529-559.

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Official URL: https://match.pmf.kg.ac.rs/issues/m87n3/m87n3_529-...

Abstract

The fundamental model of any solid crystalline material (crystal) at the atomic scale is a periodic point set. The strongest natural equivalence of crystals is rigid motion or isometry that preserves all inter-atomic distances. Past comparisons of periodic structures often used manual thresholds, symmetry groups and reduced cells, which are discontinuous under perturbations or thermal vibrations of atoms. This work defines the infinite sequence of continuous isometry invariants (Average Minimum Distances) to progressively capture distances between neighbors. The asymptotic behaviour of the new invariants is theoretically proved in all dimensions for a wide class of sets including non-periodic. The proposed near linear time algorithm identified all different crystals in the world's largest Cambridge Structural Database within a few hours on a modest desktop. The ultra fast speed and proved continuity provide rigorous foundations to continuously parameterise the space of all periodic crystals as a high-dimensional extension of Mendeleev's table of elements.

Item Type:	Article
Additional Information:	The main paper and appendices A,B are written for mathematicians and computer scientists, while appendices C,D focus on applications to crystals
Uncontrolled Keywords:	51-08 (Primary) 51K05 14L24, 74E15 (Secondary), cond-mat.mtrl-sci, cond-mat.mtrl-sci, G.0; J.2; I.3.5
Depositing User:	Symplectic Admin
Date Deposited:	21 Sep 2020 08:08
Last Modified:	15 Jan 2024 15:26
DOI:	10.46793/match.87-3.529W
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3101837