ArticleIUCrJ2026
Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry.
Article in IUCrJ, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
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 ångstroms) 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 of 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.
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