A continuous invariant-based asymmetry of a periodic crystal quantifies its deviation from higher symmetry
Authors
Surya Majumder
Daniel Widdowson
Yury Elkin
Olga Anosova
Andrew I Cooper
Graeme M Day
Vitaliy Kurlin
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 Angstroms) the deviation of a periodic crystal from a higher symmetry form. Our experiments on Crystal Structure Prediction datasets show that many simulated crystals may be non-synthesisable not only due to high energy but also due to high CIA values, which are much faster to compute. On another hand, many crystals with high Z' values in the Cambridge Structural Database (CSD) turned out to be close to more symmetric forms with Z'<=1 due to low CIA values.
