Isometry classification of periodic crystals.

19^th May 2020, 10:30
Vitaliy Kurlin
MIF

Abstract

The Crystal Structure Prediction (CSP) tools output too many simulated crystals, including many nearly identical local minima of an energy, because there was no reliable way to quantify the similarity between crystals. Since most solid crystalline materials are rigid, the similarity problem is now rigorously stated as a classification modulo rigid motions or isometries that preserve inter-point distances. Most descriptors, especially if they are based on ambiguous unit cells, are either not isometry invariants or are unstable under atomic vibrations, hence can not reliably quantify crystal similarities. The talk introduces three approaches to build stable-under-noise and complete isometry invariants of periodic crystals.