A discussion of continuous invariants and metrics on crystals.

1^st April 2022, 14:00
[open table]

Abstract

During the great discussion on 25th March with many crystallographers across the world, we agreed that the strongest possible equivalence of periodic crystals is rigid motion (or isometry), which cannot really change any crystal stucture. We also decided to continue next week in a similar format. The next step is to understand which invariants can reliably distinguish crystals up to isometry and how to avoid arbitrary thresholds to continuously quantify the similarity of crystals. One motivation is to automatically identify near duplicates that appear in experimental databases and among simulated structures obtained as different approximations of the same energy minimum in Crystal Structure Prediction.