Crystal Geomap: a visualisation and comparison tool for crystals based on ultra-fast isometry invariants.

3^rd April 2025, 14:00
Dan Widdowson
MIF

Abstract

The number of experimentally measured crystal structures has risen exponentially in recent decades. Crystals are often classified by space group, which can be the same for distinct structures and different for similar ones; yet most continuous descriptors such as density can coincide for dissimilar crystals (a false positive). The Pointwise Distance Distribution (PDD) is a continuous descriptor (isometry invariant) akin to a crystal’s genetic code with no false positives amongst real organic crystals. PDDs contain enough information to reconstruct most crystals while comparisons take only milliseconds and are fast enough to find all matches in a database of a million of structures in a few minutes, a task requiring years for comparison tools such as COMPACK. In 2021 we used invariants to find duplicates in the Cambridge Structural Database (CSD), 5 of which were investigated by curators. Since then the experiment’s speed and scope has grown considerably, culminating in a list of over 380,000 cross references between the CSD and COD (Open Crystallography Database), comprising 80% of the COD. The PDD of a crystal is considered its coordinate in a universal ‘crystal space’, motivating us to create a visualisation and comparison tool based on our invariants. Our ‘Crystal Geomap’ app allows a user to compare or cluster crystals, to export or plot on chosen x and y axes where all crystals can be seen in one space with physically meaningful coordinates.