Publication date: Dec 13, 2021
Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work, we present the simplex method that can perform the inverse operation, i.e., calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large dataset of fingerprints, we can find a particular largest simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments that can be used in a fully automatic way to analyze structures. In this way, we can, for instance, detect atoms in grain boundaries or on edges of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest simplex, we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced.
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|11.1 MiB||The C60 data set used in the paper for the classification and selection of the atomic environments|
|840.0 KiB||The code for the overlap matrix environment and the largest volume simplex developed in the paper. It is taken from the github repository https://github.com/KrumaKruma/Fingerprint|