Metrics for measuring distances in configuration spaces

TL;DR

This paper introduces a new metric based on configurational fingerprint vectors for measuring dissimilarities in molecular configurations, which correlates well with RMSD and is useful for analyzing high-dimensional configuration spaces.

Contribution

It proposes a novel configurational fingerprint metric and a Monte Carlo method to compute the global minimum RMSD for molecular structures.

Findings

The metric correlates strongly with RMSD after global minimization.

The Monte Carlo approach effectively finds the global RMSD minimum.

The metric is suitable for high-dimensional configuration space analysis.

Abstract

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. We show that these metrics correlate well with the RMSD between two configurations if this RMSD is obtained from a global minimization over all translations, rotations and permutations of atomic indices. We introduce a Monte Carlo approach to obtain this global minimum of the RMSD between configurations.