title: Metrics for measuring distances in configuration spaces.
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. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices.
authors: Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel, Switzerland.
authors: Ali
authors: A
authors: Sadeghi
authors: S Alireza
authors: SA
authors: Ghasemi
authors: Bastian
authors: B
authors: Schaefer
authors: Stephan
authors: S
authors: Mohr
authors: Markus A
authors: MA
authors: Lill
authors: Stefan
authors: S
authors: Goedecker
mesh_terms: D009010:Monte Carlo Method; D011789:Quantum Theory