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Metrics for measuring distances in configuration spaces.

Ali Sadeghi1, S Alireza Ghasemi, Bastian Schaefer

  • 1Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel, Switzerland.

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|December 11, 2013
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We introduce configurational fingerprint vectors to measure molecular structure dissimilarities. These vectors offer a computationally efficient and accurate alternative to root-mean-square distance (RMSD) for identifying identical structures.

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Area of Science:

  • Computational chemistry
  • Molecular modeling
  • Structural bioinformatics

Background:

  • Characterizing molecular structures is crucial for understanding chemical and biological processes.
  • Existing methods for comparing molecular configurations, like root-mean-square distance (RMSD), can be computationally intensive and sensitive to noise.

Purpose of the Study:

  • To introduce a novel method for characterizing molecular structures.
  • To develop a computationally efficient and robust metric for comparing molecular configurations.
  • To provide a superior alternative to RMSD for identifying structural similarities, especially with noisy data.

Main Methods:

  • Introduction of configurational fingerprint vectors.
  • Utilizing Euclidean distance to measure dissimilarities between fingerprint vectors.
  • Development of a Monte Carlo approach for global minimization of RMSD, considering all translations, rotations, and atomic permutations.

Main Results:

  • Configurational fingerprint vectors serve as effective counterparts to experimental structure identification quantities.
  • The Euclidean distance between fingerprint vectors satisfies metric properties, enabling reliable dissimilarity measurements in high-dimensional spaces.
  • Configurational fingerprint vectors provide a computationally cheap and accurate replacement for RMSD in determining the identity of noise-contaminated molecular configurations.

Conclusions:

  • Configurational fingerprint vectors offer a powerful new tool for molecular structure characterization.
  • This method enhances the efficiency and accuracy of comparing molecular structures, particularly in the presence of noise.
  • The proposed approach facilitates robust identification of identical molecular configurations.