When assessing the similarity between two isomers whose atoms are ordered identically, one typically translates and rotates their Cartesian coordinates for best alignment and computes the pairwise root mean square distance (RMSD). However, if the atoms are ordered differently, it is necessary to find the best ordering of the atoms and check for chirality before calculating a meaningful pairwise RMSD. The exponential scaling of the computational cost of finding best ordering makes it too expensive for any system with more than ten atoms. We report the use of Kuhn-Munkres matching algorithm to reduce the cost of finding the best ordering from exponential to polynomial scaling. That allows the application of this scheme to any arbitrary system in a reasonably short time. The implementation of this approach and its application to systems ranging from molecular clusters to large peptides will be demonstrated.

Optimal superposition of arbitrarily ordered molecules using the Kuhn-Munkres algorithm

251st National Meeting (2016)

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