Similarity recognition of molecular structures by optimal atomic matching and rotational superposition

Benjamin Helmich, Marek Sierka

Research output: Contribution to JournalArticleAcademicpeer-review


An algorithm for similarity recognition of molecules and molecular clusters is presented which also establishes the optimum matching among atoms of different structures. In the first step of the algorithm, a set of molecules are coarsely superimposed by transforming them into a common reference coordinate system. The optimum atomic matching among structures is then found with the help of the Hungarian algorithm. For this, pairs of structures are represented as complete bipartite graphs with a weight function that uses intermolecular atomic distances. In the final step, a rotational superposition method is applied using the optimum atomic matching found. This yields the minimum root mean square deviation of intermolecular atomic distances with respect to arbitrary rotation and translation of the molecules. Combined with an effective similarity prescreening method, our algorithm shows robustness and an effective quadratic scaling of computational time with the number of atoms.
Original languageEnglish
Pages (from-to)134-140
Number of pages7
JournalJournal of Computational Chemistry
Issue number2
Publication statusPublished - 15 Jan 2012
Externally publishedYes


  • similarity recognition, minimum RMSD, optimal atomic matching, Hungarian algorithm, molecular similarity


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