Automated least-squares molecular overlay without a priori atomic correspondence or connectivity information

A method is described for automated least-squares molecular overlay without a priori atomic correspondence and without the requirement to establish connectivity information. The method is intended to be useful for automated structure comparison where it might be difficult to establish consistent descriptions of molecular connectivity, and for unconstrained molecular overlay. The general assignment algorithm of Munkres [J. Soc. Ind. Appl. Math. (1957), 5, 32-38] is utilized to obtain the least-squares pairwise atomic correspondence for two molecules in a given relative orientation, and this step is alternated with analytical least-squares overlay using the established pairwise correspondence. Optional constraints for matching only atoms of the same type or same chemical connectivity can be applied by partitioning the molecule into corresponding groups during each Munkres match. The optimization cycle converges on a local minimum and a grid-search procedure is implemented to identify the global minimum. The method is validated and used to compare crystallographically distinct molecules in 18 941 single-component molecular crystal structures taken from the Cambridge Structural Database.