Shape recognition and chirality measure: reestablishing the link between similarity and dissimilarity in discrete space

This paper outlines a new method for matching discrete structures when atom correspondences are unknown. Instead of optimizing at once in discrete space, this method first optimizes the location of one of the two discrete entities onto a continuous interpolation of the other. On the basis of the atom correspondences obtained, the two discrete entities are overlapped. This method avoids the atom-per-atom treatment (and its inherent combinatorial problem) and considers the structures to be compared in their totality. It is shown that the method can readily handle matches of molecules with a few hundred atoms. It allows measurement of the geometric chirality of such systems as well as retrieval of given or common 3D patterns.