A general survey of molecular quantum similarity

Abstract

A comprehensive survey of the theoretical foundations and definitions associated with quantum similarity is given. In this task care has been taken to determine the primary mathematical structure which can be associated with quantum similarity measures. Due to this, the concept of a tagged set is defined to demonstrate how molecular sets can be described systematically. The definition of quantum object, a notion introduced by our laboratory and employed for a long time in quantum similarity studies, is clarified by means of a blend involving quantum theory and the tagged set structure formalism, and used afterwards as the cornerstone of the subsequent development of the theory. In the definition of quantum objects, density functions play a fundamental role. To formally construct the quantum similarity measure, it is very interesting to study the main algorithmic ideas, which may serve to compute approximate density forms, accurate enough to be employed in the practical calculation of nuclear, atomic and molecular quantum similarity measures. Thus, the atomic shell approximation is defined accompanied by all the implied computational constraints and the consequences they have in the whole theory development as well as to the physical interpretation of the results. A wide and complex field appears from all these ideas, where convex sets play a fundamental role, and a new definition emerges: one associated with vector semispaces, where the main numerical formalism of quantum similarity seems perfectly adapted. Applications of this development embrace quantum taxonomy, visual representation of molecular sets, QSAR and QSPR, topological indices, molecular alignment, etc., and among this range of procedures and fields, there appears with distinct importance the discrete representation of molecular structures.