A GENERAL SURVEY OF MOLECULAR QUANTUM SIMILARITY

A comprehensive survey of the theoretical foundations and definitions; associated with quantum similarity is given. In this task care has bee n taken to determine the primary mathematical structure which can be a ssociated with quantum similarity measures. Due to this, the concept o f a tagged set is defined to demonstrate how molecular sets can be des cribed systematically. The definition of quantum object, a notion intr oduced by our laboratory and employed for a long time in quantum simil arity studies, is clarified by means of a blend involving quantum theo ry and the tagged set structure formalism, and used afterwards as the cornerstone of the subsequent development of the theory. In the defini tion of quantum objects, density functions play a fundamental role. To formally construct the quantum similarity measure, it is very interes ting to study the main algorithmic ideas, which may serve to compute a pproximate density forms, accurate enough to be employed in the practi cal calculation of nuclear, atomic and molecular quantum similarity me asures. Thus, the atomic shell approximation is defined accompanied by all the implied computational constraints and the consequences they h ave in the whole theory development as well as to the physical interpr etation of the results. A wide and complex field appears from all thes e ideas, where convex sets play a fundamental role, and a new definiti on emerges: one associated with vector semispaces, where the main nume rical formalism of quantum similarity seems perfectly adapted. Applica tions of this development embrace quantum taxonomy, visual representat ion of molecular sets, QSAR and QSPR, topological indices, molecular a lignment, etc., and among this range of procedures and fields, there a ppears with distinct importance the discrete representation of molecul ar structures. (C) 1998 Elsevier Science B.V. All rights reserved.