Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples

Abstract

This work presents a schematic description of the theoretical foundations of quantum similarity measures and the varied usefulness of the enveloping mathematical structure. The study starts with the definition of tagged sets, continuing with inward matrix products, matrix signatures, and vector semispaces. From there, the construction and structure of quantum density functions become clear and facilitate entry into the description of quantum object sets, as well as into the construction of atomic shell approximations (ASA). An application of the ASA is presented, consisting of the density surfaces of a protein structure. Based on this previous background, quantum similarity measures are naturally constructed, and similarity matrices, composed of all the quantum similarity measures on a quantum object set, along with the quantum mechanical concept of expectation value of an operator, allow the setup of a fundamental quantitative structure-activity relationship (QSPR) equation based on quantum descriptors. An application example is presented based on the inhibition of photosynthesis produced by some naphthyridinone derivatives, which makes them good herbicide candidates. ©2004 Wiley Periodicals, Inc.