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

TLDR

This work outlines the theoretical foundations of quantum similarity measures and highlights the versatility of the underlying mathematical framework. The authors define tagged sets, inward matrix products, matrix signatures, and vector semispaces, then construct quantum density functions and atomic shell approximations, ultimately deriving quantum similarity measures, similarity matrices, and a QSPR equation based on quantum descriptors. The atomic shell approximation is applied to protein density surfaces, and naphthyridinone derivatives are shown to inhibit photosynthesis, positioning them as promising herbicide candidates. © 2004 Wiley Periodicals, Inc.; Int J Quantum Chem, 2005.

Abstract

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. Int J Quantum Chem, 2005