Communications on quantum similarity, part 3: A geometric‐quantum similarity molecular superposition algorithm

Abstract

This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric-quantum similarity molecular superposition (GQSMS) algorithm. It has been inspired by the QS Aufbau principle, already described in a previous work, to build up coherently quantum similarity matrices (QSMs). The cornerstone of the present superposition technique relies upon the fact that quantum similarity integrals (QSIs), defined using a GTO basis set, depend on the squared intermolecular atomic distances. The resulting QSM structure, constructed under the GQSMS algorithm, becomes not only optimal in terms of its QSI elements but can also be arranged to produce a positive definite matrix global structure. Kruskal minimum spanning trees are also discussed as a device to order molecular sets described in turn by means of QSM. Besides the main subject of this work, focused on MS and QS, other practical considerations are also included in this study: essentially the use of elementary Jacobi rotations as QSM refinement tools and inward functions as QSM scaling methods.

Notes on Quantitative Structure-Properties Relationships (QSPR) Part Four: Quantum Multimolecular Polyhedra, Collective Vectors, Quantum Similarity, and Quantum QSPR Fundamental Equation

“…Similarity matrices can be supposed to act as metric matrices, not necessarily positive definite (Carbó-Dorca, Besalú, & Mercado, 2011;Carbó-Dorca, 2008). This is so because QMP are usually made of essentially different molecular structures.…”

Understanding the Polar Character Trend in a Series of Diels-Alder Reactions Using Molecular Quantum Similarity and Chemical Reactivity Descriptors

“…The similarity indexes were introduced by Carbó-Dorca and coworkers almost thirty years ago [63,[70][71][72][73][74][75][76][77][78]; they defined the quantum similarity measure Z AB between molecules A and B with the electronic densities A ( 1 ) and B ( 2 ) based on the idea of minimizing the expression for the Euclidean distance as…”

Scale Alpha and Beta of Quantitative Convergence and Chemical Reactivity Analysis in Dual Cholinesterase/Monoamine Oxidase Inhibitors for the Alzheimer Disease Treatment Using Density Functional Theory (DFT)

“…First, one can hope that theoretical descriptors based on quantum similarity (QS) [17][18][19][20][21][22][23][24] and the Density Functional Theory (DFT) [25] can be used to get insights into the factors determining exact nature of the biological activity and selectivity of cholinesterase/monoamine oxidase inhibition and its interactions or at least trends, as to what factors affect the structural properties of these inhibitors molecules.…”

“…The similarity index concept was originally proposed from the perspective of quantum chemistry by Carbó and coworkers [17][18][19][20][21][22][23][24]. Similarity concepts is an omnipresent concept that permeates almost every chemistry field and other scientific fields such as physics, biology, and biochemistry among others.…”

“…From the similarity or dissimilarity concept it is possible to obtain vital information of molecular designers, who are molecular designers within the drugdevelopment context, and the molecular similarity formalism has been proved to be one of the most significant computational tools that can be used to supply novel design ideas in order to get new drugs. The present work is concerned with such methodology that is based on similarity indexes computed from molecular fields using Carbó approach [17][18][19][20][21][22][23][24].…”