Commentaries on quantum similarity (1): Density gradient quantum similarity

Abstract

Computation of density gradient quantum similarity integrals is analyzed, while comparing such integrals with overlap density quantum similarity measures. Gradient quantum similarity corresponds to another kind of numerical similarity assessment between a pair of molecular frames, which contrarily to the usual up to date quantum similarity definitions are not measures, that is: strictly positive definite integrals. As the density gradient quantum similarity integrals are defined as scalar products of three real functions, they appear to possess a richer structure than the corresponding positive definite density overlap quantum similarity measures, while preserving the overall similarity trends, when the molecular frames are relatively moved in three-dimensional space. Similarity indices are also studied when simple cases are analyzed in order to perform more comparisons with density overlap quantum similarity. Multiple gradient quantum similarity integrals are also defined. General GTO formulae are given. Numerical results within the atomic shell approximation (ASA) framework are presented as simple examples showing the new performances of the gradient density quantum similarity. Fortran 90 programs illustrating the proposed theoretical development can be downloaded from appropriate websites.

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…”

Computational study of the interaction between indene pyrazole and cyclin dependent kinase 2

“…The field of the quantum similarity was introduced by Carbó-Dorca and co-workers; [22][23][24][25][26][27][28] they defined the quantum similarity measurements Z AB between molecules A and B with the electronic density r A (r) and r B (r) taking into account the minimizing of the expression for the Euclidean distance as: (1) Considering the overlap integral involving the Z AB between the electronic density of the molecule A and B, where Z AA and Z BB represent the Self-similarity. 29 Using the cosine of the angle between the density functions 30 can be expressed mathematically 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].…”