Molecular Quantum Similarity in QSAR and Drug Design

Abstract

Includes bibliographical references and index.

Molecular Quantum Similarity: Theory and Applications

“…Over a series of five groups of benzoic acid derivatives, each containing seven to eight molecules, a correlation could be established with a regression coefficient over 96%. 174 Similar results were obtained by Carbó -Dorca et al 10 for yet another series of 12 benzoic acid derivatives. In all cases, the fragment self-similarity was calculated for a fragment F, containing the atoms a as…”

“…53 However, it has been not until recently that the mathematical and physical foundations of QS have been developed in a series of publications. 5,[8][9][10]65,68,[148][149][181][182][183][184][185][186] In those articles, several new theoretical definitions, related to old concepts, were described. The first idea described was the so-called tagged set concept.…”

Quantum similarity of isosteres coordinate versus momentum space and influence of alignment

“…As reviews on quantum similarity can be found elsewhere (see, for example, references [1][2][18][19][20][21][22]), only general definitions will be given at this point. Quantum similarity provides a quantitative measure of the resemblance between two quantum objects, A and B [4].…”

“…A quantum similarity measure in coordinate space (rQSM) involving these two objects, z AB can be constructed using their corresponding density functions. Both density functions can be multiplied and integrated over the respective electronic coordinates in a convenient domain, weighted by a positive definite operator [2,18]. That is, ( ) ρ r are the first-order molecular electron density functions of the two molecular structures being compared and ( ) 1 2 , Ω r r is a positive definite operator.…”

“…Since electron densities and the chosen operator ( ) 1 2 , Ω r r are positive definite, rQSMs are always positive real numbers. Depending on the form of the operator, different types of molecular quantum similarity measures can be defined [2,18]. The most used rQSM is the socalled overlap rQSM, in which the operator is Dirac's delta function:…”