Notes on quantitative structure-property relationships (QSPR), part 3: Density functions origin shift as a source of quantum QSPR algorithms in molecular spaces

• Published in: Journal of computational chemistry Vol. 34; no. 9; pp. 766 - 779
• Main Author: Carbó-Dorca, Ramon
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 05.04.2013; Wiley Subscription Services, Inc
• Subjects: Algorithms; causality in QQSPR; density functions; dimensionality paradox in QSPR; FORTRAN; Geometry; Mathematical functions; Molecular chemistry; molecular quantum similarity; molecular space QSPR; nested do loops; origin shifted DF; QSAR; QSPR; quantum object sets; Quantum physics; quantum QSPR
• ISSN: 0192-8651; 1096-987X; 1096-987X
• DOI: 10.1002/jcc.23198

A general algorithm implementing a useful variant of quantum quantitative structure–property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well‐described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR‐n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed. © 2012 Wiley Periodicals, Inc. Cramer steroid set experimental CBG biological activity versus estimated values of this molecular parameter are presented. Activities are computed by a quantum QSPR algorithm via molecular space (MS) definition. Every molecule is a MS point associated with a quantum mechanical (QM) density function (DF). The resultant DF set of MS points is origin‐shifted. Using shifted DF, a QQSPR operator is built up, and activities are easily computed with QM expectation values.