Molecular Spaces Quantum Quantitative Structure-Properties Relations (QQSPR): A Quantum Mechanical Comprehensive Theoretical Framework

Molecular Spaces Quantum Quantitative Structure-Properties Relations (QQSPR): A Quantum Mechanical Comprehensive Theoretical Framework

Ramon Carbó-Dorca (Institut de Química Computacional i Catàlisi, Universitat de Girona,Girona, Spain) and Silvia González (Departamento de Química, Universidad Técnica Particular de Loja,Loja, Ecuador)
DOI: 10.4018/IJQSPR.2016070101
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Abstract

Quantum QSPR can be described as a set of procedures, which can be obtained from molecular space structure, where quantum (multi)molecular polyhedra (QMP) can be defined. The collective vectors, which can be described characteristic of a given QMP and their condensed scalar values, can be used in turn to construct Hermitian QQSPR operators, which can be further employed to obtain expectation values of complex molecular properties. The linear QQSPR fundamental equation constructed from this quantum mechanical idea is able to fundament, not only an algorithm capable to obtain estimates of unknown molecular properties from the knowledge of quantum mechanical density functions, but also from the empirical, classical numerical description of molecular sets.
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Introduction

Publication of the first paper (Carbó, Leyda, & Arnau, 1980), where our laboratory introduced some seminal quantum similarity (QS) concepts, lead the way of defining and refining this quantum chemical line of work (Bultinck, Gironés, & Carbó-Dorca, 2005; Bultinck, Van Damme, & Carbó-Dorca, 2009; Carbó, Besalú, Amat, & Fradera, 1996; Carbó, Calabuig, Vera, & Besalú, 1994; Carbó & Besalú, 1995; Carbó & Calabuig, 1990; Carbó & Domingo, 1987; Carbó-Dorca, Besalú, & Mercado, 2011; Carbó-Dorca & Besalú, 1998; Carbó-Dorca, 2013d). The applications of the theoretical tools provided by this quantum chemical branch have been focused in three directions.

The Three Directions of Quantum Similarity

In a first place was developed the possibility that QS could be used to find out order within molecular sets, this could be seen in the already cited work (Carbó, Leyda, & Arnau, 1980) and certainly in subsequent publications like (Carbó & Domingo, 1987), even in one of the last publications (Carbó-Dorca, Besalú, & Mercado, 2011) on the subject.

A second topic related to QS was the systematic description of molecular sets. It started from the definition of the so-called molecular point clouds (Carbó & Calabuig, 1990, 1992a, 1992b), evolved into the definition of tagged sets and quantum object sets (QOS) (Carbó-Dorca, 1998), and finally nowadays emerged the definitions of quantum (multi)molecular polyhedra (QMP) (Carbó-Dorca & Barragán, n. d.; Carbó-Dorca & Besalú, 2012a; Carbó-Dorca & González, 2016; Carbó-Dorca, 2015d, 2012, 2013b, 2014a, 2014b, 2015a, 2015c; Mercado & Carbó-Dorca, 2011). Everyone of this issues has opened the way to multiple characterizations of molecular sets, via the construction of QMP collective parameters and condensed molecular indices (Carbó-Dorca & Barragán, n. d., 2015; Carbó-Dorca, 2013b), which not only are useful to describe from multiple points of view molecular sets, but can be also a source of order within QMP.

However, the development of QS third branch, plausibly the most important for application purposes, has to be associated to the discussion about structure-properties relations (QSPR). In this application track, QS development has been active from the earlier stages, both in a comparable way as the Hansch (Hansch & Leo, 1979) analysis (Amat, Carbó-Dorca, Cooper, Allan, & Ponec, 2003; Amat, Carbó-Dorca, & Ponec, 1999; Carbó-Dorca & Gallegos, 2009; Gironés, Carbó-Dorca, & Ponec, 2003; Ponec, Amat, & Carbó-Dorca, 1999a, 1999b) or using similarity integrals as classical molecular descriptors (Besalú, Gironés, Amat, & Carbó-Dorca, 2002; Carbó-Dorca, Amat, Besalú, Gironés, & Robert, 2000, 2001; Carbó-Dorca & Besalú, 2000, 2002; Carbó-Dorca & Gironés, 2005; Carbó-Dorca & Van Damme, 2007b, 2008, 2007a; Carbó-Dorca, 2004, 2007, 2013c, 2015b; Fradera, Amat, Besalú, & Carbó-Dorca, 1997), within an empirical or classical QSPR (CQSPR) statistically bound working frame.

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