Notes on quantitative structure‐properties relationships (QSPR) part 2: The role of the number of atoms as a molecular descriptor

Abstract

A previous analysis performed in our laboratory about the polynomial dependency of the atomic quantum self-similarity measures on the atomic number, together with recent publications on quantitative structure-properties relationships (QSPR), based on the number of molecular atoms, published by various authors, have driven us to show here that a simplified form of the fundamental quantum QSPR (QQSPR) equation, permits to theoretically demonstrate the important, but obvious, role of the number of atoms in a molecule, as a possible molecular descriptor. A discussion of the practical use of the number of atoms in QSPR is also given at the end, which also contains a discussion on the role of Ockham's razor in descriptor simplification choices.

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

“…The classical and quantum QSPR consequences of this fact, have been broadly discussed in a previous paper (Carbó-Dorca & Gallegos, 2009a), as the culmination of a wide set of studies on the modern structure of QQSPR fundamental equation and its connection with classical QSPR (Carbó-Dorca et al, 2009;Carbó-Dorca & Gallegos, 2009b;Carbó-Dorca, 2013a).…”

“…So far, this theoretical scheme corresponds to an actual alternative representation of the basic quantum QSPR abstract structure, which has been presented into the literature, since the first applicable descriptions of quantum similarity (Carbó-Dorca et al, 2009;Carbó-Dorca & Gallegos, 2009a;Carbó-Dorca, 2013a;Bultinck et al, 2005;Carbó et al, 1996;Carbó & Calabuig, 1990;1992a;1992b;Carbó-Dorca & Gallegos, 2009b;Carbó-Dorca, 2013b).…”

“…Also, once defined such an operator, for instance via an approximate computational procedure, one can calculate the corresponding expectation value α, attached to every QP DF vertex, by using the integral expression, the following references describe the evolution of theoretical and practical use of this technique with time (Bultinck, Gironés, & Carbó-Dorca, 2005;Carbó, Besalú, Amat, & Fradera, 1996;Carbó & Calabuig, 1990;1992a;1992b;Carbó-Dorca & Gallegos, 2009b;Carbó-Dorca, 2013b …”

“…Quantum similarity is theoretically and computationally based on such a quantum mechanical expectation value framework (Carbó & Calabuig, 1992a;Carbó-Dorca & Gallegos, 2009b;Carbó-Dorca, 2013b). This quantum similarity background important fact might be therefore also stated by means of the above integral (1).…”

Toward a universal quantum QSPR operator

“…In recent publications, it has been developed the theoretical background, leading into the establishment of a quantum quantitative structure–properties relations (QSPR) equation defined in molecular spaces, resulting from the quantum similarity framework development evolving in time. Recently, a basic concept for this endeavor appears grounded on the description of molecular quantum polyhedra .…”