Stochastic transformation of quantum similarity matrices and their use in quantum QSAR (QQSAR) models

A new insight on the quantum quantitative structure‐properties relationships

“…Furthermore, one can retrieve the exact value of the property for any molecule of the core set , just choosing the scalar products: The QSM for several core sets has been used in a quite large set of prediction studies 21–41, in every case employing up to date statistical tools, the usual procedures currently available in classical QSPR studies, see for example references 43–54. The use of the first order fundamental QQSPR equation to construct algorithms, which can be utilized as predictive tools independently of classical QSPR algorithms, has been previously attempted 55, but it has not been continued in practice until recently 42, 56, 57. In the present study, the reader can find, along the following sections, new theoretical developments leading to the fundamental QQSPR equation prediction ability.…”

Fundamental quantum QSAR (Q2SAR) equation: extensions, nonlinear terms, and generalizations within extended Hilbert–Sobolev spaces

“…Some years ago a paper was published 1 about a remarkable feature of Quantitative Structure‐Activity Relationships (QSAR), that is, the linear equations relating properties and structure in microscopic systems. The noteworthy characteristic consisted in the fact that a QSAR‐like equation could be easily deduced from a framework of Quantum Similarity Measures (QSM) 2–20. QSM appear to be an old set of concepts related to the geometric interpretation of some aspects of quantum theory.…”

“…QSM appear to be an old set of concepts related to the geometric interpretation of some aspects of quantum theory. Since then, a large number of applications of this newly defined quantum QSAR (Q 2 SAR) scheme has appeared in the current literature, dealing with quite a large variety of problems from nuclear structure 21–23, up to molecular properties like physical parameters and biological activity 24–35 as well as ecotoxicity 16–20, 34, 36–43. Several QSM‐related new algorithms 44–50, its general theoretical foundation 24, 25, 36, 51, 52, and some practical simplifications 53 have also been published.…”

Toward a universal quantum QSPR operator

“…Three practical numerical examples are presented, corresponding to the calculation of the polarization angle in assorted chiral molecules, the estimation of fish toxicity for perchlorobenzene within the set of chlorobenzenes and a typical quantum QSAR study on the popular Cramer steroid set. K E Y W O R D S electronic density function thermal scaling, quantum molecular polyhedra, quantum quantitative structure-properties relations, quantum quantitative structure-properties relations operator, quantum similarity, thermal voltage 1 | I N TR ODU C TI ONIn 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, [1][2][3] resulting from the quantum similarity framework development [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] evolving in time.Recently, a basic concept for this endeavor appears grounded on the description of molecular quantum polyhedra. [23][24][25][26][27] This is a linear algebra structure which defines, from the point of view of quantum mechanics, the collective description of molecular sets forming quantum object sets, a previous theoretical mathematical construct developed in this laboratory.…”

“…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, [1][2][3] resulting from the quantum similarity framework development [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] evolving in time.…”