QSPR in molecular spaces: ordering data, {de- & re-} constructing molecular similarity matrices, building their isometric vectors defining statistical-like momenta of molecular polyhedra, and analyzing the structure of a quantum QSPR operator

Abstract

AbstractA general review of quantum molecular similarity structure and applications is presented. The backbone of the discussion corresponds to the general problem of the data structure associated with the mathematical representation of a molecular set. How to standardize, and how to compare it to any other problem. This computational track describes the exact isometric vectors of the similarity matrix in a Minkowskian space. The further aim is to construct a set of origin-shifted vectors forming the vertices of a molecular polyhedron. From here, one can calculate a set of statistical-like momenta, providing a set of scalars that describe in a compact form the attached molecular set. Finally, the definition of a quantum QSPR operator permits building up a system of equations that can be further employed to determine the unknown properties of molecules in the original set. This last achievement leads to a quantum QSPR algorithm comparable with the classical QSPR counterpart but described in molecular space, not parameter space.