Quantum theory of QSAR

Abstract

Ways of developing the formalism where Quantum Similarity Measures (QSM) become a natural product issuing from a specific mathematical framework related to quantum theory are discussed. This fact is used to establish a fundamental connection between Quantum Theory and QSAR, which is analysed in turn within the realm of discrete quantum chemistry. In order to achieve such an objective several theoretical tools are revised in a previous step. The first section is devoted to constructing the concept of the Tagged Set. Next, the definition of Quantum Object (QO) is clarified by means of Quantum Theory background ideas and the previous Tagged Set formalism. In the definition of QO, Density Functions (DF) are shown to play a fundamental role and a possible simplified mathematical picture is presented for possible computational purposes. In the process of preparing the problem-solving tools, convex sets become prominent, and the notion of Vector Semispace appears as a consequence. The Transformation Rule, a device to connect Wavefunctions with DF, is defined in a new step. Various products of this preliminary discussion are described, among them the concept of Kinetic Energy distributions, issuing from the background concept of extended Hilbert and Sobolev spaces. QSM as a source of discrete representation of molecular structures is made evident in this context. Further theoretical development undertakes precise study of discretization, that is, the transformation of infinite-dimensional functional spaces into n-dimensional ones. This result adds new perspectives to the discrete representation of QO, because a) It provides a source of new QO descriptors, b) It describes the QSAR theoretical background enabling the construction of adequate models like tuned-QSAR, and c) It allows the construction of sound and general alternatives of Hammets ó or log P parameters. In this context, QSM appear to produce QSAR models constructed with unbiased descriptors, deducible from quantu