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

The nature and origin of a fundamental quantum QSPR (QQSPR) equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions (DF), a molecular set can be reconstructed as a quantum multimolecular polyhedron (QMP), whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.