Quantum polyhedra, definitions, statistics and the construction of a collective quantum similarity index

Abstract

Quantum polyhedra (QP) are geometrical constructs whose vertices are made by quantum mechanical density functions (DF). In this paper a QP centroid and a variance are defined at two levels: functional and numerical. The numerical QP variance can be shown associated to a collective QP squared distance involving the whole DF set composing the QP vertices. In this manner, a global dissimilarity index corresponding to the set of QP vertices can be defined. Extension of the mathematical and computational techniques developed on QP to shape functions polyhedra and to classical descriptor N-dimensional multimolecular polyhedra, are also discussed.