Molecular quantum similarity: Theoretical framework, ordering principles, and visualization techniques

This chapter focuses on the practical results of Quantum Similarity Measures (QSM). It defines and interprets a QSM according to quantum mechanical principles and this is accompanied by a construction of a QSM theoretical framework. The set of QSM can be transformed or combined to obtain a new kind of auxiliary terms that can be named “Similarity Indices.” There is a great deal of possible QSM manipulations leading to a variety of Quantum Similarity Index (QSI) definitions. Some of them are cosine-like similarity index, distance similarity index, and the Hodgkin-Richards or Tanimoto indices. The matrix representation of a molecular set can be associated to a set of finite dimensional vectors representing the molecules. This leads to the concept of “point-molecules” collected as a “Molecular Point Cloud.” To construct a solid theoretical body concerning QSM, a set of rules referred to as the Mendeleev Postulates are described in the chapter. © 1994 Academic Press Inc.