QUANTUM SIMILARITY MEASURES, MOLECULAR CLOUD DESCRIPTION, AND STRUCTURE PROPERTIES RELATIONSHIPS

The concept of quantum similarity permits us to obtain useful information on the relationships between members of any molecular set and their properties. Quantum molecular similarity proves to be a convenient tool with which to represent molecules as points in an Euclidean space. A projection from an infinite dimensional space to a finite dimensional one, based on principal components of some similarity index matrix taken as molecular coordinates, allows the classification and the visualization of the clustering patterns appearance within a known molecular set. We propose that the basic initial techniques to do this task need to be described within quantum mechanical principles and must obey strict geometrical considerations. After a short discussion on the theoretical structure of quantum similarity measures, there are also described triple density similarity measures, a new way to obtain a projection of the molecular density functions into finite dimensional spaces. Other concepts related to molecular quantum similarity are the description of molecular point clouds and their elements: point-molecules. In order to provide an example, visualization and classification techniques are applied to a molecular family.