Simple comparison of atomic population and shape atomic populations distributions between two molecular structures with a coherent number of atoms

Abstract

For any molecular structure and under arbitrarily varied theoretical computational levels, the concept of atomic population, initially proposed by Mulliken and now present with many variants in quantum chemical studies, can be used to obtain a set of polarized atomic charges, as it is well known. However, it has not been studied yet how atomic populations can be also the basis for constructing discrete probability distributions in the form of shape atomic population distributions. This kind of discrete molecular probability distributions can be easily used to perform numerical comparisons between various theoretical levels employed (varying computational methods and basis sets), among diverse molecular isomers or amid molecular states. Distance dissimilarity and cosine similarity indices or Shannon entropy can be employed to compare the pairs of atomic populations and at the same time to obtain new molecular descriptor parameters.