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A new family of topological information indices based on the full neighbourhood of all atoms is presented. In previous definitions, mostly partitions of atoms have been used for this purpose. We consider each atom of a molecular structure as a subsystem. For each atom the complete neighbourhood is characterized by an information functional, based on the number of atoms in all spheres around the atom. An appropriate weighting scheme summarizes the number of atoms in the different spheres, resulting in a characteristic property of the atom. The properties of all atoms are normalized to a sum of one (a probability-like measure) from which the information entropy is calculated. The entropy is scaled by the number of atoms in the structure to give a molecular descriptor E. In the current version only skeletons of the chemical structures are considered, with all atoms equal and all bonds equal.

Molecular descriptors based on entropy and the full topological neighborhood of all atoms