Extending the Characteristic Polynomial for Characterization of C20 Fullerene Congeners

The characteristic polynomial (ChP) has found its use in the characterization of chemical compounds since Huckel's method of molecular orbitals. In order to discriminate the atoms of different elements and different bonds, an extension of the classical definition is required. The extending characteristic polynomial (EChP) family of structural descriptors is introduced in this article. Distinguishable atoms and bonds in the context of chemical structures are considered in the creation of the family of descriptors. The extension finds its uses in problems requiring discrimination among same-patterned graph representations of molecules as well as in problems involving relations between the structure and the properties of chemical compounds. The ability of the EChP to explain two properties, namely, area and volume, is analyzed on a sample of C-20 fullerene congeners. The results have shown that the EChP-selected descriptors well explain the properties.