Topological Characterization of a Complete Set of Small-Sized Graphene Sheets Using Molecular Descriptors With Energy Storage Applications

Graphenes are very thin layers formed by hexagonal networks of carbon atoms that possess special mechanical, electrical, and optical properties. There is a growing interest in the study and exploitation of graphene, expressed in numerous recent studies, both theoretical and practical. Here, graphenes were theoretically investigated using molecular descriptors. The complete set of 22 graphene conformers, with five cycles of six connected carbon atoms, was subjected to the study. The Zagreb index family was used in the first instance. The analysis showed that, in the case of the analyzed graphenes, the degeneracy of the Zagreb indices is very high. In addition, when the first Zagreb index is degenerate, the structures can still be discriminated by the second Zagreb index. However, when the second Zagreb index is also degenerate, the entire Zagreb index family built with expressions involving vertex degree on adjacent ones is degenerate. Thus, its use in the case of graphenes is not recommended. In general, topological descriptors have a low power of discrimination in classes of conformers. Moreover, for a pair of conformers, even the extended Hückel energy is degenerate. In this case, the resolution can be obtained with descriptors generated from molecular geometry. Furthermore, using a pool of descriptors exploring the robustness of topology and resolution of geometry significantly increases the accuracy of structure to property prediction. The SMPI (Szeged matrix property indices) family of descriptors has been used here as an alternative, and discriminated all 22 conformers adequately. A simple linear regression, explaining over 99.97% of the extended Hückel energy using one SMPI descriptor, has been found, showing thus the potential of the SMPI family in graphene discrimination in particular and materials science-related structure-based estimations and predictions in general.