Tracing the Fingerprint of Chemical Bonds within the Electron Densities of Hydrocarbons: A Comparative Analysis of the Optimized and the Promolecule Densities

The equivalence of the molecular graphs emerging from the comparative analysis of the optimized and the promolecule electron densities in two hundred and twenty five unsubstituted hydrocarbons was recently demonstrated [Keyvani et al. Chem. Eur. J. 2016, 22, 5003]. Thus, the molecular graph of an optimized molecular electron density is not shaped by the formation of the C-H and C-C bonds. In the present study, to trace the fingerprint of the C-H and C-C bonds in the electron densities of the same set of hydrocarbons, the amount of electron density and its Laplacian at the (3, -1) critical points associated with these bonds are derived from both optimized and promolecule densities, and compared in a newly proposed comparative analysis. The analysis not only conforms to the qualitative picture of the electron density build up between two atoms upon formation of a bond in between, but also quantifies the resulting accumulation of the electron density at the (3, -1) critical points. The comparative analysis also reveals a unified mode of density accumulation in the case of 2318 studied C-H bonds, but various modes of density accumulation are observed in the case of 1509 studied C-C bonds and they are classified into four groups. The four emerging groups do not always conform to the traditional classification based on the bond orders. Furthermore, four C-C bonds described as exotic bonds in previous studies, for example the inverted C-C bond in 1,1,1-propellane, are naturally distinguished from the analysis.