Augmented Hückel molecular orbital model of π ‐electron systems: from topology to metric . II. Hydrocarbon and carbon molecules

In the previous paper (paper I, this issue), we described in detail the augmented Hückel molecular orbital (AugHMO) model of the π-electron systems and its computational realizations: the Hückel-Su-Schrieffer-Heeger (HSSH) method and the Hückel-Longuet-Higgins-Salem (HLHS) method. This methodology transforms the topological data corresponding to the topological matrix of the HMO model) into the “metric output”—the equilibrium bond lengths of a given molecule. In the present paper, we focus on the π-electron hydrocarbon and carbon molecules, for which the HMO model is a purely topological model. The necessary empirical parameters of the HSSH and HLHS methods are derived from the experimental C–C bond lengths of ethylene, benzene, and butadiene. As a byproduct, some new insights will be provided into the problem of π-electron delocalization versus bond-length alternation in butadiene. We then perform the HSSH and HLHS calculations of the C–C bond lengths in several π-electron hydrocarbon and carbon molecules (including polyacetylene, fullerene C60, and graphene). The comparison of the calculated bond lengths with the experimental data and also with the ab initio results by the Hartree-Fock and the Kohn-Sham methods (the latter in the B3LYP version) is made. In general, it is demonstrated that the HSSH and HLHS results (which almost coincide) are quite close to the experimental values, and, in general, are no worse than the B3LYP results.