Applications of Hückel-Su-Schrieffer-Heeger method: I. Carbon-carbon bond lengths in polycyclic aromatic hydrocarbons

The equilibrium carbon-carbon (C-C) bond lengths in π-electron hydrocarbons are very sensitive to the electronic ground-state characteristic. In the recent two papers by Stolarczyk and Krygowski (J Phys Org Chem, 34:e4154,e4153, 2021) a simple quantum approach, the Augmented Hückel Molecular Orbital (AugHMO) model, is proposed for the qualitative, as well as quantitative, study of this phenomenon. The simplest realization of the AugHMO model is the Hückel-Su-Schrieffer-Heeger (HSSH) method, in which the resonance integral β of the HMO model is a linear function the bond length. In the present paper, the HSSH method is applied in a study of C-C bond lengths in a set of 34 selected polycyclic aromatic hydrocarbons (PAHs). This is exactly the set of molecules analyzed by Riegel and Müllen (J Phys Org Chem, 23:315, 2010) in the context of their electronic-excitation spectra. These PAHs have been obtained by chemical synthesis, but in most cases no diffraction data (by X-rays or neutrons) of sufficient quality is available to provide us with their geometry. On the other hand, these PAHs are rather big (up to 96 carbon atoms), and ab initio methods of quantum chemistry are too expensive for a reliable geometry optimization. That makes the HSSH method a very attractive alternative. Our HSSH calculations uncover a modular architecture of certain classes of PAHs. For the studied molecules (and their fragments – modules), we calculate the values of the aromaticity index HOMA.