Applications of H\"uckel-Su-Schrieer-Heeger method. I. Carbon-carbon bond lengths in polycyclic aromatic hydrocarbons

TL;DR

This paper applies the H"uckel-Su-Schrieer-Heeger (HSSH) method to predict carbon-carbon bond lengths in 34 polycyclic aromatic hydrocarbons, providing a computationally efficient alternative to expensive quantum chemistry methods.

Contribution

The study demonstrates the effectiveness of the HSSH method in analyzing large PAHs and reveals their modular aromatic structure, which was not previously characterized using this approach.

Findings

HSSH method accurately predicts bond lengths in large PAHs

Revealed modular architecture in PAH structures

Calculated aromaticity indices for studied molecules

Abstract

The equilibrium carbon-carbon bond lengths in $\pi$-electron hydrocarbons are very sensitive to the electronic ground-state characteristic. In the recent two papers by Stolarczyk and Krygowski (to appear soon) a simple quantum approach, the Augmented H\"uckel 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 H\"uckel-Su-Schrieffer-Heeger (HSSH) method, in which the resonance integral $\beta$ of the HMO model is a linear function the bond length. In the present paper the HSSH method is applied in a study of carbon-carbon bond lengths in a set of 34 selected policyclic aromatic hydrocarbons (PAHs). This is exactly the set of molecules analyzed by Rieger and M\"ullen (\textit{J. Phys. Org. Chem.} \textbf{2010}, \textit{23}, 315) 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 \textit{ab initio} methods of quantum chemistry are too expensive for 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.