Relating vibrational energy with Kekule- and Clar-structure-based parameters

For all possible catacondensed Kekulean molecules having four, five, and six hexagons, the molecular vibrational energies were calculated within the harmonic approximation at the HF, B3LYP, and M06-2X levels of theory in combination with the 6-311G(d,p) basis set. The obtained vibrational energies were found to be a linear function of the Kekule structure count K within the sets of isomeric molecules. By employing the recently introduced generalized Zhang-Zhang polynomial, it was shown that the molecular vibrational energies can be related to the Clar-structure-based parameters. The obtained approximate formulas can accurately reproduce the vibrational energies with an average absolute error less than 1 kJ/mol. In addition, these formulas can provide further details on the structural dependence of molecular vibrational energies.