Taming semi-empirical methods for PAHs and vibrational spectra

Semi-empirical methods offer a cost-effective means of computing explicit, anharmonic vibrational frequencies for large molecules, such as polycyclic aromatic hydrocarbons (PAHs), but their default parameters produce insufficiently accurate results for comparison to experiment, especially in the hydride stretching region where the NIRSpec instrument on JWST is most effective. This work delivers several reparameterized variants of the PM6 semi-empirical method trained to reproduce the experimental vibrational frequencies of 5 small hydrocarbon molecules. When benchmarked on the experimental frequencies of benzene and naphthalene, these reparameterized methods match the empirical values to within 38.7 cm${}^{-1}$ on average. Combining these values with the default PM6 frequencies below 3000 cm${}^{-1}$ brings the average deviation below 22 cm${}^{-1}$ for naphthalene, comparing favorably with the existing state of the art in B3LYP/4-31G, for a two order of magnitude decrease in the computational cost. As such, the present work offers a promising means of extending the computation of explicit, anharmonic vibrational frequencies to PAHs larger than those that can be examined anharmonically via B3LYP. Such large and accurate data sets are necessary to disentangle the unidentified spectral features observed around myriad astronomical bodies and the influx of observational data from JWST.