Exploring the Accuracy of Density Functionals for Anharmonic Vibrations of Polycyclic Aromatic Hydrocarbons

In the zoo of density functional theory (DFT) methods, finding an optimal DFT functional to generate an accurate potential energy surface (PES) of polycyclic aromatic hydrocarbons (PAHs) for computing a vibrational structure is important since wave function-based electron-correlation methods are intractable due to the larger size of PAH molecules. The present study focuses on an extensive study of semidiagonal quartic PES computed using various DFT functionals (SVWN, BLYP, BP86, BPBE, B97D, HCTH, VSXC, τHCTH, B3LYP, B3LYP-D, B3P86, B3PW91, PBE0, B971, MPW1PW91, BHandHLYP, TPSSh, M11, MN15, M06-HF, M06-2X, M08-HF, τHCTHhyb, BMK, CAM-B3LYP, ωB97X-D, and HSEH1PBE), following the steps of Jacob's ladder based on chemical accuracy. Two different vibrational structure methods, generalized second-order vibrational perturbation theory and vibrational self-consistent field method, are used to compute the anharmonic frequencies of seven different PAH molecules. The performance of the DFT methods is assessed through statistical error parameters computed against a data set that includes 182 fundamental transitions. The results suggest that climbing a higher step of Jacob's ladder does not necessarily improve the vibrational frequency values. The commonly used hybrid GGA functionals, such as B3LYP, B3P86, B971, etc., outperform other functionals. In contrast, the meta-GGA or hybrid meta-GGA functionals often produce poor anharmonic frequencies for the PAHs. The exact HF exchange in the GGA hybrid functionals plays a significant role in reproducing the accuracy of the anharmonic frequencies.