Investigating the calculation of anharmonic vibrational frequencies using force fields derived from density functional theory

The calculation of anharmonic vibrational frequencies for a set of small molecules has been examined to explore the merit of applying such computationally expensive approaches for large molecules with density functional theory. The performance of different hybrid and gradient-corrected exchange-correlation functionals has been assessed for the calculation of anharmonic vibrational frequencies using second-order vibrational perturbation theory with two- and four-mode couplings and compared to the recently developed transition optimized shifted Hermite method. A range of exchange-correlation functionals (B3LYP, BLYP, EDF1, EDF2, B97-1, B97-2, HCTH-93, HCTH-120, HCTH-147, and HCTH-407) have been evaluated with reference to a large experimental data set comprising 88 species and 655 modes as well as a smaller set of shifts in frequency because of anharmonicity derived from experimental data. The anharmonic frequencies calculated using hybrid functionals provide the best agreement with experiment, and are not significantly improved by frequency scaling factors, indicating an absence of significant systematic error. For the molecules studied, the B97-1 and B97-2 functionals give the closest overall agreement with experiment, although the improvement over the best case for pure harmonic frequencies is modest. Predictions of the experimental anharmonic shifts are closest for the B3LYP and EDF2 functionals, with B97-1 performing well because of a good description of the harmonic force field. Investigations using modified hybrid functionals with increased fractions of Hartree-Fock exchange indicate that approximately 20% Hartree-Fock exchange is optimal.