Benchmarking DFT‑D Dispersion Corrections for Anharmonic Vibrational Frequencies and Harmonic Scaling Factors

Improvements in the form of the DFT-D empirical dispersion corrections to hybrid density functional theory are shown to have made corrections sufficiently accurate to improve the calculation of both anharmonic frequencies and scaled harmonic vibrational frequencies across a wide range of commonly tested molecules. The Becke-Johnson damping function is noted as being particularly versatile across the molecules tested, and the B3LYP-D3M­(BJ) and B3LYP-D3­(CSO) methods are found to be the most widely applicable. Dispersion corrections are shown to be important for accurately describing carbon–hydrogen bond stretching vibrations, and standard triple-dipole based three-body terms are found to cause large errors in these anharmonic frequencies. Preliminary results also indicate that there is a cancellation of error at this level of theory when using smaller finite difference step sizes to calculate anharmonic derivatives of the nuclear potential energy surface.