Calculating molecular vibrational spectra beyond the harmonic approximation

We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models—vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI)—and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules.