Van Vleck perturbation theory is a powerful tool for treating molecular vibrations and rotations. We have applied this theory to a variety of systems over the years with great success. Recently we developed a combined perturbative/variational approach and applied it to the calculation of the J=0 states of methanol. This treatment, which includes all the vibrational degrees of freedom, uses perturbation theory to reduce the coupling between the vibrations and then uses a variational calculation to find the eigenvalues of the full torsion-vibration problem. Since the vibration-vibration couplings are typically larger than the torsion-vibration couplings, the final variational calculation requires a smaller number of states that would be needed if one directly treated the torsion-vibration problem in a separable normal mode vibrational basis. The goal of the methanol work was to calculate all the torsional splittings of the fundamental vibrations. It turns out that this molecule has significant vibration-torsion couplings and these coupling profoundly affect the splittings as can be observed in the table below.
