Mode-specific hydrogen tunneling in tropolone: An instanton approach

Abstract

Calculations are reported of hydrogen and deuterium tunneling splittings in the ground state S0 (X̃,1A1) and the first excited singlet state S1 (Ã,1B2) of tropolone-d0 and -d1. The main focus of the calculations is on the splittings observed in vibrationally excited levels of S1, some of which are larger while others are smaller than the zero-point splitting. To account for these observations, a potential-energy surface is constructed by standard quantum-chemical methods and the dynamics on this surface is treated by a method derived from the instanton approach. The potential-energy surface is a complete multidimensional surface resulting from the combination of a potential-energy curve along the tunneling coordinate with a harmonic force field calculated at the stationary points. The level of calculation adopted is HF/6-31G** for S0 and CIS/6-31G** for S1. A few other, nominally more accurate, methods were tried but proved to be unsatisfactory. To deal with the dynamics, the instanton method, used previously for the calculation of zero-point level splittings, is modified so as to make it applicable to excited levels. As expected, it is found that excitation of the tunneling mode strongly promotes hydrogen transfer. The effects of exciting modes that are symmetric or antisymmetric with respect to the symmetric transition state are evaluated for all such modes with assigned splittings by a straightforward generalization of the correction terms previously derived for zero-point splittings. Of special interest are out-of-plane modes, some of which show up as overtones with splittings smaller than the zero-point splitting, despite the fact that there is no linear coupling between these modes and the tunneling mode. The effect is ascribed to anharmonic coupling and an effort is made to calculate the required anharmonicities quantum-chemically. In general the agreement between theory and experiment is satisfactory for modes that are linearly coupled while the situation is less clear for anharmonically coupled modes.