An accurate semiclassical method to predict ground-state tunneling splittings

Abstract

A new method for calculating the ground-state tunneling splitting is presented. It is based on the semiclassical theory including recently derived corrections and it is the first method, which explicitly takes into account the whole conformational space between the minima and the transition state. The density-functional theory is used to determine the qualitative shape of the potential energy surface (PES) and high level ab initio calculations provide information about the stationary points. With a dual level scheme, the low-level energy surface is mapped onto the high-level points to get a good quantitative description of the high-level PES. Therefore, the new method requires no adjustment of additional parameters like scaling of the energy barrier as is necessary in other methods. Once the high-level PES is calculated, the most probable tunneling paths are determined with a global optimization procedure. Along this representative tunneling path, the tunneling splitting is calculated with additional consideration of zero-point vibrational effects. The method is applied to three molecular systems, namely hydrofluoric acid dimer, malonaldehyde, and tropolone. These systems were chosen because their energy barriers differ strongly (1 kcal/mol–7 kcal/mol). The predicted tunneling splittings agree very well with the experimental ones, therefore, we expect our method to be generally applicable, independent of the magnitude of the energy barrier.