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 ͑PES͒ 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/mol͒. 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.

Ab initio molecular dynamics approach to tunneling splitting in polyatomic molecules

“…In principle, tunneling paths must be those that give the minimum action integral, and turning points should satisfy a condition that the momentum in a direction of tunneling is equal to zero. In general, however, it is difficult to find such an optimal tunneling path in multidimensional configuration space, [22][23][24] and thus, one should determine the way to define an appropriate tunneling path prior to AIMD simulations. In the next section, we demonstrate the way to determine the turning point and the tunneling path for two illustrative applications.…”

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

“…[23][24][25] It has been shown that the quantum mechanical tunneling is not restricted to the motion of the hydrogen atom alone but is coupled to the motion of the heavy backbone atoms. 21,26,27 Thus, the proton transfer in malonaldehyde is a truly multidimensional tunneling process. Experimentally, the ground state tunneling splitting has been determined very accurately 5,28 to be 21.583 138 29 ± ͑63͒ cm −1 .…”

Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Malonaldehyde and Tropolone

“…They also successfully applied their semiclassical method for finding the tunneling path to (HF) 2 and TRN [93], where the 7.2 kcal mol -1 quantum chemistry barrier for TRN is 50 to 100% lower than the barriers used for the computations on TRN discussed above. It is similar to the MP4/GEN results (footnote b of Table 1.3) used in the following discussion of the tautomerization of S 0 TRN that is based on an examination of the computed and spectroscopic data set for TRN(OH) and TRN(OD) [34][35][36]86].…”