Reaction rates for proton transfer over small barriers and connection to transition state theory

Reaction rates of chemical reactions can be generally well described by classical transition state theory (TST) when considering zero-point energy and tunneling effects. TST is, however, not applicable for small energy barriers comparable in size to the zero-point energy or for cases where even no energy barrier is present. These situations are common for proton transfer in bulk water. Here, energy profiles for proton transfer between water and small organic molecules were computed quantum mechanically and were used as input for solving the time-dependent Schrödinger equation in one dimension. Proton transfer over small barriers occurs very fast and is completed after 10–40 fs. Transition probabilities can reach values as high as 100%. They can easily be fitted by an analytical expression. An interpolation for proton transfer rates is then derived for connecting the low-barrier-regime that should be treated by solving the time-dependent Schrödinger equation with the high-barrier-regime where TST applies