Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems.

In recent years, many experiments have shown large kinetic isotope effects (KIEs) for hydrogen transfer reactions in condensed phases as evidence of strong quantum tunneling effects. Since accurate calculation of the tunneling dynamics in such systems still present significant challenges, previous studies have employed different types of approximations to estimate the tunneling effects and KIEs. In this work, by employing model systems consisting of a double-well coupled to a harmonic bath, we calculate the tunneling effects and KIEs using the numerically exact hierarchical equations of motion (HEOM) method. It is found that hydrogen and deuterium transfer reactions in the same system may show rather different behaviors, where hydrogen transfer is dominated by tunneling between the two lowest vibrational states and deuterium transfer is controlled by excited vibrational states close to the barrier top. The simulation results are also used to test the validity of various approximate methods. It is shown that the Wolynes theory of dissipative tunneling gives a good estimation of rate constants in the over-the-barrier regime, while the nonadiabatic reaction rate theory based on the Landau-Zener formula is more suitable for deep tunneling reactions.