Dynamics and kinetic isotope effect for the double proton transfer in formamidine monohydrated complex using direct semiempirical dynamics calculation

The dynamics of the double proton transfer in formamidine monohydrated complex has been studied by the direct semiempirical dynamics approach with variational transition-state theory using multidimensional semiclassical tunneling approximations. High-level ab initio quantum mechanical calculations were performed to estimate the energetics of the double proton transfer. Dimerization energies and the barrier height have been calculated at the G2* level of theory, which yields -7.50 and 16.6 kcal mol(-1), respectively. A quantum mechanical potential energy surface has been constructed using the AM1 Hamiltonian with specific reaction parameters (AM1-SRP) which are obtained by adjusting the standard AM1 parameters to reproduce the energetics by high-level ab initio quantum mechanical calculation. The minimum energy path has been calculated on this potential energy surface, and other characteristics of the surface were calculated as needed. The two protons are transferred synchronously, so the transition state possesses C(s) symmetry. The reaction path curvature near the transition state is small, but that far from the transition state is large. Therefore the microcanonical optimized multidimensional tunneling approximation was used to calculate the tunneling coefficient. The tunneling amplitude initiated by reaction coordinate motion as well as that initiated by the vibrational mode normal to the reaction coordinate is important over the entire reaction coordinate. The distance that the proton hops during tunneling is about 0.62 Angstrom at 300 K. This is a very long distance compared with the normal single proton transfer in solution. Before tunneling occurs, hydrogenic motion contributes minimally to the reaction path, which consists primarily of the heavy atoms moving to bring the formamidine and water molecules closer. This heavy-atom motion assists the tunneling process. The kinetic isotope effect (KIE) was also calculated. The quasi-classical contribution to the KIE is quite large due to the synchronous motion of the two protons. The tunneling contribution to the KIE determines the characteristics of the overall KIE in terms of temperature.