Promotion of the proton transfer reaction by the intermolecular stretching mode: Application of the two-dimensional finite element method to the nuclear Schrödinger equation

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Abstract
A model Hamiltonian is proposed to analyze the recently observed promotion of the proton transfer reaction by the intermolecular stretching vibrational mode. The Schrödinger equation was solved numerically with the two-dimensional finite element method. The contour maps of the wave functions clearly indicate that when the intermolecular stretching mode is excited, the proton transfers from one site to the other over the ridge, taking the detour path. Only when the intermolecular mode is in the lowest states, does the proton transfer under the barrier with the tunneling mechanism. It is demonstrated that the full two-dimensional analysis is necessary in the analysis of the large amplitude mode coupling and that the finite element method is a powerful tool to solve the Schrödinger equation for the nuclear motion in molecules.