The effects of asymmetric motions on the tunneling splittings in formic acid dimer.

We extend the reaction surface Hamiltonian model for double proton tunneling in formic acid dimer to include all in-plane modes, except the two CH stretch modes. Zero point corrections for the out-of-plane modes are also incorporated. Transition state and equilibrium normal mode representations for the description of the asymmetric modes are developed and compared. The results compare well with reduced dimensional calculations containing just symmetric in-plane modes due to a fortuitous cancellation of tunneling contributions of the out-of-plane and in-plane asymmetric modes. The effects of scaling the potential are examined as well as the effects of asymmetric vibrational excitation on tunneling splittings. Vibrational excitation of the asymmetric dimer rock, in contrast to the symmetric rock, is found to hinder tunneling. We find qualitative agreement with the experimental measurements of Ortlieb and Havenith [J. Phys. Chem. 111, 7355 (2007)] for the tunneling splitting of the ground state; the decrease in splitting upon vibrational excitation of CO stretch, however, is overestimated.