Calculation of the tunneling splitting in the zero-point level and CO-stretch fundamental of the formic acid dimer

A direct dynamics calculation based on instanton techniques is reported of tunneling splittings in the formic acid dimer and its deuterated isotopomers for the zero-point level and the lowest vibrationally excited level of a nontotally symmetric CO-stretch vibration. A new method is introduced to calculate the effect of anharmonic couplings for skeletal modes that are not linearly coupled to proton tunneling modes. The calculated splittings are in good agreement with recent observations for (DCOOH)2 provided the proposed tentative assignment is reversed such that the excited level has the smaller splitting.