An ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1-4-mode subspaces.

We report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer. This PES is a least-squares fit to 13475 CCSD(T)-F12a/haTZ (VTZ for H and aVTZ for C and O) energies. The energy-weighted, root-mean-square fitting error is 11 cm and the barrier for the double-proton transfer on the PES is 2848 cm, in good agreement with the directly-calculated ab initio value of 2853 cm. The zero-point vibrational energy of 15 337 ± 7 cm is obtained from diffusion Monte Carlo calculations. Energies of fundamentals of fifteen modes are calculated using the vibrational self-consistent field and virtual-state configuration interaction method. The ground-state tunneling splitting is computed using a reduced-dimensional Hamiltonian with relaxed potentials. The highest-level, four-mode coupled calculation gives a tunneling splitting of 0.037 cm, which is roughly twice the experimental value. The tunneling splittings of (DCOOH) and (DCOOD) from one to three mode calculations are, as expected, smaller than that for (HCOOH) and consistent with experiment.