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

Abstract

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⁻¹ and the barrier for the double-proton transfer on the PES is 2848 cm⁻¹, in good agreement with the directly-calculated ab initio value of 2853 cm⁻¹. The zero-point vibrational energy of 15 337 ± 7 cm⁻¹ 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⁻¹, which is roughly twice the experimental value. The tunneling splittings of (DCOOH)₂ and (DCOOD)₂ from one to three mode calculations are, as expected, smaller than that for (HCOOH)₂ and consistent with experiment.