In this paper the ab initio potential of mean force for the formic acid-water system is calculated in a Monte Carlo simulation using a classical fluctuating charge molecular mechanics potential to guide Monte Carlo updates. The ab initio energies in the simulation are calculated using density-functional theory (DFT) methods recently developed by Salahub [J. Chem. Phys. 107, 6770 (1997)] to describe hydrogen-bonded systems. Importance sampling methods are used to investigate structural changes and it is demonstrated that using a molecular mechanics importance function can improve the efficiency of a DFT simulation by several orders of magnitude. Monte Carlo simulation of the system in a canonical ensemble at T=300 K reveals two chemical processes at intermediate time scales: The rotation of the H2O bonded to HCOOH, which takes place on a time scale of 3 ps, and the dissociation of the complex which occurs in 24 ps. It is shown that these are the only important structural "reactions" in the formic acid-water cluster which take place on a time scale shorter than the double transfer of the proton.