  The double proton transfer (DPT) reaction in hydrated formic acid dimer (FAD)
is investigated at molecular-level detail. For this, a global and reactive
machine learned (ML) potential energy surface (PES) is developed to run
extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in
explicit molecular mechanics (MM) solvent at MP2-quality for the solute.
Simulations with fixed - as in a conventional empirical force field - and
conformationally fluctuating - as available from the ML-based PES - charge
models for FAD shows significant impact on the competition between DPT and
dissociation of FAD into two formic acid monomers. With increasing temperature
the barrier height for DPT in solution changes by about 10% ($\sim 1$ kcal/mol)
between 300 K and 600 K. The rate for DPT is largest, $\sim 1$ ns$^{-1}$, at
350 K and decreases for higher temperatures due to destabilisation and
increased probability for dissociation of FAD. The water solvent is found to
promote the first proton transfer by exerting a favourable solvent-induced
Coulomb force along the O-H$\cdots$O hydrogen bond whereas the second proton
transfer is significantly controlled by the O-O separation and other
conformational degrees of freedom. Double proton transfer in hydrated FAD is
found to involve a subtle interplay and balance between structural and
electrostatic factors.
