Activation free energy for proton transfer in solution

Path integral molecular dynamics methods are employed to compute the free energy for proton transfer reactions for strongly hydrogen bonded systems in a polar solvent. The free energy profile is calculated using several different techniques, including: integration of the mean force acting on the proton path with its centroid constrained at different values, the integral form of the free energy calculation in the constrained-reaction-coordinate-dynamics ensemble and direct simulation of the unconstrained dynamics. The results show that estimates of the free energy barrier obtained by harmonic extrapolation are likely to be in error. Both quantum and classical results for the free energy are obtained and compared with simulations using adiabatic quantum dynamics. Comparison of the quantum and classical results show that there are quantum corrections to the solvent contributions to the free energy.