The mean reaction force: a method to study the influence of the environment on reaction mechanisms.

The mean reaction force is introduced as the negative derivative of the free energy along a predefined reaction path. In analogy to the reaction force, this descriptor allows detailed characterization of different processes of the reaction mechanism and the assignment of electronic and structural free energy contributions to activation barriers. Due to its free energy dependence, the mean reaction force represents a new tool to study the influence of the environment on the reaction mechanism. Moreover, it enables the separation of catalytic effects in structural and electronic components responsible for the free energy barrier reduction of a reaction. To validate the method, the intramolecular proton transfer in tryptophan was studied in the gas phase, in aqueous solution and at the vacuum-water interface employing molecular dynamics simulation in combination with ab initio calculations and the quantum molecular/molecular mechanics (QM/MM) methodology. The obtained results were compared to static vacuum and continuum calculations. The mean reaction force distinguishes structural rearrangements as the dominant free energy component to reach the transition state from the neutral form, whereas electronic reorganization predominates the activation of the zwitterion in aqueous solution. In addition, it identifies the origin of the reduction of the activation barrier for desolvated functional groups at the water-vacuum interface as the absence of hydrogen bonds which stabilize charge delocalized species.