Biasing the center of charge in molecular dynamics simulations with empirical valence bond models: free energetics of an excess proton in a water droplet

摘要

Multistate empirical valence bond (EVB) models provide an accuratedescription of the energetics of proton transfer and solvation in complexmolecular systems and can be efficiently used in molecular dynamics computersimulations. Within such models, the location of the moving protonic charge canbe specified by the so called center of charge, defined as a weighted averageover the diabatic states of the EVB model. In this paper, we use first orderperturbation theory to calculate the molecular forces that arise if a biaspotential is applied to the center of charge. Such bias potentials are oftennecessary when molecular dynamics simulations are used to determine freeenergies related to proton transfer and not all relevant proton positions aresampled with sufficient frequency during the available computing time. Theforce expressions we derive are easy to evaluate and do not create anysignificant computational cost compared with unbiased EVB-simulations. As anillustration of the method, we study proton transfer in a small liquid waterdroplet consisting of 128 water molecules plus an excess proton. Contrary topredictions of continuum electrostatics but in agreement with previous computersimulations of similar systems, we observe that the excess proton ispredominantly located at the surface of the droplet. Using the formalismdeveloped in this paper, we calculate the reversible work required to carry theprotonic charge from the droplet surface to its core finding a value of roughly4 $k_{\rm B}T$.