Targeted Molecular Dynamics Calculations of Free Energy Profiles Using a Nonequilibrium Friction Correction

As standard unbiased molecular dynamics (MD) simulations become impractical for sampling rare events, “targeted MD” employs a moving distance constraint to enforce rare transitions along some reaction coordinate x . To calculate free energy profiles from these nonequilibrium simulations via Δ G ( x ) = W ( x ) – W diss ( x ), apart from the (readily obtained) work W ( x ) performed on the system, the dissipated work W diss ( x ) is also required. By employing a second-order cumulant expansion of Jarzynski’s equality combined with an analysis within Langevin theory, the dissipated work can be expressed via a nonequilibrium friction coefficient Γ NEQ ( x ) that may be calculated on-the-fly from constraint force fluctuations. Adopting the ion dissociation of NaCl in water as a test system, this friction correction is shown to result in accurate free energy profiles, even for a modest number of simulations and at high constraint velocities. As a bonus, the analysis of Γ NEQ ( x ) may yield valuable insight into the microscopic mechanism of friction.