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 Delta 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 Gamma(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 Gamma(NEQ)(x) may yield valuable insight into the microscopic mechanism of friction.