Diffusion and friction from force correlations

Friction from solute-solvent interactions governs processes from molecular diffusion to protein folding and is fundamental for understanding molecular dynamics in liquids. While the fluctuation-dissipation relation determines friction and diffusivity via the velocity autocorrelation function, this exact relation is inconvenient for interfacial systems involving extended surfaces. For interfacial systems, alternative approximate friction formulas based on the force autocorrelation function (FACF) have been introduced. However, these approaches face limitations due to the so-called plateau problem, where the FACF integral decays to zero at long times, complicating friction estimation in particular for small systems. We address these challenges by introducing an exact integral method that is based on the FACF and eliminates the plateau problem, ensuring robust convergence even for small systems. Validated through molecular dynamics simulations of molecular diffusion in SPC/E water, our approach accurately yields diffusivity and friction coefficients and enables decomposing diffusivity contributions into electrostatic and Lennard-Jones forces. Our findings provide a framework for estimating friction from molecular simulations and elucidating the dissipative effects of microscopic forces.