A Residence-Time Approach for Determining Position-Dependent Diffusivities from Biased Molecular Simulations.

Position-dependent diffusivities are central parameters in reduced stochastic descriptions of molecular transport in heterogeneous environments, but their reliable estimation from molecular dynamics simulations remains challenging. We present a residence-time approach (RTA) that extracts local diffusivities from first-exit statistics measured in biased simulations after compensation of the mean free-energy gradient. We apply the method to oxygen diffusion across a hexadecane/water slab, water permeation across a POPC lipid bilayer, and transport of water and volatile organic compounds through a model skin-barrier membrane. In the slab system, RTA diffusivities agree with independently determined bulk reference values. In the membrane systems, propagator predictions based on RTA-derived diffusivities reproduce unbiased molecular dynamics propagators over substantial lag-time ranges, while also revealing that, in some cases, no single lag-time-independent diffusivity profile captures the dynamics across all time scales. These results support residence-time statistics as a practical route for determining effective position-dependent diffusivities from biased molecular simulations.