High-accuracy estimation of 'slow' molecular diffusion rates in zeolite nanopores, based on free energy calculations at an ultrahigh temperature

We present a methodology to estimate 'slow' molecular diffusivities through nanopores, which have been difficult to calculate from conventional molecular dynamics (MD), combining statistical-mechanical theory with MD simulations. In this method, the hopping rate of a guest molecule is calculated by transition state theory (TST) and used to estimate self-diffusivities. To obtain hopping rates from TST, it is essential to obtain free energy profiles along the reaction coordinate, However, the free energy calculation can involve considerable error because of insufficient statistical samplings, especially simulating 'slow' molecular diffusion. To solve this problem, Helmholtz free energy profiles at much lower temperatures are predicted from ultrahigh temperature MD, based on classical statistical-mechanical theory. Using these predicted profiles, self-diffusivities at lower temperatures were estimated. This methodology was applied to estimate molecular diffusivities of CH4 through an LTA-type zeolite. Our predicted diffusivities showed excellent agreement with those obtained from conventional MD. Our methodology is a promising approach to the systematic prediction of 'slow' molecular diffusivity in various types of nanoporous material.