Ideal conductor/dielectric model (ICDM): A generalized technique to correct for finite-size effects in molecular simulations of hindered ion transport

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study (\href{https://doi.org/10.1021/acs.jctc.2c00375}{Shoemaker,~\emph{et al.},~\emph{J. Chem. Theory Comput.}, 18: 7142, {\bf 2022}}), we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (ICDM), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the ICDM model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The ICDM model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.