Secondary finite-size effects and multi-barrier free energy landscapes in molecular simulations of hindered ion transport

Abstract

Ion transport through nanoscale channels and pores is pivotal to numerous natural processes and industrial applications. Experimental investigation of the kinetics and mechanisms of such processes is, however, hampered by the limited spatiotemporal resolution of existing experimental techniques. While molecular simulations have become indispensable for unraveling the underlying principles of nanoscale transport, they also suffer from some important technical limitations. In our previous works, we identified strong polarization-induced finite-size effects in molecular dynamics simulations of hindered ion transport, caused by spurious long-range interactions between the traversing ion and the periodic replicates of other ions. To rectify these artifacts, we introduced the Ideal Conductor/Dielectric Model (\textsc{Icdm}), which treats the system as a combination of conductors and dielectrics, and constructs an analytical correction to the translocation free energy profile. Here, we investigate some limitations of this model. Firstly, we propose a generalized approach based on Markov State models that is capable of estimating translocation timescales in the thermodynamic limit for free energy profiles with multiple comparable barriers. Second, we identify a new category of polarization-induced finite-size effects, which significantly alter the spatial distribution of non-traversing ions in smaller systems. These secondary effects cannot be corrected by the ICDM model and must be avoided by selecting sufficiently large system sizes. Additionally, we demonstrate through multiple case studies that finite-size artifacts can reverse expected trends in ion transport kinetics. Our findings underscore the necessity for careful selection of system sizes and the judicious application of the \textsc{Icdm} model to rectify residual finite-size artifacts.