Prediction of the Diffusion Coefficient through Machine Learning Based on Transition-State Theory Descriptors

Nanoporous materials serve as very effective media for storing and separating small molecules. To design the best materials for a given application based on adsorption, one usually assesses the equilibrium performance by using key thermodynamic quantities such as Henry constants or adsorption loading values. To go beyond standard methodologies, we probe here the transport effects occurring in the material by studying the self-diffusion coefficients of xenon inside the nanopores of the framework materials. We find good correlations between the diffusion coefficients and the pore aperture size as well as other geometrical and energetic descriptors. We used extensive molecular dynamics simulations to calculate the diffusion coefficient of xenon in 4873 MOFs from the CoRE MOF 2019 database, the first large-scale database of transport properties published at this scale. Based on these data, we present a tool to quickly evaluate the diffusion energy barrier that proved to be very correlated to the diffusion rate. This descriptor, alongside other geometrical characterizations, was then used to build a machine learning model that can predict the xenon diffusion coefficients in MOFs. The final trained model is quite accurate and shows a root-mean-square error on the log10 of the diffusion coefficient equal to 0.25.