Free-energy simulation methods are applied toward the calculation of cluster integrals that appear in diagrammatic methods of statistical mechanics. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of the integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. Virial coefficients, up to the sixth for the Lennard-Jones model and the fifth for the SPCE model of water, are calculated as a demonstration.

We establish a robust and broadly applicable multistep workflow using machine learning algorithms to construct well-trained data-driven models for predicting the hydrogen evolution reaction activity of 4500 MM′XT₂-type MXenes.

We studied the structural and dynamical properties of methane and ethane in montmorillonite (MMT) slit pore of sizes 10, 20 and 30 Å using grand canonical Monte Carlo and classical molecular dynamics (MD) simulations. The isotherm, at 298.15 K, is generated for pressures up to 60 bar. The molecules preferentially adsorb at the surface as indicated by the density profile. In case of methane, we observe only a single layer, at the pore wall, whose density increases with increasing pressure. However, ethane also displays a second layer, though of low density in case of pore widths 20 and 30 Å. In-plane self-diffusion coefficient, D_‖, of methane and ethane is of the order of 10^− 6 m²/s. At low pressure, D_‖ increases significantly with the pore size. However, D_‖ decreases rapidly with increasing pressure. Furthermore, the effect of pore size on D_‖ diminishes at high pressure. Ideal adsorbed solution theory is used to understand the adsorption behaviour of the binary mixture of methane (80%) and ethane (20%) at 298.15 K. Furthermore, we calculate the selectivity of the gases at various pressures of the mixture, and found high selectivity for ethane in MMT pores. However, selectivity of ethane decreases with increase in pressure or pore size.