“…As a result, they have been applied in a wide range of contexts such as investigating the binding of hydrogen to metal–organic frameworks and simulating the movement of ions through channels in membranes. − Sampling the grand canonical ensemble requires the chemical potential (μ), volume ( V ), and temperature ( T ) to be held constant. − Simulating at a constant chemical potential allows the number of particles in the system to fluctuate, which can be used to bypass kinetic barriers to the sampling of buried water molecules through randomly attempting their insertion and deletion within a user-defined region of interest such as a binding site. ,,,− These attempted moves are accepted and rejected based on rigorous probabilities derived using the Metropolis-Hastings algorithm. The use of GCMC sampling has been found to significantly improve the accuracy of ligand binding free energy calculations, where displaced waters that are not expelled sufficiently quickly from the binding site can have a serious impact on the free energy results, when using conventional sampling methods. ,,, However, the acceptance rates for unbiased and instantaneous particle insertions and deletions in condensed phases are typically very low, with around 1 in every 10,000 moves attempting to insert/delete water molecules to/from a bulk water system being accepted . A number of enhanced sampling techniques have been developed to improve the acceptance rates of GCMC, including cavity biasing, continuous fractional component Monte Carlo, configurational biasing, and molecular exchange approaches .…”