Free energy differences and coexistence of clathrate structures II and H via lattice-switch Monte Carlo
We introduce a simulation technique to compute the free energy difference between two hydrate structures of different stoichiometry connected to a reservoir of gas molecules at a prescribed pressure. The method permits the determination of coexistence parameters for the system when the two hydrate structures have the same number of water molecules $N_w$. The approach is based on performing isobaric Lattice Switch Monte Carlo simulations to measure free energy differences between the hydrate structures when they are either fully occupied by gas molecules, or fully empty. This measurement is combined with thermodynamic integration within an ensemble in which the number of guest molecules $N_g$ can fluctuate under the control of a chemical potential $μ_g$. We analyze the properties of the resulting constant-$N_w,μ_g,P,T$ ensemble and show how it can be used to calculate coexistence points via a thermodynamic cycle. Applying the method to argon and methane structures, we find coexistence pressures that are in good agreement overall with the available experimental data.