Activation energies in the grand canonical ensemble: Diffusion of methane in a zeolite

We introduce a method for calculating activation energies in the grand canonical ensemble. This is an extension of the previously developed fluctuation theory for dynamics approach that determines the activation energy for any dynamical timescale from simulations at a single temperature. In the grand canonical ensemble, there are two contributions to the activation energy: An intrinsic energetic barrier for the dynamics and effects on the timescale due to changes in the number of molecules within the system as temperature is varied. We demonstrate the approach by calculating both of these contributions for the diffusion of methane molecules (at different chemical potentials) in a zeolite framework using a combination of grand canonical Monte Carlo and molecular dynamics simulations. The contributions to the activation energy from different energetic components and intermolecular interactions are further explored. In addition, we show how the dependence of the diffusion coefficient on the chemical potential can be determined locally from simulations at a single chemical potential and globally from multiple such simulations.