the number of degrees of freedom for the guest molecule (3 for Xe, 5 for CO 2 and 6 for CH 4 .), and N g the number of guest molecules per simulation cell. The main difficulty in lattice dynamics lies in the poor convergence of the vibrational energy with respect to Brillouin zone sampling. We performed simulations on supercells, the dimensions of which were determined from the requirement that the reciprocal lattice vectors of the empty host structure were all smaller than 2π × 0.07 Å -1 . In addition, we used Debye's method to model phonon dispersion of the three acoustic modes, as described elsewhere . A linear phonon dispersion can be assumed for the acoustic modes near the Γ-point and the dispersion relation is determined from the elastic tensor and the Christoffel equation. Phonon dispersion around other k-points was modelled as a kernel density estimate (KDE) . We and others have previously used Gaussian kernel density estimates for this purpose . However, invoking Debye's assumption of a linear phonon dispersion within a small sphere around each k-point , it can be shown that the dispersion can be effectively modelled by substituting each discrete phonon frequency ω i with an Epanechnikov kernel function ;