Building on our previous work (J. Phys. Chem. C, 2016, 120, 16561), using an empirical model we run both classical and path-integral molecular dynamics simulations for a type II clathrate hydrate containing different amounts of guest H-2 molecules from 1 to 5 molecules per large cage, with results presented at temperatures of 50, 100 K and 200 K. We present results for the density isosurfaces of the guest molecules at all different occupations and temperatures, showing how the density approaches the perfect tetrahedral structure which has been found for the n = 4 case in which each molecule sits on the vertex of a tetrahedron about the centre of each large cage. We calculate free-energy profiles of the molecules over the volume interior to the cage, and using umbrella sampling, we also calculate the free energy barrier for the molecule to hop between cages. We show that this barrier reduces almost linearly for n = 1-3 molecules per large cage, but becomes larger than would be expected (from extrapolation) for the n = 4 case, with this departure from linearity becoming larger at lower temperatures. We show that, perhaps counter-intuitively, these barriers tend to increase with raising the temperature, and also counter-intuitively that quantisation of the nuclei acts to increase the barriers. Finally, for the n = 4 case, a comparison is made between the empirical model results and those from an ab initio molecular dynamics calculation, which shows that qualitative agreement exists between the two models.