Molecular dynamics simulations of hydrogen-containing type-sII clathrate hydrate slabs have been performed. A range of water-water interaction potentials were tested. Three potentials that yield water ice melting points close to 273 K gave very different clathrate stabilities. The TIP5P potential was found to give the closest match to experimentally observed clathrate stabilities. Using this potential, we investigated molecular hydrogen mobility within the clathrate. It was found that hydrogen molecules within the large clathrate cages were highly mobile, migrating rapidly from cage to cage and giving instantaneous cage occupations of up to six hydrogen molecules per cage. Self-diffusion coefficients for hydrogen migration were calculated and found to obey an Arrhenius relation. Hydrogen in the small cages was not mobile on the time scale of the simulations. Simulations including the known promoter molecule tetrahydrofuran demonstrated enhanced stability of the clathrate, consistent with experimental data.