The isotope effect and orientational potentials of methane molecules in gas hydrates

We report an inelastic neutron scattering experiment at $\text{T=2\hspace{0.05em}}\mathrm{K}$ of a fully deuterated methane hydrate ${\mathrm{CD}}_{\mathrm{4}}\mathrm{\cdot 5.75}$ ${\mathrm{D}}_{\mathrm{2}}\mathrm{O}.$ In the experiment the $\text{J=0→J=1}$ rotational transition of an almost free quantum ${\mathrm{CD}}_4$ rotor at an energy transfer of 0.4 meV has been found. No line splitting due to the two different kinds of cages, which are occupied by the methane molecules in the host lattice, has been found. Using a simple electrostatic model of the orientational interaction between the methane molecules and the water molecules in the host lattice we are able to explain the measured spectra of both the deuterated and protonated samples. The intrinsic linewidth found for the rotational transition in deuterated and protonated samples can be attributed to the frozen in disorder of the water dipole moments in the cages. The contribution of the van der Waals interaction has also been calculated on the basis of empirical atom–atom interaction parameters and has been found to be one order of magnitude smaller than the electrostatic interaction. In addition the calculated orientational scattering length density of the ${\mathrm{CD}}_4$ molecules is found to be in good agreement with experimental values. It is shown, that previous diffraction experiments lead to only limited information about the orientational distribution function due to the proton disorder.