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In methane hydrate the dominant peak in the density of states above 3 meV represents a rattling mode of the guest molecule CH(4) in the large ice cages. This mode shifts from 6.7 meV at T=4.5 K to T=30 K to 7.14 meV with conversion of CH(4) guest molecules into the tunneling ground state. The less symmetric angular density distribution PsiPsi(*) in the excited rotational state compared to the ground state allows the methane to fit better in the orientation dependent cage potential surface. This leads to a larger average distance to the cage-forming molecules with a weaker potential and a reduced rattling energy. A two state single particle model with characteristic rattling energies of 5.20 meV for pure T-methane and 7.3 meV for pure A-methane weighted by the population factors can fit the data

Methane clathrate: CH4 quantum rotor state dependent rattling potential