Coupled translation-rotation eigenstates of H ₂, HD, and D ₂ in the large cage of structure II clathrate hydrate: comparison with the small cage and rotational raman spectroscopy

We report fully coupled quantum five-dimensional calculations of the translation-rotation (T-R) energy levels of one H ₂, HD, and D ₂ molecule confined inside the large hexakaidecahedral (5 ¹²6 ⁴) cage of the structure II clathrate hydrate. Highly converged T-R eigenstates have been obtained for excitation energies beyond the; = 2 rotational levels of the guest molecules, in order to allow comparison with the recent Raman spectroscopic measurements. The translationally excited T-R states are assigned with the quantum numbers n and l of the 3D isotropic harmonic oscillator. However, the translational excitations are not harmonic, since the level energies depend not only on n but also on I. For I > 1, the T-R levels having the same n,l values are split into groups of almost degenerate levels. The splitting patterns follow the predictions of group theory for the environment of T _d symmetry, which is created by the configuration of the oxygen atoms of the large cage. The 2j + 1 degeneracy of the j = 1 and 2 rotational levels of the encapsulated hydrogen molecule is lifted entirely by the angular anisotropy of the H ₂-cage interaction potential. The patterns and magnitudes of the j = 1, 2 rotational level splittings, and the energies of the subleveis, in the large cage are virtually identical with those calculated for the small cage. This is in agreement with, and sheds light on, the observation that the S ₀(O) (j = 0→2) bands in the rotational Raman spectra measured for simple H ₂ hydrate and the binary hydrate of H ₂ with tetrahydrofuran are remarkably similar with respect to their frequencies, widths, shapes, and internal structure, when the H ₂ occupancy of the large cage of simple H ₂ hydrate is low.