Quantum dynamics of a hydrogen molecule inside an anisotropic open-cage fullerene: coupled translation-rotation eigenstates and comparison with inelastic neutron scattering spectroscopy.

We report rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H(2) inside aza-thia-open-cage fullerene (ATOCF). Translational and rotational excitations of this endohedral complex have been measured in a recent inelastic neutron scattering (INS) study, enabling direct comparison between theory and experiment. ATOCF has no symmetry, and therefore the intermolecular potential energy surface (PES) governing the T-R dynamics of H(2) is strongly anisotropic. A pairwise additive PES is employed in the calculations. Inspection of the wave functions shows three regular quasi-1D translational modes aligned with the Cartesian x, y, and z axes, respectively. These and other translational excitations can be assigned with the Cartesian quantum numbers v(x), v(y), and v(z). The radial anisotropy of the cage environment causes the splitting of the translational fundamental into three excitations whose frequencies differ substantially; the z mode directed toward the ATOCF orifice has the lowest frequency and is the most anharmonic. All three translational modes exhibit negative anharmonicity. The j = 1 rotational level of H(2) is also split into a triplet, due to the angular anisotropy of the cage. The complete lifting of the degeneracies of the translational fundamental and the j = 1 triplet of the encapsulated H(2) molecule that emerges from the calculations is also observed in the INS spectra of H(2)@ATOCF. The calculated magnitudes of both splittings, as well as the energies of the individual sublevels, rotational and translational, are in good agreement with the INS data.