H₂ in solid C₆₀: Coupled translation-rotation eigenstates in the octahedral interstitial site from quantum five-dimensional calculations

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (TR) energy levels and wave functions of an H ₂ molecule, in the ground (ν = 0) and vibrationally excited (ν = 1) states, confined inside the octahedral interstitial site of solid C ₆₀ with S₆ symmetry. Translational and rotational excitations of H₂ in this nanocavity have been measured by the inelastic neutron scattering (INS) and infrared (IR) spectroscopy, enabling direct comparison between theory and experiment. A pairwise additive 5D intermolecular potential energy surface (PES) was employed in the calculations. The quantum calculations cover the range of energies and types of translational and rotational excitations of the guest molecule which go substantially beyond those considered in the earlier theoretical investigations of this system, revealing new information about the TR energy level structure. The computed j = 1 and j = 2 rotational levels and their splittings, as well as the translational fundamental, are in semi-quantitative agreement with the available INS and IR data, indicating the need for a more accurate intermolecular PES. Our calculations reveal a strong dependence of the TR energy levels, in particular their splittings, on the setting angle which defines the orientation of the C₆₀ molecules relative to their local threefold axes.