H2, HD, and D2 inside C60: Coupled translation-rotation eigenstates of the endohedral molecules from quantum five-dimensional calculations

We have performed rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H2, HD, and D2 inside C60. This work is an extension of our earlier investigation of the quantum T-R dynamics of H2 @ C60 [M. Xu, J. Chem. Phys. 128, 011101 (2008)] and uses the same computational methodology. Two 5D intermolecular potential energy surfaces (PESs) were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H2, HD, and D2. The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic three-dimensional harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H2 HD D2. The quantum number j associated with the rotation of H2, HD, and D2 was found to be a good quantum number for H2 and D2 on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.