Interaction of endohedral molecular hydrogen with C$_{60}$: infrared study*

We report on the dynamics of isotopically different hydrogen molecules, H$_2$, D$_2$ and HD, trapped in the molecular cages of a fullerene C$_{60}$[Min Ge et al., J. Chem. Phys. {\bf 134}, 054507 (2011), {\bf 135}, 114511 (2011)]. The infrared spectra were measured at temperatures from 5K to 300K and analyzed using a model of a vibrating rotor trapped in a spherical potential. The interaction potential was determined in the ground and in the first excited vibrational state of a hydrogen molecule. The isotropic part of the potential is similar for all three molecules studied. In HD@C$_{60}$ we observe the mixing of rotational states and an interference effect of the dipole moment terms due to the displacement of the HD rotation center from the fullerene cage center. A three-site Lennard-Jones potential in the pairwise additive five-dimensional potential energy surface reproduces the hydrogen IR spectrum with great accuracy[M. Xu et al., J. Chem. Phys.{\bf 130}, 224306 (2009)].