Rotational and vibrational dynamics of interstitial molecular hydrogen

Abstract

The calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum J is a good quantum number. One goal of this program is to interpret the energy-resolved neutron time-of-flight spectrum previously obtained for ${\mathrm{H}}_{2}{\mathrm{C}}_{60}.$ This spectrum gives direct information on the energy-level spectrum of ${\mathrm{H}}_{2}$ molecules confined to the octahedral interstitial sites of solid ${\mathrm{C}}_{60}.$ We treat this problem of coupled translational and orientational degrees of freedom (i) by construction of an effective Hamiltonian to describe the splitting of the manifold of states characterized by a given value of J and having a fixed total number of phonon excitations, (ii) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and (iii) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an ${\mathrm{H}}_{2}$ molecule with a surrounding array of C atoms has not yet been developed.