Rotational and Vibrational Dynamics of Interstitial Molecular Hydrogen

TL;DR

This paper systematically analyzes the rotational and vibrational energy levels of interstitial hydrogen molecules in C60, combining theoretical models and numerical solutions to interpret neutron scattering data and understand molecular confinement.

Contribution

It introduces an effective Hamiltonian and numerical methods to study coupled translation-rotation states of H2 in C60, providing insights into experimental spectra and highlighting the need for improved interaction potentials.

Findings

Theoretical models explain previously unexplained experimental features.

Numerical solutions are consistent with symmetry analysis.

Current interaction potentials are insufficient for full accuracy.

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 H$_{2}$C$_{60}$. This spectrum gives direct information on the energy level spectrum of H$_2$ molecules confined to the octahedral interstitial sites of solid C$_{60}$. We treat this problem of coupled translational and orientational degrees of freedom a) 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, b) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and c) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several hitherto uninterpreted aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an H$_2$ molecule with a surrounding array of C atoms has not yet been developed.