Quantum dynamics of interstitialH2in solidC60

We present a neutron-scattering study of the quantum dynamics of molecular hydrogen trapped inside solid ${\mathrm{C}}_{60}.$ The loading isotherm is shown to deviate significantly from a standard Langmuir response and follows instead an exponential form, increasing from 40% filling at 130 atm to 90% at 700 atm. Diffraction data confirm that the adsorbed molecules are randomly oriented and sit exclusively at the octahedral site. Inelastic neutron scattering clearly shows the ortho to para conversion of the interstitial hydrogen, which occurs via a transition from the $J=1\mathrm{}$ to $J=0\mathrm{}$ rotational levels. The level scheme shows relatively minor deviations (on the order of a few percent) from the free rotor model with the splitting in the excited level being the same, 0.7 meV, for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2.$ In contrast the shift in the overall level, which is shown to depend critically upon zero-point motion is almost three times greater for ${\mathrm{H}}_2$ than ${\mathrm{D}}_2.$ We also identify the translational modes of the trapped molecules which occur at a much higher energy than would be classically predicted and have an isotopic shift on the order of $\sqrt{2.2}.$ Quantum-mechanical model calculations within the self-consistent harmonic approximation indicate that zero-point motion of ${\mathrm{H}}_2$ molecules in the ground state play the central role in understanding the experimental results, and in particular the high energy of the translational modes and the magnitude of their isotopic shift.