Quantum dynamics of coupled translational and rotational motions of H2 inside C60

Abstract

We report rigorous quantum calculations of the translation-rotation (T-R) eigenstates of the H2 molecule in C60. The resulting level structure can be explained in terms of a few dominant features. These include the coupling between the orbital and the rotational angular momenta of H2 to give the total angular momentum lambda, and the splitting of the sevenfold degeneracy of T-R levels with lambda=3 by the nonsphericity of C60, according to the rules of the icosahedral I h group.

HD in C 60 : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

“…They have revealed strong coupling between the orbital angular momentum associated with the translational motions of H 2 /HD and the rotational angular momentum of the molecule. This T-R coupling manifests conspicuously through the entire T-R energy level structure, partially lifting the degeneracies, and splitting the eigenstates, of H 2 and HD in C 60 with simultaneous translational and rotational excitation [2,3,5]. Shortly thereafter, the first infrared (IR) spectra measured for H 2 @C 60 [6] showed absorption lines split into distinct peaks owing to the T-R coupling, as predicted by our calculations [2,3].…”

“…This T-R coupling manifests conspicuously through the entire T-R energy level structure, partially lifting the degeneracies, and splitting the eigenstates, of H 2 and HD in C 60 with simultaneous translational and rotational excitation [2,3,5]. Shortly thereafter, the first infrared (IR) spectra measured for H 2 @C 60 [6] showed absorption lines split into distinct peaks owing to the T-R coupling, as predicted by our calculations [2,3]. Subsequent IR spectroscopic studies of H 2 @C 60 [4] as well as of endohedral HD and D 2 in C 60 [7] have provided a great deal of valuable information about the T-R energy levels of the guest molecules and their interaction potentials with C 60 .…”

“…Our quantum five-dimensional calculations of the T-R eigenstates of H 2 and HD in C 60 [2,3,5] have characterized quantitatively the 'rattling' dynamics of the endohedral hydrogen. They have revealed strong coupling between the orbital angular momentum associated with the translational motions of H 2 /HD and the rotational angular momentum of the molecule.…”

“…These studies have determined the energies of the majority of the lower lying T-R eigenstates of H 2 @C 60 [16]. In their interpretation and assignment of the measured INS spectra, Horsewill and co-workers have been guided by the general theoretical framework developed by us [2,3], in particular the T-R coupling scheme, and the accurately calculated T-R energy levels of H 2 @C 60 [5].…”

“…The endohedral complexes of C 60 with H 2 and HD have received a great deal of attention [1] because of the profoundly quantum character of the dynamics of the guest molecule, which is surprisingly complex despite the apparent simplicity of these systems [2,3]. Large quantum effects dominate the translational motions of the centre of mass of H 2 /HD as well as the rotation of the molecule; they arise from the combination of the lightness of H 2 or HD and the small size of the C 60 cavity.…”