Coupled translation-rotation eigenstates of H2 in C60 and C70 on the spectroscopically optimized interaction potential: Effects of cage anisotropy on the energy level structure and assignments

Abstract

We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H(2) in C(60) through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H(2) in the vibrationally excited nu=1 state. The PES is based on the three-site H(2)-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H(2) has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H(2)@C(60) to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H(2)-fullerene interaction afforded by the three-site H(2)-C pair potential. The same H(2)-C pair potential spectroscopically optimized for H(2)@C(60) was also used to construct the pairwise additive 5D PES of H(2) (nu=1) in C(70). This PES, because of the lower symmetry of C(70) (D(5h)) relative to that of C(60) (I(h)), exhibits pronounced anisotropy with respect to the direction of the translational motion of H(2) away from the cage center, unlike that of H(2) in C(60). As a result, the T-R energy level structure of H(2) in C(70) from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H(2) are all qualitatively different from those determined previously for H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008).

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].…”

“…Our approach to the rigorous calculation of the coupled five-dimensional T-R energy levels and wave functions of a hydrogen molecule inside fullerenes, applied in this study to HD@C 60 , has evolved in our group over a number of years, in the course of the theoretical investigations of the quantum T-R dynamics of H 2 and its isotopologues entrapped in the cages of clathrate hydrates [19][20][21], fullerenes C 60 and C 70 [2,5], and an open-cage derivative of C 60 (ATOCF) [22]. A detailed description of the quantum five-dimensional methodology is available in [18], and therefore only the salient features are given here.…”

“…Computational parameters used in this work. (in cm −1 ) and σ (in angstrom) are the LJ parameters, and ω [5] is dimensionless. They define the five-dimensional intermolecular PES of H 2 @C 60 and have been optimized by fitting the computed T-R energy levels to the IR spectroscopic measurements for H 2 @C 60 [7].…”

“…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].…”