Reports: AC6
47202-AC6 Quantum Dynamics of Hydrogen Molecules Confined Inside Cages of Clathrate Hydrates
We have performed fully coupled quantum five-dimensional calculations of the translation-rotation (T-R) energy levels of one H2, HD, and D2 molecule confined inside the large hexakaidecahedral (51264) cage of the structure II clathrate hydrate. Highly converged T-R eigenstates have been obtained for excitation energies beyond the j=2 rotational levels of the guest molecules, in order to allow comparison with the recent Raman spectroscopic measurements. The translationally excited T-R states are assigned with the quantum numbers n and l of the 3D isotropic harmonic oscillator. However, the translational excitations are not harmonic, since the level energies depend not only on n but also on l. For l > 1, the T-R levels having the same n,l values are split into groups of almost degenerate levels. The splitting patterns follow the predictions of group theory for the environment of Td symmetry, which is created by the configuration of the oxygen atoms of the large cage. The 2j+1 degeneracy of the j=1 and j=2 rotational levels of the encapsulated hydrogen molecule is lifted entirely by the angular anisotropy of the H2-cage interaction potential. The patterns and magnitudes of the j=1,2 rotational level splittings, and the energies of the sub-levels, in the large cage are virtually identical to those calculated for the small cage. This is in agreement with, and sheds light on, the observation that the S0(0) j=0 to j=2 bands in the rotational Raman spectra measured for simple H2 hydrate and the binary hydrate of H2 with tetrahydrofuran are remarkably similar with respect to their frequencies, widths, shapes, and internal structure, when the H2 occupancy of the large cage of simple H2 hydrate is low.
In a related work, we have developed a quantitatively accurate pairwise additive 5D potential energy surface (PES) for H2 in C60 through fitting to the recently published infrared (IR) spectroscopic measurements of this system, for H2 in the vibrationally excited v=1 state. The PES is based on the three-site H2-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H2 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 T-R energy levels observed so far in the IR spectra of H2@C60 to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H2-fullerene interaction afforded by the three-site H2-C pair potential. The same H2-C pair potential spectroscopically optimized for H2@C60 was also used to construct the pairwise additive 5D PES of H2 (v=1) in C70. This PES, because of the lower symmetry of C70 (D5h) relative to that of C60 (Ih), exhibits pronounced anisotropy with respect to the direction of the translational motion of H2 away from the cage center, unlike that of H2 in C60. As a result, the T-R energy level structure of H2 in C70 from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the translation-rotation coupling for translationally excited H2, are all qualitatively different from those determined previously for H2@C60 [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)].
