47202-AC6
Quantum Dynamics of Hydrogen Molecules Confined Inside Cages of Clathrate Hydrates
We have performed rigorous quantum five-dimensional (5D) calculations and analysis of the translation-rotation (T-R) energy levels of one H2, D2, and HD molecule inside the small dodecahedral (H2O)20 cage of the structure II clathrate hydrate, which was treated as rigid. The H2-cage intermolecular potential energy surface (PES) used previously in the molecular dynamics simulations of the hydrogen hydrates was employed. This PES, denoted as SPC/E, combines an effective, empirical water-water pair potential and electrostatic interactions between the partial charges placed on H2O and H2. The 5D T-R eigenstates of HD were calculated also on another 5D H2-cage PES denoted PA-D, used by us earlier to investigate the quantum T-R dynamics of H2 and D2 in the small cage. In the PA-D PES, the hydrogen-water pair potential is described by the ab initio 5D PES of the isolated H2-H2O dimer. The quality of the SPC/E and the PA-D H2-cage PESs was tested by direct comparison of the T-R excitation energies calculated on them with the results of two recent inelastic neutron scattering (INS) studies of H2 and HD inside the small clathrate cage. The translational fundamental and overtone excitations, as well as the triplet splittings of the j=1 rotational excitation, of H2 and HD in the small cage calculated on the SPC/E PES agree very well with the INS results, and represent a significant improvement over the results computed on the PA-D PES. Our calculations on the SPC/E PES also make predictions about several spectroscopic observables for the encapsulated H2, D2, and HD which have not been measured yet. In addition, we have performed diffusion Monte Carlo (DMC) calculations of the size evolution of the energetics and the vibrationally averaged spatial distributions of small (para-H2 )n and (ortho-D2)n clusters, with n=1-5, inside the large cage of the structure II clathrate hydrate. Our DMC results concerning the maximum occupancy of four H2 and D2 molecules, their distances from the cage center, the D2-D2 separation, and the specific orientation of the tetrahedral (H2)4 and (D2)4 clusters relative to the framework of the large cage, are in excellent agreement with experiments.
We have investigated by means of rigorous quantum 5D calculations the T-R energy levels and wave functions of H2, D2, and HD inside the fullerene C60. Two 5D intermolecular PESs were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H2, D2, and HD. The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic 3D harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H2/HD/D2 to give the total angular momentum L. The 7-fold degeneracy of T-R levels with L=3 is split by the non-sphericity of C60, according to the rules of the icosahedral Ih group. The quantum number j associated with the rotation of H2, D2, and HD, was found to be a good quantum number for H2 and D2 on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.
