Quantum dynamics of H2, D2, and HD in the small dodecahedral cage of clathrate hydrate: Evaluating H2-water nanocage interaction potentials by comparison of theory with inelastic neutron scattering experiments

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 [Alavi et al., J. Chem. Phys. 123, 024507 (2005)] was employed. This PES, denoted here as SPC/E, combines an effective, empirical water-water pair potential [Berendsen et al., J. Phys. Chem. 91, 6269 (1987)] 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 [Xu et al., J. Phys. Chem. B 110, 24806 (2006)]. 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 to 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=0→j=1 rotational transitions, 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.