Intramolecular stretching vibrational states and frequency shifts of (H) confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H) encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H moieties and a rigid clathrate structure but is otherwise fully coupled. The (H)-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H-HO pair potential for flexible H and rigid HO [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H-H potential energy surface [R. J. Hinde, J. Chem. Phys. 128, 154308 (2008)]. The calculations are performed by first solving for the eigenstates of a reduced-dimension 6D "intermolecular" Hamiltonian extracted from the full 8D Hamiltonian by taking the H moieties to be rigid. An 8D contracted product basis for the solution of the full problem is then constructed from a small number of the lowest-energy 6D intermolecular eigenstates and two discrete variable representations covering the H-monomer internuclear distances. Converged results are obtained already by including just the two lowest intermolecular eigenstates in the final 8D basis of dimension 128. The two HH vibrational stretching fundamentals are computed for three hydrate domains having an increasing number of HO molecules. For the largest domain, the two fundamentals are found to be site-split by ∼0.5 cm and to be redshifted by about 24 cm from the free-H monomer stretch frequency, in excellent agreement with the experimental value of 26 cm. A first-order perturbation theory treatment gives results that are nearly identical to those of the 8D quantum calculations.