Abstract
We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H2)2 encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H2 moieties and a rigid clathrate structure but is otherwise fully coupled. The (H2)2-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H2-H2O pair potential for flexible H2 and rigid H2O [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H2-H2 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 H2 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 H2-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 H2O molecules. For the largest domain, the two fundamentals are found to be site-split by ∼0.5 cm-1 and to be redshifted by about 24 cm-1 from the free-H2 monomer stretch frequency, in excellent agreement with the experimental value of 26 cm-1. A first-order perturbation theory treatment gives results that are nearly identical to those of the 8D quantum calculations.
Highlights
The quantum 8D calculations are performed for three clathrate hydrate domains of increasing size, the largest of which contains 98 H2O molecules
The results pertain to all three clathrate hydrate domains, and are given for both the rotationless basis and for the basis that allows for H2@small cage to (H2) rotational motion
The (H2)2-hydrate interaction potential employed is constructed in a pairwise-additive fashion by combining the ab initio H2-H2O pair potential[47] for flexible H2 and rigid H2O and the 6D H2-H2 potential energy surface.[49]
Summary
Hydrogen clathrate hydrates are inclusion compounds in which one or more hydrogen molecules are confined inside closely packed polyhedral cavities within the three-dimensional (3D) crystalline framework created by hydrogen-bonded water molecules.[1,2,3] Simple hydrogen clathrate hydrates, with only hydrogen molecules as guests, first identified by Dyadin et al.,[4] and subsequently studied in more detail by Mao et al.,[5] adopt the classical structure II (sII).[1,2,5] Its unit cell is cubic, comprised of two types of cages: (a) sixteen small cages, each consisting of 20 H2O molecules and denoted 512 due to its 12 pentagonal faces, and (b) eight large cages, each formed by 28 H2O molecules arranged in 12 pentagonal and 4 hexagonal faces, and denoted as 51264. Recently,[30] this constraint was relaxed partially, by performing quantum 5D calculations of the TR levels of (rigid) H2 in the small sII hydrate cage, while taking into account the quantum delocalization of the proton nuclei of the framework water molecules arising from their hindered rotations about the fixed positions of their O atoms Another spectroscopic manifestation of the encapsulation of hydrogen molecules in the cages of clathrate hydrates, relevant for this study, is the shift in the frequency of the H2 intramolecular stretching vibration away from that in the gas phase. In our recent study,[47] we presented the results of the first fully coupled quantum 6D calculations of the vibration-translation-rotation (VTR) eigenstates of a single flexible H2, HD and D2 molecule entrapped in the (rigid) small cage of the sII hydrate, that extended to the first excited (v = 1) vibrational state of H2. V summarizes the work and outlines possible directions of further research
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