Abstract
We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H2, HD, and D2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H2O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H2 in the hydrate domain, based on an ab initio 6D H2-H2O pair potential for flexible H2 and rigid H2O. They extend to the first excited (v = 1) vibrational state of H2, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm-1 for H2). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H2, our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H2) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of -43 cm-1 for H2 is only 14% away from the experimental value at 20 K.
Highlights
Hydrogen clathrate hydrates are crystalline inclusion compounds where one or more hydrogen molecules are encapsulated inside the cavities, or cages, created by the threedimensional (3D) framework of hydrogen-bonded water molecules.1–3 Simple hydrogen clathrate hydrates, that have only hydrogen molecules as guests, were first identified by Dyadin et al.,4 and later characterized by Mao et al in more detail.5 They have the classical structure II,1,2,5 whose cubic unit cell consists of two types of cages
The disparity between the nodal patterns of the states involved, completely irregular for the highly excited TR states vs. a smooth one, with a single node for the v = 1 state, are likely to figure prominently in any theoretical model. Both the Smolyak scheme approach and filter-diagonalization calculations demonstrate that in order to compute a highly converged H2 stretch fundamental one needs to use a basis for the intermolecular DOFs that can provide an accurate description of the vibrational averaging over the large-amplitude TR motions in the delocalized quantum ground state of the system
Their positive values result from the relative magnitudes of two contributions: (i) The interaction between H2 and the cage; this contribution is negative since the reference energy corresponds to H2 at large distance from the cage. (ii) The zero-point energy (ZPE) of the H2 intramolecular vibration, about 2179 cm−1 for the free H2
Summary
Hydrogen clathrate hydrates are crystalline inclusion compounds where one or more hydrogen molecules are encapsulated inside the cavities, or cages, created by the threedimensional (3D) framework of hydrogen-bonded water molecules. Simple hydrogen clathrate hydrates, that have only hydrogen molecules as guests, were first identified by Dyadin et al., and later characterized by Mao et al in more detail. They have the classical structure II (sII), whose cubic unit cell consists of two types of cages. Besides giving rise to the TR energy level structure, the encapsulation of hydrogen molecules in the cages of clathrate hydrates results in the shift in the frequency of the H2 intramolecular stretching vibration away from that in the gas phase. One can ask whether it is possible to perform quantum 6D calculation of the bound states of H2 in the small cage up to, and including, the energy of the first excited (v = 1) intramolecular vibrational state (the stretch fundamental), around 4100 cm−1, treating the intra- and intermolecular (TR) degrees of freedom as fully coupled, i.e., not invoking their separability.
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