Does cage quantum delocalisation influence the translation–rotational bound states of molecular hydrogen in clathrate hydrate?

Abstract

In this study, we examine the effect of a flexible description of the clathrate hydrate framework on the translation-rotation (TR) eigenstates of guest molecules such as molecular hydrogen. Traditionally, the water cage structure is assumed to be rigid, thus ignoring the quantum nature of hydrogen nuclei in the water framework. However, it has been shown that protons in a water molecule possess a marked delocalised character in many situations, ranging from water clusters to proton transfer in the bulk. In the case of water clathrates, all previous TR bound-state calculations of guest molecules consider that the caging water molecules are fixed at their equilibrium geometry. Only recently, a static investigation of the role of proton configurations was performed by Bačić and co-workers by sampling a very large number of different static structures of water clathrates. Here, we investigate the importance of the rotational degrees of freedom of the water cage on the TR levels of the guest molecule using an efficient adiabatic decoupling scheme. Our approach combines rigid body diffusion Monte Carlo calculations for the description of the rotational degree of freedom of water molecules surrounding the guest molecular hydrogen to an efficient Smolyak sparse-grid technique for the calculation of the TR levels. This approach allows us to take into account the highly anharmonic nature of the rotational water motions in a high-dimensional system. The clathrate-induced splittings of the j = 1 rotational levels are much more sensitive to the quantum hydrogen delocalisation than the translational transitions. This result is in good agreement with the previous static study of Bačić and co-workers.

Quasistructural molecules

“…Allowing for the nonrigidity of the lattice, not considered in the Devonshire cell model, 112 introduces two effects changing the quantum treatment of these systems: (a) the host-guest (molecule-crystal) interaction energy is minimized by the relaxation of the lattice, and (b) the orientation-dependent lattice relaxations, through coupling of the guest rotations with pseudorotation of the host, induce a significant change, in fact a decrease of the effective rotational constants. Recently, quantum studies 113 of molecules trapped in cages 113,114 found renewed interest, especially with regard to the joint treatment of translation-rotation states. Answering the question whether these systems are quasistructural or not would require detailed experimental high-resolution spectroscopic studies and variational rovibrational treatments, both hindered by the size of some of these systems.…”

H2, HD, and D2 in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates

“…[22][23][24] In all these calculations, the hydrogen-bonded clathrate hydrate framework was treated as rigid. In a recent study, 25 this constraint was relaxed partially, by performing quantum 5D calculations of the TR levels of H 2 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.…”

Intramolecular stretching vibrational states and frequency shifts of (H2)2 confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets

“…In all these calculations, both the H 2 molecules and the hydrogen-bonded clathrate hydrate framework were treated as rigid. Recently, 30 this constraint was relaxed partially, by performing quantum 5D calculations of the TR levels of (rigid) H 2 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.…”