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.