Path Integral Molecular Dynamics Study of Small H2 Clusters in the Large Cage of Structure II Clathrate Hydrate: Temperature Dependence of Quantum Spatial Distributions

Abstract

We report a path integral molecular dynamics (PIMD) study of the temperature dependence of the spatial distribution of two and four H2 molecules inside the large cage of the structure II clathrate hydrate. The PIMD calculations were performed at five temperatures ranging from 25 to 200 K. Their results were combined with those from an earlier diffusion Monte Carlo (DMC) study of this system at T = 0 K [Sebastianelli, F.; Xu, M.; Bačić, Z. J. Chem. Phys. 2008, 129, 244706]. The spatial distribution of the confined H2 molecules at each of the temperatures considered was characterized with the help of several one-dimensional (1D) and three-dimensional (3D) distribution functions of suitably chosen intermolecular coordinates, generated by the PIMD and DMC calculations. The 1D distribution that proved to be the most strongly temperature dependent, and also the most revealing about the structural properties of the system as a function of temperature, involves the H2−cage center−H2 angle. In the case of four caged H2 molecules, this angular distribution provides clear evidence that between 50 and ∼100 K the system undergoes a qualitative change. At 50 K and below, the system is fully localized in the global minimum of the intermolecular potential, corresponding to a tetrahedral configuration of H2 molecules with a unique orientation relative to the cage frame. At temperatures of 75−100 K and higher, nearly degenerate local minima ∼200 cm−1 above the global minimum become accessible and are increasingly sampled by the system. The 3D spatial distributions also show this growing delocalization above 75−100 K. Our findings are in accord with the localization−delocalization transition observed experimentally to occur at 50 K for four D2 molecules in the large cage [Lokshin, K. A.; Zhao, Y.; He, D.; Mao, W. L.; Mao, H. K.; Hemley, R. J.; Lobanov, M. V.; Greenblatt, M. Phys. Rev. Lett. 2004, 93, 125503].