Direct Space Methods for Powder X-ray Diffraction for Guest−Host Materials: Applications to Cage Occupancies and Guest Distributions in Clathrate Hydrates

Structural determination of crystalline powders, especially those of complex materials, is not a trivial task. For non-stoichiometric guest−host materials, the difficulty lies in how to determine dynamical disorder and partial cage occupancies of the guest molecules without other supporting information or constraints. Here, we show how direct space methods combined with Rietveld analysis can be applied to a class of host−guest materials, in this case the clathrate hydrates. We report crystal structures in the three important hydrate crystal classes, sI, sII, and sH, for the guests CO₂, C₂H₆, C₃H₈, and methylcyclohexane + CH₄. The results obtained for powder samples are found to be in good agreement with the experimental data from single crystal X-ray diffraction and ¹³C solid-state NMR spectroscopy. This method is also used to determine the guest disorder and cage occupancies of neohexane and tert-butyl methyl ether binary hydrates with CH₄ in the structure H clathrate hydrates. The results are found to be in good agreement with the results from the ¹³C solid-state NMR and molecular dynamics simulations. It is demonstrated that the ab initio crystal structure determination methodology reported here is able to determine absolute cage occupancies and the dynamical disorder of guest molecules in clathrate hydrates from powdered crystalline samples.