Theoretical studies of CH₄(H₂O)₂₀, (H₂O)₂₁, (H₂O)₂₀, and fused dodecahedral and tetrakaidecahedral structures: How do natural gas hydrates form?

Ab initio geometry optimizations (HF/6-31G*) followed by single point energy calculations (MP2/6-31G*) suggest that the CH₄(H₂O)₂₀ cluster with a CH₄ molecule within the (H₂O)₂₀ dodecahedral cavity has a stabilization energy (SE) of around 7 kcal/mol relative to separated CH₄ and (H₂O)₂₀ molecules. The cavity of a 20 mer fused cubic or edge-shared prismic structure is too small to enclose a methane molecule. Even though the (H₂O)₂₁ cluster with a water molecule within the dodecahedral cavity is significantly more stable (by around 28 kcal/mol) than CH₄(H₂O)₂₀, the dodecahedral cage is too distorted in (H₂O)₂₁ to form a fused hydrate structure. In CH₄(H₂O)₂₀, on the other hand, the dodecahedral cage remains almost undistorted and hence, can form a fused hydrate structure. The present study also suggests that during a fused structure formation, each pentagonal ring sharing between two dodecahedral structures or a dodecahedral and a tetrakaidecahedral structures results in stabilization by around 20-23 kcal/mol.