Nonstandard cages in the formation process of methane clathrate: Stability, structure, and spectroscopic implications from first-principles

Endohedral CH ₄ at (H ₂O) _n (n 16, 18, 20, 22, 24) clusters with standard and nonstandard cage configurations containing four-, five-, six-, seven-membered rings were generated by spiral algorithm and were systematically explored using DFT-D methods. The geometries of all isomers were optimized in vacuum and aqueous solution. In vacuum, encapsulation of methane molecules can stabilize the hollow (H ₂O) _n cage by 2.31∼5.44 kcalmol; but the endohedral CH ₄ at (H ₂O) _n cages are still less stable than the pure (H ₂O) _n clusters. Aqueous environment could promote the stabilities of the hollow (H ₂O) _n cages as well as the CH ₄ at (H ₂O) _n clusters, and the CH ₄ at (H ₂O) _n clusters possess larger stabilization energies with regard to the pure (H ₂O) _n clusters except for n 24. The lowest energy structures of the CH ₄ at (H ₂O) ₂₀ and CH ₄ at (H ₂O) ₂₄ cages are identical to the building units in the crystalline sI clathrate hydrate. All of the low-energy cages (including both regular and irregular ones) have large structural similarity and can be connected by dimer-insertion operation and Stone-Wales transformation. Our calculation also showed that in the range of cluster size n 16-24, the relative energies of cage isomers tend to decrease with increasing number of the adjacent pentagons in the oxygen skeleton structures. In addition to the regular endohedral CH ₄ at (H ₂O) ₂₀ and CH ₄ at (H ₂O) ₂₄ cage structures, some nonstandard CH ₄ at (H ₂O) _n (n 18, 20, 22, 24) cages have lower energies and might appear during nucleation process of methane hydrate. For the methane molecules in these low-energy cage isomers, we found that the C-H symmetric stretching frequencies show a red-shift trend and the ¹³C NMR chemical shifts generally move toward negative values as the cavity size increases. These theoretical results are comparable to the available experimental data and might help experimental identification of the endohedral water cages during nucleation.