PNNL

Abstract

We provide a detailed study of the hydrogen bonding arrangements, the relative stability, and an analysis of the many-body effects in the (H2O)20 (D-cage), (H2O)24 (T-cage) and (H2O)28 (H-cage) hollow cages making up the structure I (sI) and structure II (sII) clathrate hydrate structures. Based on the enumeration of the possible hydrogen bonding networks for a fixed oxygen atom scaffold, the residual entropy (S_0) of these gas phase cages was estimated at 0.75482, 0.7544 and 0.75417 ·Nk_b, where N is the number of molecules and k_b is Boltzmann’s constant for the D-, T- and H-cages, respectively. We show that previously identified descriptors of enhanced stability of the (H2O)20 cage based on the relative arrangement and connectivity of nearest-neighbor fragments on the polyhedral water cluster, as described by the Strong-Weak-Effective-Bond model, are also contributing to the relative stability of networks for the larger (H2O)24 and (H2O)28 hollow cages. The three cages considered in this study contain a maximum of 7, 9 and 11 such preferable arrangements of nearest neighbor dimers (t1d dimers). We report the optimization of all 30,026 hydrogen bond arrangements of (H2O)20, all structures containing 7 to 9 (t1d) dimers for (H2O)24 and all structures containing 9 to 11 (t1d) dimers in (H2O)28. We have found that many possible hydrogen-bond arrangements do not correspond to local minima and collapse to lower-energy structures upon optimization, usually by bridging one of the pentagonal rings in the cage structure. To better understand the subtle hydrogen-bonding interactions in these cages, we report the Many-Body Expansion (MBE) up to the 4-body term for the optimized structures of the three cages. The MBE analysis suggests that the many-body terms vary nearly linearly with the cluster binding energy and that the 2- and 3-body energies have nearly the same slope with respect to the total energy. By using a hierarchical approach of screening the relative stability of networks starting from optimizations with the TIP4P, TTM2.1-F and MB-pol classical potentials, subsequently refining at more accurate levels of electronic structure theory (DFT and MP2) and finally correcting for zero-point energy, we were able to identify a group of 4 low-lying isomers of the (H2O)24 T-cage, two of which are antisymmetric and the other two form a pair of antipode configurations.