Assessing Intermolecular Interactions in Guest-Free Clathrate Hydrate Systems

Recently, empty hydrate structures sI, sII, sH, and others have been proposed as low-density ice structures by both experimental observations and computer simulations. Some of them have been synthesized in the laboratory, which motivates further investigations on the stability of such guest-free clathrate structures. Using semiempirical and <i>ab initio</i>-based water models, as well as dispersion-corrected density functional theory approaches, we predict their stability, including cooperative many-body effects, in comparison with reference data from converged wave function-based DF-MP2 electronic structure calculations. We show that large basis sets and counterpoise corrections are required to improve convergence in the interaction/binding energies for such systems. Therefore, extrapolation schemes based on triple/quadruple and quadruple/quintuple ζ quality basis sets are used to reach high accuracy. Eleven different water structures corresponding to dodecahedron, edge sharing, face sharing, and fused cubes, as a part of the WATER27 database, as well as cavities from the sI, sII, and sH clathrate hydrates formed by 20, 24, 28, and 36 water molecules, are employed, and new benchmark energies are reported. Using these benchmark sets of interaction energies, we assess the performance of both analytical models and direct DFT calculations for such clathrate-like systems. In particular, seven popular water models (TIP4P/ice, TIP4P/2005, q-TIP4P/F, TTM2-F, TTM3-F, TTM4-F, and MB-pol) available in the literature, and nine density functional approximations (3 meta-GGAs, 3 hybrids, and 3 range separated functionals) are used to investigate their accuracy. By including dispersion corrections, our results show that errors in the interaction energies are reduced for most of the DFT functionals. Despite the difficulties faced by current water models and DFT functionals to accurately describe the interactions in such water systems, we found some general trends that could serve to extend their applicability to larger systems.