Effects of finite size and proton disorder on lattice-dynamics estimates of the free energy of clathrate hydrates

We consider lattice dynamics methods for calculation of the free energy of clathrate hydrate phases, specifically the cubic structure I (sI), cubic structure II (sII), and hexagonal structure H (sH) phases, in the absence of guest molecules; water molecules are modeled with the TIP4P potential. We examine in particular the effects of finite size and proton disorder on the calculated free energies and consider these in the context of the free-energy differences between the phases. We find that at 300 K, the finite-size, proton-disorder, and quantum effects between phases are, respectively, on the order of 0.4, 0.03, and 0.1 kJ/mol. Details of the calculations are provided, with emphasis on efficiencies developed to handle various aspects related to rigid-molecule lattice dynamics with electrostatic interactions in large crystalline systems.