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Residual entropy of ices and clathrates from Monte Carlo simulation.

We calculated the residual entropy of ices (Ih, Ic, III, V, VI) and clathrates (I, II, H), assuming the same energy of all configurations satisfying the Bernal-Fowler ice rules. The Metropolis Monte Carlo simulations in the range of temperatures from infinity to a size-dependent threshold were followed by the thermodynamic integration. Convergence of the simulation and the finite-size effects were analyzed using the quasichemical approximation and the Debye-Hückel theory applied to the Bjerrum defects. The leading finite-size error terms, ln N/N, 1/N, and for the two-dimensional square ice model also 1/N(3/2), were used for an extrapolation to the thermodynamic limit. Finally, we discuss the influence of unequal energies of proton configurations.