TIP4P-ice

Our results for different water models (TIP4P/Ice, TIP4P/2005, and SPC/E) are shown in Fig. 5. 

Table 1. Potential parameters of TIP4P/Ice (water) [17] and OPLS-UA (methane) [18] models. The distance, in A, between oxygen and hydrogen or the virtual site (M) is don or doM, respectively. The angle, in degrees, formed at the oxygen atom separating the two hydrogen atoms is zH-O-H. The positive charge on the proton is qn- The Lennard-Jones parameters are denoted by crand s/ks, where a and e are the distance and energy parameters, respectively, and ks is Boltzmann s constant.

As can be seen from Figure 4, the predicted three phase coexistence temperatures for the three tested pressures in this woik are consistently below the experimentally measured values by about 3 K. This result could be due to the usage of the TIP4P/Ice force field to model water. The direct coexistence method nsed in this study had been previously used to predict the melting point of ice in the range between 266 and 270 K [14], 3 to 7 K below the experimental melting point. This resnlt is consistent with the prediction of the eqnilibrinm temperatnre of hydrates that is presented in this woik. 

C. Vega, J. L. F. Abascal, I. Nezbeda, Vapor-liquid equilibria from the triple point up to the critical point for the new generation of TIP4P-like models TIP4P/Ew, TIP4P/2005, and TIP4P/ice, J. Chem. Phys. 125 (2006) 034503. 

J. L. F. Abascal, E. Sanz, R. Garcia Fernandez, and C. Vega,/. Chem. Phys., 122, 234511 (2005). A Potential Model for the Study Of Ices and Amorphous Water TIP4P/Ice. 

Besides the six-site model, there are several other models that have been proposed for simulations of ice and water. The KKY (Kumagai, Kawamura, and Yokokawa) potential model is an atomistic model for simulations of ice and water [63]. This model enables analysis of the lattice vibrations of H2O molecules not only for their translational and rotational motions but also for their internal vibrations [64]. The TIP4P/Ice model [65] is a modification of the TIP4P model that can reproduce the real of ice. 

TIP4P/Ice [65], and TIP4P/2005 [72] models. The results of the simulations using aU of the models indicated that QLL thickness near is larger for the basal plane surface than that for the prismatic plane surface and that it is larger for the prismatic plane surface than that for the secondary prismatic plane surface. The simulation results also indicated that the QLL thickness was similar for all models when it was measured at the same supercooling with respect to of the model. 

Transferability from the solid state to the liquid state is equally problematic. A truly transferable potential in this region of the phase diagram must reproduce not only the freezing point, but also the temperature of maximum density and the relative stability of the various phases of ice. This goal remains out of reach at present, and few existing models demonstrate acceptable transferability from solid to liquid phases.One feature of water that has been demonstrated by both an EE model study and an ab initio study °° is that the dipole moments of the liquid and the solid are different, so polarization is likely to be important for an accurate reproduction of both phases. In addition, while many nonpolarizable water models exhibit a computed temperature of maximum density for the liquid, the temperature is not near the experimental value of 277 Eor example, TIP4P and... 

The WK model completely reparametrizes TIP4P. Charges are scaled to reproduce the quadrupole moment of the isolated molecule. The dipole moment, on the other hand, is close to its value in the liquid phase, assumed 2.6 D as in ice [158-161]. The LJ parameters are then adjusted to reproduce internal energy, density and 0-0 pair correlation function of the liquid at 25 C. 

In order to demonstrate the size effect, Burnham [26] has made a series of MD calculations with different lattice-cells, having 64, 128, 256 and 512 water molecules at 100 K. The potential function used was again TIP4P. As one can see from Fig. 6, the size effect is quite dramatic. The 64 and 128 water cells give a DOS with highly structured noise. In more complex systems, some of these features could be mistaken for real peaks. Indeed, in the case of ice the noise at 28 meV was often believed to be one of the two peaks observed in the INS spectrum. This incomplete sampling of the BZ is also demonstrated LD simulation in Fig. 3. 

Fig. 6. MD simulations for ice Ih with different sizes of super-lattice cells, 64, 128, 256 and 512 water molecules using TIP4P potentials. The calculations show that intensities for 64 and 128 molecules are very noisy . The 512 molecule cell shows a good agreement with LD simulation result see Fig. 16, indicating the BZ integration is about acceptable with at least 512 molecules.

Recently, there were many attempts of MD simulations for the vibrational dynamics of ice. In these calculations more realistic, either non-rigid or polarizable, potentials were used. One such calculation was made by Itoh et al [72] using the KKY potential [9] which has three separate pair-wise terms yoo(r), VoH(r), VnH(r) and an extra three-body term for H-O-H and H-0—H bending. These calculations produced the all the fundamental modes up to 450 meV (or 3622 cm" ). The resulting spectra show very similar features to results from the MCY and TIP4P potentials in the translational and librational regions (see Fig. 16 and 17). 

Figure 2. Pair interaction energy distribution for individual water molecules in hexagonal (solid line) and cubic (dotted line) ices. The potential model is TIP4P.

Figure 9. Density of state for intermolecular vibrational motions for empty hydrate II (dotted line) and ice Ic (solid line). The water dimer interactions are (a) TIP4P and (b) CC potential.

Among the different two-phase liquid/crystal systems, ice/water interfaces are of great interest because of their fundamental presence in nature and importance in chemical, biological, environmental and atmospheric processes [14]. Systematic studies of ice/water interfaces by molecular dynamics simulations began in 1987, when Karim and Haymet [15] simulated for the first time the two-phase coexistence using the SPC model of water molecules. Since 1987, ice/water interfaces were studied with TIP4P [16], CF1 [17], SPC/E [18, 19] and six-site [20] models of water molecules. 

Figure 4 also shows that the equilibrium temperatures predicted by Tung et al. [9] are consistently about 5 K below the measured experimental values, which is similar to the results of this woik. It is interesting to note that in that particular woik the TIP4P-Ew force field for water was used, which is known to predict a melting temperature of ice that is 31 K below the experimental melting temperature [14]. 

Dielectric properties for this water model have been simulated by Neumann (1986) and Alper and Levy (1989). Motakabbir and Berkowitz (1991) and Karim and Haymet (1988) have simulated vapor/liquid and ice/liquid interfaces, respectively. De Pablo and Prausnitz (1989) and Vlot et al. (1999) have studied vapor-liquid equilibrium properties of the TIP4P model, and have shown that it overestimates the vapor pressure and underestimates the critical temperature of water. 

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