M. M. Conde

Determining the three-phase coexistence line in methane hydrates using computer simulations

Molecular dynamics simulations have been performed to estimate the three-phase (solid hydrate-liquid water-gaseous methane) coexistence line for the water-methane binary mixture. The temperature at which the three phases are in equilibrium was determined for three different pressures, namely, 40, 100, and 400 bar by using direct coexistence simulations. In the simulations water was described by using either TIP4P, TIP4P/2005, or TIP4P/Ice models and methane was described as simple Lennard-Jones interaction site. Lorentz-Berthelot combining rules were used to obtain the parameters of the cross interactions. For the TIP4P/2005 model positive deviations from the energetic Lorentz-Berthelot rule were also considered to indirectly account for the polarization of methane when introduced in liquid water. To locate the three-phase coexistence point, two different global compositions were used, which yielded (to within statistical uncertainty) the same predictions for the three-phase coexistence temperatures, although with a somewhat different time evolution. The three-phase coexistence temperatures obtained at different pressures when using the TIP4P/Ice model of water were in agreement with the experimental results. The main reason for this is that the TIP4P/Ice model reproduces the melting point of ice I(h).

The thickness of a liquid layer on the free surface of ice as obtained from computer simulation

Molecular dynamic simulations were performed for ice I(h) with a free surface by using four water models, SPC/E, TIP4P, TIP4P/Ice, and TIP4P/2005. The behavior of the basal plane, the primary prismatic plane, and of the secondary prismatic plane when exposed to vacuum was analyzed. We observe the formation of a thin liquid layer at the ice surface at temperatures below the melting point for all models and the three planes considered. For a given plane it was found that the thickness of a liquid layer was similar for different water models, when the comparison is made at the same undercooling with respect to the melting point of the model. The liquid layer thickness is found to increase with temperature. For a fixed temperature it was found that the thickness of the liquid layer decreases in the following order: the basal plane, the primary prismatic plane, and the secondary prismatic plane. For the TIP4P/Ice model, a model reproducing the experimental value of the melting temperature of ice, the first clear indication of the formation of a liquid layer, appears at about -100 degrees C for the basal plane, at about -80 degrees C for the primary prismatic plane, and at about -70 degrees C for the secondary prismatic plane.

Heat capacity of water : a signature of nuclear quantum effects

In this note we present results for the heat capacity at constant pressure for the TIP4PQ/2005 model, as obtained from path-integral simulations. The model does a rather good job of describing both the heat capacity of ice I(h) and of liquid water. Classical simulations using the TIP4P/2005, TIP3P, TIP4P, TIP4P-Ew, simple point charge/extended, and TIP5P models are unable to reproduce the heat capacity of water. Given that classical simulations do not satisfy the third law of thermodynamics, one would expect such a failure at low temperatures. However, it seems that for water, nuclear quantum effects influence the heat capacities all the way up to room temperature. The failure of classical simulations to reproduce C(p) points to the necessity of incorporating nuclear quantum effects to describe this property accurately.

Computing the free energy of molecular solids by the Einstein molecule approach: Ices XIII and XIV, hard-dumbbells and a patchy model of proteins

The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. In order to show its applicability, we have computed the free energy of a hard-dumbbell solid, of two recently discovered solid phases of water, namely, ice XIII and ice XIV, where the interactions between water molecules are described by the rigid nonpolarizable TIP4P/2005 model potential, and of several solid phases that are thermodynamically stable for an anisotropic patchy model with octahedral symmetry which mimics proteins. Our calculations show that both the Einstein crystal method and the Einstein molecule approach yield the same results within statistical uncertainty. In addition, we have studied in detail some subtle issues concerning the calculation of the free energy of molecular solids. First, for solids with noncubic symmetry, we have studied the effect of the shape of the simulation box on the free energy. Our results show that the equilibrium shape of the simulation box must be used to compute the free energy in order to avoid the appearance of artificial stress in the system that will result in an increase in the free energy. In complex solids, such as the solid phases of water, another difficulty is related to the choice of the reference structure. As in some cases there is no obvious orientation of the molecules; it is not clear how to generate the reference structure. Our results will show that, as long as the structure is not too far from the equilibrium structure, the calculated free energy is invariant to the reference structure used in the free energy calculations. Finally, the strong size dependence of the free energy of solids is also studied.

The phase diagram of water at negative pressures: virtual ices.

The phase diagram of water at negative pressures as obtained from computer simulations for two models of water, TIP4P/2005 and TIP5P is presented. Several solid structures with lower densities than ice Ih, so-called virtual ices, were considered as possible candidates to occupy the negative pressure region of the phase diagram of water. In particular the empty hydrate structures sI, sII, and sH and another, recently proposed, low-density ice structure. The relative stabilities of these structures at 0 K was determined using empirical water potentials and density functional theory calculations. By performing free energy calculations and Gibbs-Duhem integration the phase diagram of TIP4P/2005 was determined at negative pressures. The empty hydrates sII and sH appear to be the stable solid phases of water at negative pressures. The phase boundary between ice Ih and sII clathrate occurs at moderate negative pressures, while at large negative pressures sH becomes the most stable phase. This behavior is in reasonable agreement with what is observed in density functional theory calculations.

Determining the phase diagram of water from direct coexistence simulations: the phase diagram of the TIP4P/2005 model revisited.

Direct coexistence simulations between the fluid and solid phases are performed for several ices. For ices Ih and VII it has already been shown that the methodology is successful and the melting point is in agreement with that obtained from free energy calculations. In this work the methodology is applied to ices II, III, V, and VI. The lengths of the direct coexistence runs for the high pressure polymorphs are not too long and last less than 20 ns for all ices except for ice II where longer runs (of about 150 ns) are needed. For ices II, V, and VI the results obtained are completely consistent with those obtained from free energy calculations. However, for ice III it is found that the melting point from direct coexistence simulations is higher than that obtained from free energy calculations, the difference being greater than the statistical error. Since ice III presents partial proton orientational disorder, the departure is attributed to differences in the partial proton order in the water model with respect to that found in the experiment. The phase diagram of the TIP4P/2005 model is recalculated using the melting points obtained from direct coexistence simulations. The new phase diagram is similar to the previous one except for the coexistence lines where ice III is involved. The range of stability of ice III on the p-T plot of the phase diagram increases significantly. It is seen that the model qualitatively describes the phase diagram of water. In this work it is shown that the complete phase diagram of water including ices Ih, II, III, V, VI, VII, and the fluid phase can be obtained from direct coexistence simulations without the need of free energy calculations.Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.

Can gas hydrate structures be described using classical simulations

Quantum path-integral simulations of the hydrate solid structures have been performed using the recently proposed TIP4PQ/2005 model. By also performing classical simulations using this model, the impact of the nuclear quantum effects on the hydrates is highlighted; nuclear quantum effects significantly modify the structure, densities, and energies of the hydrates, leading to the conclusion that nuclear quantum effects are important not only when studying the solid phases of water but also when studying the hydrates. To analyze the validity of a classical description of hydrates, a comparison of the results of the TIP4P/2005 model (optimized for classical simulations) with those of TIP4PQ/2005 (optimized for path-integral simulations) was undertaken. A classical description of hydrates is able to correctly predict the densities at temperatures above 150 K and the relative stabilities between the hydrates and ice I(h). The inclusion of nuclear quantum effects does not significantly modify the sequence of phases found in the phase diagram of water at negative pressures, namely, I(h)-->sII-->sH. In fact the transition pressures are little affected by the inclusion of nuclear quantum effects; the phase diagram predictions for hydrates can be performed with reasonable accuracy using classical simulations. However, for a reliable calculation of the densities below 150 K, the sublimation energies, the constant pressure heat capacity, and the radial distribution functions, the incorporation of nuclear quantum effects is indeed required.

Competition between ices Ih and Ic in homogeneous water freezing

The role of cubic ice, ice Ic, in the nucleation of ice from supercooled water has been widely debated in the past decade. Computer simulations can provide insightful information about the mechanism of ice nucleation at a molecular scale. In this work, we use molecular dynamics to study the competition between ice Ic and hexagonal ice, ice Ih, in the process of ice nucleation. Using a seeding approach, in which classical nucleation theory is combined with simulations of ice clusters embedded in supercooled water, we estimate the nucleation rate of ice for a pathway in which the critical nucleus has an Ic structure. Comparing our results with those previously obtained for ice Ih [Sanz et al., J. Am. Chem. Soc. 135, 15008 (2013)], we conclude that within the accuracy of our calculations both nucleation pathways have the same rate for the studied water models (TIP4P/Ice and TIP4P/2005). We examine in detail the factors that contribute to the nucleation rate and find that the chemical potential difference with the fluid, the attachment rate of particles to the cluster, and the ice-water interfacial free energy are the same within the estimated margin of error for both ice polymorphs. Furthermore, we study the morphology of the ice clusters and conclude that they have a spherical shape.

The phase diagram of water from quantum simulations.

The phase diagram of water has been calculated from the TIP4PQ/2005 model, an empirical rigid non-polarisable model. The path integral Monte Carlo technique was used, permitting the incorporation of nuclear quantum effects. The coexistence lines were traced out using the Gibbs-Duhem integration method, once having calculated the free energies of the liquid and solid phases in the quantum limit, which were obtained via thermodynamic integration from the classical value by scaling the mass of the water molecule. The resulting phase diagram is qualitatively correct, being displaced to lower temperatures by 15-20 K. It is found that the influence of nuclear quantum effects is correlated to the tetrahedral order parameter.

Path integral Monte Carlo simulations for rigid rotors and their application to water

In this work the path integral formulation for rigid rotors, proposed by Müser and Berne [Phys. Rev. Lett. 77, 2638 (1996)], is described in detail. It is shown how this formulation can be used to perform Monte Carlo simulations of water. Our numerical results show that whereas some properties of water can be accurately reproduced using classical simulations with an empirical potential which, implicitly, includes quantum effects, other properties can only be described quantitatively when quantum effects are explicitly incorporated. In particular, quantum effects are extremely relevant when it comes to describing the equation of state of the ice phases at low temperatures, the structure of the ices at low temperatures, and the heat capacity of both liquid water and the ice phases. They also play a minor role in the relative stability of the ice phases.