Comparison of selected polarizable and nonpolarizable water models in molecular dynamics simulations of ice I(h)

We present a molecular dynamics simulation study in which we determined the melting point of ice I(h) for the polarizable SWM4-NDP water model (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245-249) and compared the performance of several popular water force fields, both polarizable and nonpolarizable, in terms of melting temperature, stability and orientational structuring of ice. The simulations yield the melting temperature of SWM4-NDP ice as low as T(m) = 185 ± 10 K, despite the quadrupole moment of a SWM4-NDP water molecule being close to the experimental gas phase value. The results thus show that the dependence of T(m) on the molecular quadrupole, observed for the three- and four-site water models, is generally lost if polarization is explicitly included. The study also shows that adding polarizability to a planar three-charge water model increases orientational disorder in hexagonal ice. In addition, analysis of the tetrahedral order in bulk ice reveals a correlation between the pre-existing degree of orientational disorder in ice simulated using different polarizable and nonpolarizable models and the melting temperature of the models. Our findings thus suggest some new considerations regarding the role of polarization forces in a crystalline solid that may guide future development of reliable polarizable water models for ice.     

A classical polarizable model for simulations of water and ice

We develop a classical rigid polarizable model of water for molecular simulations of water and ice. The model uses the Rowlinson five-site geometry: oxygen bearing the Lennard-Jones interaction and linearly polarizable point dipole, two positively charged hydrogens, and two massless negative charges placed symmetrically off oxygen so that the experimental dipole moment is reproduced. The target properties are the densities of water and ice Ih, diffusivity, enthalpies of fusion and vaporization, and the ice Ih melting point. The surface tension at lower temperatures is by 7% underestimated whereas the dielectric constant by 6% overestimated. Diffusivity and viscosity worsen at higher temperatures, although the Stokes radius is overestimated only by 2-7%. The ice Ih melting temperature is 260 K and the temperature of maximum density is 269 K. Rescaling the charges by a factor of 1.01 and Lennard-Jones energy by 1.0201 improves the melting point and energy-related quantities but shifts the agreement of kinetic properties to higher temperatures. For the model we propose abbreviation POL4D.     

The melting point of ice Ih for common water models calculated from direct coexistence of the solid-liquid interface

In this work we present an implementation for the calculation of the melting point of ice I(h) from direct coexistence of the solid-liquid interface. We use molecular dynamics simulations of boxes containing liquid water and ice in contact. The implementation is based on the analysis of the evolution of the total energy along NpT simulations at different temperatures. We report the calculation of the melting point of ice I(h) at 1 bar for seven water models: SPC/E, TIP4P, TIP4P-Ew, TIP4P/ice, TIP4P/2005, TIP5P, and TIP5P-E. The results for the melting temperature from the direct coexistence simulations of this work are in agreement (within the statistical uncertainty) with those obtained previously by us from free energy calculations. By taking into account the results of this work and those of our free energy calculations, recommended values of the melting point of ice I(h) at 1 bar for the above mentioned water models are provided.     

The melting temperature of the most common models of water

The melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E,TIP3P,TIP4P, TIP4P/Ew, and TIP5P) is obtained from computer simulations at p = 1 bar. Since the melting temperature of ice I(h) for the TIP4P model is now known [E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 (2004)], it is possible to use the Gibbs-Duhem methodology [D. Kofke, J. Chem. Phys. 98, 4149 (1993)] to evaluate the melting temperature of ice I(h) for other potential models of water. We have found that the melting temperatures of ice I(h) for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T = 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I(h) with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II (so that ice I(h) is not a thermodynamically stable phase for these models). For TIP4P and TIP4P/Ew, ice I(h) is the stable solid phase at the standard melting point. The location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters.     

Calculations of the free energy of interaction of the c-Fos-c-Jun coiled coil: effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein-protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson-Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos-c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos-c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.     

Communication: The effect of dispersion corrections on the melting temperature of liquid water

The melting temperature (T(m)) of liquid water with the Becke-Lee-Yang-Parr (BLYP) density functional including dispersion corrections (BLYP-D) and the Thole-type, version 3 (TTM3-F) ab-initio based flexible, polarizable classical potential is reported via constant pressure and constant enthalpy (NPH) molecular dynamics simulations of an ice I(h)-liquid coexisting system. Dispersion corrections to BLYP lower T(m) to about 360 K, a large improvement over the value of T(m) > 400 K previously obtained with the original BLYP functional under the same simulation conditions. For TTM3-F, T(m) = 248 K from classical molecular dynamics simulations.     

Kinetic aspects of the thermostatted growth of ice from supercooled water in simulations

In experiments, the growth rate of ice from supercooled water is seen to increase with the degree of supercooling, that is, the lower the temperature, the faster the crystallization takes place. In molecular dynamics simulations of the freezing process, however, the temperature is usually kept constant by means of a thermostat that artificially removes the heat released during the crystallization by scaling the velocities of the particles. This direct removal of energy from the system replaces a more realistic heat-conduction mechanism and is believed to be responsible for the curious observation that the thermostatted ice growth proceeds fastest near the melting point and more slowly at lower temperatures, which is exactly opposite to the experimental findings [M. A. Carignano, P. B. Shepson, and I. Szleifer, Mol. Phys. 103, 2957 (2005)]. This trend is explained by the diffusion and the reorientation of molecules in the liquid becoming the rate-determining steps for the crystal growth, both of which are slower at low temperatures. Yet, for a different set of simulations, a kinetic behavior analogous to the experimental finding has been reported [H. Nada and Y. Furukawa, J. Crystal Growth 283, 242 (2005)]. To clarify this apparent contradiction, we perform relatively long simulations of the TIP4P/Ice model in an extended range of temperatures. The temperature dependence of the thermostatted ice growth is seen to be more complex than was previously reported: The crystallization process is very slow close to the melting point at 270 K, where the thermodynamic driving force for the phase transition is weak. On lowering the temperature, the growth rate initially increases, but displays a maximum near 260 K. At even lower temperatures, the freezing process slows down again due to the reduced diffusivity in the liquid. The velocity of the thermostatted melting process, in contrast, shows a monotonic increase upon raising the temperature beyond the normal melting point. In this case, the effects of the increasing thermodynamic driving force and the faster diffusion at higher temperatures reinforce each other. In the context of this study, we also report data for the diffusion coefficient as a function of temperature for the water models TIP4P/Ice and TIP4P/2005.     

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.     

Effect of flexibility on surface tension and coexisting densities of water

Molecular dynamics simulations of pure water at the liquid-vapor interface are performed using direct simulation of interfaces in a liquid slab geometry. The effect of intramolecular flexibility on coexisting densities and surface tension is analyzed. The dipole moment profile across the liquid-vapor interface shows different values for the liquid and vapor phases. The flexible model is a polarizable model. This effect is minor for liquid densities and is large for surface tension. The liquid densities increase from 2% at 300 K to 9% at 550 K when the force field is changed from a fully rigid simple point charge extended (SPCE) model to that of a fully flexible model with the same intermolecular interaction parameters. The increases in surface tension at both temperatures are around 11% and 36%, respectively. The calculated properties of the flexible models are closer to the experimental data than those of the rigid SPCE. The effect of the maximum number of reciprocal vectors (h(z) (max)) and the surface area on the calculated properties at 300 K is also analyzed. The coexiting densities are not sensitive to those variables. The surface tension fluctuates with h(z) (max) with an amplitude larger than 10 mN m(-1). The effect of using small interfacial areas is slightly larger than the error in the simulations.     

Relation between the melting temperature and the temperature of maximum density for the most common models of water

Water exhibits a maximum in density at normal pressure at 4 degrees above its melting point. The reproduction of this maximum is a stringent test for potential models used commonly in simulations of water. The relation between the melting temperature and the temperature of maximum density for these potential models is unknown mainly due to our ignorance about the melting temperature of these models. Recently we have determined the melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P). In this work we locate the temperature of maximum density for these models. In this way the relative location of the temperature of maximum density with respect to the melting temperature is established. For SPC, SPC/E, TIP3P, TIP4P, and TIP4P/Ew the maximum in density occurs at about 21-37 K above the melting temperature. In all these models the negative charge is located either on the oxygen itself or on a point along the H-O-H bisector. For the TIP5P and TIP5P-E models the maximum in density occurs at about 11 K above the melting temperature. The location of the negative charge appears as a geometrical crucial factor to the relative position of the temperature of maximum density with respect to the melting temperature.     

Surface relaxation in water clusters: evidence from theoretical analysis of the oxygen 1s photoelectron spectrum

We present a theoretical interpretation of the oxygen 1s photoelectron spectrum published by Ohrwall et al. [J. Chem. Phys. 123, 054310 (2005)]. A water cluster that contains 200 molecules was simulated at 215 K using the polarizable AMOEBA force field. The force field predicts longer O...O distances at the cluster surface than in the bulk. Comparisons to ab initio molecular dynamics (MD) simulations indicate that the force field underestimates the degree of surface relaxation. By comparing cluster lineshape models, computed from MD simulations, to the experimental spectrum we find further evidence of surface relaxation.     

Ab initio parameterization of an all-atom polarizable and dissociable force field for water

A novel all-atom, dissociative, and polarizable force field for water is presented. The force field is parameterized based on forces, stresses, and energies obtained form ab initio calculations of liquid water at ambient conditions. The accuracy of the force field is tested by calculating structural and dynamical properties of liquid water and the energetics of small water clusters. The transferability of the force field to dissociated states is studied by considering the solvation of a proton and the ionization of water at extreme conditions of pressure and temperature. In the case of the solvated proton, the force field properly describes the presence of both Eigen and Zundel configurations. In the case of the pressure-induced ice VIII/ice X transition and the temperature-induced transition to a superionic phase, the force field is found to describe accurately the proton symmetrization and the melting of the proton sublattice, respectively.     

Crystallization, melting, and structure of water nanoparticles at atmospherically relevant temperatures

Water nanoparticles play an important role in atmospheric processes, yet their equilibrium and nonequilibrium liquid-ice phase transitions and the structures they form on freezing are not yet fully elucidated. Here we use molecular dynamics simulations with the mW water model to investigate the nonequilibrium freezing and equilibrium melting of water nanoparticles with radii R between 1 and 4.7 nm and the structure of the ice formed by crystallization at temperatures between 150 and 200 K. The ice crystallized in the particles is a hybrid form of ice I with stacked layers of the cubic and hexagonal ice polymorphs in a ratio approximately 2:1. The ratio of cubic ice to hexagonal ice is insensitive to the radius of the water particle and is comparable to that found in simulations of bulk water around the same temperature. Heating frozen particles that contain multiple crystallites leads to Ostwald ripening and annealing of the ice structures, accompanied by an increase in the amount of ice at the expense of the liquid water, before the particles finally melt from the hybrid ice I to liquid, without a transition to hexagonal ice. The melting temperatures T(m) of the nanoparticles are not affected by the ratio of cubic to hexagonal layers in the crystal. T(m) of the ice particles decreases from 255 to 170 K with the particle size and is well described by the Gibbs-Thomson equation, T(m)(R) = T(m)(bulk) - K(GT)/(R - d), with constant K(GT) = 82 ± 5 K·nm and a premelted liquid of width d = 0.26 ± 0.05 nm, about one monolayer. The freezing temperatures also decrease with the particles' radii. These results are important for understanding the composition, freezing, and melting properties of ice and liquid water particles under atmospheric conditions.     

Polarizable simulations with second order interaction model (POSSIM) force field: Developing parameters for protein side‐chain analogues

A previously introduced polarizable simulations with second‐order interaction model (POSSIM) force field has been extended to include parameters for small molecules serving as models for peptide and protein side‐chains. Parameters have been fitted to permit reproducing many‐body energies, gas‐phase dimerization energies, and geometries and liquid‐phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second‐order approximation of the full‐scale induced point dipole polarization formalism. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters are currently being used in further development of the POSSIM fast polarizable force field for proteins. © 2012 Wiley Periodicals, Inc.     

Structural properties and thermodynamics of water clusters: a Wang-Landau study

The temperature dependence of structural properties and thermodynamic behavior of water clusters has been studied using Wang-Landau sampling. Four potential models, simple point charge/extended (SPC/E), transferable intermolecular potential 3 point (TIP3P), transferable intermolecular potential 4 point (TIP4P), and Gaussian charge polarizable (GCP), are compared for ground states and properties at finite temperatures. Although the hydrogen bond energy and the distance of the nearest-neighbor oxygen pair are significantly different for TIP4P and GCP models, they approach to similar ground state structures and melting transition temperatures in cluster sizes we considered. Comparing with TIP3P, SPC/E model provides properties closer to that of TIP4P and GCP.     

Temperature dependence of crystal growth of hexagonal ice (I(h))

The transformations between water and ice have many implications across numerous fields of study. A better understanding of this process would benefit many areas of science and technology such as medicine, biology, and atmospheric and material sciences. In the present work the temperature dependence of the rate of growth (melting) of the basal face of hexagonal ice I(h) and the effect of system size are investigated in molecular dynamics simulations. Using an effective pair potential model of water, systems are studied over temperatures ranging from T(M) - 40 to T(M) + 16 K, where T(M) is the melting temperature of the model. It is found that the growth rates reach a maximum value of 0.7 ? ns(-1) (7 cm s(-1)) at about 12 K below the melting temperature. A noticeable effect of the system size on the melting temperature and ice growth rates is observed; it is shown that the size effect arises in smaller systems due to the artificial ordering under periodic conditions. The decrease in melting entropy in the smallest system by 0.4 J (mol K)(-1) relative to the largest system results in an up-shift in the melting temperature by about 2 K. An almost 60% increase in the maximum growth rate is observed for the smallest system.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.     

Free energy of solvation of simple ions: molecular-dynamics study of solvation of Cl- and Na+ in the ice/water interface

Molecular-dynamics simulations of Cl(-) and Na(+) ions are performed to calculate ionic solvation free energies in both bulk simple point-charge/extended water and ice 1 h at several different temperatures, and at the basal ice 1 h/water interface. For the interface we calculate the free energy of "transfer" of the ions across the ice/water interface. For the ions in bulk water in the NPT ensemble at 298 K and 1 atm, results are found to be in good agreement with experiments, and with other simulation results. Simulations performed in the NVT ensemble are shown to give equivalent solvation free energies, and this ensemble is used for the interfacial simulations. Solvation free energies of Cl(-) and Na(+) ions in ice at 150 K are found to be approximately 30 and approximately 20 kcal mol(-1), respectively, less favorable than for water at room temperature. Near the melting point of the model the solvation of the ions in water is the same (within statistical error) as that measured at room temperature, and in the ice is equivalent and approximately 10 kcal mol(-1) less favorable than the liquid. The free energy of transfer for each ion across ice/water interface is calculated and is in good agreement with the bulk observations for the Cl(-) ion. However, for the model of Na(+) the long-range electrostatic contribution to the free energy was more negative in the ice than the liquid, in contrast with the results observed in the bulk calculations.     

An application of flexible constraints in Monte Carlo simulations of the isobaric--isothermal ensemble of liquid water and ice Ih with the polarizable and flexible mobile charge densities in harmonic oscillators model

The method of flexible constraints was implemented in a Monte Carlo code to perform numerical simulations of liquid water and ice Ih in the constant number of molecules, volume, and temperature and constant pressure, instead of volume ensembles, using the polarizable and flexible mobile charge densities in harmonic oscillators (MCDHO) model. The structural and energetic results for the liquid at T=298 K and rho=997 kg m(-3) were in good agreement with those obtained from molecular dynamics. The density obtained at P=1 atm with flexible constraints, rho=1008 kg m(-3), was slightly lower than with the classical sampling of the intramolecular vibrations, rho=1010 kg m(-3). The comparison of the structures and energies found for water hexamers and for ice Ih with six standard empirical models to those obtained with MCDHO, show this latter to perform better in describing water far from ambient conditions: the MCDHO minimum lattice energy, density, and lattice constants were in good agreement with experiment. The average angle HOH of the water molecule in ice was predicted to be slightly larger than in the liquid, yet 1.2% smaller than the experimental value.