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.     

Transport coefficients of the TIP4P-2005 water model

A detailed understanding of the dynamics of liquid water at molecular level is of fundamental importance as well as have applications in many branches of science and technology. In this work, the diffusion of the TIP4P-2005 model of water is systematically investigated in liquid phase in the temperature range 210-310 K. The translational and rotational diffusions, as well as correlations between them, are examined. The effects of system size and shape are also probed in this study. The results suggest the presence of a temperature of dynamical arrest of molecular translations in the range of 150-180 K and of molecular rotations in the range of 80-130 K, depending on specific direction. A substantial change in the preferred directions of translations and rotations relative to the molecular coordinate system is observed slightly below (≈15 K) the melting temperature of the model. It is shown that there is a correlation between translational and rotational molecular motions essential for diffusion in the liquid. The presence of hydrodynamic size effects is confirmed and quantified; it is also shown that using a non-cubic simulation box for a liquid system leads to an anisotropic splitting in the diffusion tensor. The findings of this study enhance our general understanding of models of water, specifically the TIP4P-2005 model, as well as provide evidences of the direct connection between thermodynamics of liquid water and dynamics of its molecules.     

Common features of orientational order at the temperature of maximum density for various water models: molecular dynamics study

Canonical ensembles for liquid water were obtained from molecular dynamics simulations at various temperatures using the TIP5P, TIP4P-FQ, TIP4P, and SPC/E water models at a fixed density of 1 g/cm3. From these ensembles, it was found that the distributions of the orientational order parameter q of these models showed similar patterns as temperature changed except that the distributions were shifted relative to each other by the difference of their temperature of maximum density (TMD). The four models exhibited similar distributions and average values of orientational order around their respective TMDs, and these common features were investigated in detail especially. The current study suggests that the unique microscopic configuration of water molecules cause TMD phenomenon in any reasonable water model. This finding provides a useful tool in the development of new water potentials by offering guidelines to predict the TMD, avoiding troublesome isothermal-isobaric ensemble simulations.     

Chemometric study of liquid water simulations. I. The parameters of the TIP4P model potential

The multivariate chemometric techniques two level factorial design (TLFD) and principal component analysis (PCA) were used to investigate the TIP4P model potential behavior with respect to perturbations on all intermolecular interaction parameters. The effects of these perturbations were calculated for the enthalpy of vaporization, the density, the first maximum of the radial distribution functions of the O-H and O-O pairs, and the second maximum of the radial distribution function of the O-H pair obtained from Monte Carlo simulations of liquid water at 25 degrees C. The principal effects were quantified and rationalized in terms of the pair-wise interaction potential of the TIP4P model. They also corroborate previously published sensitivity analysis results using molecular dynamics and other model potentials. In addition, significant interaction effects between some parameters of the TIP4P model potential were observed and quantified, which hardly could be obtained without such a statistic approach. These interaction effects are very regular and systematic, and their behavior has not been encountered in other chemometric studies and cannot be rationalized in terms of the functional form of the pair-wise potential.     

Influence of water-protein hydrogen bonding on the stability of Trp-cage miniprotein. A comparison between the TIP3P and TIP4P-Ew water models

We report extensive replica exchange molecular dynamics (REMD) simulations on the folding/unfolding equilibrium of Trp-cage miniprotein using the Amber ff99SB all atom forcefield and TIP3P and TIP4P-Ew explicit water solvent models. REMD simulation-lengths in the 500 ns to the microsecond regime per replica are required to adequately sample the folding/unfolding equilibrium. We observe that this equilibrium is significantly affected by the choice of the water model. Compared with experimental data, simulations using the TIP3P solvent describe the stability of the Trp-cage quite realistically, providing a melting point which is just a few Kelvins above the experimental transition temperature of 317 K. The TIP4P-Ew model shifts the equilibrium towards the unfolded state and lowers the free energy of unfolding by about 3 kJ mol(-1) at 280 K, demonstrating the need to fine-tune the protein-forcefield depending on the chosen water model. We report evidence that the main difference between the two water models is mostly due to the different solvation of polar groups of the peptide. The unfolded state of the Trp-cage is stabilized by an increasing number of hydrogen bonds, destabilizing the α-helical part of the molecule and opening the R-D salt bridge. By reweighting the strength of solvent-peptide hydrogen bonds by adding a hydrogen bond square well potential, we can fully recover the effect of the different water models and estimate the shift in population as due to a difference in hydrogen bond-strength of about 0.4 kJ mol(-1) per hydrogen bond.     

Quantum effects in liquid water and ice: model dependence

This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.     

Characterization of the TIP4P-Ew water model: vapor pressure and boiling point

The liquid-vapor-phase equilibrium properties of the previously developed TIP4P-Ew water model have been studied using thermodynamic integration free-energy simulation techniques in the temperature range of 274-400 K. We stress that free-energy results from simulations need to be corrected in order to be compared to the experiment. This is due to the fact that the thermodynamic end states accessible through simulations correspond to fictitious substances (classical rigid liquids and classical rigid ideal gases) while experiments operate on real substances (liquids and real gases, with quantum effects). After applying analytical corrections the vapor pressure curve obtained from simulated free-energy changes is in excellent agreement with the experimental vapor pressure curve. The boiling point of TIP4P-Ew water under ambient pressure is found to be at 370.3+/-1.9 K, about 7 K higher than the boiling point of TIP4P water (363.7+/-5.1 K; from simulations that employ finite range treatment of electrostatic and Lennard-Jones interactions). This is in contrast to the approximately +15 K by which the temperature of the density maximum and the melting temperature of TIP4P-Ew are shifted relative to TIP4P, indicating that the temperature range over which the liquid phase of TIP4P-Ew is stable is narrower than that of TIP4P and resembles more that of real water. The quality of the vapor pressure results highlights the success of TIP4P-Ew in describing the energetic and entropic aspects of intermolecular interactions in liquid water.     

Dynamical properties of liquid water from ab initio molecular dynamics performed in the complete basis set limit

Dynamical properties of liquid water were studied using Car-Parrinello [Phys. Rev. Lett. 55, 2471 (1985)] ab initio molecular dynamics (AIMD) simulations within the Kohn-Sham (KS) density functional theory employing the Becke-Lee-Yang-Parr exchange-correlation functional for the electronic structure. The KS orbitals were expanded in a discrete variable representation basis set, wherein the complete basis set limit can be easily reached and which, therefore, provides complete convergence of ionic forces. In order to minimize possible nonergodic behavior of the simulated water system in a constant energy (NVE) ensemble, a long equilibration run (30 ps) preceded a 60 ps long production run. The temperature drift during the entire 60 ps trajectory was found to be minimal. The diffusion coefficient [0.055 A2/ps] obtained from the present work for 32 D2O molecules is a factor of 4 smaller than the most up to date experimental value, but significantly larger than those of other recent AIMD studies. Adjusting the experimental result so as to match the finite-sized system used in the present study brings the comparison between theory and experiment to within a factor of 3. More importantly, the system is not observed to become "glassy" as has been reported in previous AIMD studies. The computed infrared spectrum is in good agreement with experimental data, especially in the low frequency regime where the translational and librational motions of water are manifested. The long simulation length also made it possible to perform detailed studies of hydrogen bond dynamics. The relaxation dynamics of hydrogen bonds observed in the present AIMD simulation is slower than those of popular force fields, such as the TIP4P potential, but comparable to that of the TIP5P potential.     

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.     

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to (2), where is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.     

Water rotational relaxation and diffusion in hydrated lysozyme

This paper is concerned with the dynamics of water around a small globular protein. Dipolar second-rank relaxation time and diffusion properties of surface water were computed by extensive molecular dynamics simulations of lysozyme in water which lasted a total of 28 ns. Our results indicate that the rotational relaxation of water in the vicinity of lysozyme is 3-7 times slower than that in the bulk depending on how the hydration shell is defined in the calculation. We have also verified that the dynamics of water translational diffusion in the vicinity of lysozyme have retardations similar to rotational relaxation. This is a common assumption in nuclear magnetic relaxation dispersion (NMRD) studies to derive residence times. In contrast to bulk water dynamics, surface water is in a dispersive diffusion regime or subdiffusion. Very good agreement of dipolar second-rank relaxation time with NMRD estimates is obtained by using appropriate dimensions of the hydration shell. Although our computed second-rank dipolar retardations are independent of the water model, SPC/E describes more realistically the time scale of the water dynamics around lysozyme than does TIP3P.     

A potential model for the study of ices and amorphous water: TIP4P/Ice

The ability of several water models to predict the properties of ices is discussed. The emphasis is put on the results for the densities and the coexistence curves between the different ice forms. It is concluded that none of the most commonly used rigid models is satisfactory. A new model specifically designed to cope with solid-phase properties is proposed. The parameters have been obtained by fitting the equation of state and selected points of the melting lines and of the coexistence lines involving different ice forms. The phase diagram is then calculated for the new potential. The predicted melting temperature of hexagonal ice (Ih) at 1 bar is 272.2 K. This excellent value does not imply a deterioration of the rest of the properties. In fact, the predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.     

Effects of water model and simulation box size on protein diffusional motions

We performed molecular dynamics simulations of ubiquitin with the distinct water models, TIP3P, SPC, SPC/E, and SPC/Fw, in different system sizes with different box shapes. The translational diffusion constants of pure water linearly depend on the effective box length, which is known as finite size effect, whereas the first and second rotational times of pure water are nearly constant. We then observed that both the overall translation and rotational motions of the protein are linearly correlated to the viscosity of pure water. As expected from the finite size effect in pure water, the translational diffusion of the protein is significantly affected by the system size, and rotational diffusion is nearly size-independent. After correction for the finite size effect, the SPC/E and SPC/Fw models reproduce both the translational and rotational motion of the protein relatively well. Thus, water models that reproduce the experimentally derived diffusional properties of pure water accurately are expected to also be suitable for simulating protein diffusion quantitatively.     

Temperature and structural changes of water clusters in vacuum due to evaporation

This paper presents a study on evaporation of pure water clusters. Molecular dynamics simulations between 20 ns and 3 micros of clusters ranging from 125 to 4096 molecules in vacuum were performed. Three different models (SPC, TIP4P, and TIP5P) were used to simulate water, starting at temperatures of 250, 275, and 300 K. We monitored the temperature, the number of hydrogen bonds, the tetrahedral order, the evaporation, the radial distribution functions, and the diffusion coefficients. The three models behave very similarly as far as temperature and evaporation are concerned. Clusters starting at a higher temperature show a higher initial evaporation rate and therefore reach the point where evaporation stop (around 240 K) sooner. The radius of the clusters is decreased by 0.16-0.22 nm after 0.5 micros (larger clusters tend to decrease their radius slightly more), which corresponds to around one evaporated molecule per nm(2). The cluster temperature seems to converge towards 215 K independent of cluster size, when starting at 275 K. We observe only small structural changes, but the clusters modeled by TIP5P show a larger percentage of molecules with low diffusion coefficient as t-->infinity, than those using the two other water models. TIP4P seems to be more structured and more hydrogen bonds are formed than in the other models as the temperature falls. The cooling rates are in good agreement with experimental results, and evaporation rates agree well with a phenomenological expression based on experimental observations.     

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 molecular dynamics study of water nucleation using the TIP4P/2005 model

Extensive molecular dynamics simulations were conducted using the TIP4P/2005 water model of Abascal and Vega [J. Chem. Phys. 123, 234505 (2005)] to investigate its condensation from supersaturated vapor to liquid at 330 K. The mean first passage time method [J. Wedekind, R. Strey, and D. Reguera, J. Chem. Phys. 126, 134103 (2007); L. S. Bartell and D. T. Wu, 125, 194503 (2006)] was used to analyze the influence of finite size effects, thermostats, and charged species on the nucleation dynamics. We find that the Nose?-Hoover thermostat and the one proposed by Bussi et al. [J. Chem. Phys. 126, 014101 (2007)] give essentially the same averages. We identify the maximum thermostat coupling time to guarantee proper thermostating for these simulations. The presence of charged species has a dramatic impact on the dynamics, inducing a marked change towards a pure growth regime, which highlights the importance of ions in the formation of liquid droplets in the atmosphere. It was found a small but noticeable sign preference at intermediate cluster sizes (between 5 and 30 water molecules) corresponding mostly to the formation of the second solvation shell around the ion. The TIP4P/2005 water model predicts that anions induce faster formation of water clusters than cations of the same magnitude of charge.     

Computer simulation of two new solid phases of water: Ice XIII and ice XIV

NpT Monte Carlo simulations have been performed for two recently discovered solid phases of water which have been denoted as ice XIII and ice XIV C. G. Salzmann et al. [Science311, 1758 (2006)]. Several potential models of water were considered, namely, the traditional SPC/E, TIP4P, and TIP5P and the more recent TIP5P-E, TIP4P-Ew, TIP4P/Ice, and TIP4P/2005 models. Significant differences in density and oxygen-oxygen radial distribution functions are found between the predictions of the SPC/E, TIP5P, and the models of the TIP4P family. The models TIP4P/Ice and TIP4P/2005 provide the best estimates of the density.     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.