Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Pressure in Molecular Simulations with Scaled Charges. 1. Ionic Systems

Charge scaling, rationalized as MDEC (molecular dynamics in electronic continuum) or ECC (electronic continuum correction), has become a widely used simple approach to how to avoid self-consistent induced dipoles yet approximately take into account the effects of electronic polarizability. It has been assumed that the continuum permittivity does not depend on density; in turn, pressure is calculated by standard formulas. In this work, we elaborate a complementary approximation of density-independent molecular polarizability and derive formulas for pressure corrections within the MDEC framework; real behavior lies between these two extremes. The pressure corrections for test ionic systems are huge and negative, leading to sizable densities in constant-pressure MDEC simulations. A comparison of MDEC results with equivalent polarizable systems gives a good pressure match for a crystal but very low MDEC pressures for ionic liquids. These results witness about the importance of a correct density dependence not only of continuum permittivity in MDEC simulations but also of polarizability in polarizable simulations.

Residual entropy of ice III from Monte Carlo simulation

We calculated the residual entropy of ice III as a function of the occupation probabilities of hydrogen positions α and β assuming equal energies of all configurations. To do this, a discrete ice model with Bjerrum defect energy penalty and harmonic terms to constrain the occupation probabilities was simulated by the Metropolis Monte Carlo method for a range of temperatures and sizes followed by thermodynamic integration and extrapolation to N = ∞. Similarly as for other ices, the residual entropies are slightly higher than the mean-field (no-loop) approximation. However, the corrections caused by fluctuation of energies of ice samples calculated using molecular models of water are too large for accurate determination of the chemical potential and phase equilibria.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

Hydrothermal properties of the COS/D2 water model: a polarizable charge-on-spring water model, at elevated temperatures and pressures

Molecular simulations have been conducted to assess the pVT properties and static permittivity of the charge-on-spring polarizable water model COS/D2 at hydrothermal conditions from 300 to 450 °C and bulk densities of 0.001 to 1.0 g cm⁻³.

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.

Surface Tension of Supercooled Water: No Inflection Point down to -25 °C

A dramatic increase in the surface tension of water with decreasing temperature in the supercooled liquid region has appeared as one of the many anomalies of water. This claimed anomaly characterized by the second inflection point at about +1.5 °C was observed in older surface tension data and was partially supported by some molecular simulations and theoretical considerations. In this study, two independent sets of experimental data for the surface tension of water in the temperature range between +33 and -25 °C are reported. The two data sets are mutually consistent, and they lie on a line smoothly extrapolating from the stable region. No second inflection point and no other anomalies in the course of the surface tension were observed. The new data lies very close to the extrapolated IAPWS correlation for the surface tension of ordinary water, which hence can be recommended for use, e.g., in atmospheric modeling.

Polarizable six-point water models from computational and empirical optimization

Tröster et al. (J. Phys. Chem B 2013, 117, 9486-9500) recently suggested a mixed computational and empirical approach to the optimization of polarizable molecular mechanics (PMM) water models. In the empirical part the parameters of Buckingham potentials are optimized by PMM molecular dynamics (MD) simulations. The computational part applies hybrid calculations, which combine the quantum mechanical description of a H2O molecule by density functional theory (DFT) with a PMM model of its liquid phase environment generated by MD. While the static dipole moments and polarizabilities of the PMM water models are fixed at the experimental gas phase values, the DFT/PMM calculations are employed to optimize the remaining electrostatic properties. These properties cover the width of a Gaussian inducible dipole positioned at the oxygen and the locations of massless negative charge points within the molecule (the positive charges are attached to the hydrogens). The authors considered the cases of one and two negative charges rendering the PMM four- and five-point models TL4P and TL5P. Here we extend their approach to three negative charges, thus suggesting the PMM six-point model TL6P. As compared to the predecessors and to other PMM models, which also exhibit partial charges at fixed positions, TL6P turned out to predict all studied properties of liquid water at p0 = 1 bar and T0 = 300 K with a remarkable accuracy. These properties cover, for instance, the diffusion constant, viscosity, isobaric heat capacity, isothermal compressibility, dielectric constant, density, and the isobaric thermal expansion coefficient. This success concurrently provides a microscopic physical explanation of corresponding shortcomings of previous models. It uniquely assigns the failures of previous models to substantial inaccuracies in the description of the higher electrostatic multipole moments of liquid phase water molecules. Resulting favorable properties concerning the transferability to other temperatures and conditions like the melting of ice are also discussed.

A systematic development of a polarizable potential of water

Based on extensive studies of existing potentials we propose a new molecular model for water. The new model is rigid and contains three Gaussian charges. Contrary to other models, all charges take part in the polarization of the molecule. They are connected by harmonic springs to their gas-phase positions: the negative charge to a prescribed point on the main axis of the molecule; the positive charges to the hydrogens. The mechanical equilibrium between the electrostatic forces and the spring forces determines the polarization of the molecule which is established by iteration at every timestep. The model gives excellent estimates for ambient liquid properties and reasonably good results from high-pressure solids to gas-phase clusters. We present a detailed description of the development of this model and a large number of calculated properties compared to the estimates of the nonpolarizable TIP4P∕2005 [J. L. F. Abascal and C. Vega, J. Chem. Phys. 123, 234505 (2005)], the polarizable GCPM [P. Paricaud, M. Predota, A. A. Chialvo, and P. T. Cummings, J. Chem. Phys. 122, 244511 (2005)], and our earlier BKd3 model [P. T. Kiss and A. Baranyai, J. Chem. Phys. 137, 084506 (2012)]. The best overall performance is shown by the new model.

The Microscopic Physical Cause for the Density Maximum of Liquid Water

The existence of a density maximum at 277 K is probably the most prominent anomaly among the many very special thermodynamic properties of liquid water. While usually attributed to so-called hydrogen bonding, the microscopic physical cause of this prominent anomaly is still elusive. Here we show that the density anomaly is caused by those short-range electrostatic forces, which are generated by the quadrupole and higher moments of the charge distributions present in liquid-phase water molecules. This conclusion derives from 20 ns replica exchange molecular-dynamics simulations with closely related polarizable four-, five-, and six-point water models. As soon as the model complexity suffices to represent the higher electrostatic moments with sufficient accuracy, the density temperature profile n(T) calculated for T ∈ [250,320] K at the standard pressure 1 bar locks in to the experimental observation. The corresponding six-point model is, therefore, the most simple available cartoon for liquid-phase water molecules.

Polarizable water models from mixed computational and empirical optimization

Here we suggest a mixed computational and empirical approach serving to optimize the parameters of complex and polarizable molecular mechanics (PMM) models for complicated liquids. The computational part of the parameter optimization relies on hybrid calculations combining density functional theory (DFT) for a solute molecule with a PMM treatment of its solvent environment at well-defined thermodynamic conditions. As an application we have developed PMM models for water featuring ν = 3, 4, and 5 points of force action, a Gaussian inducible dipole and a Buckingham potential at the oxygen, the experimental liquid phase geometry, the experimental gas phase polarizability α(exp)(g) = 1.47 ų, and, for ν = 4 and 5, the gas phase value μ(exp)(g) = 1.855 D for the static dipole moment. The widths of the Gaussian dipoles and, for ν = 4 and 5, also the electrostatic geometries of these so-called TLνP models are derived from self-consistent DFT/PMM calculations, and the parameters of the Buckingham potentials (and the static TL3P dipole moment) are estimated from molecular dynamics (MD) simulations. The high quality of the resulting models is demonstrated for the observables targeted during optimization (potential energy per molecule, pressure, radial distribution functions) and a series of predicted properties (quadrupole moments, density at constant pressure, dielectric constant, diffusivity, viscosity, compressibility, heat capacity) at certain standard conditions. Remaining deficiencies and possible ways for their removal are discussed.

Six-site polarizable model of water based on the classical Drude oscillator

A polarizable water model, SWM6, was developed and optimized for liquid phase simulations under ambient conditions. Building upon the previously developed SWM4-NDP model, additional sites representing oxygen lone-pairs were introduced. The geometry of the sites is assumed to be rigid. Considering the large number of adjustable parameters, simulated annealing together with polynomial fitting was used to facilitate model optimization. The new water model was shown to yield the correct self-diffusion coefficient after taking the system size effect into account, and the dimer geometry is better reproduced than in the SWM4 models. Moreover, the experimental oxygen-oxygen radial distribution is better reproduced, indicating that the new model more accurately describes the local hydrogen bonding structure of bulk phase water. This was further validated by its ability to reproduce the experimental nuclear magnetic shielding and related chemical shift of the water hydrogen in the bulk phase, a property sensitive to the local hydrogen bonding structure. In addition, comparison of the liquid properties of the SWM6 model is made with those of a number of widely used additive and polarizable models. Overall, improved balance between the description of monomer, dimer, clustered, and bulk phase water is obtained with the new model compared to its SWM4-NDP polarizable predecessor, though application of the model requires an approximately twofold increase on computational resources.