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Molecular simulations employing empirical force fields have provided valuable knowledge about the ice growth process in the past decade. The development of novel computational techniques allows us to study this process, which requires long simulations of relatively large systems, with ab initio accuracy. In this work, we use a neural-network potential for water trained on the revised Perdew–Burke–Ernzerhof functional to describe the kinetics of the ice–water interface. We study both ice melting and growth processes. Our results for the ice growth rate are in reasonable agreement with previous experiments and simulations. We find that the kinetics of ice melting presents a different behavior (monotonic) than that of ice growth (non-monotonic). In particular, a maximum ice growth rate of 6.5 Å/ns is found at 14 K of supercooling. The effect of the surface structure is explored by investigating the basal and primary and secondary prismatic facets. We use the Wilson–Frenkel relation to explain these results in terms of the mobility of molecules and the thermodynamic driving force. Moreover, we study the effect of pressure by complementing the standard isobar with simulations at a negative pressure (−1000 bar) and at a high pressure (2000 bar). We find that prismatic facets grow faster than the basal one and that pressure does not play an important role when the speed of the interface is considered as a function of the difference between the melting temperature and the actual one, i.e., to the degree of either supercooling or overheating. [ABSTRACT FROM AUTHOR]

We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal–isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation. [ABSTRACT FROM AUTHOR]

The application of the Young–Laplace equation to a solid–liquid interface is considered. Computer simulations show that the pressure inside a solid cluster of hard spheres is smaller than the external pressure of the liquid (both for small and large clusters). This would suggest a negative value for the interfacial free energy. We show that in a Gibbsian description of the thermodynamics of a curved solid–liquid interface in equilibrium, the choice of the thermodynamic (rather than mechanical) pressure is required, as suggested by Tolman for the liquid–gas scenario. With this definition, the interfacial free energy is positive, and the values obtained are in excellent agreement with previous results from nucleation studies. Although, for a curved fluid–fluid interface, there is no distinction between mechanical and thermal pressures (for a sufficiently large inner phase), in the solid–liquid interface, they do not coincide, as hypothesized by Gibbs. [ABSTRACT FROM AUTHOR]

We analyze the changes in the interfacial free energy between a spherical solid cluster and a fluid due to the change of the radius of the solid. Interfacial free energies from nucleation studies using the seeding technique for four different systems, being hard spheres, Lennard-Jones, and two models of water (mW and TIP4P/ICE), were plotted as a function of the inverse of the radius of the solid cluster. In all cases, the interfacial free energy was a linear function of the inverse of the radius of the solid cluster and this is consistent with Tolman's equation. This linear behavior is shown not only in isotherms but also along isobars. The effect of curvature on the interfacial free energy is more pronounced in water, followed by hard spheres, and smaller for Lennard-Jones particles. We show that it is possible to estimate nucleation rates of Lennard-Jones particles at different pressures by using information from simple NpT simulations and taking into account the variation of the interfacial free energy with the radius of the solid cluster. Neglecting the effects of the radius on the interfacial free energy (capillarity approximation) leads to incorrect values of the nucleation rate. For the Lennard-Jones system, the homogeneous nucleation curve is not parallel to the melting curve as was found for water in previous work. This is due to the increase in the interfacial free energy along the coexistence curve as the pressure increases. This work presents a simple and relatively straightforward way to approximately estimate nucleation rates. [ABSTRACT FROM AUTHOR]

The transformation of liquid water into solid ice is arguably the most important phase transition on Earth. A key aspect of such transformation is the speed with which ice grows once it is nucleated. There are contradictory experimental results as to whether the ice growth rate shows a maximum on cooling. Previous simulation results point to the existence of such a maximum. However, simulations were performed at constant temperature with the aid of a thermostat that dissipates the heat released at the ice-water interface unrealistically fast. Here, we perform simulations of ice growth without any thermostat. Large systems are required to perform these simulations at constant overall thermodynamic conditions (pressure and temperature). We obtain the same growth rate as in previous thermostatted simulations. This implies that the dynamics of ice growth is not affected by heat dissipation. Our results strongly support the experiments predicting the existence of a maximum in the ice growth rate. By using the Wilson-Frenkel kinetic theory, we argue that such maximum is due to a competition between an increasing crystallization thermodynamic driving force and a decreasing molecular mobility on cooling. [ABSTRACT FROM AUTHOR]

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young-Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We investigate the density isobar of water and the melting temperature of ice using six different density functionals. Machine-learning potentials are employed to ensure computational affordability. Our findings reveal significant discrepancies between various base functionals. Notably, even the choice of damping can result in substantial differences. Overall, the outcomes obtained through density functional theory are not entirely satisfactory across most utilized functionals. All functionals exhibit significant deviations either in the melting temperature or equilibrium volume, with most of them even predicting an incorrect volume difference between ice and water. Our heuristic analysis indicates that a hybrid functional with 25% exact exchange and van der Waals damping averaged between zero and Becke-Johnson dampings yields the closest agreement with experimental data. This study underscores the necessity for further enhancements in the treatment of van der Waals interactions and, more broadly, density functional theory to enable accurate quantitative predictions for molecular liquids., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

As the most important solvent, water has been at the center of interest since the advent of computer simulations. While early molecular dynamics and Monte Carlo simulations had to make use of simple model potentials to describe the atomic interactions, accurate ab initio molecular dynamics simulations relying on the first-principles calculation of the energies and forces have opened the way to predictive simulations of aqueous systems. Still, these simulations are very demanding, which prevents the study of complex systems and their properties. Modern machine learning potentials (MLPs) have now reached a mature state, allowing us to overcome these limitations by combining the high accuracy of electronic structure calculations with the efficiency of empirical force fields. In this Perspective, we give a concise overview about the progress made in the simulation of water and aqueous systems employing MLPs, starting from early work on free molecules and clusters via bulk liquid water to electrolyte solutions and solid-liquid interfaces., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Among the numerous anomalies of water, the acceleration of dynamics under pressure is particularly puzzling. Whereas the diffusivity anomaly observed in experiments has been reproduced in several computer studies, the parallel viscosity anomaly has received less attention. Here we simulate viscosity and the self-diffusion coefficient of the TIP4P/2005 water model over a broad temperature and pressure range. We reproduce the experimental behavior and find additional anomalies at negative pressure. The anomalous effect of pressure on dynamic properties becomes more pronounced upon cooling, reaching two orders of magnitude for viscosity at 220 K. We analyze our results with a dynamic extension of a thermodynamic two-state model, an approach which has proved successful in describing experimental data. Water is regarded as a mixture of interconverting species with contrasting dynamic behaviors, one being strong (Arrhenius) and the other fragile (non-Arrhenius). The dynamic parameters of the two-state models are remarkably close between experiment and simulations. The larger pressure range accessible to simulations suggests a modification of the dynamic two-state model, which in turn also improves the agreement with experimental data. Furthermore, our simulations demonstrate the decoupling between viscosity η and self-diffusion coefficient D as a function of temperature T . The Stokes-Einstein relation, which predicts a constant Dη / T , is violated when T is lowered, in connection with the Widom line defined by an equal fraction of the two interconverting species. These results provide a unifying picture of thermodynamics and dynamics in water and call for experiments at negative pressure.

In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014)PNASA60027-842410.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.