Local order parameters for use in driving homogeneous ice nucleation with all-atom models of water

Machine Learning Classification of Local Environments in Molecular Crystals

Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of molecular crystals using learning models that employ either flexibly learned or handcrafted molecular representations. In the first case, we follow our earlier work on graph learning in molecular crystals, deploying an atomistic graph convolutional network combined with molecule-wise aggregation to enable per-molecule environmental classification. For the second model, we develop a new set of descriptors based on symmetry functions combined with a point-vector representation of the molecules, encoding information about the positions and relative orientations of the molecule. We demonstrate very high classification accuracy for both approaches on urea and nicotinamide crystal polymorphs and practical applications to the analysis of dynamical trajectory data for nanocrystals and solid-solid interfaces. Both architectures are applicable to a wide range of molecules and diverse topologies, providing an essential step in the exploration of complex condensed matter phenomena.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

Simulations of disordered matter in 3D with the morphological autoregressive protocol (MAP) and convolutional neural networks

Disordered molecular systems, such as amorphous catalysts, organic thin films, electrolyte solutions, and water, are at the cutting edge of computational exploration at present. Traditional simulations of such systems at length scales relevant to experiments in practice require a compromise between model accuracy and quality of sampling. To address this problem, we have developed an approach based on generative machine learning called the Morphological Autoregressive Protocol (MAP), which provides computational access to mesoscale disordered molecular configurations at linear cost at generation for materials in which structural correlations decay sufficiently rapidly. The algorithm is implemented using an augmented PixelCNN deep learning architecture that, as we previously demonstrated, produces excellent results in 2 dimensions (2D) for mono-elemental molecular systems. Here, we extend our implementation to multi-elemental 3D and demonstrate performance using water as our test system in two scenarios: (1) liquid water and (2) samples conditioned on the presence of pre-selected motifs. We trained the model on small-scale samples of liquid water produced using path-integral molecular dynamics simulations, including nuclear quantum effects under ambient conditions. MAP-generated water configurations are shown to accurately reproduce the properties of the training set and to produce stable trajectories when used as initial conditions in quantum dynamics simulations. We expect our approach to perform equally well on other disordered molecular systems in which structural correlations decay sufficiently fast while offering unique advantages in situations when the disorder is quenched rather than equilibrated.

Preferential Ordering and Organization of Hydration Water Favor Nucleation of Ice by Ice-Nucleating Proteins over Antifreeze Proteins

Bacteria containing ice-nucleating proteins (INPs) evolved in nature to nucleate ice at the high sub-zero ambiance. The ability of the INPs to induce order in the hydration layer and their aggregation propensity appear to be key factors of their ice nucleation abilities. However, the mechanism of the process of ice nucleation by INPs is yet to be understood clearly. Here, we have performed all-atom molecular dynamics simulations and analyzed the structure and dynamics of the hydration layer around the proposed ice-nucleating surface of a model INP. Results are compared with the hydration of a topologically similar non-ice-binding protein (non-IBP) and another ice-growth inhibitory antifreeze protein (sbwAFP). We observed that the hydration structure around the ice-nucleating surface of INP is highly ordered and the dynamics of the hydration water are slower, compared to the non-IBP. Even the ordering of the hydration layer is more evident around the ice-binding surface of INP, compared to the antifreeze protein sbwAFP. Particularly with increasing repeat units of INP, we observe an increased population of ice-like water. Interestingly, the distances between the hydroxyl groups of the threonine ladder and its associated channel water of the ice-binding surface (IBS) of INP in the X and Y direction mimic the oxygen atom distances of the basal plane of hexagonal ice. However, the structural synergies between the hydroxyl group distances of the threonine ladder and its associated channel water of the IBS of sbwAFP and oxygen atom distances of the basal plane are less evident. This difference makes the IBS of the INP a better template for ice nucleation than AFP, although both of them bind to the ice surface efficiently.

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier (TΔΩv/min*) does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the TΔΩv/min* and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Molecular cluster analysis using local order parameters selected by machine learning

Accurately extracting local molecular structures is essential for understanding the mechanisms of phase and structural transitions. A promising method to characterize the local molecular structure is defining the value of the local order parameter (LOP) for each particle. This work develops the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO), a machine learning package that can propose an optimal (set of) LOP(s) quickly and automatically for a huge number of LOP species and various methods of selecting neighboring particles for the calculation. We applied this package to distinguish between the nematic and smectic phases of uniaxial liquid crystal molecules, and selected candidate LOPs that could be used to precisely observe the nematic-smectic phase transition. The LOP candidates were used to observe the nucleation and subsequent percolation transition, and the effect of the choice of LOP species and neighboring particles on the statistics of local molecular structures (clusters) was examined. The procedure revealed the time evolution of the number of clusters and the dependence of the percolation curve on the number of neighboring particles for each LOP species. The LOP species with the lowest dependence on the number of neighboring particles was the best-performing LOP species in the MALIO screening strategy. These results not only show that machine learning can powerfully screen a huge number of LOP species and suggest only a few promising candidates, but also indicate that MALIO can select the best LOP species.

Molecular Factors of Ice Growth Inhibition for Hyperactive and Globular Antifreeze Proteins: Insights from Molecular Dynamics Simulation

The molecular mechanism behind the ice growth inhibition by antifreeze proteins (AFPs) is yet to be understood completely. Also, what physical parameters differentiate between the AFP and non-AFP are largely unknown. Thus, to get an atomistic overview of the differential antifreeze activities of different classes of AFPs, we have studied ice growth from different ice surfaces in the presence of a moderately active globular type III AFP and a hyperactive spruce budworm (sbw) AFP. Results are compared with the observations of ice growth simulations in the presence of topologically similar non-AFPs using all-atom molecular dynamics simulations. Simulation data suggest that the ice surface coverage is a critical factor in ice growth inhibition. Due to the presence of an ice binding surface (IBS), AFPs form a high affinity complex with ice, accompanied by a transition of hydration water around the IBS from clathrate-like to ice-like. Several residues around the periphery of the IBS anchor the AFP to the curved ice surface mediated by multiple strong hydrogen bonds, stabilizing the complex immensely. In the high surface coverage regime, the slow unbinding kinetics dominates over the ice growth kinetics and thus facilitates the ice growth inhibition. Due to the non-availability of a proper IBS, non-AFPs form a low-affinity complex with the growing ice surface. As a result, the non-AFPs are continuously repelled by the surface. If the concentration of AFPs is low, then the effective surface coverage is reduced significantly. In this low surface coverage regime, AFPs can also behave like impurities and are engulfed by the growing ice crystal.

Crystal Prediction via Genetic Algorithms in a Model Chiral System

Chiral crystals and their constituent molecules play a prominent role in theories about the origin of biological homochirality and in drug discovery, design, and stability. Although the prediction and identification of stable chiral crystal structures is crucial for numerous technologies, including separation processes and polymorph selection and control, predictive ability is often complicated by a combination of many-body interactions and molecular complexity and handedness. In this work, we address these challenges by applying genetic algorithms to predict the ground-state crystal lattices formed by a chiral tetramer molecular model, which we have previously shown to exhibit complex fluid-phase behavior. Using this approach, we explore the relative stability and structures of the model's conglomerate and racemic crystals, and present a structural phase diagram for the stable Bravais crystal types in the zero-temperature limit.

Phase Transition between Crystalline Variants of Ordinary Ice

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

Effect of sodium chloride adsorption on the surface premelting of ice

We characterise the structural properties of the quasi-liquid layer (QLL) at two low-index ice surfaces in the presence of sodium chloride (Na⁺/Cl^-) ions by molecular dynamics simulations. We find that the presence of a high surface density of Na⁺/Cl^- pairs changes the surface melting behaviour from step-wise to gradual melting. The ions lead to an overall increase of the thickness and the disorder of the QLL, and to a low-temperature roughening transition of the air-ice interface. The local molecular structure of the QLL is similar to that of liquid water, and the differences between the basal and primary prismatic surface are attenuated by the presence of Na⁺/Cl^- pairs. These changes modify the crystal growth rates of different facets and the solvation environment at the surface of sea-water ice with a potential impact on light scattering and environmental chemical reactions.

Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations

Water freezing is the most common liquid-to-crystal phase transition on Earth, however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih, Ic and a stacking mixture of ice Ih/Ic; reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner which contributes to benchmarking the freezing behaviour of two popular water models.

The role of the diffusion in the predictions of the classical nucleation theory for quasi-real systems differ in dipole moment value

In this paper, we examine the crystallization tendency for two quasi-real systems, which differ exclusively in the dipole moment's value. The main advantage of the studied system is the fact that despite that their structures are entirely identical, they exhibit different physical properties. Hence, the results obtained for one of the proposed model systems cannot be scaled to reproduce the results for another corresponding system, as it can be done for simple model systems, where structural differences are modeled by the different parameters of the intermolecular interactions. Our results show that both examined systems exhibit similar stability behavior below the melting temperature. This finding is contrary to the predictions of the classical nucleation theory, which suggests a significantly higher crystallization tendency for a more polar system. Our studies indicate that the noted discrepancies are caused by the kinetic aspect of the classical nucleation theory, which overestimates the role of diffusion in the nucleation process.

Investigating the quasi-liquid layer on ice surfaces: a comparison of order parameters

Ice surfaces are characterized by pre-melted quasi-liquid layers (QLLs), which mediate both crystal growth processes and interactions with external agents. Understanding QLLs at the molecular level is necessary to unravel the mechanisms of ice crystal formation. Computational studies of the QLLs heavily rely on the accuracy of the methods employed for identifying the local molecular environment and arrangements, discriminating between solid-like and liquid-like water molecules. Here we compare the results obtained using different order parameters to characterize the QLLs on hexagonal ice (Ih) and cubic ice (Ic) model surfaces investigated with molecular dynamics (MD) simulations in a range of temperatures. For the classification task, in addition to the traditional Steinhardt order parameters in different flavours, we select an entropy fingerprint and a deep learning neural network approach (DeepIce), which are conceptually different methodologies. We find that all the analysis methods give qualitatively similar trends for the behaviours of the QLLs on ice surfaces with temperature, with some subtle differences in the classification sensitivity limited to the solid-liquid interface. The thickness of QLLs on the ice surface increases gradually as the temperature increases. The trends of the QLL size and of the values of the order parameters as a function of temperature for the different facets may be linked to surface growth rates which, in turn, affect crystal morphologies at lower vapour pressure. The choice of the order parameter can be therefore informed by computational convenience except in cases where a very accurate determination of the liquid-solid interface is important.

Simulation of the carbon dioxide hydrate-water interfacial energy

HYPOTHESIS

Carbon dioxide hydrates are ice-like nonstoichiometric inclusion solid compounds with importance to global climate change, and gas transportation and storage. The thermodynamic and kinetic mechanisms that control carbon dioxide nucleation critically depend on hydrate-water interfacial free energy. Only two independent indirect experiments are available in the literature. Interfacial energies show large uncertainties due to the conditions at which experiments are performed. Under these circumstances, we hypothesize that accurate molecular models for water and carbon dioxide combined with computer simulation tools can offer an alternative but complementary way to estimate interfacial energies at coexistence conditions from a molecular perspective.

CALCULATIONS

We have evaluated the interfacial free energy of carbon dioxide hydrates at coexistence conditions (three-phase equilibrium or dissociation line) implementing advanced computational methodologies, including the novel Mold Integration methodology. Our calculations are based on the definition of the interfacial free energy, standard statistical thermodynamic techniques, and the use of the most reliable and used molecular models for water (TIP4P/Ice) and carbon dioxide (TraPPE) available in the literature.

FINDINGS

We find that simulations provide an interfacial energy value, at coexistence conditions, consistent with the experiments from its thermodynamic definition. Our calculations are reliable since are based on the use of two molecular models that accurately predict: (1) The ice-water interfacial free energy; and (2) the dissociation line of carbon dioxide hydrates. Computer simulation predictions provide alternative but reliable estimates of the carbon dioxide interfacial energy. Our pioneering work demonstrates that is possible to predict interfacial energies of hydrates from a truly computational molecular perspective and opens a new door to the determination of free energies of hydrates.

Self-Diffusion of Individual Adsorbed Water Molecules at Rutile (110) and Anatase (101) TiO2 Interfaces from Molecular Dynamics

The distribution of individual water molecules’ self-diffusivities in adsorbed layers at TiO2 surfaces anatase (101) and rutile (110) have been determined at 300 K for inner and outer adsorbed layers, via classical molecular-dynamics methods. The layered-water structure has been identified and classified in layers making use of local order parameters, which proved to be an equally valid method of “self-ordering” molecules in layers. Significant distinctness was observed between anatase and rutile in disturbing these molecular distributions, more specifically in the adsorbed outer layer. Anatase (101) presented significantly higher values of self-diffusivity, presumably due to its “corrugated” structure that allows more hydrogen bonding interaction with adsorbed molecules beyond the first hydration layer. On the contrary, rutile (110) has adsorbed water molecules more securely “trapped” in the region between Ob atoms, resulting in less mobile adsorbed layers.

Screening toward the Development of Fingerprints of Atomic Environments Using Bond-Orientational Order Parameters

A combination of atomic numbers and bond-orientational order parameters is considered a candidate for a simple representation that involves information on both the atomic species and their positional relation. The 504 candidates are applied as the fingerprint of the molecules stored in QM9, a data set of computed geometric, energetic, electronic, and thermodynamic properties for 133 885 stable small organic molecules made up of carbon, hydrogen, oxygen, nitrogen, and fluorine atoms. To screen the fingerprints, a regression analysis of the atomic charges given by Open Babel was performed by supervised machine learning. The regression results indicate that the 60 fingerprints successfully estimate Open Babel charges. The results of the dipole moments, an example of a property expressed by charge and position, also had a high accuracy in comparison with the values computed from Open Babel charges. Therefore, the screened 60 fingerprints have the potential to precisely describe the chemical and structural information on the atomic environment of molecules.

Impact of surface nanostructure and wettability on interfacial ice physics

Ice accumulation on solid surfaces is a severe problem for safety and functioning of a large variety of engineering systems, and its control is an enormous challenge that influences the safety and reliability of many technological applications. The use of molecular dynamics (MD) simulations is popular, but as ice nucleation is a rare event when compared to simulation timescales, the simulations need to be accelerated to force ice to form on a surface, which affects the accuracy and/or applicability of the results obtained. Here, we present an alternative seeded MD simulation approach, which reduces the computational cost while still ensuring accurate simulations of ice growth on surfaces. In addition, this approach enables, for the first time, brute-force all-atom water simulations of ice growth on surfaces unfavorable for nucleation within MD timescales. Using this approach, we investigate the effect of surface wettability and structure on ice growth in the crucial surface-ice interfacial region. Our main findings are that the surface structure can induce a flat or buckled overlayer to form within the liquid, and this transition is mediated by surface wettability. The first overlayer and the bulk ice compete to structure the intermediate water layers between them, the relative influence of which is traced using density heat maps and diffusivity measurements. This work provides new understanding on the role of the surface properties on the structure and dynamics of ice growth, and we also present a useful framework for future research on surface icing simulations.

Pressure Dependence of the Crystallization Rate for the S-Enantiomer and a Racemic Mixture of Ibuprofen

This paper examines the pressure effect on the crystallization rate of the pharmaceutically active enantiomerically pure S-enantiomer and the racemic mixture of the well-known drug ibuprofen. Performed experimental studies revealed that at ambient pressure S-ibuprofen crystallizes faster than the racemic mixture. When the pressure increases, the crystallization rate slows down for both systems, but interestingly it is more apparent in the case of the S-enantiomer. It is found that this experimentally observed trend can be understood based on the predictions of the classical nucleation theory. We suggest that the solid-liquid interfacial free energy is the main reason for the observed variations in S- and RS-ibuprofen's stability behaviors. Employing a special method of computational studies, i.e., the capillary fluctuation method, we show that the increase in pressure affects the solid-liquid interfacial free energy for S- and RS-ibuprofen in an entirely different way. Importantly, the detected differences correspond to the experimentally observed variations in the overall crystallization rates.

Mining of Effective Local Order Parameters to Classify Ice Polymorphs

Order parameters make it possible to quantify the degree of structural ordering in a material and thus to apply as the reaction coordinates during the free-energy analysis of phase or structure transitions. Furthermore, order parameters are useful in determining the local structures of molecular groups during transition stages. However, identifying or developing local order parameters (LOPs) that are sensitive for specific materials and phases is a non-trivial task. In this study, the ability of LOPs to classify the solid and liquid structures of water at coexistence or triple points is investigated with the aid of supervised machine learning. The classification accuracy of a total of 179,738,433 combinations of 493 LOPs is automatically and systematically compared for water structures at the ice Ih-Ic-liquid coexistence point and the ice III-V-liquid and ice V-VI-liquid triple points. The optimal sets of two LOPs are found for each point, and sets of three LOPs are suggested for better accuracy.

Searching for local order parameters to classify water structures at triple points

The diversity of ice polymorphs is of interest in condensed-matter physics, engineering, astronomy, and biosphere and climate studies. In particular, their triple points are critical to elucidate the formation of each phase and transitions among phases. However, an approach to distinguish their molecular structures is lacking. When precise molecular geometries are given, order parameters are often computed to quantify the degree of structural ordering and to classify the structures. Many order parameters have been developed for specific or multiple purposes, but their capabilities have not been exhaustively investigated for distinguishing ice polymorphs. Here, 493 order parameters and their combinations are considered for two triple points involving the ice polymorphs ice III-V-liquid and ice V-VI-liquid. Supervised machine learning helps automatic and systematic searching of the parameters. For each triple point, the best set of two order parameters was found that distinguishes three structures with high accuracy. A set of three order parameters is also suggested for better accuracy.

Liquid Water and Interfacial, Cubic, and Hexagonal Ice Classification through Eclipsed and Staggered Conformation Template Matching

We propose a novel method based on template matching for the recognition of liquid water, cubic ice (ice I_c), hexagonal ice (ice I_h), clathrate hydrates, and different interfacial structures in atomistic and coarse-grained simulations of water and ice. The two template matrices represent staggered and eclipsed conformations, which are the building blocks of hexagonal and cubic ice and clathrate crystals. The algorithm is rotationally invariant and highly robust against imperfections in the ice structure, and its sensitivity for recognizing ice-like structures can be tuned for different applications. Unlike most other algorithms, it can discriminate between cubic, hexagonal, clathrate, mixed, and other interfacial ice types and is therefore well suited to study complex systems and heterogeneous ice nucleation.

On the Gibbs-Thomson equation for the crystallization of confined fluids

The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e., kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could, for example, be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an atomic force microscope and a substrate.

Role of Nanoscale Interfacial Proximity in Contact Freezing in Water

Contact freezing is a mode of atmospheric ice nucleation in which a collision between a dry ice nucleating particle (INP) and a water droplet results in considerably faster heterogeneous nucleation. The molecular mechanism of such an enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface. By simulating the heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids, we demonstrate that such nanoscale proximity is sufficient for inducing rate increases commensurate with those observed in contact freezing experiments, but only if the free interface has a tendency to enhance homogeneous nucleation. Water is suspected of possessing this latter property, known as surface freezing propensity. Our findings therefore establish a connection between the surface freezing propensity and kinetic enhancement during contact nucleation. We also observe that faster nucleation proceeds through a mechanism markedly distinct from classical heterogeneous nucleation, involving the formation of hourglass-shaped crystalline nuclei that conceive at either interface and that have a lower free energy of formation due to the nanoscale proximity of the interfaces and the modulation of the free interfacial structure by the INP. In addition to providing valuable insights into the physics of contact nucleation, our findings can assist in improving the accuracy of heterogeneous nucleation rate measurements in experiments and in advancing our understanding of ice nucleation on nonuniform surfaces such as organic, polymeric, and biological materials.

Quantum-mechanical exploration of the phase diagram of water

The set of known stable phases of water may not be complete, and some of the phase boundaries between them are fuzzy. Starting from liquid water and a comprehensive set of 50 ice structures, we compute the phase diagram at three hybrid density-functional-theory levels of approximation, accounting for thermal and nuclear fluctuations as well as proton disorder. Such calculations are only made tractable because we combine machine-learning methods and advanced free-energy techniques. The computed phase diagram is in qualitative agreement with experiment, particularly at pressures ≲ 8000 bar, and the discrepancy in chemical potential is comparable with the subtle uncertainties introduced by proton disorder and the spread between the three hybrid functionals. None of the hypothetical ice phases considered is thermodynamically stable in our calculations, suggesting the completeness of the experimental water phase diagram in the region considered. Our work demonstrates the feasibility of predicting the phase diagram of a polymorphic system from first principles and provides a thermodynamic way of testing the limits of quantum-mechanical calculations.

Numerical calculation of free-energy barriers for entangled polymer nucleation

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.

Deciphering the Role of the Non-ice-binding Surface in the Antifreeze Activity of Hyperactive Antifreeze Proteins

Antifreeze proteins (AFPs) show thermal hysteresis through specific interaction with the ice crystal. Hyperactive AFPs interact with the ice surface through a threonine-rich motif present at their ice-binding surface (IBS). Ordering of water around the IBS was extensively investigated. However, the role of non-IBS in ice growth inhibition is yet to be understood completely. The present study explores the nature of hydration and its length-scale evaluation around the non-IBS for hyperactive AFPs. We observed that the hydration layer of non-IBS is liquid-like, even in highly supercooled conditions, and the nature of hydration is drastically different from the hydration pattern of non-AFP surfaces. In similar conditions, the hydration layer around the IBS is ice-like ordered. Non-IBS of the hyperactive AFP exposes toward the bulk and is able to maintain the liquid-like character of its hydration water up to 15 Å. We also find that the amino acid compositions and their spatial distribution on the non-IBS are markedly different from those of the IBS and non-AFP surfaces. These results elucidate the combined role of IBS and non-IBS in ice-growth inhibition. While IBS is required to adsorb on ice efficiently, the exposed non-IBS may prevent ice nucleation/growth on top of the bound AFPs.

Mechanical Unfolding of Spectrin Repeats Induces Water-Molecule Ordering

Mechanical processes are involved at many stages of the development of living cells, and often external forces applied to a biomolecule result in its unfolding. Although our knowledge of the unfolding mechanisms and the magnitude of the forces involved has evolved, the role that water molecules play in the mechanical unfolding of biomolecules has not yet been fully elucidated. To this end, we investigated with steered molecular dynamics simulations the mechanical unfolding of dystrophin's spectrin repeat 1 and related the changes in the protein's structure to the ordering of the surrounding water molecules. Our results indicate that upon mechanically induced unfolding of the protein, the solvent molecules become more ordered and increase their average number of hydrogen bonds. In addition, the unfolded structures originating from mechanical pulling expose an increasing amount of the hydrophobic residues to the solvent molecules, and the uncoiled regions adapt a convex surface with a small radius of curvature. As a result, the solvent molecules reorganize around the protein's small protrusions in structurally ordered waters that are characteristic of the so-called "small-molecule regime," which allows water to maintain a high hydrogen bond count at the expense of an increased structural order. We also determined that the response of water to structural changes in the protein is localized to the specific regions of the protein that undergo unfolding. These results indicate that water plays an important role in the mechanically induced unfolding of biomolecules. Our findings may prove relevant to the ever-growing interest in understanding macromolecular crowding in living cells and their effects on protein folding, and suggest that the hydration layer may be exploited as a means for short-range allosteric communication.

Hydrogen polarity of interfacial water regulates heterogeneous ice nucleation

Using all-atomic molecular dynamics (MD) simulations, we show that the structure of interfacial water (IW) induced by substrates characterizes the ability of a substrate to nucleate ice. We probe the shape and structure of ice nuclei and the corresponding supercooling temperatures to measure the ability of IW with various hydrogen polarities for ice nucleation, and find that the hydrogen polarization of IW even with the ice-like oxygen lattice increases the contact angle of the ice nucleus on IW, thus lifting the free energy barrier of heterogeneous ice nucleation. The results show that not only the oxygen lattice order but the hydrogen disorder of IW on substrates are required to effectively facilitate the freezing of top water.

Machine learning-aided analysis for complex local structure of liquid crystal polymers

Elucidation of mesoscopic structures of molecular systems is of considerable scientific and technological interest for the development and optimization of advanced materials. Molecular dynamics simulations are a promising means of revealing macroscopic physical properties of materials from a microscopic viewpoint, but analysis of the resulting complex mesoscopic structures from microscopic information is a non-trivial and challenging task. In this study, a Machine Learning-aided Local Structure Analyzer (ML-LSA) is developed to classify the complex local mesoscopic structures of molecules that have not only simple atomistic group units but also rigid anisotropic functional groups such as mesogens. The proposed ML-LSA is applied to classifying the local structures of liquid crystal polymer (LCP) systems, which are of considerable scientific and technological interest because of their potential for sensors and soft actuators. A machine learning (ML) model is constructed from small, and thus computationally less costly, monodomain LCP trajectories. The ML model can distinguish nematic- and smectic-like monodomain structures with high accuracy. The ML-LSA is applied to large, complex quenched LCP structures, and the complex local structures are successfully classified as either nematic- or smectic-like. Furthermore, the results of the ML-LSA suggest the best order parameter for distinguishing the two mesogenic structures. Our ML model enables automatic and systematic analysis of the mesogenic structures without prior knowledge, and thus can overcome the difficulty of manually determining the specific order parameter required for the classification of complex structures.

A generalized deep learning approach for local structure identification in molecular simulations

Identifying local structure in molecular simulations is of utmost importance. The most common existing approach to identify local structure is to calculate some geometrical quantity referred to as an order parameter. In simple cases order parameters are physically intuitive and trivial to develop (e.g., ion-pair distance), however in most cases, order parameter development becomes a much more difficult endeavor (e.g., crystal structure identification). Using ideas from computer vision, we adapt a specific type of neural network called a PointNet to identify local structural environments in molecular simulations. A primary challenge in applying machine learning techniques to simulation is selecting the appropriate input features. This challenge is system-specific and requires significant human input and intuition. In contrast, our approach is a generic framework that requires no system-specific feature engineering and operates on the raw output of the simulations, i.e., atomic positions. We demonstrate the method on crystal structure identification in Lennard-Jones (four different phases), water (eight different phases), and mesophase (six different phases) systems. The method achieves as high as 99.5% accuracy in crystal structure identification. The method is applicable to heterogeneous nucleation and it can even predict the crystal phases of atoms near external interfaces. We demonstrate the versatility of our approach by using our method to identify surface hydrophobicity based solely upon positions and orientations of surrounding water molecules. Our results suggest the approach will be broadly applicable to many types of local structure in simulations.

Temperature Dependence of Homogeneous Nucleation in Ice

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Heating- and pressure-induced transformations in amorphous and hexagonal ice: A computer simulation study using the TIP4P/2005 model

We characterize the phase behavior of glassy water by performing extensive out-of-equilibrium molecular dynamics simulations using the TIP4P/2005 water model. Specifically, we study (i) the pressure-induced transformations between low-density (LDA) and high-density amorphous ice (HDA), (ii) the pressure-induced amorphization (PIA) of hexagonal ice (I_h), (iii) the heating-induced LDA-to-HDA transformation at high pressures, (iv) the heating-induced HDA-to-LDA transformation at low and negative pressures, (v) the glass transition temperatures of LDA and HDA as a function of pressure, and (vi) the limit of stability of LDA upon isobaric heating and isothermal decompression (at negative pressures). These transformations are studied systematically, over a wide range of temperatures and pressures, allowing us to construct a P-T phase diagram for glassy TIP4P/2005 water. Our results are in qualitative agreement with experimental observations and with the P-T phase diagram obtained for glassy ST2 water that exhibits a liquid-liquid phase transition and critical point. We also discuss the mechanism for PIA of ice I_h and show that this is a two-step process where first, the hydrogen-bond network (HBN) is distorted and then the HBN abruptly collapses. Remarkably, the collapse of the HB in ice I_h occurs when the average molecular orientations order, a measure of the tetrahedrality of the HBN, is of the same order as in LDA, suggesting a common mechanism for the LDA-to-HDA and I_h-to-HDA transformations.

Hybrid Monte Carlo with LAMMPS

We describe a strategy for performing canonical and isothermal-isobaric ensemble hybrid Monte Carlo (HMC) simulations with the widely-used Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics (MD) software package. The overall workflow for the HMC simulations is handled using an external Python driver script, which invokes LAMMPS’ library interface to perform numerically intensive tasks such as MD integration. We document several rigorous consistency checks that have been used to validate our HMC implementation. We also demonstrate that our approach can be readily extended to implement biased HMC sampling schemes for computing free energies. Codes and input files from the documented examples are available on the web.

Operation of Kelvin Effect in the Activities of an Antifreeze Protein: A Molecular Dynamics Simulation Study

Ice growth and melting inhibition activities of antifreeze proteins (AFPs) are better explained by the adsorption-inhibition mechanism. Inhibition occurs as a result of the Kelvin effect induced by adsorbed protein molecules onto the surface of seed ice crystal. However, the Kelvin effect has not been explored by the state-of-the-art experimental techniques. In this work, atomistic molecular dynamics simulations have been carried out with Tenebrio molitor antifreeze protein ( TmAFP) placed at ice-water interface to probe the Kelvin effect in the mechanism of AFPs. Simulations show that, below equilibrium melting temperature, ice growth is inhibited through the convex ice-water interface formation toward the water phase and, above equilibrium melting temperature, ice melting is inhibited through the concave ice-water interface formation inward to ice phase. Simulations further reveal that the radius of curvature of the interface formed to stop the ice growth increases with decrease in the degree of supercooling. Our results are in qualitative agreement with the theoretical prediction of the Kelvin effect and thus reveal its operation in the activities of AFPs.

Heterogeneous Ice Nucleation: Interplay of Surface Properties and Their Impact on Water Orientations

Ice is ubiquitous in nature, and heterogeneous ice nucleation is the most common pathway of ice formation. How surface properties affect the propensity to observe ice nucleation on that surface remains an open question. We present results of molecular dynamics studies of heterogeneous ice nucleation on model surfaces. The models surfaces considered emulate the chemistry of kaolinite, an abundant component of mineral dust. We investigate the interplay of surface lattice and hydrogen bonding properties in affecting ice nucleation. We find that lattice matching and hydrogen bonding are necessary but not sufficient conditions for observing ice nucleation at these surfaces. We correlate this behavior to the orientations sampled by the metastable supercooled water in contact with the surfaces. We find that ice is observed in cases where water molecules not only sample orientations favorable for bilayer formation but also do not sample unfavorable orientations. This distribution depends on both surface-water and water-water interactions and can change with subtle modifications to the surface properties. Our results provide insights into the diverse behavior of ice nucleation observed at different surfaces and highlight the complexity in elucidating heterogeneous ice nucleation.