A first-principles machine-learning force field for heterogeneous ice nucleation on microcline feldspar.

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water under deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high-fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. Our training set includes configurations of bulk supercooled water, hexagonal and cubic ice, microcline, and fully-hydroxylated feldspar surfaces exposed to a vacuum, liquid water, and ice. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to a vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in a vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 10 Å from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30 000 atoms. Future work will be directed towards the calculation of nucleation free-energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces in ice nucleation.

Critical behavior in a chiral molecular model.

Understanding the condensed-phase behavior of chiral molecules is important in biology as well as in a range of technological applications, such as the manufacture of pharmaceuticals. Here, we use molecular dynamics simulations to study a chiral four-site molecular model that exhibits a second-order symmetry-breaking phase transition from a supercritical racemic liquid into subcritical D-rich and L-rich liquids. We determine the infinite-size critical temperature using the fourth-order Binder cumulant, and we show that the finite-size scaling behavior of the order parameter is compatible with the 3D Ising universality class. We also study the spontaneous D-rich to L-rich transition at a slightly subcritical temperature of T = 0.985Tc, and our findings indicate that the free energy barrier for this transformation increases with system size as N2/3, where N is the number of molecules, consistent with a surface-dominated phenomenon. The critical behavior observed herein suggests a mechanism for chirality selection in which a liquid of chiral molecules spontaneously forms a phase enriched in one of the two enantiomers as the temperature is lowered below the critical point. Furthermore, the increasing free energy barrier with system size indicates that fluctuations between the L-rich and D-rich phases are suppressed as the size of the system increases, trapping it in one of the two enantiomerically enriched phases. Such a process could provide the basis for an alternative explanation for the origin of biological homochirality. We also conjecture the possibility of observing nucleation at subcritical temperatures under the action of a suitable chiral external field.

Melting curves of ice polymorphs in the vicinity of the liquid-liquid critical point.

The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164-168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid-liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid-liquid critical point lies between the melting curves of ice III and ice V. We explore this conjecture using molecular dynamics simulations with a machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid-liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.

Comparison of On-the-Fly Probability Enhanced Sampling and Parallel Tempering Combined with Metadynamics for Atomistic Simulations of RNA Tetraloop Folding.

Atomistic simulations with reliable models are extremely useful in providing exquisitely detailed pictures of biomolecular phenomena that are not always accessible to experiments. One such biomolecular phenomenon is RNA folding, which often requires exhaustive simulations with combined advanced sampling techniques. In this work, we employed the multithermal-multiumbrella on-the-fly probability enhanced sampling (MM-OPES) technique and compared it against combined parallel tempering and metadynamics simulations. We found that MM-OPES simulations were successful in reproducing the free energy surfaces from combined parallel tempering and metadynamics simulations. Importantly, we also investigated a wide range of temperature sets (minimum and maximum temperatures) for MM-OPES simulations in order to identify some guidelines for deciding the temperature limits for an accurate and efficient exploration of the free energy landscapes. We found that most temperature sets yielded almost the same accuracy in reproducing the free energy surface at the ambient conditions as long as (i) the maximum temperature is reasonably high, (ii) the temperature at which we run the simulation is reasonably high (in our simulations, running temperature is defined as [minimum temperature + maximum temperature]/2), and (iii) the effective sample size at the temperature of interest is statistically reasonable. In terms of the computational cost, all MM-OPES simulations were nearly 4 times less costly than the combined parallel tempering and metadynamics simulations. We concluded that the demanding combined parallel tempering and metadynamics simulations can safely be replaced with approximately 4 times less costly MM-OPES simulations (with carefully selected temperature limits) to obtain the same information.

Homogeneous ice nucleation in an ab initio machine-learning model of water.

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

Phase diagram of the TIP4P/Ice water model by enhanced sampling simulations.

We studied the phase diagram for the TIP4P/Ice water model using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice-liquid free energy differences from biased coexistence simulations that reversibly sample the melting and growth of layers of ice. We computed a total of 19 melting points for five different ice polymorphs, which are in excellent agreement with the melting lines obtained from the integration of the Clausius-Clapeyron equation. For proton-ordered and fully proton-disordered ice phases, the results are in very good agreement with previous calculations based on thermodynamic integration. For the partially proton-disordered ice III, we find a large increase in stability that is in line with previous observations using direct coexistence simulations for the TIP4P/2005 model. This issue highlights the robustness of the approach employed here for ice polymorphs with diverse degrees of proton disorder. Our approach is general and can be applied to the calculation of other complex phase diagrams.

Liquid-Liquid Transition in Water from First Principles.

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States.

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

Phase Equilibrium of Water with Hexagonal and Cubic Ice Using the SCAN Functional.

Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye toward studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ices Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic.

Signatures of a liquid-liquid transition in an ab initio deep neural network model for water.

The possible existence of a metastable liquid-liquid transition (LLT) and a corresponding liquid-liquid critical point (LLCP) in supercooled liquid water remains a topic of much debate. An LLT has been rigorously proved in three empirically parametrized molecular models of water, and evidence consistent with an LLT has been reported for several other such models. In contrast, experimental proof of this phenomenon has been elusive due to rapid ice nucleation under deeply supercooled conditions. In this work, we combined density functional theory (DFT), machine learning, and molecular simulations to shed additional light on the possible existence of an LLT in water. We trained a deep neural network (DNN) model to represent the ab initio potential energy surface of water from DFT calculations using the Strongly Constrained and Appropriately Normed (SCAN) functional. We then used advanced sampling simulations in the multithermal-multibaric ensemble to efficiently explore the thermophysical properties of the DNN model. The simulation results are consistent with the existence of an LLCP, although they do not constitute a rigorous proof thereof. We fit the simulation data to a two-state equation of state to provide an estimate of the LLCP's location. These combined results-obtained from a purely first-principles approach with no empirical parameters-are strongly suggestive of the existence of an LLT, bolstering the hypothesis that water can separate into two distinct liquid forms.

Erratum: Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations [Phys. Rev. Lett. 119, 015701 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.015701.

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations.

We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. We analyze the effect of the system size on the ice Ih-liquid free energy differences, and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih.

Ab initio phase diagram and nucleation of gallium.

Elemental gallium possesses several intriguing properties, such as a low melting point, a density anomaly and an electronic structure in which covalent and metallic features coexist. In order to simulate this complex system, we construct an ab initio quality interaction potential by training a neural network on a set of density functional theory calculations performed on configurations generated in multithermal-multibaric simulations. Here we show that the relative equilibrium between liquid gallium, α-Ga, ß-Ga, and Ga-II is well described. The resulting phase diagram is in agreement with the experimental findings. The local structure of liquid gallium and its nucleation into α-Ga and ß-Ga are studied. We find that the formation of metastable ß-Ga is kinetically favored over the thermodinamically stable α-Ga. Finally, we provide insight into the experimental observations of extreme undercooling of liquid Ga.

Molecular Dynamics Simulations of Crystal Nucleation from Solution at Constant Chemical Potential.

A widespread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. The nucleation process, polymorph selection, and crystal habits depend crucially on this thermodynamic parameter. When performing molecular dynamics simulations with a fixed number of molecules in the canonical ensemble, crystal growth is accompanied by a decrease in the solution concentration. This modification of the thermodynamic condition leads to significant artifacts. Inspired by the recent development of the constant chemical potential molecular dynamics simulation method by Perego et al. [ J. Chem. Phys. 2015 , 142 , 144113 ] , we develop a spherical variant of it to study nucleation from solution. Our method allows determining the crystal nucleus size and nucleation rates at constant supersaturation. As an example, we study the homogeneous nucleation of sodium chloride from its supersaturated aqueous solution.

Calculation of phase diagrams in the multithermal-multibaric ensemble.

From the Ising model and the Lennard-Jones fluid to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. Despite the effort of the simulation community, the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here, we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end, we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way, in a single molecular dynamics simulation, we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum.

A local fingerprint for hydrophobicity and hydrophilicity: From methane to peptides.

An important characteristic that determines the behavior of a solute in water is whether it is hydrophobic or hydrophilic. The traditional classification is based on chemical experience and heuristics. However, this does not reveal how the local environment modulates this important property. We present a local fingerprint for hydrophobicity and hydrophilicity inspired by the two body contribution to the entropy. This fingerprint is an inexpensive, quantitative, and physically meaningful way of studying hydrophilicity and hydrophobicity that only requires as input the water-solute radial distribution functions. We apply our fingerprint to octanol, benzene, and 20 proteinogenic amino acids. Our measure of hydrophilicity is coherent with chemical experience, and moreover, it also shows how the character of an atom can change as its environment is changed. Finally, we use the fingerprint as a collective variable in a funnel metadynamics simulation of a host-guest system. The fingerprint serves as a desolvation collective variable that enhances transitions between the bound and unbound states.

Multithermal-Multibaric Molecular Simulations from a Variational Principle.

We present a method for performing multithermal-multibaric molecular dynamics simulations that sample entire regions of the temperature-pressure (TP) phase diagram. The method uses a variational principle [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.090601] in order to construct a bias that leads to a uniform sampling in energy and volume. The intervals of temperature and pressure are taken as inputs and the relevant energy and volume regions are determined on the fly. In this way the method guarantees adequate statistics for the chosen TP region. We show that our multithermal-multibaric simulations can be used to calculate all static physical quantities for all temperatures and pressures in the targeted region of the TP plane. We illustrate our approach by studying the density anomaly of TIP4P/ice water.