Liquid water contains the building blocks of diverse ice phases

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks

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.

Descriptors of water aggregation

We rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (rOH) and HOH bond angle (θHOH), (ii) two-body: OO distance (rOO), OHO angle (θOHO), and HOOX dihedral angle (ϕHOOX), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θOOO), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (qm, m = 2, 3, 4, 5) and radius of gyration (Rg). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H2O)n, n = 3-25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that rOH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.

ZundEig: The Structure of the Proton in Liquid Water from Unsupervised Learning

The structure of the excess proton in liquid water has been the subject of lively debate on both experimental and theoretical fronts for the last century. Fluctuations of the proton are typically interpreted in terms of limiting states referred to as the Eigen and Zundel species. Here, we put these ideas under the microscope, taking advantage of recent advances in unsupervised learning that use local atomic descriptors to characterize environments of acidic water combined with advanced clustering techniques. Our agnostic approach leads to the observation of only one charged cluster and two neutral ones. We demonstrate that the charged cluster involving the excess proton is best seen as an ionic topological defect in water's hydrogen bond network, forming a single local minimum on the global free-energy landscape. This charged defect is a highly fluxional moiety, where the idealized Eigen and Zundel species are neither limiting configurations nor distinct thermodynamic states. Instead, the ionic defect enhances the presence of neutral water defects through strong interactions with the network. We dub the combination of the charged and neutral defect clusters as ZundEig, demonstrating that the fluctuations between these local environments provide a general framework for rationalizing more descriptive notions of the proton in the existing literature.

Neural Network Water Model Based on the MB-Pol Many-Body Potential

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

Detecting dynamic domains and local fluctuations in complex molecular systems via timelapse neighbors shuffling

It is known that the behavior of many complex systems is controlled by local dynamic rearrangements or fluctuations occurring within them. Complex molecular systems, composed of many molecules interacting with each other in a Brownian storm, make no exception. Despite the rise of machine learning and of sophisticated structural descriptors, detecting local fluctuations and collective transitions in complex dynamic ensembles remains often difficult. Here, we show a machine learning framework based on a descriptor which we name Local Environments and Neighbors Shuffling (LENS), that allows identifying dynamic domains and detecting local fluctuations in a variety of systems in an abstract and efficient way. By tracking how much the microscopic surrounding of each molecular unit changes over time in terms of neighbor individuals, LENS allows characterizing the global (macroscopic) dynamics of molecular systems in phase transition, phases-coexistence, as well as intrinsically characterized by local fluctuations (e.g., defects). Statistical analysis of the LENS time series data extracted from molecular dynamics trajectories of, for example, liquid-like, solid-like, or dynamically diverse complex molecular systems allows tracking in an efficient way the presence of different dynamic domains and of local fluctuations emerging within them. The approach is found robust, versatile, and applicable independently of the features of the system and simply provided that a trajectory containing information on the relative motion of the interacting units is available. We envisage that "such a LENS" will constitute a precious basis for exploring the dynamic complexity of a variety of systems and, given its abstract definition, not necessarily of molecular ones.

Are Neural Network Potentials Trained on Liquid States Transferable to Crystal Nucleation? A Test on Ice Nucleation in the mW Water Model

Neural network potentials (NNPs) are increasingly being used to study processes that happen on long time scales. A typical example is crystal nucleation, which rate is controlled by the occurrence of a rare fluctuation, i.e., the appearance of the critical nucleus. Because the properties of this nucleus are far from those of the bulk crystal, it is yet unclear whether NN potentials trained on equilibrium liquid states can accurately describe nucleation processes. So far, nucleation studies on NNPs have been limited to ab initio models whose nucleation properties are unknown, preventing an accurate comparison. Here we train a NN potential on the mW model of water─a classical three-body potential whose nucleation time scale is accessible in standard simulations. We show that a NNP trained only on a small number of liquid state points can reproduce with great accuracy the nucleation rates and free energy barriers of the original model, computed from both spontaneous and biased trajectories, strongly supporting the use of NNPs to study nucleation events.

Do Machine-Learning Atomic Descriptors and Order Parameters Tell the Same Story? The Case of Liquid Water

Machine-learning (ML) has become a key workhorse in molecular simulations. Building an ML model in this context involves encoding the information on chemical environments using local atomic descriptors. In this work, we focus on the Smooth Overlap of Atomic Positions (SOAP) and their application in studying the properties of liquid water both in the bulk and at the hydrophobic air-water interface. By using a statistical test aimed at assessing the relative information content of different distance measures defined on the same data space, we investigate if these descriptors provide the same information as some of the common order parameters that are used to characterize local water structure such as hydrogen bonding, density, or tetrahedrality to name a few. Our analysis suggests that the ML description and the standard order parameters of the local water structure are not equivalent. In particular, a combination of these order parameters probing local water environments can predict SOAP similarity only approximately, and vice versa, the environments that are similar according to SOAP are not necessarily similar according to the standard order parameters. We also elucidate the role of some of the metaparameters in the SOAP definition in encoding chemical information.

A neural network potential with self-trained atomic fingerprints: A test with the mW water potential

We present a neural network (NN) potential based on a new set of atomic fingerprints built upon two- and three-body contributions that probe distances and local orientational order, respectively. Compared with the existing NN potentials, the atomic fingerprints depend on a small set of tunable parameters that are trained together with the NN weights. In addition to simplifying the selection of the atomic fingerprints, this strategy can also considerably increase the overall accuracy of the network representation. To tackle the simultaneous training of the atomic fingerprint parameters and NN weights, we adopt an annealing protocol that progressively cycles the learning rate, significantly improving the accuracy of the NN potential. We test the performance of the network potential against the mW model of water, which is a classical three-body potential that well captures the anomalies of the liquid phase. Trained on just three state points, the NN potential is able to reproduce the mW model in a very wide range of densities and temperatures, from negative pressures to several GPa, capturing the transition from an open random tetrahedral network to a dense interpenetrated network. The NN potential also reproduces very well properties for which it was not explicitly trained, such as dynamical properties and the structure of the stable crystalline phases of mW.

Preparation of pure active water for auto-catalytic reactions performed in it

In catalyzed electrochemical reactions, a general strategy is to modify electrode materials to increase the efficiency of the reaction. From the viewpoint of environmental protection, electrochemical reactions should be performed in an inert green water phase. In this study, we report active pure liquid water (named PV), which was collected from the condensed vapor of heated gold (Au)-containing plasmon-activated water (PAW) with a distinct structure of electron-doping and reduced hydrogen bonding (HB). The resulting PV also exhibited distinct properties of the formation of stronger intermolecular HB with alcohols, and notable activities in catalytic electrochemical reactions, compared to bulk deionized water (DIW). Moreover, the measured diffusion coefficients of water increased by ca. 30% in PV solutions. Two typical electrochemical reactions significantly increased peak currents observed in oxidation-reduction cycles (ORCs) with roughening of the Au substrate and in a model of reversible oxidation-reduction reactions on a platinum (Pt) substrate. Also, PV enhanced hydrogen evolution reactions (HERs) on catalytic Pt and inert stainless steel substrates in PV-based solutions at different pH values, compared to DIW. Moreover, these activities of PV were more marked, even better than those of PAW, when PV was collected under a higher heating rate used to heat PAW. Active pure PV has emerged as a promising green solvent applicable to various chemical reactions with more efficiency.

Size and Quality of Quantum Mechanical Data Set for Training Neural Network Force Fields for Liquid Water

Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT) and thus is limited to small systems and a relatively short simulation time. In this scenario, Neural Network Force Fields (NNFFs) have an important role, since they provide a way to circumvent these caveats. In this work, we investigate NNFFs designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data set considered. We show that structural properties are less dependent on the size of the training data set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for the training process) can lead to a small sample with good precision.

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.

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.

Dimensionality reduction of local structure in glassy binary mixtures

We consider unsupervised learning methods for characterizing the disordered microscopic structure of supercooled liquids and glasses. Specifically, we perform dimensionality reduction of smooth structural descriptors that describe radial and bond-orientational correlations and assess the ability of the method to grasp the essential structural features of glassy binary mixtures. In several cases, a few collective variables account for the bulk of the structural fluctuations within the first coordination shell and also display a clear connection with the fluctuations of particle mobility. Fine-grained descriptors that characterize the radial dependence of bond-orientational order better capture the structural fluctuations relevant for particle mobility but are also more difficult to parameterize and to interpret. We also find that principal component analysis of bond-orientational order parameters provides identical results to neural network autoencoders while having the advantage of being easily interpretable. Overall, our results indicate that glassy binary mixtures have a broad spectrum of structural features. In the temperature range we investigate, some mixtures display well-defined locally favored structures, which are reflected in bimodal distributions of the structural variables identified by dimensionality reduction.

The biosensor based on electrochemical dynamics of fermentation in yeast Saccharomyces cerevisiae

The zymase activity of the yeast Saccharomyces cerevisiae is sensitive to environmental parameters and is therefore used as a microbiological sensor for water quality assessment, ecotoxicological characterization or environmental monitoring. Comparing to bacterial bioluminescence approach, this method has no toxicity, excludes usage of genetically modified microorganisms, and enables low-cost express analysis. This work focuses on measuring the yeast fermentation dynamics based on multichannel pressure sensing and electrochemical impedance spectroscopy (EIS). Measurement results are compared with each other in terms of accuracy, reproducibility and ease of use in field conditions. It has been shown that EIS provides more information about ionic dynamics of metabolic processes and requires less complex measurements. The conducted experiments demonstrated the sensitivity of this approach for assessing biophotonic phenomena, non-chemical water treatments and impact of environmental stressors.

Classifying soft self-assembled materials via unsupervised machine learning of defects

Unlike molecular crystals, soft self-assembled fibers, micelles, vesicles, etc., exhibit a certain order in the arrangement of their constitutive monomers but also high structural dynamicity and variability. Defects and disordered local domains that continuously form-and-repair in their structures impart to such materials unique adaptive and dynamical properties, which make them, e.g., capable to communicate with each other. However, objective criteria to compare such complex dynamical features and to classify soft supramolecular materials are non-trivial to attain. Here we show a data-driven workflow allowing us to achieve this goal. Building on unsupervised clustering of Smooth Overlap of Atomic Position (SOAP) data obtained from equilibrium molecular dynamics simulations, we can compare a variety of soft supramolecular assemblies via a robust SOAP metric. This provides us with a data-driven "defectometer" to classify different types of supramolecular materials based on the structural dynamics of the ordered/disordered local molecular environments that statistically emerge within them.

Toward High-level Machine Learning Potential for Water Based on Quantum Fragmentation and Neural Networks

Accurate and efficient simulation of liquids, such as water and salt solutions, using high-level wave function theories is still a formidable task for computational chemists owing to the high computational costs. In this study, we develop a deep machine learning potential based on fragment-based second-order Møller-Plesset perturbation theory (DP-MP2) for water through neural networks. We show that the DP-MP2 potential predicts the structural, dynamical, and thermodynamic properties of liquid water in better agreement with the experimental data than previous studies based on density functional theory (DFT). The nuclear quantum effects (NQEs) on the properties of liquid water are also examined, which are noticeable in affecting the structural and dynamical properties of liquid water under ambient conditions. This work provides a general framework for quantitative predictions of the properties of condensed-phase systems with the accuracy of high-level wave function theory while achieving significant computational savings compared to ab initio simulations.

Ephemeral ice-like local environments in classical rigid models of liquid water

Despite great efforts over the past 50 years, the simulation of water still presents significant challenges and open questions. At room temperature and pressure, the collective molecular interactions and dynamics of water molecules may form local structural arrangements that are non-trivial to classify. Here, we employ a data-driven approach built on Smooth Overlap of Atomic Position (SOAP) that allows us to compare and classify how widely used classical models represent liquid water. Macroscopically, the obtained results are rationalized based on water thermodynamic observables. Microscopically, we directly observe how transient ice-like ordered environments may dynamically/statistically form in liquid water, even above freezing temperature, by comparing the SOAP spectra for different ice structures with those of the simulated liquid systems. This confirms recent ab initio-based calculations but also reveals how the emergence of ephemeral local ice-like environments in liquid water at room conditions can be captured by classical water models.

Water clusters and density fluctuations in liquid water based on extended hierarchical clustering methods

The microscopic structures of liquid water at ambient temperatures remain a hot debate, which relates with structural and density fluctuations in the hydrogen bond network. Here, we use molecular dynamics simulations of liquid water to study the properties of three-dimensional cage-like water clusters, which we investigate using extended graph-based hierarchical clustering methods. The water clusters can cover over 95% of hydrogen bond network, among which some clusters maximally encompass thousands of molecules extending beyond 3.0 nm. The clusters imply fractal behaviors forming percolating networks and the morphologies of small and large clusters show different scaling rules. The local favored clusters and the preferred connections between adjacent clusters correspond to lower energy and conformational entropy depending on cluster topologies. Temperature can destroy large clusters into small ones. We show further that the interior of clusters favors high-density patches. The water molecules in the small clusters, inside which are the void regarded as hydrophobic objects, have a preference for being more tetrahedral. Our results highlight the properties and changes of water clusters as the fundamental building blocks of hydrogen bond networks. In addition, the water clusters can elucidate structural and density fluctuations on different length scales in liquid water.

High-Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning

The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free-energy landscape of water starting from encoding the water environment using local atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy under ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space, which we characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates. We demonstrate that a combination of both types of variables is needed in order to adequately capture the complexity of the fluctuations in the hydrogen bond network at different length scales both at room temperature and also close to the critical point of water. Our results provide a general framework for examining fluctuations in water under different conditions.

Predicting properties of periodic systems from cluster data: A case study of liquid water

The accuracy of the training data limits the accuracy of bulk properties from machine-learned potentials. For example, hybrid functionals or wave-function-based quantum chemical methods are readily available for cluster data but effectively out of scope for periodic structures. We show that local, atom-centered descriptors for machine-learned potentials enable the prediction of bulk properties from cluster model training data, agreeing reasonably well with predictions from bulk training data. We demonstrate such transferability by studying structural and dynamical properties of bulk liquid water with density functional theory and have found an excellent agreement with experimental and theoretical counterparts.

A complete description of thermodynamic stabilities of molecular crystals

Predicting stable polymorphs of molecular crystals remains one of the grand challenges of computational science. Current methods invoke approximations to electronic structure and statistical mechanics and thus fail to consistently reproduce the delicate balance of physical effects determining thermodynamic stability. We compute the rigorous ab initio Gibbs free energies for competing polymorphs of paradigmatic compounds, using machine learning to mitigate costs. The accurate description of electronic structure and full treatment of quantum statistical mechanics allow us to predict the experimentally observed phase behavior. This constitutes a key step toward the first-principles design of functional materials for applications from photovoltaics to pharmaceuticals.

Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expansion. The importance of these effects has been individually established, but rigorous free energy calculations for general molecular compounds, which simultaneously account for all effects, have hitherto not been computationally viable. Here we present an efficient “end to end” framework that seamlessly combines state-of-the art electronic structure calculations, machine-learning potentials, and advanced free energy methods to calculate ab initio Gibbs free energies for general organic molecular materials. The facile generation of machine-learning potentials for a diverse set of polymorphic compounds—benzene, glycine, and succinic acid—and predictions of thermodynamic stabilities in qualitative and quantitative agreement with experiments highlight that predictive thermodynamic studies of industrially relevant molecular materials are no longer a daunting task.

Static and dynamic water structures at interfaces: A case study with focus on Pt(111)

An accurate atomistic treatment of aqueous solid-liquid interfaces necessitates the explicit description of interfacial water ideally via ab initio molecular dynamics simulations. Many applications, however, still rely on static interfacial water models, e.g., for the computation of (electro)chemical reaction barriers and focus on a single, prototypical structure. In this work, we systematically study the relation between density functional theory-derived static and dynamic interfacial water models with specific focus on the water-Pt(111) interface. We first introduce a general construction protocol for static 2D water layers on any substrate, which we apply to the low index surfaces of Pt. Subsequently, we compare these with structures from a broad selection of reference works based on the Smooth Overlap of Atomic Positions descriptor. The analysis reveals some structural overlap between static and dynamic water ensembles; however, static structures tend to overemphasize the in-plane hydrogen bonding network. This feature is especially pronounced for the widely used low-temperature hexagonal ice-like structure. In addition, a complex relation between structure, work function, and adsorption energy is observed, which suggests that the concentration on single, static water models might introduce systematic biases that are likely reduced by averaging over consistently created structural ensembles, as introduced here.

Phase classification using neural networks: application to supercooled, polymorphic core-softened mixtures

Characterization of phases of soft matter systems is a challenge faced in many physical chemical problems. For polymorphic fluids it is an even greater challenge. Specifically, glass forming fluids, as water, can have, besides solid polymorphism, more than one liquid and glassy phases, and even a liquid-liquid critical point. In this sense, we apply a neural network algorithm to analyze the phase behavior of a mixture of core-softened fluids that interact through the continuous-shouldered well (CSW) potential, which have liquid polymorphism and liquid-liquid critical points, similar to water. We also apply the neural network to mixtures of CSW fluids and core-softened alcohols models. We combine and expand methods based on bond-orientational order parameters to study mixtures, applied to mixtures of hardcore fluids and to supercooled water, to include longer range coordination shells. With this, the trained neural network was able to properly predict the crystalline solid phases, the fluid phases and the amorphous phase for the pure CSW and CSW-alcohols mixtures with high efficiency. More than this, information about the phase populations, obtained from the network approach, can help verify if the phase transition is continuous or discontinuous, and also to interpret how the metastable amorphous region spreads along the stable high density fluid phase. These findings help to understand the behavior of supercooled polymorphic fluids and extend the comprehension of how amphiphilic solutes affect the phases behavior.

AENET-LAMMPS and AENET-TINKER: Interfaces for accurate and efficient molecular dynamics simulations with machine learning potentials

Machine-learning potentials (MLPs) trained on data from quantum-mechanics based first-principles methods can approach the accuracy of the reference method at a fraction of the computational cost. To facilitate efficient MLP-based molecular dynamics and Monte Carlo simulations, an integration of the MLPs with sampling software is needed. Here, we develop two interfaces that link the atomic energy network (ænet) MLP package with the popular sampling packages TINKER and LAMMPS. The three packages, ænet, TINKER, and LAMMPS, are free and open-source software that enable, in combination, accurate simulations of large and complex systems with low computational cost that scales linearly with the number of atoms. Scaling tests show that the parallel efficiency of the ænet-TINKER interface is nearly optimal but is limited to shared-memory systems. The ænet-LAMMPS interface achieves excellent parallel efficiency on highly parallel distributed-memory systems and benefits from the highly optimized neighbor list implemented in LAMMPS. We demonstrate the utility of the two MLP interfaces for two relevant example applications: the investigation of diffusion phenomena in liquid water and the equilibration of nanostructured amorphous battery materials.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

A Data-Driven Dimensionality Reduction Approach to Compare and Classify Lipid Force Fields

Molecular dynamics simulations of all-atom and coarse-grained lipid bilayer models are increasingly used to obtain useful insights for understanding the structural dynamics of these assemblies. In this context, one crucial point concerns the comparison of the performance and accuracy of classical force fields (FFs), which sometimes remains elusive. To date, the assessments performed on different classical potentials are mostly based on the comparison with experimental observables, which typically regard average properties. However, local differences of the structure and dynamics, which are poorly captured by average measurements, can make a difference, but these are nontrivial to catch. Here, we propose an agnostic way to compare different FFs at different resolutions (atomistic, united-atom, and coarse-grained), by means of a high-dimensional similarity metrics built on the framework of Smooth Overlap of Atomic Position (SOAP). We compare and classify a set of 13 FFs, modeling 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. Our SOAP kernel-based metrics allows us to compare, discriminate, and correlate different FFs at different model resolutions in an unbiased, high-dimensional way. This also captures differences between FFs in modeling nonaverage events (originating from local transitions), for example, the liquid-to-gel phase transition in dipalmitoylphosphatidylcholine (DPPC) bilayers, for which our metrics allows us to identify nucleation centers for the phase transition, highlighting some intrinsic resolution limitations in implicit versus explicit solvent FFs.

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.

Identification of synthesisable crystalline phases of water – a prototype for the challenges of computational materials design

We discuss the identification of experimentally realisable crystalline phases of water to outline and contextualise some of the diverse building blocks of a computational materials design process.