How van der Waals interactions determine the unique properties of water

Evidence of ferroelectric features in low-density supercooled water from ab initio deep neural-network simulations

Over the last decade, an increasing body of evidence has emerged, supporting the existence of a metastable liquid-liquid critical point in supercooled water whereby two distinct liquid phases of different densities coexist. Analyzing long molecular dynamics simulations performed using deep neural-network force fields trained to accurate quantum mechanical data, we demonstrate that the low-density liquid phase displays a strong propensity toward spontaneous polarization, as witnessed by large and long-lived collective dipole fluctuations. Our findings suggest that the dynamical stability of the low-density phase, and hence the transition from high-density to low-density liquid, is triggered by a collective process involving an accumulation of rotational angular jumps, which could ignite large dipole fluctuations. This dynamical transition involves subtle changes in the electronic polarizability of water molecules which affects their rotational mobility within the two phases. These findings hold the potential for catalyzing activity in the search for dielectric-based probes of the putative second critical point.

Accuracy limit of non-polarizable four-point water models: TIP4P/2005 vs OPC. Should water models reproduce the experimental dielectric constant?

The last generation of four center non-polarizable models of water can be divided into two groups: those reproducing the dielectric constant of water, as OPC, and those significantly underestimating its value, as TIP4P/2005. To evaluate the global performance of OPC and TIP4P/2005, we shall follow the test proposed by Vega and Abascal in 2011 evaluating about 40 properties to fairly address this comparison. The liquid-vapor and liquid-solid equilibria are computed, as well as the heat capacities, isothermal compressibilities, surface tensions, densities of different ice polymorphs, the density maximum, equations of state at high pressures, and transport properties. General aspects of the phase diagram are considered by comparing the ratios of different temperatures (namely, the temperature of maximum density, the melting temperature of hexagonal ice, and the critical temperature). The final scores are 7.2 for TIP4P/2005 and 6.3 for OPC. The results of this work strongly suggest that we have reached the limit of what can be achieved with non-polarizable models of water and that the attempt to reproduce the experimental dielectric constant deteriorates the global performance of the water force field. The reason is that the dielectric constant depends on two surfaces (potential energy and dipole moment surfaces), whereas in the absence of an electric field, all properties can be determined simply from just one surface (the potential energy surface). The consequences of the choice of the water model in the modeling of electrolytes in water are also discussed.

Learning a reactive potential for silica-water through uncertainty attribution

The reactivity of silicates in aqueous solution is relevant to various chemistries ranging from silicate minerals in geology, to the C-S-H phase in cement, nanoporous zeolite catalysts, or highly porous precipitated silica. While simulations of chemical reactions can provide insight at the molecular level, balancing accuracy and scale in reactive simulations in the condensed phase is a challenge. Here, we demonstrate how a machine-learning reactive interatomic potential trained on PaiNN architecture can accurately capture silicate-water reactivity. The model was trained on a dataset comprising 400,000 energies and forces of molecular clusters at the ωB97X-D3/def2-TZVP level. To ensure the robustness of the model, we introduce a general active learning strategy based on the attribution of the model uncertainty, that automatically isolates uncertain regions of bulk simulations to be calculated as small-sized clusters. The potential reproduces static and dynamic properties of liquid water and solid crystalline silicates, despite having been trained exclusively on cluster data. Furthermore, we utilize enhanced sampling simulations to recover the self-ionization reactivity of water accurately, and the acidity of silicate oligomers, and lastly study the silicate dimerization reaction in a water solution at neutral conditions and find that the reaction occurs through a flanking mechanism.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water

The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.

Predicting Emission Spectra of Heteroleptic Iridium Complexes Using Artificial Chemical Intelligence

We report a deep learning-based approach to accurately predict the emission spectra of phosphorescent heteroleptic [Ir(C ∧ N ${{\rm{C}}^\wedge {\rm{N}}}$ )2(N ∧ N ${{\rm{N}}^\wedge {\rm{N}}}$ )]+ complexes, enabling the rapid discovery of novel Ir(III) chromophores for diverse applications including organic light-emitting diodes and solar fuel cells. The deep learning models utilize graph neural networks and other chemical features in architectures that reflect the inherent structure of the heteroleptic complexes, composed ofC ∧ N ${{\rm{C}}^\wedge {\rm{N}}}$ andN ∧ N ${{\rm{N}}^\wedge {\rm{N}}}$ ligands, and are thus geared towards efficient training over the dataset. By leveraging experimental emission data, our models reliably predict the full emission spectra of these complexes across various emission profiles, surpassing the accuracy of conventional DFT and correlated wavefunction methods, while simultaneously achieving robustness to the presence of imperfect (noisy, low-quality) training spectra. We showcase the potential applications for these and related models for in silico prediction of complexes with tailored emission properties, as well as in "design of experiment" contexts to reduce the synthetic burden of high-throughput screening. In the latter case, we demonstrate that the models allow us to exploit a limited amount of experimental data to explore a wide range of chemical space, thus leveraging a modest synthetic effort.

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.

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Origin of dielectric polarization suppression in confined water from first principles

It has long been known that the dielectric constant of confined water should be different from that in bulk. Recent experiments have shown that it is vanishingly small, however the origin of the phenomenon remains unclear. Here we used ab initio molecular dynamics simulations (AIMD) and AIMD-trained machine-learning potentials to understand water's structure and electronic properties underpinning this effect. For the graphene and hexagonal boron-nitride substrates considered, we find that it originates in the spontaneous anti-parallel alignment of the water dipoles in the first two water layers near the solid interface. The interfacial layers exhibit net ferroelectric ordering, resulting in an overall anti-ferroelectric arrangement of confined water. Together with constrained hydrogen-bonding orientations, this leads to much reduced out-of-plane polarization. Furthermore, we directly contrast AIMD and simple classical force-field simulations, revealing important differences. This work offers insight into a property of water that is critical in modulating surface forces, the electric-double-layer formation and molecular solvation, and shows a way to compute it.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

Accuracy Assessment of Atomistic Neural Network Potentials: The Impact of Cutoff Radius and Message Passing

Atomistic neural network potentials have achieved great success in accelerating atomistic simulations in complicated systems in recent years. They are typically based on the atomic decomposition of total properties, truncating the interatomic correlations to a local environment within a given cutoff radius. A more recently developed message passing (MP) neural network framework can, in principle, incorporate nonlocal effects through iteratively correlating some atoms outside the cutoff sphere with atoms inside, a process referred to as MP. However, how the model accuracy depends on the cutoff radius and the MP process has rarely been discussed. In this work, we investigate this dependence using a recursively embedded atom neural network method that possesses both local and MP features, in two representative systems: liquid H2O and solid Al2O3. We focus on how these settings influence predictions for structural and vibrational properties, namely, radial distribution functions (RDFs) and vibrational density of states (VDOSs). We find that while MP lowers test errors of energy and forces in general, it may not improve the prediction for RDFs and/or VDOSs if direct interatomic correlations in the local environment are insufficiently described. A cutoff radius exceeding the first neighbor shell is necessary, beyond which involving MP quickly enhances the model accuracy until convergence. This is a potentially more efficient way to increase the model accuracy than directly increasing the cutoff radius, especially with more memory savings in the GPU implementation. Our findings also suggest that using the mean test error as the measure of the model accuracy alone is inadequate.

High-Dimensional Neural Network Potentials for Accurate Prediction of Equation of State: A Case Study of Methane

Machine learning-based interatomic potentials, such as those provided by neural networks, are increasingly important in molecular dynamics simulations. In the present work, we consider the applicability and robustness of machine learning molecular dynamics to predict the equation of state properties of methane by using high-dimensional neural network potentials (HDNNPs). We investigate two different strategies for generating training data: one strategy based upon bulk representations using periodic cells and another strategy based upon clusters of molecules. We assess the accuracy of the trained potentials by predicting the equilibrium mass density for a wide range of thermodynamic conditions to characterize the liquid phase, supercritical fluid, and gas phase, as well as the liquid-vapor coexistence curve. Our results show an excellent agreement with reference phase diagrams, with an average error below ∼2% for all studied phases. Moreover, we confirm the applicability of models trained on cluster data sets for producing accurate and reliable results.

Machine Learning Density Functionals from the Random-Phase Approximation

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

Mechanistic Insights into Water Autoionization through Metadynamics Simulation Enhanced by Machine Learning

Characterizing the free energy landscape of water ionization has been a great challenge due to the limitations from expensive ab initio calculations and strong rare-event features. Lacking equilibrium sampling of the ionization pathway will cause ambiguities in the mechanistic study. Here, we obtain convergent free energy surfaces through nanosecond timescale metadynamics simulations with classical nuclei enhanced by atomic neural network potentials, which yields good reproduction of the equilibrium constant (pK_{w}=14.14) and ionization rate constant (1.369×10^{-3}  s^{-1}). The character of transition state unveils the triple-proton transfer occurs through a concerted but asynchronous mechanism. Conditional ensemble average analyses establish the dual-presolvation mechanism, where a pair of hypercoordinated and undercoordinated waters bridged by one H_{2}O cooperatively constitutes the initiation environment for autoionization, and contributes extremely to the local electric field fluctuation to promote water dissociation.

Reducing the Cost of Neural Network Potential Generation for Reactive Molecular Systems

Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

A Status Report on "Gold Standard" Machine-Learned Potentials for Water

Owing to the central importance of water to life as well as its unusual properties, potentials for water have been the subject of extensive research over the past 50 years. Recently, five potentials based on different machine learning approaches have been reported that are at or near the "gold standard" CCSD(T) level of theory. The development of such high-level potentials enables efficient and accurate simulations of water systems using classical and quantum dynamical approaches. This Perspective serves as a status report of these potentials, focusing on their methodology and applications to water systems across different phases. Their performances on the energies of gas phase water clusters, as well as condensed phase structural and dynamical properties, are discussed.

Characterization of the Hydrogen-Bond Network in High-Pressure Water by Deep Potential Molecular Dynamics

The hydrogen-bond (H-bond) network of high-pressure water is investigated by neural-network-based molecular dynamics (MD) simulations with first-principles accuracy. The static structure factors (SSFs) of water at three densities, i.e., 1, 1.115, and 1.24 g/cm3, are directly evaluated from 512 water MD trajectories, which are in quantitative agreement with the experiments. We propose a new method to decompose the computed SSF and identify the changes in the SSF with respect to the changes in H-bond structures. We find that a larger water density results in a higher probability for one or two non-H-bonded water molecules to be inserted into the inner shell, explaining the changes in the tetrahedrality of water under pressure. We predict that the structure of the accepting end of water molecules is more easily influenced by the pressure than by the donating end. Our work sheds new light on explaining the SSF and H-bond properties in related fields.

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations

The transport of excess protons and hydroxide ions in water underlies numerous important chemical and biological processes. Accurately simulating the associated transport mechanisms ideally requires utilizing ab initio molecular dynamics simulations to model the bond breaking and formation involved in proton transfer and path-integral simulations to model the nuclear quantum effects relevant to light hydrogen atoms. These requirements result in a prohibitive computational cost, especially at the time and length scales needed to converge proton transport properties. Here, we present machine-learned potentials (MLPs) that can model both excess protons and hydroxide ions at the generalized gradient approximation and hybrid density functional theory levels of accuracy and use them to perform multiple nanoseconds of both classical and path-integral proton defect simulations at a fraction of the cost of the corresponding ab initio simulations. We show that the MLPs are able to reproduce ab initio trends and converge properties such as the diffusion coefficients of both excess protons and hydroxide ions. We use our multi-nanosecond simulations, which allow us to monitor large numbers of proton transfer events, to analyze the role of hypercoordination in the transport mechanism of the hydroxide ion and provide further evidence for the asymmetry in diffusion between excess protons and hydroxide ions.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

Physics-inspired machine learning of localized intensive properties

Machine learning (ML) has been widely applied to chemical property prediction, most prominently for the energies and forces in molecules and materials. The strong interest in predicting energies in particular has led to a 'local energy'-based paradigm for modern atomistic ML models, which ensures size-extensivity and a linear scaling of computational cost with system size. However, many electronic properties (such as excitation energies or ionization energies) do not necessarily scale linearly with system size and may even be spatially localized. Using size-extensive models in these cases can lead to large errors. In this work, we explore different strategies for learning intensive and localized properties, using HOMO energies in organic molecules as a representative test case. In particular, we analyze the pooling functions that atomistic neural networks use to predict molecular properties, and suggest an orbital weighted average (OWA) approach that enables the accurate prediction of orbital energies and locations.

Common Cations Are Not Polarizable: Effects of Dispersion Correction on Hydration Structures from Ab Initio Molecular Dynamics

We employed density functional theory-based ab initio molecular dynamics simulations to examine the hydration structure of several common alkali and alkali earth metal cations. We found that the commonly used atom pairwise dispersion correction scheme D3, which assigns dispersion coefficients based on the neutral form of the atom rather than its actual oxidation state, leads to inaccuracies in the hydration structures of these cations. We evaluated this effect for lithium, sodium, potassium, and calcium and found that the inaccuracies are particularly pronounced for sodium and potassium compared to the experiment. To remedy this issue, we propose disabling the D3 correction specifically for all cation-including pairs, which leads to a much better agreement with experimental data.

Fine Tuning the Intermolecular Interactions of Water Clusters Using the Dispersion-Corrected Density Functional Theory

Dispersion-inclusive density functional theory (DFT) methods have unequivocally demonstrated improved performances with respect to standard DFT approximations for modeling large and extended molecular systems at the quantum mechanical level. Yet, in some cases, disagreements with highly accurate reference calculations, such as CCSD(T) and quantum Monte Carlo (MC) calculations, still remain. Furthermore, the application of general-purpose corrections, such as the popular Grimme's semi-classical models (DFT-D), to different Kohn-Sham exchange-correlation functionals sometimes leads to variable and inconsistent results, which recommend a careful prior evaluation. In a recent study, we proposed a simple optimization protocol for enhancing the accuracy of these DFT-D methods by following an alternative and system-specific approach. Here, adopting the same computational strategy, we show how the accurate MC intermolecular interactions of a large set of water clusters of variable sizes (i.e., 300 (H₂O)_n structures, n = 9, 15, 27) can be reproduced remarkably well by dispersion-corrected DFT models (i.e., B3LYP-D4, PBE-D4, revPBE(0)-D4) upon re-optimization, reaching a mean absolute error per monomer of ~0.1 kcal/mol. Hence, the obtained results support the use of this procedure for fine-tuning tailored DFT-D models for the accurate description of targeted molecular systems.

High-pressure and temperature neural network reactive force field for energetic materials

Reactive force fields for molecular dynamics have enabled a wide range of studies in numerous material classes. These force fields are computationally inexpensive compared with electronic structure calculations and allow for simulations of millions of atoms. However, the accuracy of traditional force fields is limited by their functional forms, preventing continual refinement and improvement. Therefore, we develop a neural network-based reactive interatomic potential for the prediction of the mechanical, thermal, and chemical responses of energetic materials at extreme conditions. The training set is expanded in an automatic iterative approach and consists of various CHNO materials and their reactions under ambient and shock-loading conditions. This new potential shows improved accuracy over the current state-of-the-art force fields for a wide range of properties such as detonation performance, decomposition product formation, and vibrational spectra under ambient and shock-loading conditions.

Proton Transport in Perfluorinated Ionomer Simulated by Machine-Learned Interatomic Potential

Polymers are a class of materials that are highly challenging to deal with using first-principles methods. Here, we present an application of machine-learned interatomic potentials to predict structural and dynamical properties of dry and hydrated perfluorinated ionomers. An improved active-learning algorithm using a small number of descriptors allows to efficiently construct an accurate and transferable model for this multielemental amorphous polymer. Molecular dynamics simulations accelerated by the machine-learned potentials accurately reproduce the heterogeneous hydrophilic and hydrophobic domains formed in this material as well as proton and water diffusion coefficients under a variety of humidity conditions. Our results reveal pronounced contributions of Grotthuss chains consisting of two to three water molecules to the high proton mobility under strongly humidified conditions.

Machine Learning Interatomic Potentials and Long-Range Physics

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Effects of molecular size and orientation on the interfacial properties and wetting behavior of water/n-alkane systems: a molecular-dynamics study

Molecular dynamics simulations (MD) are performed to study the interfacial structure/tension and wetting behavior of water/n-alkane systems (water/nC5 to water/nC16 where nCx = CxH(2x + 2)). In particular, we study complete-to-partial wetting transitions by changing the n-alkane chain length (N_C) at a constant temperature, T = 295 K. Simulations are carried out with a united-atom TraPPE model for n-alkanes and the TIP4P-2005 model of water. Simulation results are in excellent agreement with the initial spreading coefficients and contact angles calculated using experimental values of the surface and interfacial tensions. In addition, it has been determined that water/(nC5-nC7) and water/(nC8-nC16), respectively, exhibit complete and partial initial wetting modes. Simulations show that the interfacial structures of water/(nC5-nC7) are different from water/(nC8-nC16) systems. In the latter, water preferentially orients near the interface to increase the number of hydrogen bonds and the charge and mass densities. Moreover, the orientation of n-alkane molecules at water/(nC8-nC16) interfaces has a long-range persistence, resulting in layered structures that increase with N_C. In addition, simulation results of the orientational order parameter S_z show alignment behavior of the n-alkane molecules with respect to the interfaces. Simulations predict that the central segments of n-alkane are strongly packed in the interfaces while the end segments (methyl groups) form smaller peaks in the outer edge of the layer. This observation confirms the "horseshoe" or "C-shaped" structure of n-alkane molecules in the water/n-alkane interfaces. At constant temperature, the interface widths of both water and the n-alkanes decrease with increasing n-alkane molecular length. These results suggest that increasing the n-alkane chain length affects the water/n-alkane interfacial properties in a manner similar to that of cooling.

A first-principles exploration of the conformational space of sodiated pyranose assisted by neural network potentials

Sampling the conformational space of monosaccharides using the first-principles methods is important and as a database of local minima provides a solid base for interpreting experimental measurements such as infrared photo-dissociation (IRPD) spectroscopy or collision-induced dissociation (CID). IRPD emphasizes low-energy conformers and CID can distinguish conformers with distinct reaction pathways. A typical computational approach is to engage empirical or semi-empirical methods to sample the conformational space first, and only selected minima are reoptimized at first-principles levels. In this work, we propose a computational scheme to explore the configurational space of 12 types of sodiated pyranoses with the assistance of a neural network potential (NNP). We demonstrated that it is possible to train an NNP based on the density functional calculations extracted from a previous study on sodiated glucose (Glc), galactose (Gal), and mannose (Man). This NNP yields a better description of the other five types of aldohexoses than the four types of ketohexoses. We further show that such a discrepancy in the accuracy of NNP can be resolved by an active learning scheme where the NNP model is engaged in generating the data and has itself updated. Through this iterative process, we can locate more than 17 000 distinct local minima at the B3LYP/6-311+G(d,p) level and an NNP with an accuracy of 1 kJ mol^-1 was created, which can be used for further studies.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

Spectroscopy from Machine Learning by Accurately Representing the Atomic Polar Tensor

Vibrational spectroscopy is a key technique to elucidate microscopic structure and dynamics. Without the aid of theoretical approaches, it is, however, often difficult to understand such spectra at a microscopic level. Ab initio molecular dynamics has repeatedly proved to be suitable for this purpose; however, the computational cost can be daunting. Here, the E(3)-equivariant neural network e3nn is used to fit the atomic polar tensor of liquid water a posteriori on top of existing molecular dynamics simulations. Notably, the introduced methodology is general and thus transferable to any other system as well. The target property is most fundamental and gives access to the IR spectrum, and more importantly, it is a highly powerful tool to directly assign IR spectral features to nuclear motion─a connection which has been pursued in the past but only using severe approximations due to the prohibitive computational cost. The herein introduced methodology overcomes this bottleneck. To benchmark the machine learning model, the IR spectrum of liquid water is calculated, indeed showing excellent agreement with the explicit reference calculation. In conclusion, the presented methodology gives a new route to calculate accurate IR spectra from molecular dynamics simulations and will facilitate the understanding of such spectra on a microscopic level.

Coupled Cluster Molecular Dynamics of Condensed Phase Systems Enabled by Machine Learning Potentials: Liquid Water Benchmark

Coupled cluster theory is a general and systematic electronic structure method, but in particular the highly accurate "gold standard" coupled cluster singles, doubles and perturbative triples, CCSD(T), can only be applied to small systems. To overcome this limitation, we introduce a framework to transfer CCSD(T) accuracy of finite molecular clusters to extended condensed phase systems using a high-dimensional neural network potential. This approach, which is automated, allows one to perform high-quality coupled cluster molecular dynamics, CCMD, as we demonstrate for liquid water including nuclear quantum effects. The machine learning strategy is very efficient, generic, can be systematically improved, and is applicable to a variety of complex systems.

Machine learning interatomic potentials for aluminium: application to solidification phenomena

In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphization requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and the liquid states. Taking into account rare nucleation events or structural relaxation under deep undercooling conditions requires much larger length scales and longer time scales than those achievable byab initiomolecular dynamics (AIMD). This problem is addressed by means of classical molecular dynamics simulations using a well established high dimensional neural network potential trained on a set of configurations generated by AIMD relevant for solidification phenomena. Our dataset contains various crystalline structures and liquid states at different pressures, including their time fluctuations in a wide range of temperatures. Applied to elemental aluminium, the resulting potential is shown to be efficient to reproduce the basic structural, dynamics and thermodynamic quantities in the liquid and undercooled states. Early stages of crystallization are further investigated on a much larger scale with one million atoms, allowing us to unravel features of the homogeneous nucleation mechanisms in the fcc phase at ambient pressure as well as in the bcc phase at high pressure with unprecedented accuracy close to theab initioone. In both cases, a single step nucleation process is observed.

Quantum neural networks force fields generation

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning (ML) methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum ML is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network (NN) potentials. To this end, we design a quantum NN architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum ML.

Combining Machine Learning Approaches and Accurate Ab Initio Enhanced Sampling Methods for Prebiotic Chemical Reactions in Solution

The study of the thermodynamics, kinetics, and microscopic mechanisms of chemical reactions in solution requires the use of advanced free-energy methods for predictions to be quantitative. This task is however a formidable one for atomistic simulation methods, as the cost of quantum-based ab initio approaches, to obtain statistically meaningful samplings of the relevant chemical spaces and networks, becomes exceedingly heavy. In this work, we critically assess the optimal structure and minimal size of an ab initio training set able to lead to accurate free-energy profiles sampled with neural network potentials. The results allow one to propose an ab initio protocol where the ad hoc inclusion of a machine-learning (ML)-based task can significantly increase the computational efficiency, while keeping the ab initio accuracy and, at the same time, avoiding some of the notorious extrapolation risks in typical atomistic ML approaches. We focus on two representative, and computationally challenging, reaction steps of the classic Strecker-cyanohydrin mechanism for glycine synthesis in water solution, where the main precursors are formaldehyde and hydrogen cyanide. We demonstrate that indistinguishable ab initio quality results are obtained, thanks to the ML subprotocol, at about 1 order of magnitude less of computational load.

Water Flow in Single-Wall Nanotubes: Oxygen Makes It Slip, Hydrogen Makes It Stick

Experimental measurements have reported ultrafast and radius-dependent water transport in carbon nanotubes which are absent in boron nitride nanotubes. Despite considerable effort, the origin of this contrasting (and fascinating) behavior is not understood. Here, with the aid of machine learning-based molecular dynamics simulations that deliver first-principles accuracy, we investigate water transport in single-wall carbon and boron nitride nanotubes. Our simulations reveal a large, radius-dependent hydrodynamic slippage on both materials, with water experiencing indeed a ≈5 times lower friction on carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms across the two materials reveals that the fast water transport on carbon is governed by facile oxygen motion, whereas the higher friction on boron nitride arises from specific hydrogen-nitrogen interactions. This work not only delivers a clear reference of quantum mechanical accuracy for water flow in single-wall nanotubes but also provides detailed mechanistic insight into its radius and material dependence for future technological application.

Accurate diffusion coefficients of the excess proton and hydroxide in water via extensive ab initio simulations with different schemes

Despite its simple molecular formula, obtaining an accurate in silico description of water is far from straightforward. Many of its very peculiar properties are quite elusive, and in particular, obtaining good estimations of the diffusion coefficients of the solvated proton and hydroxide at a reasonable computational cost has been an unsolved challenge until now. Here, I present extensive results of several unusually long ab initio molecular dynamics (MD) simulations employing different combinations of the Born-Oppenheimer and second-generation Car-Parrinello MD propagation methods with different ensembles (NVE and NVT) and thermostats, which show that these methods together with the RPBE-D3 functional provide a very accurate estimation of the diffusion coefficients of the solvated H₃O⁺ and OH^- ions, together with an extremely accurate description of several properties of neutral water (such as the structure of the liquid and its diffusion and shear viscosity coefficients). In addition, I show that the estimations of D_H3O⁺ and D_OH^- depend dramatically on the simulation length, being necessary to reach timescales in the order of hundreds of picoseconds to obtain reliable results.

Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials

Metal oxide/water interfaces play an important role in biology, catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by experimental techniques, whilst results from ab initio molecular dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems containing more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio molecular dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water molecules from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calculation of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water molecules are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochemistry with explicit solvent molecules.

Machine learning molecular dynamics simulations toward exploration of high-temperature properties of nuclear fuel materials: case study of thorium dioxide

Predicting materials properties of nuclear fuel compounds is a challenging task in materials science. Their thermodynamical behaviors around and above the operational temperature are essential for the design of nuclear reactors. However, they are not easy to measure, because the target temperature range is too high to perform various standard experiments safely and accurately. Moreover, theoretical methods such as first-principles calculations also suffer from the computational limitations in calculating thermodynamical properties due to their high calculation-costs and complicated electronic structures stemming from f-orbital occupations of valence electrons in actinide elements. Here, we demonstrate, for the first time, machine-learning molecular-dynamics to theoretically explore high-temperature thermodynamical properties of a nuclear fuel material, thorium dioxide. The target compound satisfies first-principles calculation accuracy because f-electron occupation coincidentally diminishes and the scheme meets sampling sufficiency because it works at the computational cost of classical molecular-dynamics levels. We prepare a set of training data using first-principles molecular dynamics with small number of atoms, which cannot directly evaluate thermodynamical properties but captures essential atomistic dynamics at the high temperature range. Then, we construct a machine-learning molecular-dynamics potential and carry out large-scale molecular-dynamics calculations. Consequently, we successfully access two kinds of thermodynamic phase transitions, namely the melting and the anomalous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}λ transition induced by large diffusions of oxygen atoms. Furthermore, we quantitatively reproduce various experimental data in the best agreement manner by selecting a density functional scheme known as SCAN. Our results suggest that the present scale-up simulation-scheme using machine-learning techniques opens up a new pathway on theoretical studies of not only nuclear fuel compounds, but also a variety of similar materials that contain both heavy and light elements, like thorium dioxide.

Connection between water's dynamical and structural properties: Insights from ab initio simulations

SignificanceFirst-principles calculations, which explicitly account for the electronic structure of matter, can shed light on the molecular structure and dynamics of water in its supercooled state. In this work, we use density functional theory, which relies on a functional to describe electronic exchange and correlations, to evaluate which functional best describes the temperature evolution of bulk water transport coefficients. We also assess the validity of the Stokes-Einstein relation for all the functionals in the temperature range studied, and explore the link between structure and dynamics. Based on these results, we show how transport coefficients can be computed from structural descriptors, which require shorter simulation times to converge, and we point toward strategies to develop better functionals.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Graph neural networks accelerated molecular dynamics

Molecular Dynamics (MD) simulation is a powerful tool for understanding the dynamics and structure of matter. Since the resolution of MD is atomic-scale, achieving long timescale simulations with femtosecond integration is very expensive. In each MD step, numerous iterative computations are performed to calculate energy based on different types of interaction and their corresponding spatial gradients. These repetitive computations can be learned and surrogated by a deep learning model, such as a Graph Neural Network (GNN). In this work, we developed a GNN Accelerated MD (GAMD) model that directly predicts forces, given the state of the system (atom positions, atom types), bypassing the evaluation of potential energy. By training the GNN on a variety of data sources (simulation data derived from classical MD and density functional theory), we show that GAMD can predict the dynamics of two typical molecular systems, Lennard-Jones system and water system, in the NVT ensemble with velocities regulated by a thermostat. We further show that GAMD’s learning and inference are agnostic to the scale, where it can scale to much larger systems at test time. We also perform a comprehensive benchmark test comparing our implementation of GAMD to production-level MD software, showing GAMD’s competitive performance on the large-scale simulation.

Assessing the persistence of chalcogen bonds in solution with neural network potentials

Non-covalent bonding patterns are commonly harvested as a design principle in the field of catalysis, supramolecular chemistry and functional materials to name a few. Yet, their computational description generally neglects finite temperature and environment effects, which promote competing interactions and alter their static gas-phase properties. Recently, neural network potentials (NNPs) trained on Density Functional Theory (DFT) data have become increasingly popular to simulate molecular phenomena in condensed phase with an accuracy comparable to ab initio methods. To date, most applications have centered on solid-state materials or fairly simple molecules made of a limited number of elements. Herein, we focus on the persistence and strength of chalcogen bonds involving a benzotelluradiazole in condensed phase. While the tellurium-containing heteroaromatic molecules are known to exhibit pronounced interactions with anions and lone pairs of different atoms, the relevance of competing intermolecular interactions, notably with the solvent, is complicated to monitor experimentally but also challenging to model at an accurate electronic structure level. Here, we train direct and baselined NNPs to reproduce hybrid DFT energies and forces in order to identify what are the most prevalent non-covalent interactions occurring in a solute-Cl$^-$-THF mixture. The simulations in explicit solvent highlight competition with chalcogen bonds formed with the solvent and the short-range directionality of the interaction with direct consequences for the molecular properties in the solution. The comparison with other potentials (e.g., AMOEBA, direct NNP and continuum solvent model) also demonstrates that baselined NNPs offer a reliable picture of the non-covalent interaction interplay occurring in solution.

Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network — a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions — and demonstrate its utility by modeling liquid water with and without applied fields.

Machine learning-based neural network potentials often cannot describe long-range interactions. Here the authors present an approach for building neural network potentials that can describe the electronic and nuclear response of molecular systems to long-range electrostatics.

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.