Ab initio thermodynamics of liquid and solid water

From flat to stepped: active learning frameworks for investigating local structure at copper-water interfaces

Understanding processes at solid-liquid interfaces at the atomic level is important for applications such as electrocatalysis. Here we explore the effects of different step densities on the structure of interfacial water at the copper-water interface. Utilizing spatially resolved uncertainties, we develop an active learning framework and train a machine-learning force field (MLFF) based on dispersion-corrected density functional theory data. Using molecular dynamics simulations, we investigate structural properties of water molecules in the contact layer, including density profiles, angular distributions, and 2D pair correlation functions. In accordance with previous studies, we observe the formation of two sublayers within the contact layer at the Cu(111) surface, whereas the structure on surfaces with a high step density is dominated by the undercoordinated ridge atoms. By systematically decreasing the step density, we identify the cross-over to when the behavior observed at the flat surface can be locally recovered. Using dimensionality reduction, we identify four distinct types of Cu environments at the interfaces, providing insights into analyzing less idealized surfaces with MLFFs.

The evolution of machine learning potentials for molecules, reactions and materials

Recent years have witnessed the fast development of machine learning potentials (MLPs) and their widespread applications in chemistry, physics, and material science. By fitting discrete ab initio data faithfully to continuous and symmetry-preserving mathematical forms, MLPs have enabled accurate and efficient atomistic simulations in a large scale from first principles. In this review, we provide an overview of the evolution of MLPs in the past two decades and focus on the state-of-the-art MLPs proposed in the last a few years for molecules, reactions, and materials. We discuss some representative applications of MLPs and the trend of developing universal potentials across a variety of systems. Finally, we outline a list of open challenges and opportunities in the development and applications of MLPs.

Revealing the photochemical pathways of nitrate in water through first-principles simulations

The nitrate anion (NO3-) is abundant in environmental aqueous phases, including aerosols, surface waters, and snow, where its photolysis releases nitrogen oxides back into the atmosphere. Nitrate photolysis occurs via two channels: (1) the formation of NO2 and O- and (2) the formation of NO2- and O(3P). The occurrence of two reaction channels with very low quantum yield (∼1%) highlights the critical role of the solvation environment and spin-forbidden electronic transitions, which remain unexplained at the molecular level. We investigate the two photolysis channels in water using quantum chemical calculations and first-principles molecular dynamics simulations with hybrid density functional theory and enhanced sampling. We find that spin-forbidden absorption to the triplet state (T1) is possible but occurs at a rate ∼15 times weaker than the spin-allowed transition to the singlet state (S1). A metastable solvation cage complex requires additional thermal energy to dissociate the N-O bond, allowing for recombination or non-radiative deactivation. Our results explain the temperature dependence of photolysis, linked to hydrogen bond rearrangement in the solvation shell. This work provides new molecular insights into nitrate photolysis and its low quantum yield under environmental conditions.

Extending atomic decomposition and many-body representation with a chemistry-motivated approach to machine learning potentials

Most widely used machine learning potentials for condensed-phase applications rely on many-body permutationally invariant polynomial or atom-centered neural networks. However, these approaches face challenges in achieving chemical interpretability in atomistic energy decomposition and fully matching the computational efficiency of traditional force fields. Here we present a method that combines aspects of both approaches and balances accuracy and force-field-level speed. This method utilizes a monomer-centered representation, where the potential energy is decomposed into the sum of chemically meaningful monomeric energies. The structural descriptors of monomers are described by one-body and two-body effective interactions, enforced by appropriate sets of permutationally invariant polynomials as inputs to the feed-forward neural networks. Systematic assessments of models for gas-phase water trimer, liquid water, methane-water cluster and liquid carbon dioxide are performed. The improved accuracy, efficiency and flexibility of this method have promise for constructing accurate machine learning potentials and enabling large-scale quantum and classical simulations for complex molecular systems.

Understanding hydrogen and heat diffusion across c-Si/a-Si:H heterojunctions for improved thermal management in solar cells fabrication

c-Si/a-Si:H-based solar cells are characterized by impressive efficiencies for silicon based devices. In this paper, we present a comprehensive atomistic simulation study of the structural and transport properties of crystalline silicon and hydrogenated amorphous silicon heterostructures for photovoltaic applications. By leveraging state-of-the-art molecular dynamics simulations with a machine-learned force field, we explore the effects of thermal boundary resistance as well as hydrogen diffusion on device performance. The simulations reveal the dependence of thermal properties on crystalline orientations, cooling rates of the amorphous layer, and interface morphology. A systematic investigation of hydrogen diffusion demonstrates its impact on heat transport and structural stability, highlighting the role of moderate hydrogenation (⩽10%) and specific orientations in enhancing thermal dissipation and reducing degradation. These findings provide atomistic insights into optimizing c-Si/a-Si:H interfaces, enabling improved thermal management and long-term stability for high-performance solar cells.

IceCoder: Identification of Ice Phases in Molecular Simulation Using Variational Autoencoder

The identification and classification of different phases of ice within molecular simulations are challenging tasks due to the complex and varied phase space of ice, which includes numerous crystalline and amorphous forms. Traditional order parameters often struggle to differentiate between these phases, especially under the conditions of thermal fluctuations. In this work, we present a novel machine learning-based framework, IceCoder, which combines a variational autoencoder (VAE) with the smooth overlap of atomic position (SOAP) descriptor to classify a large number of ice phases effectively. Our approach compresses high-dimensional SOAP vectors into a two-dimensional latent space using VAE, facilitating the visualization and distinction of various ice phases. We trained the model on a comprehensive data set generated through molecular dynamics simulations and demonstrated its ability to accurately detect various phases of crystalline ice as well as liquid water at the molecular level. IceCoder provides a robust and generalizable tool for tracking ice phase transitions in simulations, overcoming the limitations of traditional methods. This approach may also be generalized to detect polymorphs in other molecular crystals, leading to new insights into the microscopic mechanisms underlying nucleation, growth, and phase transitions while maintaining computational efficiency.

Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials

Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity often makes it challenging to address potential finite-size effects. Here, we present a specialized graphics processing units (GPUs) implementation of PIMD methods, including ring-polymer molecular dynamics (RPMD) and thermostatted ring-polymer molecular dynamics (TRPMD), into the open-source Graphics Processing Units Molecular Dynamics (GPUMD) package, combined with highly accurate and efficient machine-learned neuroevolution potential (NEP) models. This approach achieves almost the accuracy of first-principles calculations with the computational efficiency of empirical potentials, enabling large-scale atomistic simulations that incorporate nuclear quantum effects, effectively overcoming finite-size limitations at a relatively affordable computational cost. We validate and demonstrate the efficacy of the combined NEP-PIMD approach by examining various thermal properties of diverse materials, including lithium hydride (LiH), three porous metal-organic frameworks (MOFs), liquid water, and elemental aluminum. For LiH, our NEP-PIMD simulations successfully capture the isotope effect, reproducing the experimentally observed dependence of the lattice parameter on the reduced mass. For MOFs, our results reveal that achieving good agreement with experimental data requires consideration of both nuclear quantum effects and dispersive interactions. For water, our PIMD simulations capture the significant impact of nuclear quantum effects on its microscopic structure. For aluminum, the TRPMD method effectively captures thermal expansion and phonon properties, aligning well with quantum mechanical predictions. This efficient GPU-accelerated NEP-PIMD implementation in the GPUMD package provides an alternative, accessible, accurate, and scalable tool for exploring complex material properties influenced by nuclear quantum effects, with potential applications across a broad range of materials.

PiNN: Equivariant Neural Network Suite for Modeling Electrochemical Systems

Electrochemical energy storage and conversion play increasingly important roles in electrification and sustainable development across the globe. A key challenge therein is to understand, control, and design electrochemical energy materials with atomistic precision. This requires inputs from molecular modeling powered by machine learning (ML) techniques. In this work, we have upgraded our pairwise interaction neural network Python package PiNN via introducing equivariant features to the PiNet2 architecture for fitting potential energy surfaces along with PiNet2-dipole for dipole and charge predictions as well as PiNet2-χ for generating atom-condensed charge response kernels. By benchmarking publicly accessible data sets of small molecules, crystalline materials, and liquid electrolytes, we found that the equivariant PiNet2 shows significant improvements over the original PiNet architecture and provides a state-of-the-art overall performance. Furthermore, leveraging on plug-ins such as PiNNAcLe for an adaptive learn-on-the-fly workflow in generating ML potentials and PiNNwall for modeling heterogeneous electrodes under external bias, we expect PiNN to serve as a versatile and high-performing ML-accelerated platform for molecular modeling of electrochemical systems.

Data-efficient fine-tuning of foundational models for first-principles quality sublimation enthalpies

Calculating sublimation enthalpies of molecular crystal polymorphs is relevant to a wide range of technological applications. However, predicting these quantities at first-principles accuracy - even with the aid of machine learning potentials - is a challenge that requires sub-kJ mol-1 accuracy in the potential energy surface and finite-temperature sampling. We present an accurate and data-efficient protocol for training machine learning interatomic potentials by fine-tuning the foundational MACE-MP-0 model and showcase its capabilities on sublimation enthalpies and physical properties of ice polymorphs. Our approach requires only a few tens of training structures to achieve sub-kJ mol-1 accuracy in the sublimation enthalpies and sub-1% error in densities at finite temperature and pressure. Exploiting this data efficiency, we perform preliminary NPT simulations of hexagonal ice at the random phase approximation level and demonstrate a good agreement with experiments. Our results show promise for finite-temperature modelling of molecular crystals with the accuracy of correlated electronic structure theory methods.

Automatic feature selection and weighting in molecular systems using Differentiable Information Imbalance

Feature selection is essential in the analysis of molecular systems and many other fields, but several uncertainties remain: What is the optimal number of features for a simplified, interpretable model that retains essential information? How should features with different units be aligned, and how should their relative importance be weighted? Here, we introduce the Differentiable Information Imbalance (DII), an automated method to rank information content between sets of features. Using distances in a ground truth feature space, DII identifies a low-dimensional subset of features that best preserves these relationships. Each feature is scaled by a weight, which is optimized by minimizing the DII through gradient descent. This allows simultaneously performing unit alignment and relative importance scaling, while preserving interpretability. DII can also produce sparse solutions and determine the optimal size of the reduced feature space. We demonstrate the usefulness of this approach on two benchmark molecular problems: (1) identifying collective variables that describe conformations of a biomolecule, and (2) selecting features for training a machine-learning force field. These results show the potential of DII in addressing feature selection challenges and optimizing dimensionality in various applications. The method is available in the Python library DADApy.

Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by committee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy.

Efficient Parametrization of Transferable Atomic Cluster Expansion for Water

We present a highly accurate and transferable parametrization of water using the atomic cluster expansion (ACE). To efficiently sample liquid water, we propose a novel approach that involves sampling static calculations of various ice phases and utilizing the active learning (AL) feature of the ACE-based D-optimality algorithm to select relevant liquid water configurations, bypassing computationally intensive ab initio molecular dynamics simulations. Our results demonstrate that the ACE descriptors enable a potential initially fitted solely on ice structures, which is later upfitted with few configurations of liquid, identified with AL to provide an excellent description of liquid water. The developed potential exhibits remarkable agreement with first-principles reference, accurately capturing various properties of liquid water, including structural characteristics such as pair correlation functions, covalent bonding profiles, and hydrogen bonding profiles, as well as dynamic properties like the vibrational density of states, diffusion coefficient, and thermodynamic properties such as the melting point of the ice Ih. Our research introduces a new and efficient sampling technique for machine learning potentials in water simulations while also presenting a transferable interatomic potential for water that reveals the accuracy of first-principles reference. This advancement not only enhances our understanding of the relationship between ice and liquid water at the atomic level but also opens up new avenues for studying complex aqueous systems.

The Dynamic Diversity and Invariance of Ab Initio Water

Comprehending water dynamics is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While ab initio molecular dynamics (AIMD) accurately portray water's structure, computing its dynamic properties over nanosecond time scales proves cost-prohibitive. This study employs machine learning potentials (MLPs) to accurately determine the dynamic properties of liquid water with ab initio accuracy. Our findings reveal diversity in the calculated diffusion coefficient (D) and viscosity of water (η) across different methodologies. Specifically, while the GGA, meta-GGA, and hybrid functional methods struggle to predict dynamic properties under ambient conditions, methods on the higher level of Jacob's ladder of DFT approximation perform significantly better. Intriguingly, we discovered that both D and η adhere to the established Stokes-Einstein (SE) relation for all of the ab initio water. The diversity observed across different methods can be attributed to distinct structural entropy, affirming the applicability of excess entropy scaling relations across all functionals. The correlation between D and η provides valuable insights for identifying the ideal temperature to accurately replicate the dynamic properties of liquid water. Furthermore, our findings can validate the rationale behind employing artificially high temperatures in the simulation of water via AIMD. These outcomes not only pave the path to designing better functionals for water but also underscore the significance of water's many-body characteristics.

Density isobar of water and melting temperature of ice: Assessing common density functionals

We investigate the density isobar of water and the melting temperature of ice using six different density functionals. Machine-learning potentials are employed to ensure computational affordability. Our findings reveal significant discrepancies between various base functionals. Notably, even the choice of damping can result in substantial differences. Overall, the outcomes obtained through density functional theory are not entirely satisfactory across most utilized functionals. All functionals exhibit significant deviations either in the melting temperature or equilibrium volume, with most of them even predicting an incorrect volume difference between ice and water. Our heuristic analysis indicates that a hybrid functional with 25% exact exchange and van der Waals damping averaged between zero and Becke-Johnson dampings yields the closest agreement with experimental data. This study underscores the necessity for further enhancements in the treatment of van der Waals interactions and, more broadly, density functional theory to enable accurate quantitative predictions for molecular liquids.

Quantum-level machine learning calculations of Levodopa

Many drug molecules contain functional groups, resulting in a torsional barrier corresponding to rotation around the bond linking the fragments. In medicinal chemistry and pharmaceutical sciences, inclusive of drug design studies, the exact calculation of the potential energy surface (PES) of these molecular torsions is extremely important and precious. Machine learning (ML), including deep learning (DL), is currently one of the most rapidly evolving tools in computer-aided drug discovery and molecular simulations. In this work, we used ANI-1x neural network potential as a quantum-level ML to predict the PESs of the L-3,4-dihydroxyphenylalanine (Levodopa) antiparkinsonian drug molecule. The electronic energies and structural parameters calculated by density functional theory (DFT) using the wB97X method and all possible Pople's basis sets indicated the 6-31G(d) basis set, when used with the wB97X functional, exhibits behavior similar to that of the ANI-1x model. The vibrational frequencies investigation showed a linear correlation between DFT and ML data. All ANI-1x calculations were completed quickly in a very short computing time. From this perspective, we expect the ANI-1x dataset applied in this work to be appreciably efficient and effective in computational structure-based drug design studies.

The heterogeneity of aqueous solutions: the current situation in the context of experiment and theory

The advancement of experimental methods has provided new information about the structure and structural fluctuations of water. Despite the appearance of numerous models, which aim to describe a wide range of thermodynamic and electrical characteristics of water, there is a deficit in systemic understanding of structuring in aqueous solutions. A particular challenge is the fact that even pure water is a heterogeneous, multicomponent system composed of molecular and supramolecular structures. The possibility of the existence of such structures and their nature are of fundamental importance for various fields of science. However, great difficulties arise in modeling relatively large supramolecular structures (e.g. extended hydration shells), where the bonds between molecules are characterized by low energy. Generally, such structures may be non-equilibrium but relatively long-lived. Evidently, the short times of water microstructure exchanges do not mean short lifetimes of macrostructures, just as the instability of individual parts does not mean the instability of the entire structure. To explain this paradox, we review the data from experimental and theoretical research. Today, only some of the experimental results on the lifetime of water structures have been confirmed by modeling, so there is not a complete theoretical picture of the structure of water yet. We propose a new hierarchical water macrostructure model to resolve the issue of the stability of water structures. In this model, the structure of water is presented as consisting of many hierarchically related levels (the stratification model). The stratification mechanism is associated with symmetry breaking at the formation of the next level, even with minimal changes in the properties of the previous level. Such a hierarchical relationship can determine the unique physico-chemical properties of water systems and, in the future, provide a complete description of them.

The role of the water contact layer on hydration and transport at solid/liquid interfaces

Understanding the structure in the nanoscopic region of water that is in direct contact with solid surfaces, so-called contact layer, is key to quantifying macroscopic properties that are of interest to e.g. catalysis, ice nucleation, nanofluidics, gas adsorption, and sensing. We explore the structure of the water contact layer on various technologically relevant solid surfaces, namely graphene, MoS[Formula: see text], Au(111), Au(100), Pt(111), and Pt(100), which have been previously hampered by time and length scale limitations of ab initio approaches or force field inaccuracies, by means of molecular dynamics simulations based on ab initio machine learning potentials built using an active learning scheme. Our results reveal that the in-plane intermolecular correlations of the water contact layer vary greatly among different systems: Whereas the contact layer on graphene and on Au(111) is predominantly homogeneous and isotropic, it is inhomogeneous and anisotropic on MoS[Formula: see text], on Au(100), and on the Pt surfaces, where it additionally forms two distinct sublayers. We apply hydrodynamics and the theory of the hydrophobic effect, to relate the energy corrugation and the characteristic length-scales of the contact layer with wetting, slippage, the hydration of small hydrophobic solutes and diffusio-osmotic transport. Thus, this work provides a microscopic picture of the water contact layer and links it to macroscopic properties of liquid/solid interfaces that are measured experimentally and that are relevant to wetting, hydrophobic solvation, nanofluidics, and osmotic transport.

Five-Site Water Models for Ice and Liquid Water Generated by a Series-Parallel Machine Learning Strategy

Icing, a common natural phenomenon, always originates from a molecule. Molecular simulation is crucial for understanding the relevant process but still faces a great challenge in obtaining a uniform and accurate description of ice and liquid water with limited model parameters. Here, we propose a series-parallel machine learning (ML) approach consisting of a classification back-propagation neural network (BPNN), parallel regression BPNNs, and a genetic algorithm to establish conventional TIP5P-BG and temperature-dependent TIP5P-BGT models. The established water models exhibit a comprehensive balance among the crucial physical properties (melting point, density, vaporization enthalpy, self-diffusion coefficient, and viscosity) with mean absolute percentage errors of 2.65 and 2.40%, respectively, and excellent predictive performance on the related properties of liquid water. For ice, the simulation results on the critical nucleus size and growth rate are in good accordance with experiments. This work offers a powerful molecular model for phase transition and icing in nanoconfinement and a construction strategy for a complex molecular model in the extreme case.

Ab Initio Simulation of Liquid Water without Artificial High Temperature

Comprehending the structure and dynamics of water is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While reported works show that the ab initio molecular dynamics (AIMD) can accurately portray water's structure, the artificial high temperature (AHT) from 120 to 30 K is needed to mimic the quantum nature of hydrogen-bond network from GGA, metaGGA to hybrid functionals. The AHT proves to be an inadequate approach for systems involving aqueous multiphase mixtures, such as water-solid interfaces and aqueous solutions. This is due to the activation of additional phonons in other phases, which can lead to an overestimation of the dynamics of nearby water molecules. In this work, we find that the regularized SCAN (rSCAN) functional effectively captures both the structure and dynamics of liquid water at ambient conditions without AHT. Moreover, rSCAN closely matches experimental results for the hydration structures of alkali, alkali earth, and halide ions. We anticipate that the versatile and accurate rSCAN functional will emerge as a key tool based on ab initio simulation for investigating chemical processes in aqueous environments.

Ice Phase Classification Made Easy with Score-Based Denoising

Accurate identification of ice phases is essential for understanding various physicochemical phenomena. However, such classification for structures simulated with molecular dynamics is complicated by the complex symmetries of ice polymorphs and thermal fluctuations. For this purpose, both traditional order parameters and data-driven machine learning approaches have been employed, but they often rely on expert intuition, specific geometric information, or large training data sets. In this work, we present an unsupervised phase classification framework that combines a score-based denoiser model with a subsequent model-free classification method to accurately identify ice phases. The denoiser model is trained on perturbed synthetic data of ideal reference structures, eliminating the need for large data sets and labeling efforts. The classification step utilizes the smooth overlap of atomic position (SOAP) descriptors as the atomic fingerprint, ensuring Euclidean symmetries and transferability to various structural systems. Our approach achieves a remarkable 100% accuracy in distinguishing ice phases of test trajectories using only seven ideal reference structures of ice phases as model inputs. This demonstrates the generalizability of the score-based denoiser model in facilitating phase identification for complex molecular systems. The proposed classification strategy can be broadly applied to investigate structural evolution and phase identification for a wide range of materials, offering new insights into the fundamental understanding of water and other complex systems.

Spatially Resolved Uncertainties for Machine Learning Potentials

Machine learning potentials have become an essential tool for atomistic simulations, yielding results close to ab initio simulations at a fraction of computational cost. With recent improvements on the achievable accuracies, the focus has now shifted on the data set composition itself. The reliable identification of erroneously predicted configurations to extend a given data set is therefore of high priority. Yet, uncertainty estimation techniques have achieved mixed results for machine learning potentials. Consequently, a general and versatile method to correlate energy or atomic force uncertainties with the model error has remained elusive to date. In the current work, we show that epistemic uncertainty cannot correlate with model error by definition but can be aggregated over groups of atoms to yield a strong correlation. We demonstrate that our method correctly estimates prediction errors both globally per structure and locally resolved per atom. The direct correlation of local uncertainty and local error is used to design an active learning framework based on identifying local subregions of a large simulation cell and performing ab initio calculations only for the subregion subsequently. We successfully utilized this method to perform active learning in the low-data regime for liquid water.

Quasi-one-dimensional hydrogen bonding in nanoconfined ice

The Bernal-Fowler ice rules stipulate that each water molecule in an ice crystal should form four hydrogen bonds. However, in extreme or constrained conditions, the arrangement of water molecules deviates from conventional ice rules, resulting in properties significantly different from bulk water. In this study, we employ machine learning-driven first-principles simulations to identify a new stabilization mechanism in nanoconfined ice phases. Instead of forming four hydrogen bonds, nanoconfined crystalline ice can form a quasi-one-dimensional hydrogen-bonded structure that exhibits only two hydrogen bonds per water molecule. These structures consist of strongly hydrogen-bonded linear chains of water molecules that zig-zag along one dimension, stabilized by van der Waals interactions that stack these chains along the other dimension. The unusual interplay of hydrogen bonding and van der Waals interactions in nanoconfined ice results in atypical proton behavior such as potential ferroelectric behavior, low dielectric response, and long-range proton dynamics.

Direct Visualization of Molecular Stacking in Quasi-2D Hexagonal Ice

Understanding ice nucleation and growth is of great interest to researchers due to its importance in the biological, cryopreservation, and environmental fields. However, microstructural investigations of ice on the molecular scale are still lacking. In this paper, a simple method is proposed to prepare quasi-2-dimensional ice Ih films, which have been characterized via cryogenic transmission electron microscope. The intersecting stacking faults of basal (BSF) and prismatic (PSF) types have been directly visualized and resolved with a notable first-time report of PSF in ice Ih. Moreover, the possible growth pathways of BSF, namely, the Ic phase, were elucidated by the theoretical calculations and the chair conformation of H2O molecules. This study offers valuable insights that can enhance researchers' understanding of the growth kinetics of crystalline ice.

i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations

Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.

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.

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

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.

Learning Electronic Polarizations in Aqueous Systems

The polarization of periodically repeating systems is a discontinuous function of the atomic positions, a fact which seems at first to stymie attempts at their statistical learning. Two approaches to build models for bulk polarizations are compared: one in which a simple point charge model is used to preprocess the raw polarization to give a learning target that is a smooth function of atomic positions and the total polarization is learned as a sum of atom-centered dipoles and one in which instead the average position of Wannier centers around atoms is predicted. For a range of bulk aqueous systems, both of these methods perform perform comparatively well, with the former being slightly better but often requiring an extra effort to find a suitable point charge model. As a challenging test, we also analyze the performance of the models at the air-water interface. In this case, while the Wannier center approach delivers accurate predictions without further modifications, the preprocessing method requires augmentation with information from isolated water molecules to reach similar accuracy. Finally, we present a simple protocol to preprocess the polarizations in a data-driven way using a small number of derivatives calculated at a much lower level of theory, thus overcoming the need to find point charge models without appreciably increasing the computation cost. We believe that the training strategies presented here help the construction of accurate polarization models required for the study of the dielectric properties of realistic complex bulk systems and interfaces with ab initio accuracy.

Path Integral Simulations of Condensed-Phase Vibrational Spectroscopy

Recent theoretical and algorithmic developments have improved the accuracy with which path integral dynamics methods can include nuclear quantum effects in simulations of condensed-phase vibrational spectra. Such methods are now understood to be approximations to the delocalized classical Matsubara dynamics of smooth Feynman paths, which dominate the dynamics of systems such as liquid water at room temperature. Focusing mainly on simulations of liquid water and hexagonal ice, we explain how the recently developed quasicentroid molecular dynamics (QCMD), fast-QCMD, and temperature-elevated path integral coarse-graining simulations (Te PIGS) methods generate classical dynamics on potentials of mean force obtained by averaging over quantum thermal fluctuations. These new methods give very close agreement with one another, and the Te PIGS method has recently yielded excellent agreement with experimentally measured vibrational spectra for liquid water, ice, and the liquid-air interface. We also discuss the limitations of such methods.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for TensorNet models, with performance gains ranging from 2× to 10× over previous, nonoptimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Amorphous MoS2 from a machine learning inter-atomic potential

Amorphous molybdenum disulfide has shown potential as a hydrogen evolution catalyst, but the origin of its high activity is unclear, as is its atomic structure. Here, we have developed a classical inter-atomic potential using the charge equilibration neural network method, and we have employed it to generate atomic models of amorphous MoS2 by melting and quenching processes. The amorphous phase contains an abundance of molybdenum and sulfur atoms in low coordination. Besides the 6-coordinated molybdenum typical of the crystalline phases, a substantial fraction displays coordinations 4 and 5. The amorphous phase is also characterized by the appearance of direct S-S bonds. Density functional theory shows that the amorphous phase is metallic, with a considerable contribution of the 4-coordinated molybdenum to the density of states at the Fermi level. S-S bonds are related to the reduction of sulfur, with the excess electrons spread over several molybdenum atoms. Moreover, S-S bond formation is associated with a distinctive broadening of the 3s states, which could be exploited for experimental characterization of the amorphous phases. The large variety of local environments and the high density of electronic states at the Fermi level may play a positive role in increasing the electrocatalytic activity of this compound.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in the TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for Tensor-Net models, with performance gains ranging from 2x to 10x over previous, non-optimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Theoretical insight into H2O impact on V2O5/TiO2 catalysts for selective catalytic reduction of NOx

H2O in flue gas causes the deactivation of V2O5/TiO2 catalysts for selective catalytic reduction (SCR) of NOx with NH3 at low temperatures. Developing water resistance requires understanding the theoretical mechanism of H2O impact on the catalysts. The aim of this work was to clarify the adsorption process of H2O and the deactivation mechanism induced by H2O through density functional theory (DFT). The process of H2O adsorption was studied based on a modeled V2O5/TiO2 catalyst surface. It was found that H2O had a strong interaction with exposed titanium atoms. Water adsorption on the catalyst surface significantly alters the electronic structure of VOx sites, transforming Lewis acid sites into Brønsted acid sites. Exposed titanium sites contribute to the decrease of Lewis acidity via adsorbed water. Ab initio thermodynamic calculations show that H2O adsorption on V2O5/TiO2 is stable at low coverage but less favorable at high coverage. Adsorption of NH3 is the most critical step for the SCR of NOx, and the adsorption of H2O can hinder this process. The H2O coverage below 15% of adsorption sites could enhance the NH3 adsorption rate and have a limited effect on the acidity, while higher coverage impeded the adsorption ability of VOx sites. This work provided electron-scale insight into the adsorption impact of H2O on the surface of V2O5/TiO2 catalysts, presented thermodynamic analysis of the adsorption of H2O and NH3, paving the way for the exploration of V2O5/TiO2 catalysts with improved water resistance.

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

Collaboration on Machine-Learned Potentials with IPSuite: A Modular Framework for Learning-on-the-Fly

The field of machine learning potentials has experienced a rapid surge in progress, thanks to advances in machine learning theory, algorithms, and hardware capabilities. While the underlying methods are continuously evolving, the infrastructure for their deployment has lagged. The community, due to these rapid developments, frequently finds itself split into groups built around different implementations of machine-learned potentials. In this work, we introduce IPSuite, a Python-driven software package designed to connect different methods and algorithms from the comprehensive field of machine-learned potentials into a single platform while also providing a collaborative infrastructure, helping ensure reproducibility. Furthermore, the data management infrastructure of the IPSuite code enables simple model sharing and deployment in simulations. Currently, IPSuite supports six state-of-the-art machine learning approaches for the fitting of interatomic potentials as well as a variety of methods for the selection of training data, running of ab initio calculations, learning-on-the-fly strategies, model evaluation, and simulation deployment.

Highly efficient molecular film for inhibiting volatilization of hazardous nitric acid

Nitric acid, an important basic chemical raw material, plays an important role in promoting the development of national economy. However, such liquid hazardous chemicals are easy to cause accidental leakage during production, transportation, storage and use. The high concentration and corrosive toxic gas generated from decomposition shows tremendous harm to the surrounding environment and human life safety. Therefore, how to inhibit the volatilization of nitric acid and effectively control and block the generation of the toxic gas in the first time are the key to deal with the nitric acid leakage accident. Herein, a new method of molecular film obstruction is proposed to inhibit the nitric acid volatilization. The molecular film inhibitor spontaneously spread and form an insoluble molecular film on the gas-liquid interface, changing the state of nitric acid liquid surface and inhibiting the volatilization on the molecular scale. The inhibition rate up to 96% can be achieved below 45 °C within 400 min. Cluster structure simulation and energy barrier calculation is performed to elucidate the inhibition mechanism. Theoretical analysis of energy barrier shows that the specific resistance of the inhibitor significantly increased to 460 s·cm-1 at 45 °C, and the generated energy barrier is about 17,000 kJ·mol-1, which is much higher than the maximum energy required for nitric acid volatilization of 107.97 kJ·mol-1. The molecular film obstruction strategy can effectively inhibit the volatilization of nitric acid. This strategy paves the way for preventing the volatilization of liquid hazardous chemicals in accidental leakage treatment.

Electronic Excited States from Physically Constrained Machine Learning

Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or combined explicitly with physically grounded operations. We present an example of an integrated modeling approach in which a symmetry-adapted ML model of an effective Hamiltonian is trained to reproduce electronic excitations from a quantum-mechanical calculation. The resulting model can make predictions for molecules that are much larger and more complex than those on which it is trained and allows for dramatic computational savings by indirectly targeting the outputs of well-converged calculations while using a parametrization corresponding to a minimal atom-centered basis. These results emphasize the merits of intertwining data-driven techniques with physical approximations, improving the transferability and interpretability of ML models without affecting their accuracy and computational efficiency and providing a blueprint for developing ML-augmented electronic-structure methods.

Dynamics of the charge transfer to solvent process in aqueous iodide

Charge-transfer-to-solvent states in aqueous halides are ideal systems for studying the electron-transfer dynamics to the solvent involving a complex interplay between electronic excitation and solvent polarization. Despite extensive experimental investigations, a full picture of the charge-transfer-to-solvent dynamics has remained elusive. Here, we visualise the intricate interplay between the dynamics of the electron and the solvent polarization occurring in this process. Through the combined use of ab initio molecular dynamics and machine learning methods, we investigate the structure, dynamics and free energy as the excited electron evolves through the charge-transfer-to-solvent process, which we characterize as a sequence of states denoted charge-transfer-to-solvent, contact-pair, solvent-separated, and hydrated electron states, depending on the distance between the iodine and the excited electron. Our assignment of the charge-transfer-to-solvent states is supported by the good agreement between calculated and measured vertical binding energies. Our results reveal the charge transfer process in terms of the underlying atomic processes and mechanisms.

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.

GenIce-core: Efficient algorithm for generation of hydrogen-disordered ice structures

Ice is different from ordinary crystals because it contains randomness, which means that statistical treatment based on ensemble averaging is essential. Ice structures are constrained by topological rules known as the ice rules, which give them unique anomalous properties. These properties become more apparent when the system size is large. For this reason, there is a need to produce a large number of sufficiently large crystals that are homogeneously random and satisfy the ice rules. We have developed an algorithm to quickly generate ice structures containing ions and defects. This algorithm is provided as an independent software module that can be incorporated into crystal structure generation software. By doing so, it becomes possible to simulate ice crystals on a previously impossible scale.

Absolute energy levels of liquid water from many-body perturbation theory with effective vertex corrections

We demonstrate the importance of addressing the Γ vertex and thus going beyond the GW approximation for achieving the energy levels of liquid water in many-body perturbation theory. In particular, we consider an effective vertex function in both the polarizability and the self-energy, which does not produce any computational overhead compared with the GW approximation. We yield the band gap, the ionization potential, and the electron affinity in good agreement with experiment and with a hybrid functional description. The achieved electronic structure and dielectric screening further lead to a good description of the optical absorption spectrum, as obtained through the solution of the Bethe-Salpeter equation. In particular, the experimental peak position of the exciton is accurately reproduced.

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.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

Developing an Implicit Solvation Machine Learning Model for Molecular Simulations of Ionic Media

Molecular dynamics (MD) simulations of biophysical systems require accurate modeling of their native environment, i.e., aqueous ionic solution, as it critically impacts the structure and function of biomolecules. On the other hand, the models should be computationally efficient to enable simulations of large spatiotemporal scales. Here, we present the deep implicit solvation model for sodium chloride solutions that satisfies both requirements. Owing to the use of the neural network potential, the model can capture the many-body potential of mean force, while the implicit water treatment renders the model inexpensive. We demonstrate our approach first for pure ionic solutions with concentrations ranging from physiological to 2 M. We then extend the model to capture the effective ion interactions in the vicinity and far away from a DNA molecule. In both cases, the structural properties are in good agreement with all-atom MD, showcasing a general methodology for the efficient and accurate modeling of ionic media.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

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.

Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects

We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.

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.

Probing the self-ionization of liquid water with ab initio deep potential molecular dynamics

The chemical equilibrium between self-ionized and molecular water dictates the acid-base chemistry in aqueous solutions, yet understanding the microscopic mechanisms of water self-ionization remains experimentally and computationally challenging. Herein, Density Functional Theory (DFT)-based deep neural network (DNN) potentials are combined with enhanced sampling techniques and a global acid-base collective variable to perform extensive atomistic simulations of water self-ionization for model systems of increasing size. The explicit inclusion of long-range electrostatic interactions in the DNN potential is found to be crucial to accurately reproduce the DFT free energy profile of solvated water ion pairs in small (64 and 128 H2O) cells. The reversible work to separate the hydroxide and hydronium to a distance [Formula: see text] is found to converge for simulation cells containing more than 500 H2O, and a distance of [Formula: see text] 8 Å is the threshold beyond which the work to further separate the two ions becomes approximately zero. The slow convergence of the potential of mean force with system size is related to a restructuring of water and an increase of the local order around the water ions. Calculation of the dissociation equilibrium constant illustrates the key role of long-range electrostatics and entropic effects in the water autoionization process.