A deep potential model with long-range electrostatic interactions

Transferability and Accuracy of Ionic Liquid Simulations with Equivariant Machine Learning Interatomic Potentials

Ionic liquids (ILs) are an exciting class of electrolytes finding applications in many areas from energy storage to solvents, where they have been touted as "designer solvents" as they can be mixed to precisely tailor the physiochemical properties. As using machine learning interatomic potentials (MLIPs) to simulate ILs is still relatively unexplored, several questions need to be answered to see if MLIPs can be transformative for ILs. Since ILs are often not pure, but are either mixed together or contain additives, we first demonstrate that a MLIP can be trained to be compositionally transferable; i.e., the MLIP can be applied to mixtures of ions not directly trained on, while only being trained on a few mixtures of the same ions. We also investigated the accuracy of MLIPs for a novel IL, which we experimentally synthesize and characterize. Our MLIP trained on ∼200 DFT frames is in reasonable agreement with our experiments and DFT.

FeNNol: An efficient and flexible library for building force-field-enhanced neural network potentials

Neural network interatomic potentials (NNPs) have recently proven to be powerful tools to accurately model complex molecular systems while bypassing the high numerical cost of ab initio molecular dynamics simulations. In recent years, numerous advances in model architectures as well as the development of hybrid models combining machine-learning (ML) with more traditional, physically motivated, force-field interactions have considerably increased the design space of ML potentials. In this paper, we present FeNNol, a new library for building, training, and running force-field-enhanced neural network potentials. It provides a flexible and modular system for building hybrid models, allowing us to easily combine state-of-the-art embeddings with ML-parameterized physical interaction terms without the need for explicit programming. Furthermore, FeNNol leverages the automatic differentiation and just-in-time compilation features of the Jax Python library to enable fast evaluation of NNPs, shrinking the performance gap between ML potentials and standard force-fields. This is demonstrated with the popular ANI-2x model reaching simulation speeds nearly on par with the AMOEBA polarizable force-field on commodity GPUs (graphics processing units). We hope that FeNNol will facilitate the development and application of new hybrid NNP architectures for a wide range of molecular simulation problems.

Insights into the structure and dynamics of K+ ions at the muscovite-water interface from machine learning potential simulations

The surfaces of many minerals are covered by naturally occurring cations that become partially hydrated and can be replaced by hydronium or other cations when the surface is exposed to water or an aqueous solution. These ion exchange processes are relevant to various chemical and transport phenomena, yet elucidating their microscopic details is challenging for both experiments and simulations. In this work, we make a first step in this direction by investigating the behavior of the native K+ ions at the interface between neat water and the muscovite mica (001) surface with ab-initio-based machine learning molecular dynamics and enhanced sampling simulations. Our results show that the desorption of the surface K+ ions in pure ion-free water has a significant free energy barrier irrespective of their local surface arrangement. In contrast, facile K+ diffusion between mica's ditrigonal cavities characterized by different Al/Si orderings is observed. This behavior suggests that the K+ ions may favor a dynamic disordered surface arrangement rather than complete desorption when exposed to deionized water.

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.

Aqueous Titania Interfaces

Water-metal oxide interfaces are central to many phenomena and applications, ranging from material corrosion and dissolution to photoelectrochemistry and bioengineering. In particular, the discovery of photocatalytic water splitting on TiO2 has motivated intensive studies of water-TiO2 interfaces for decades. So far, a broad understanding of the interaction of water vapor with several TiO2 surfaces has been obtained. However, much less is known about liquid water-TiO2 interfaces, which are more relevant to many practical applications. Probing these complex systems at the molecular level is experimentally challenging and is sometimes possible only through computational studies. This review summarizes recent advances in the atomistic understanding, mostly through computational simulations, of the structure and dynamics of interfacial water on TiO2 surfaces. The main focus is on the nature, molecular or dissociated, of water in direct contact with low-index defect-free crystalline surfaces. The hydroxyls resulting from water dissociation are essential in the photooxidation of water and critically affect the surface chemistry of TiO2.

Accelerating Computation of Acidity Constants and Redox Potentials for Aqueous Organic Redox Flow Batteries by Machine Learning Potential-Based Molecular Dynamics

Due to the increased concern about energy and environmental issues, significant attention has been paid to the development of large-scale energy storage devices to facilitate the utilization of clean energy sources. The redox flow battery (RFB) is one of the most promising systems. Recently, the high cost of transition-metal complex-based RFB has promoted the development of aqueous RFBs with redox-active organic molecules. To expand the working voltage, computational chemistry has been applied to search for organic molecules with lower or higher redox potentials. However, redox potential computation based on implicit solvation models would be challenging due to difficulty in parametrization when considering the complex solvation of supporting electrolytes. Besides, although ab initio molecular dynamics (AIMD) describes the supporting electrolytes with the same level of electronic structure theory as the redox couple, the application is impeded by the high computation costs. Recently, machine learning molecular dynamics (MLMD) has been illustrated to accelerate AIMD by several orders of magnitude without sacrificing the accuracy. It has been established that redox potentials can be computed by MLMD with two separated machine learning potentials (MLPs) for reactant and product states, which is redundant and inefficient. In this work, an automated workflow is developed to construct a universal MLP for both states, which can compute the redox potentials or acidity constants of redox-active organic molecules more efficiently. Furthermore, the predicted redox potentials can be evaluated at the hybrid functional level with much lower costs, which would facilitate the design of aqueous organic RFBs.

The Potential of Neural Network Potentials

In the next half-century, physical chemistry will likely undergo a profound transformation, driven predominantly by the combination of recent advances in quantum chemistry and machine learning (ML). Specifically, equivariant neural network potentials (NNPs) are a breakthrough new tool that are already enabling us to simulate systems at the molecular scale with unprecedented accuracy and speed, relying on nothing but fundamental physical laws. The continued development of this approach will realize Paul Dirac's 80-year-old vision of using quantum mechanics to unify physics with chemistry and providing invaluable tools for understanding materials science, biology, earth sciences, and beyond. The era of highly accurate and efficient first-principles molecular simulations will provide a wealth of training data that can be used to build automated computational methodologies, using tools such as diffusion models, for the design and optimization of systems at the molecular scale. Large language models (LLMs) will also evolve into increasingly indispensable tools for literature review, coding, idea generation, and scientific writing.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

The emergence of machine learning force fields in drug design

In the field of molecular simulation for drug design, traditional molecular mechanic force fields and quantum chemical theories have been instrumental but limited in terms of scalability and computational efficiency. To overcome these limitations, machine learning force fields (MLFFs) have emerged as a powerful tool capable of balancing accuracy with efficiency. MLFFs rely on the relationship between molecular structures and potential energy, bypassing the need for a preconceived notion of interaction representations. Their accuracy depends on the machine learning models used, and the quality and volume of training data sets. With recent advances in equivariant neural networks and high-quality datasets, MLFFs have significantly improved their performance. This review explores MLFFs, emphasizing their potential in drug design. It elucidates MLFF principles, provides development and validation guidelines, and highlights successful MLFF implementations. It also addresses potential challenges in developing and applying MLFFs. The review concludes by illuminating the path ahead for MLFFs, outlining the challenges to be overcome and the opportunities to be harnessed. This inspires researchers to embrace MLFFs in their investigations as a new tool to perform molecular simulations in drug design.

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

Biomolecular dynamics with machine-learned quantum-mechanical force fields trained on diverse chemical fragments

The GEMS method enables molecular dynamics simulations of large heterogeneous systems at ab initio quality.

AI in computational chemistry through the lens of a decade-long journey

This article gives a perspective on the progress of AI tools in computational chemistry through the lens of the author's decade-long contributions put in the wider context of the trends in this rapidly expanding field. This progress over the last decade is tremendous: while a decade ago we had a glimpse of what was to come through many proof-of-concept studies, now we witness the emergence of many AI-based computational chemistry tools that are mature enough to make faster and more accurate simulations increasingly routine. Such simulations in turn allow us to validate and even revise experimental results, deepen our understanding of the physicochemical processes in nature, and design better materials, devices, and drugs. The rapid introduction of powerful AI tools gives rise to unique challenges and opportunities that are discussed in this article too.

Charge-Optimized Electrostatic Interaction Atom-Centered Neural Network Algorithm

Machine-learning algorithms have been proposed to capture electrostatic interactions by using effective partial charges. These algorithms often rely on a pretrained model for partial charge prediction using density functional theory-calculated partial charges as references, which introduces complexity to the force field model. The accuracy of the trained model also depends on the reliability of charge partition methods, which can be dependent on the specific system and methodology employed. In this study, we propose an atom-centered neural network (ANN) algorithm that eliminates the need for reference charges. Our algorithm requires only a single NN model for each element to obtain both atomic energy and charges. These atomic charges are then employed to compute electrostatic energies using the Ewald summation algorithm. Subsequently, the force field model is trained on total energy and forces, with the inclusion of electrostatic energy. To evaluate the performance of our algorithm, we conducted tests on three benchmark systems, including a Ge slab with an O adatom system, a TiO2 crystalline system, and a Pd-O nanoparticle system. Our results demonstrate reasonably accurate predictions of partial charges and electrostatic interactions. This algorithm provides a self-consistent charge prediction strategy and possibilities for robust and reliable modeling of electrostatic interactions in machine-learning potentials.

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

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

Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment

Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

Water Electric Field Induced Modulation of the Wetting of Hexagonal Boron Nitride: Insights from Multiscale Modeling of Many-Body Polarization

Understanding the behavior of water contacting two-dimensional materials, such as hexagonal boron nitride (hBN), is important in practical applications, including seawater desalination and energy harvesting. Water, being a polar solvent, can strongly polarize the hBN surface via the electric fields that it generates. However, there is a lack of molecular-level understanding about the role of polarization effects at the hBN/water interface, including its effect on the wetting properties of water. In this study, we develop a theoretical framework that introduces an all-atomistic polarizable force field to accurately model the interactions of water molecules with hBN surfaces. The force field is then utilized to self-consistently describe the water-induced polarization of hBN using the classical Drude oscillator model, including predicting the hBN-water binding energies which are found to be in excellent agreement with diffusion Monte Carlo (DMC) predictions. By carrying out molecular dynamics (MD) simulations, we demonstrate that the polarizable force field yields a water contact angle on multilayered hBN which is in close agreement with the recent experimentally reported values. Conversely, an implicit modeling of the hBN-water polarization energy utilizing a Lennard-Jones (LJ) potential, a commonly utilized approximation in previous MD simulation studies, leads to a considerably lower water contact angle. This difference in the predicted contact angles is attributed to the significant energy-entropy compensation resulting from the incorporation of polarization effects at the hBN-water interface. Our work highlights the importance of self-consistently modeling the hBN-water polarization energy and offers insights into the wetting-related interfacial phenomena of water on polarizable materials.

Two-Step Machine Learning Approach for Charge-Transfer Coupling with Structurally Diverse Data

Electronic coupling is important in determining charge-transfer rates and dynamics. Coupling strength is sensitive to both intermolecular, e.g., orientation or distance, and intramolecular degrees of freedom. Hence, it is challenging to build an accurate machine learning model to predict electronic coupling of molecular pairs, especially for those derived from the amorphous phase, for which intermolecular configurations are much more diverse than those derived from crystals. In this work, we devise a new prediction algorithm that employs two consecutive KRR models. The first model predicts molecular orbitals (MOs) from structural variation for each fragment, and coupling is further predicted by using the overlap integral included in a second model. With our two-step procedure, we achieved mean absolute errors of 0.27 meV for an ethylene dimer and 1.99 meV for a naphthalene pair, much improved accuracy amounting to 14-fold and 3-fold error reductions, respectively. In addition, MOs from the first model can also be the starting point to obtain other quantum chemical properties from atomistic structures. This approach is also compatible with a MO predictor with sufficient accuracy.

PhyNEO: A Neural-Network-Enhanced Physics-Driven Force Field Development Workflow for Bulk Organic Molecule and Polymer Simulations

An accurate, generalizable, and transferable force field plays a crucial role in the molecular dynamics simulations of organic polymers and biomolecules. Conventional empirical force fields often fail to capture precise intermolecular interactions due to their negligence of important physics, such as polarization, charge penetration, many-body dispersion, etc. Moreover, the parameterization of these force fields relies heavily on top-down fittings, limiting their transferabilities to new systems where the experimental data are often unavailable. To address these challenges, we introduce a general and fully ab initio force field construction strategy, named PhyNEO. It features a hybrid approach that combines both the physics-driven and the data-driven methods and is able to generate a bulk potential with chemical accuracy using only quantum chemistry data of very small clusters. Careful separations of long-/short-range interactions and nonbonding/bonding interactions are the key to the success of PhyNEO. By such a strategy, we mitigate the limitations of pure data-driven methods in long-range interactions, thus largely increasing the data efficiency and the scalability of machine learning models. The new approach is thoroughly tested on poly(ethylene oxide) and polyethylene glycol systems, giving superior accuracies in both microscopic and bulk properties compared to conventional force fields. This work thus offers a promising framework for the development of advanced force fields in a wide range of organic molecular systems.

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.

Global Neural Network Potential with Explicit Many-Body Functions for Improved Descriptions of Complex Potential Energy Surface

The high dimensional machine learning potential (MLP) that has developed rapidly in the past decade represents a giant step forward in large-scale atomic simulation for complex systems. The long-range interaction and the poor description of chemical reactions are typical problems of high dimensional MLP, which are mainly caused by the poor structure discrimination of the atom-centered ML model. Herein, we propose a low-cost neural-network-based MLP architecture for fitting global potential energy surface data, namely, G-MBNN, that can offer improved energy and force resolution on a complex potential energy surface. In G-MBNN, a set of many-body energy terms based on the local atomic environment are explicitly included in computing the total energy─the total energy of the system is written as the sum of atomic energy and many-body energy contributions. These extra many-body energy terms are computationally low-cost and, importantly, can provide easy access to delicate energy terms in complex systems such as very short repulsion, long-range attractions, and sensitive angular-dependent covalent interactions. We implement G-MBNN in the LASP code and demonstrate the improved accuracy of the new framework in representative systems, including ternary-element energy materials LiCoOx, TiO2 with defects, and a series of organic reactions.

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.

Physics-Inspired Equivariant Descriptors of Nonbonded Interactions

One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects such as electrostatic or dispersion interactions. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body nonbonded interactions in the data-driven modeling of matter.

How to train a neural network potential

The introduction of modern Machine Learning Potentials (MLPs) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow us to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations, provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form, the construction of MLPs has to be done with great care. In this Tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.

Acid-Base Chemistry of a Model IrO2 Catalytic Interface

Iridium oxide (IrO2) is one of the most efficient catalytic materials for the oxygen evolution reaction (OER), yet the atomic scale structure of its aqueous interface is largely unknown. Herein, the hydration structure, proton transfer mechanisms, and acid-base properties of the rutile IrO2(110)-water interface are investigated using ab initio based deep neural-network potentials and enhanced sampling simulations. The proton affinities of the different surface sites are characterized by calculating their acid dissociation constants, which yield a point of zero charge in agreement with experiments. A large fraction (≈80%) of adsorbed water dissociation is observed, together with a short lifetime (≈0.5 ns) of the resulting terminal hydroxy groups, due to rapid proton exchanges between adsorbed H2O and adjacent OH species. This rapid surface proton transfer supports the suggestion that the rate-determining step in the OER may not involve proton transfer across the double layer into solution, as indicated by recent experiments.

Why Dissolving Salt in Water Decreases Its Dielectric Permittivity

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters.

Accelerating explicit solvent models of heterogeneous catalysts with machine learning interatomic potentials

Realistically modelling how solvents affect catalytic reactions is a longstanding challenge due to its prohibitive computational cost. Typically, an explicit atomistic treatment of the solvent molecules is needed together with molecular dynamics (MD) simulations and enhanced sampling methods. Here, we demonstrate the utility of machine learning interatomic potentials (MLIPs), coupled with active learning, to enable fast and accurate explicit solvent modelling of adsorption and reactions on heterogeneous catalysts. MLIPs trained on-the-fly were able to accelerate ab initio MD simulations by up to 4 orders of magnitude while reproducing with high fidelity the geometrical features of water in the bulk and at metal-water interfaces. Using these ML-accelerated simulations, we accurately predicted key catalytic quantities such as the adsorption energies of CO*, OH*, COH*, HCO*, and OCCHO* on Cu surfaces and the free energy barriers of C-H scission of ethylene glycol over Cu and Pd surfaces, as validated with ab initio calculations. We envision that such simulations will pave the way towards detailed and realistic studies of solvated catalysts at large time- and length-scales.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

Efficient interatomic descriptors for accurate machine learning force fields of extended molecules

Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges remain to be addressed to enable predictive MLFF simulations of realistic molecules, including: (1) developing efficient descriptors for non-local interatomic interactions, which are essential to capture long-range molecular fluctuations, and (2) reducing the dimensionality of the descriptors to enhance the applicability and interpretability of MLFFs. Here we propose an automatized approach to substantially reduce the number of interatomic descriptor features while preserving the accuracy and increasing the efficiency of MLFFs. To simultaneously address the two stated challenges, we illustrate our approach on the example of the global GDML MLFF. We found that non-local features (atoms separated by as far as 15 Å in studied systems) are crucial to retain the overall accuracy of the MLFF for peptides, DNA base pairs, fatty acids, and supramolecular complexes. Interestingly, the number of required non-local features in the reduced descriptors becomes comparable to the number of local interatomic features (those below 5 Å). These results pave the way to constructing global molecular MLFFs whose cost increases linearly, instead of quadratically, with system size.

Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects

Deep-HP is a scalable extension of the Tinker-HP multi-GPU molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Network (DNN) models. Deep-HP increases DNNs' MD capabilities by orders of magnitude offering access to ns simulations for 100k-atom biosystems while offering the possibility of coupling DNNs to any classical (FFs) and many-body polarizable (PFFs) force fields. It allows therefore the introduction of the ANI-2X/AMOEBA hybrid polarizable potential designed for ligand binding studies where solvent-solvent and solvent-solute interactions are computed with the AMOEBA PFF while solute-solute ones are computed by the ANI-2X DNN. ANI-2X/AMOEBA explicitly includes AMOEBA's physical long-range interactions via an efficient Particle Mesh Ewald implementation while preserving ANI-2X's solute short-range quantum mechanical accuracy. The DNN/PFF partition can be user-defined allowing for hybrid simulations to include key ingredients of biosimulation such as polarizable solvents, polarizable counter ions, etc.… ANI-2X/AMOEBA is accelerated using a multiple-timestep strategy focusing on the model's contributions to low-frequency modes of nuclear forces. It primarily evaluates AMOEBA forces while including ANI-2X ones only via correction-steps resulting in an order of magnitude acceleration over standard Velocity Verlet integration. Simulating more than 10 μs, we compute charged/uncharged ligand solvation free energies in 4 solvents, and absolute binding free energies of host-guest complexes from SAMPL challenges. ANI-2X/AMOEBA average errors are discussed in terms of statistical uncertainty and appear in the range of chemical accuracy compared to experiment. The availability of the Deep-HP computational platform opens the path towards large-scale hybrid DNN simulations, at force-field cost, in biophysics and drug discovery.

Monitoring the melting behavior of boron nanoparticles using a neural network potential

The melting behavior of metal additives is fundamental for various propulsion and energy-conversion applications. A neural network potential (NNP) is proposed to examine the size-dependent melting behaviors of boron nanoparticles. Our NNP model is proven to possess a desirable computational efficiency and retain ab initio accuracy, allowing investigation of the physicochemical properties of bulk boron crystals from an atomic perspective. In this work, a series of NNP-based molecular dynamics simulations were conducted and numerical evidence of the size-dependent melting behavior of boron nanoparticles with diameters from 3 to 6 nm was reported for the first time. Evolution of the intermolecular energy and the Lindemann index are used to monitor the melting process. A liquid layer forms on the particle surface and further expands with increased temperature. Once the liquid layer reaches the core region, the particle is completely molten. The reduced melting temperature of the boron nanoparticle decreases with its particle size following a linear relationship with reciprocal size, similar to other commonly used metals (Al and Mg). Additionally, boron nanoparticles are more sensitive to particle size than Al particles and less sensitive than Mg particles. These findings provide an atomistic perspective for developing manufacturing techniques and tailoring combustion performance in practical applications.

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

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

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.

Machine Learning Assisted Simulations of Electrochemical Interfaces: Recent Progress and Challenges

The electrochemical interface, where the adsorption of reactants and electrocatalytic reactions take place, has long been a focus of attention. Some of the important processes on it tend to possess relatively slow kinetic characteristics, which are usually beyond the scope of ab initio molecular dynamics. The newly emerging technique, machine learning methods, provides an alternative approach to achieve thousands of atoms and nanosecond time scale while ensuring precision and efficiency. In this Perspective, we summarize in detail the recent progress and achievements made by the introduction of machine learning to simulate electrochemical interfaces, and focus on the limitations of current machine learning models, such as accurate descriptions of long-range electrostatic interactions and the kinetics of the electrochemical reactions occurring at the interface. Finally, we further point out the future directions for machine learning to expand in the field of electrochemical interfaces.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Dynamics of Aqueous Electrolyte Solutions: Challenges for Simulations

This Perspective article focuses on recent simulation work on the dynamics of aqueous electrolytes. It is well-established that full-charge, nonpolarizable models for water and ions generally predict solution dynamics that are too slow in comparison to experiments. Models with reduced (scaled) charges do better for solution diffusivities and viscosities but encounter issues describing other dynamic phenomena such as nucleation rates of crystals from solution. Polarizable models show promise, especially when appropriately parametrized, but may still miss important physical effects such as charge transfer. First-principles calculations are starting to emerge for these properties that are in principle able to capture polarization, charge transfer, and chemical transformations in solution. While direct ab initio simulations are still too slow for simulations of large systems over long time scales, machine-learning models trained on appropriate first-principles data show significant promise for accurate and transferable modeling of electrolyte solution dynamics.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

Transferable Deep Learning Potential Reveals Intermediate-Range Ordering Effects in LiF-NaF-ZrF4 Molten Salt

LiF-NaF-ZrF₄ multicomponent molten salts are promising candidate coolants for advanced clean energy systems owing to their desirable thermophysical and transport properties. However, the complex structures enabling these properties, and their dependence on composition, is scarcely quantified due to limitations in simulating and interpreting experimental spectra of highly disordered, intermediate-ranged structures. Specifically, size-limited ab initio simulations and accuracy-limited classical models used in the past are unable to capture a wide range of fluctuating motifs found in the extended heterogeneous structures of liquid salt. This greatly inhibits our ability to design tailored compositions and materials. Here, accurate, efficient, and transferable machine learning potentials are used to predict structures far beyond the first coordination shell in LiF-NaF-ZrF₄. Neural networks trained at only eutectic compositions with 29% and 37% ZrF₄ are shown to accurately simulate a wide range of compositions (11-40% ZrF₄) with dramatically different coordination chemistries, while showing a remarkable agreement with theoretical and experimental Raman spectra. The theoretical Raman calculations further uncovered the previously unseen shift and flattening of bending band at ∼250 cm^-1 which validated the simulated extended-range structures as observed in compositions with higher than 29% ZrF₄ content. In such cases, machine learning-based simulations capable of accessing larger time and length scales (beyond 17 Å) were critical for accurately predicting both structure and ionic diffusivities.

Quantifying the Structure of Water and Hydrated Monovalent Ions by Density Functional Theory-Based Molecular Dynamics

The accurate description of the structures of water and hydrated ions is important in electrochemical desalination, ion separation, and supercapacitors. In this work, we present an ab initio atomistic simulation-based study to explore the structure of water and hydrated monovalent ions (Li⁺, Na⁺, K⁺, Rb⁺, F^-, and Cl^-) at ambient conditions using generalized gradient approximation (GGA)-based methods with and without van der Waals correction (PBE, PBE + D3, and revPBE + D3) and recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. We find that both revPBE + D3 and SCAN can well capture the structure of bulk water with +30 K artificial high temperature in contrast to overstructuring water using PBE and PBE + D3. However, being the same as PBE + D3, revPBE + D3 overestimates the structure of the hydration shell, especially for monovalent cations. Surprisingly, SCAN can well match the experimental results of hydrated monovalent ions. Detailed structure analyzes of entropy reveal that the hydration shell under the level of PBE + D3 and revPBE + D3 is more disordered and looser than SCAN. The successful prediction of the flexible SCAN functional could facilitate the exploration of complex ionic processes in the aqueous phase, the interactions of hydrated ions with surfaces, and solvation states in nanopores at an accurate, efficient, predictive, and ab initio level.

Defect-free and crystallinity-preserving ductile deformation in semiconducting Ag2S

Typical ductile materials are metals, which deform by the motion of defects like dislocations in association with non-directional metallic bonds. Unfortunately, this textbook mechanism does not operate in most inorganic semiconductors at ambient temperature, thus severely limiting the development of much-needed flexible electronic devices. We found a shear-deformation mechanism in a recently discovered ductile semiconductor, monoclinic-silver sulfide (Ag2S), which is defect-free, omni-directional, and preserving perfect crystallinity. Our first-principles molecular dynamics simulations elucidate the ductile deformation mechanism in monoclinic-Ag2S under six types of shear systems. Planer mass movement of sulfur atoms plays an important role for the remarkable structural recovery of sulfur-sublattice. This in turn arises from a distinctively high symmetry of the anion-sublattice in Ag2S, which is not seen in other brittle silver chalcogenides. Such mechanistic and lattice-symmetric understanding provides a guideline for designing even higher-performance ductile inorganic semiconductors.

Towards fully ab initio simulation of atmospheric aerosol nucleation

Atmospheric aerosol nucleation contributes to approximately half of the worldwide cloud condensation nuclei. Despite the importance of climate, detailed nucleation mechanisms are still poorly understood. Understanding aerosol nucleation dynamics is hindered by the nonreactivity of force fields (FFs) and high computational costs due to the rare event nature of aerosol nucleation. Developing reactive FFs for nucleation systems is even more challenging than developing covalently bonded materials because of the wide size range and high dimensional characteristics of noncovalent hydrogen bonding bridging clusters. Here, we propose a general workflow that is also applicable to other systems to train an accurate reactive FF based on a deep neural network (DNN) and further bridge DNN-FF-based molecular dynamics (MD) with a cluster kinetics model based on Poisson distributions of reactive events to overcome the high computational costs of direct MD. We found that previously reported acid-base formation rates tend to be significantly underestimated, especially in polluted environments, emphasizing that acid-base nucleation observed in multiple environments should be revisited.

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab initio molecular dynamics simulations. In this study, we present a deep neural network potential trained using accurate ab initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK_a, as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab initio methods is required.

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

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

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.