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

PW-SMD: A Plane-Wave Implicit Solvation Model Based on Electron Density for Surface Chemistry and Crystalline Systems in Aqueous Solution

Electron density-based implicit solvation models are a class of techniques for quantifying solvation effects and calculating free energies of solvation without an explicit representation of solvent molecules. Integral to the accuracy of solvation modeling is the proper definition of the solvation shell separating the solute molecule from the solvent environment, allowing for a physical partitioning of the free energies of solvation. Unlike state-of-the-art implicit solvation models for molecular quantum chemistry calculations, e.g., the solvation model based on solute electron density (SMD), solvation models for systems under periodic boundary conditions with plane-wave (PW) basis sets have been limited in their accuracy. Furthermore, a unified implicit solvation model with both homogeneous solution-phase and heterogeneous interfacial structures treated on equal footing is needed. In order to address this challenge, we developed a high-accuracy solvation model for periodic PW calculations that is applicable to molecular, ionic, interfacial, and bulk-phase chemistry. Our model, PW-SMD, is an extension of the SMD molecular solvation model to periodic systems in water. The free energy of solvation is partitioned into the electrostatic and cavity-dispersion-solvent structure (CDS) contributions. The electrostatic contributions of the solvation shell surrounding solute structures are parametrized based on their geometric and physical properties. In addition, the nonelectrostatic contribution to the solvation energy is accounted for by extending the CDS formalism of SMD to incorporate periodic boundary conditions. We validate the accuracy and robustness of our solvation model by comparing predicted solvation free energies against experimental data for molecular and ionic systems, carved-cluster composite energetic models of solvated reaction energies and barriers on surface systems, and deep-learning-accelerated ab initio molecular dynamics (AIMD). Our developed periodic implicit solvation model shows significantly improved accuracy compared to previous work (namely, solvation models in aqueous solution) and can be applied to simulate solvent effects in a wide range of surface and crystalline materials.

Hydroxide and Hydronium Ions Modulate the Dynamic Evolution of Nitrogen Nanobubbles in Water

It has been widely recognized that the pH environment influences the nanobubble dynamics and hydroxide ions adsorbed on the surface may be responsible for the long-term survival of the nanobubbles. However, understanding the distribution of hydronium and hydroxide ions in the vicinity of a bulk nanobubble surface at a microscopic scale and the consequent impact of these ions on the nanobubble behavior remains a challenging endeavor. In this study, we carried out deep potential molecular dynamics simulations to explore the behavior of a nitrogen nanobubble under neutral, acidic, and alkaline conditions and the inherent mechanism, and we also conducted a theoretical thermodynamic and dynamic analysis to address constraints related to simulation duration. Our simulations and theoretical analyses demonstrate a trend of nanobubble dissolution similar to that observed experimentally, emphasizing the limited dissolution of bulk nanobubbles in alkaline conditions, where hydroxide ions tend to reside slightly farther from the nanobubble surface than hydronium ions, forming more stable hydrogen bond networks that shield the nanobubble from dissolution. In acidic conditions, the hydronium ions preferentially accumulating at the nanobubble surface in an orderly manner drive nanobubble dissolution to increase the entropy of the system, and the dissolved nitrogen molecules further strengthen the hydrogen bond networks of systems by providing a hydrophobic environment for hydronium ions, suggesting both entropy and enthalpy effects contribute to the instability of nanobubbles under acidic conditions. These results offer fresh insights into the double-layer distribution of hydroxide and hydronium near the nitrogen-water interface that influences the dynamic behavior of bulk nanobubbles.

The Reconstruction of Pt(001) Surface and the Shell-Like Reconstruction of the Vicinal Pt(001) Surfaces Revealed by Neural Network Potential

In this work, a highly accurate neural network potential (NNP) is presented, named PtNNP, and the exploration of the reconstruction of the Pt(001) surface and its vicinal surfaces with it. Contrary to the most accepted understanding of the Pt(001) surface reconstruction, the study reveals that the main driving force behind Pt(001) quasi-hexagonal reconstruction is not the surface stress relaxation but the increased coordination number of the surface atoms resulting in stronger intralayer binding in the reconstructed surface layer. In agreement with experimental observations, the optimized supercell size of the reconstructed Pt(001) surface contains (5 × 20) unit cells. Surprisingly, the reconstruction of the vicinal Pt(001) surfaces leads to a smooth shell-like surface layer covering the whole surface and diminishing sharp step edges.

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

Tuning Interfacial Water Friction through Moiré Twist

Foundations of nanofluidics can enable advances in diverse applications such as water desalination, energy harvesting, and biological analysis. Dynamically manipulating nanofluidic properties, such as diffusion and friction, is an area of great scientific interest. Twisted bilayer graphene, particularly at the magic angle, has garnered attention for its unconventional superconductivity and correlated insulator behavior due to strong electronic correlations. The impact of the electronic properties of moiré patterns in twisted bilayer graphene on structural and dynamic properties of water remains largely unexplored. Computational challenges, stemming from simulating large unit cells using density functional theory, have hindered progress. This study addresses this gap by investigating water behavior on twisted bilayer graphene, employing a deep neural network potential (DP) model trained with a data set from ab initio molecular dynamics simulations. It is found that as the twisted angle approaches the magic angle, interfacial water friction increases, leading to a reduced water diffusion. Notably, the analysis shows that at smaller twisted angles with larger moiré patterns, water is more likely to reside in AA stacking regions than AB (or BA) stacking regions, a distinction that diminishes with smaller moiré patterns. This study illustrates the potential for leveraging the distinctive properties of moiré systems to effectively control and optimize interfacial fluid behavior.

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Prebiotic chemical reactivity in solution with quantum accuracy and microsecond sampling using neural network potentials

While RNA appears as a good candidate for the first autocatalytic systems preceding the emergence of modern life, the synthesis of RNA oligonucleotides without enzymes remains challenging. Because the uncatalyzed reaction is extremely slow, experimental studies bring limited and indirect information on the reaction mechanism, the nature of which remains debated. Here, we develop neural network potentials (NNPs) to study the phosphoester bond formation in water. While NNPs are becoming routinely applied to nonreactive systems or simple reactions, we demonstrate how they can systematically be trained to explore the reaction phase space for complex reactions involving several proton transfers and exchanges of heavy atoms. We then propagate at moderate computational cost hundreds of nanoseconds of a variety of enhanced sampling simulations with quantum accuracy in explicit solvent conditions. The thermodynamically preferred reaction pathway is a concerted, dissociative mechanism, with the transient formation of a metaphosphate transition state and direct participation of water solvent molecules that facilitate the exchange of protons through the nonbridging phosphate oxygens. Associative-dissociative pathways, characterized by a much tighter pentacoordinated phosphate, are higher in free energy. Our simulations also suggest that diprotonated phosphate, whose reactivity is never directly assessed in the experiments, is significantly less reactive than the monoprotonated species, suggesting that it is probably never the reactive species in normal pH conditions. These observations rationalize unexplained experimental results and the temperature dependence of the reaction rate, and they pave the way for the design of more efficient abiotic catalysts and activating groups.

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.

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

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

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.

Competing Reaction Mechanisms of Peptide Bond Formation in Water Revealed by Deep Potential Molecular Dynamics and Path Sampling

The formation of an amide bond is an essential step in the synthesis of materials and drugs, and in the assembly of amino acids to form peptides. The mechanism of this reaction has been studied extensively, in particular to understand how it can be catalyzed, but a representation capable of explaining all the experimental data is still lacking. Numerical simulation should provide the necessary molecular description, but the solvent involvement poses a number of challenges. Here, we combine the efficiency and accuracy of neural network potential-based reactive molecular dynamics with the extensive and unbiased exploration of reaction pathways provided by transition path sampling. Using microsecond-scale simulations at the density functional theory level, we show that this method reveals the presence of two competing distinct mechanisms for peptide bond formation between alanine esters in aqueous solution. We describe how both reaction pathways, via a general base catalysis mechanism and via direct cleavage of the tetrahedral intermediate respectively, change with pH. This result contrasts with the conventional mechanism involving a single pathway in which only the barrier heights are affected by pH. We show that this new proposal involving two competing mechanisms is consistent with the experimental data, and we discuss the implications for peptide bond formation under prebiotic conditions and in the ribosome. Our work shows that integrating deep potential molecular dynamics with path sampling provides a powerful approach for exploring complex chemical mechanisms.

Ultra-flat bands at large twist angles in group-V twisted bilayer materials

Flat bands in 2D twisted materials are key to the realization of correlation-related exotic phenomena. However, a flat band often was achieved in the large system with a very small twist angle, which enormously increases the computational and experimental complexity. In this work, we proposed group-V twisted bilayer materials, including P, As, and Sb in the β phase with large twist angles. The band structure of twisted bilayer materials up to 2524 atoms has been investigated by a deep learning method DeepH, which significantly reduces the computational time. Our results show that the bandgap and the flat bandwidth of twisted bilayer β-P, β-As, and β-Sb reduce gradually with the decreasing of twist angle, and the ultra-flat band with bandwidth approaching 0 eV is achieved. Interestingly, we found that a twist angle of 9.43° is sufficient to achieve the band flatness for β-As comparable to that of twist bilayer graphene at the magic angle of 1.08°. Moreover, we also find that the bandgap reduces with decreasing interlayer distance while the flat band is still preserved, which suggests interlayer distance as an effective routine to tune the bandgap of flat band systems. Our research provides a feasible platform for exploring physical phenomena related to flat bands in twisted layered 2D materials.

Intramolecular and Water Mediated Tautomerism of Solvated Glycine

Understanding tautomerism and characterizing solvent effects on the dynamic processes pose significant challenges. Using enhanced-sampling molecular dynamics based on state-of-the-art deep learning potentials, we investigated the tautomeric equilibria of glycine in water. We observed that the tautomerism between neutral and zwitterionic glycine can occur through both intramolecular and intermolecular proton transfers. The latter proceeds involving a contact anionic-glycine-hydronium ion pair or separate cationic-glycine-hydroxide ion pair. These pathways with comparable barriers contribute almost equally to the reaction flux.

Long-range proton and hydroxide ion transfer dynamics at the water/CeO2 interface in the nanosecond regime: reactive molecular dynamics simulations and kinetic analysis

The structural properties, dynamical behaviors, and ion transport phenomena at the interface between water and cerium oxide are investigated by reactive molecular dynamics (MD) simulations employing neural network potentials (NNPs). The NNPs are trained to reproduce density functional theory (DFT) results, and DFT-based MD (DFT-MD) simulations with enhanced sampling techniques and refinement schemes are employed to efficiently and systematically acquire training data that include diverse hydrogen-bonding configurations caused by proton hopping events. The water interfaces with two low-index surfaces of (111) and (110) are explored with these NNPs, and the structure and long-range proton and hydroxide ion transfer dynamics are examined with unprecedented system sizes and long simulation times. Various types of proton hopping events at the interface are categorized and analyzed in detail. Furthermore, in order to decipher the proton and hydroxide ion transport phenomena along the surface, a counting analysis based on the semi-Markov process is formulated and applied to the MD trajectories to obtain reaction rates by considering the transport as stochastic jump processes. Through this model, the coupling between hopping events, vibrational motions, and hydrogen bond networks at the interface are quantitatively examined, and the high activity and ion transport phenomena at the water/CeO2 interface are unequivocally revealed in the nanosecond regime.

Quasi-Classical Trajectory Calculation of Rate Constants Using an Ab Initio Trained Machine Learning Model (aML-MD) with Multifidelity Data

Machine learning (ML) provides a great opportunity for the construction of models with improved accuracy in classical molecular dynamics (MD). However, the accuracy of a ML trained model is limited by the quality and quantity of the training data. Generating large sets of accurate ab initio training data can require significant computational resources. Furthermore, inconsistent or incompatible data with different accuracies obtained using different methods may lead to biased or unreliable ML models that do not accurately represent the underlying physics. Recently, transfer learning showed its potential for avoiding these problems as well as for improving the accuracy, efficiency, and generalization of ML models using multifidelity data. In this work, ab initio trained ML-based MD (aML-MD) models are developed through transfer learning using DFT and multireference data from multiple sources with varying accuracy within the Deep Potential MD framework. The accuracy of the force field is demonstrated by calculating rate constants for the H + HO2 → H2 + 3O2 reaction using quasi-classical trajectories. We show that the aML-MD model with transfer learning can accurately predict the rate constants while reducing the computational cost by more than five times compared to the use of more expensive quantum chemistry training data sets. Hence, the aML-MD model with transfer learning shows great potential in using multifidelity data to reduce the computational cost involved in generating the training set for these potentials.

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.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Generating Minimal Training Sets for Machine Learned Potentials

This Letter presents a novel approach for identifying uncorrelated atomic configurations from extensive datasets with a nonstandard neural network workflow known as random network distillation (RND) for training machine-learned interatomic potentials (MLPs). This method is coupled with a DFT workflow wherein initial data are generated with cheaper classical methods before only the minimal subset is passed to a more computationally expensive ab initio calculation. This benefits training not only by reducing the number of expensive DFT calculations required but also by providing a pathway to the use of more accurate quantum mechanical calculations. The method's efficacy is demonstrated by constructing machine-learned interatomic potentials for the molten salts KCl and NaCl. Our RND method allows accurate models to be fit on minimal datasets, as small as 32 configurations, reducing the required structures by at least 1 order of magnitude compared to alternative methods. This reduction in dataset sizes not only substantially reduces computational overhead for training data generation but also provides a more comprehensive starting point for active-learning procedures.

Insights into Lithium Sulfide Glass Electrolyte Structures and Ionic Conductivity via Machine Learning Force Field Simulations

Sulfide-based solid electrolytes (SEs) are important for advancing all-solid-state batteries (ASSBs), primarily due to their high ionic conductivities and robust mechanical stability. Glassy SEs (GSEs) comprising mixed Si and P glass formers are particularly promising for their synthesis process and their ability to prevent lithium dendrite growth. However, to date, the complexity of their glassy structures hinders a complete understanding of the relationships between their structures and properties. This study introduces a new machine learning force field (ML-FF) tailored for lithium sulfide-based GSEs, enabling the exploration of their structural characteristics, mechanical properties, and lithium ionic conductivities. Using molecular dynamic (MD) simulations with this ML-FF, we explore the glass structures in varying compositions, including binary Li2S-SiS2 and Li2S-P2S5 as well as ternary Li2S-SiS2-P2S5. Our simulations yielded consistent results in terms of density, elastic modulus, radial distribution functions, and neutron structure factors compared to DFT and experimental work. Our findings reveal distinct local environments for Si and P within these glasses, with most Si atoms in edge-sharing configurations in Li2S-SiS2 and a mix of corner- and edge-sharing tetrahedra in the ternary Li2S-SiS2-P2S5 composition. For lithium ionic conductivity at 300 K, the 50Li2S-50SiS2 glass displayed the lowest conductivity at 2.1 mS/cm, while the 75Li2S-25P2S5 composition exhibited the highest conductivity at 3.6 mS/cm. The ternary glass showed a conductivity of 2.6 mS/cm, sitting between the two. Moreover, an in-depth analysis of lithium ion diffusion over the MD trajectory in the ternary glass demonstrated a significant correlation between diffusion pathways and the rotational dynamics of nearby SiS4 or PS4 tetrahedra. The ML-FF developed in this study provides an important tool for exploring a broad spectrum of solid-state and mixed former sulfide-based electrolytes.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

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.

Homogeneous water vapor condensation with a deep neural network potential model

Molecular-level nucleation has not been clearly understood due to the complexity of multi-body potentials and the stochastic, rare nature of the process. This work utilizes molecular dynamics (MD) simulations, incorporating a first-principles-based deep neural network (DNN) potential model, to investigate homogeneous water vapor condensation. The nucleation rates and critical nucleus sizes predicted by the DNN model are compared against commonly used semi-empirical models, namely extended simple point charge (SPC/E), TIP4P, and OPC, in addition to classical nucleation theory (CNT). The nucleation rates from the DNN model are comparable with those from the OPC model yet surpass the rates from the SPC/E and TIP4P models, a discrepancy that could mainly arise from the overestimated bulk free energy by SPC/E and TIP4P. The surface free energy predicted by CNT is lower than that in MD simulations, while its bulk free energy is higher than that in MD simulations, irrespective of the potential model used. Further analysis of cluster properties with the DNN model unveils pronounced variations of O-H bond length and H-O-H bond angle, along with averaged bond lengths and angles that are enlarged during embryonic cluster formation. Properties such as cluster surface free energy and liquid-to-vapor density transition profiles exhibit significant deviations from CNT assumptions.

Neural Network-Based Sum-Frequency Generation Spectra of Pure and Acidified Water Interfaces with Air

The affinity of hydronium ions (H3O+) for the air-water interface is a crucial question in environmental chemistry. While sum-frequency generation (SFG) spectroscopy has been instrumental in indicating the preference of H3O+ for the interface, key questions persist regarding the molecular origin of the SFG spectral changes in acidified water. Here we combine nanosecond long neural network (NN) reactive simulations of pure and acidified water slabs with NN predictions of molecular dipoles and polarizabilities to calculate SFG spectra of long reactive trajectories including proton transfer events. Our simulations show that H3O+ ions cause two distinct changes in phase-resolved SFG spectra: first, a low-frequency tail due to the vibrations of H3O+ and its first hydration shell, analogous to the bulk proton continuum, and second, an enhanced hydrogen-bonded band due to the ion-induced static field polarizing molecules in deeper layers. Our calculations confirm that changes in the SFG spectra of acidic solutions are caused by hydronium ions preferentially residing at the interface.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows

Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

Mechanism of Charge Transport in Lithium Thiophosphate

Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.

Atomistic Scale Modeling of Anode/Electrolyte Interfaces in Li-Ion Batteries

A key issue in lithium-ion batteries is understanding the solid electrolyte interphase (SEI) resulting from a reductive reaction on the anode/electrolyte interface. The presence of the SEI layer affects the transport behavior of the ions and electrons between the anode and electrolyte. Despite the influence on interfacial properties, the formation and evolution mechanism of the SEI layer are unclear owing to their complexity and dynamic nature. Atomistic-scale simulations have promoted the understanding of the reaction mechanism on the anode/electrolyte interface, the formation and evolution of the SEI layer, and their fundamental properties. This Perspective discusses the modeling and interpretations of anode/SEI/electrolyte interfaces through computational methods at the atomic-scale and highlights interfacial modeling techniques for a realistic interface design, which can overcome the limited time and length scale with high accuracy.

DP/MM: A Hybrid Model for Zinc-Protein Interactions in Molecular Dynamics

Zinc-containing proteins are vital for many biological processes, yet accurately modeling them using classical force fields is hindered by complicated polarization and charge transfer effects. This study introduces DP/MM, a hybrid force field scheme that utilizes a deep potential model to correct the atomic forces of zinc ions and their coordinated atoms, elevating them from MM to QM levels of accuracy. Trained on the difference between MM and QM atomic forces across diverse zinc coordination groups, the DP/MM model faithfully reproduces structural characteristics of zinc coordination during simulations, such as the tetrahedral coordination of Cys4 and Cys3His1 groups. Furthermore, DP/MM allows water exchange in the zinc coordination environment. With its unique blend of accuracy, efficiency, flexibility, and transferability, DP/MM serves as a valuable tool for studying structures and dynamics of zinc-containing proteins and also represents a pioneering approach in the evolving landscape of machine learning potentials for molecular modeling.

Nuclear quantum effects in the acetylene:ammonia plastic co-crystal

Organic molecular solids can exhibit rich phase diagrams. In addition to structurally unique phases, translational and rotational degrees of freedom can melt at different state points, giving rise to partially disordered solid phases. The structural and dynamic disorder in these materials can have a significant impact on the physical properties of the organic solid, necessitating a thorough understanding of disorder at the atomic scale. When these disordered phases form at low temperatures, especially in crystals with light nuclei, the prediction of material properties can be complicated by the importance of nuclear quantum effects. As an example, we investigate nuclear quantum effects on the structure and dynamics of the orientationally disordered, translationally ordered plastic phase of the acetylene:ammonia (1:1) co-crystal that is expected to exist on the surface of Saturn's moon Titan. Titan's low surface temperature (∼90 K) suggests that the quantum mechanical behavior of nuclei may be important in this and other molecular solids in these environments. By using neural network potentials combined with ring polymer molecular dynamics simulations, we show that nuclear quantum effects increase orientational disorder and rotational dynamics within the acetylene:ammonia (1:1) co-crystal by weakening hydrogen bonds. Our results suggest that nuclear quantum effects are important to accurately model molecular solids and their physical properties in low-temperature environments.

Accurate and Transferable Machine Learning Potential for Molecular Dynamics Simulation of Sodium Silicate Glasses

An accurate and transferable machine learning (ML) potential for the simulation of binary sodium silicate glasses over a wide range of compositions (from 0 to 50% Na2O) was developed. The potential energy surface is approximated by the sum of atomic energy contributions mapped by a neural network algorithm from the local geometry comprising information on atomic distances and angles with neighboring atoms using the DeePMD code [Wang, H. Comput. Phys. Commun. 2018, 228, 178-184]. Our model was trained on a large data set of total energies and atomic forces computed at the density functional theory level on structures extracted from classical molecular dynamics (MD) simulations performed at several temperatures from 300 to 3000 K. This allows for the generation of a robust and transferable ML potential applicable over the full compositional range of glass formability at different temperatures that outperforms the empirical potentials available in the literature in reproducing structures and properties such as bond angle distribution, total distribution functions, and vibrational density of state. The generality of the approach enables the future training of a potential with other or more elements allowing for simulations of structures, properties, and behavior of ternary and multicomponent oxide glasses with nearly ab initio accuracy at a fraction of the computational cost.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Understanding the Anomalous Diffusion of Water in Aqueous Electrolytes Using Machine Learned Potentials

The diffusivity of water in aqueous cesium iodide solutions is larger than that in neat liquid water and vice versa for sodium chloride solutions. Such peculiar ion-specific behavior, called anomalous diffusion, is not reproduced in typical force field based molecular dynamics (MD) simulations due to inadequate treatment of ion-water interactions. Herein, this hurdle is tackled by using machine learned atomic potentials (MLPs) trained on data from density functional theory calculations. MLP based atomistic MD simulations of aqueous salt solutions reproduce experimentally determined thermodynamic, structural, dynamical, and transport properties, including their varied trends in water diffusivities across salt concentration. This enables an examination of their intermolecular structure to unravel the microscopic underpinnings of the differences in their transport properties. While both ions in CsI solutions contribute to the faster diffusion of water molecules, the competition between the heavy retardation by Na ions and the slight acceleration by Cl ions in NaCl solutions reduces their water diffusivity.

Thermal transport across TiO2-H2O interface involving water dissociation: Ab initio-assisted deep potential molecular dynamics

Water dissociation on TiO2 surfaces has been known for decades and holds great potential in various applications, many of which require a proper understanding of thermal transport across the TiO2-H2O interface. Molecular dynamics (MD) simulations play an important role in characterizing complex systems' interfacial thermal transport properties. Nevertheless, due to the imprecision of empirical force field potentials, the interfacial thermal transport mechanism involving water dissociation remains to be determined. To cope with this, a deep potential (DP) model is formulated through the utilization of ab initio datasets. This model successfully simulates interfacial thermal transport accompanied by water dissociation on the TiO2 surfaces. The trained DP achieves a total energy accuracy of ∼238.8 meV and a force accuracy of ∼197.05 meV/Å. The DPMD simulations show that water dissociation induces the formation of hydrogen bonding networks and molecular bridges. Structural modifications further affect interfacial thermal transport. The interfacial thermal conductance estimated by DP is ∼8.54 × 109 W/m2 K, smaller than ∼13.17 × 109 W/m2 K by empirical potentials. The vibrational density of states (VDOS) quantifies the differences between the DP model and empirical potentials. Notably, the VDOS disparity between the adsorbed hydrogen atoms and normal hydrogen atoms demonstrates the influence of water dissociation on heat transfer processes. This work aims to understand the effect of water dissociation on thermal transport at the TiO2-H2O interface. The findings will provide valuable guidance for the thermal management of photocatalytic devices.

ChecMatE: A workflow package to automatically generate machine learning potentials and phase diagrams for semiconductor alloys

Semiconductor alloy materials are highly versatile due to their adjustable properties; however, exploring their structural space is a challenging task that affects the control of their properties. Traditional methods rely on ad hoc design based on the understanding of known chemistry and crystallography, which have limitations in computational efficiency and search space. In this work, we present ChecMatE (Chemical Material Explorer), a software package that automatically generates machine learning potentials (MLPs) and uses global search algorithms to screen semiconductor alloy materials. Taking advantage of MLPs, ChecMatE enables a more efficient and cost-effective exploration of the structural space of materials and predicts their energy and relative stability with ab initio accuracy. We demonstrate the efficacy of ChecMatE through a case study of the InxGa1-xN system, where it accelerates structural exploration at reduced costs. Our automatic framework offers a promising solution to the challenging task of exploring the structural space of semiconductor alloy materials.

PANNA 2.0: Efficient neural network interatomic potentials and new architectures

We present the latest release of PANNA 2.0 (Properties from Artificial Neural Network Architectures), a code for the generation of neural network interatomic potentials based on local atomic descriptors and multilayer perceptrons. Built on a new back end, this new release of PANNA features improved tools for customizing and monitoring network training, better graphics processing unit support including a fast descriptor calculator, new plugins for external codes, and a new architecture for the inclusion of long-range electrostatic interactions through a variational charge equilibration scheme. We present an overview of the main features of the new code, and several benchmarks comparing the accuracy of PANNA models to the state of the art, on commonly used benchmarks as well as richer datasets.