Deep Potential Research Articles

Understanding melting behavior of aluminum clusters using machine learned deep neural network potential energy surfaces.

Deep neural network-based deep potentials (DP), developed by Tuo et al., have been used to compute the thermodynamic properties of free aluminum clusters with accuracy close to that of density functional theory. Although Jarrold and collaborators have reported extensive experimental measurements on the melting temperatures and heat capacities of free aluminum clusters, no reports exist for finite-temperature abinitio simulations on larger clusters (N > 55 atoms). We report the heat capacities and melting temperatures for 32 clusters in the size range of 48-342 atoms, computed using the multiple histogram technique. Extensive molecular dynamics (MD) simulations at twenty four temperatures have been performed for all the clusters. Our results are in very good agreement with the experimental melting temperatures for 19 clusters. Except for a few sizes, the interesting features in the heat capacities have been reproduced. To gain insight into the striking features reported in the experiments, we used structural and dynamical descriptors such as temperature-dependent mean squared displacements and the Lindemann index. Bimodal features observed in Al116 and the weak shoulder seen in Al52 are attributed to solid-solid structural transitions. In confirmation of the earlier reports, we observe that the behavior of the heat capacities is significantly influenced by the nature of the ground state geometries. Our findings show that the sharp drop in the melting temperature of the 56-atom cluster is a consequence of the change in the geometry of Al55. Mulliken population analysis of Al55 reveals that the charge-induced local electric field is responsible for the strong bonding between core and surface atoms, leading to the higher melting temperature. Our calculations do not support the lower melting temperature observed in experimental studies of Al69. Our results indicate that Al48 is in a liquid state above 600K and does not support the high melting temperature reported in the experiment. It turns out that the accuracy of the DP model by Tuo et al. is not reliable for MD simulations beyond 750K. We also report low-lying equilibrium geometries and thermodynamics of 11 larger clusters (N = 147-342) that have not been previously reported, and the melting temperatures of these clusters are in good agreement with the experimental ones.

Formation and Dynamics of Imidazole Supramolecular Chains Investigated by Deep Potential Molecular Dynamics Simulation.

Imidazole-based materials have attracted considerable attention due to their promising potential for facilitating anhydrous proton transport at high temperatures. Herein, a machine learning-based deep potential (DP) model for bulk imidazole with first-principles accuracy is developed. The trained model exhibits remarkable accuracy in predicting energies and forces, with minor errors of 4.71 × 10-4 eV/atom and 3.23 × 10-2 eV/Å, respectively. Utilizing DP molecular dynamics simulations, we have systematically investigated the temperature-dependent formation and dynamics of imidazole supramolecular chains through the partial radial distribution function, quantification of hydrogen bond numbers, incoherent intermediate scattering function, and diffusion coefficient. The findings reveal the influence of temperature on the proton transport path following either the "Grotthuss" and "vehicle" mechanism.

Simulation of lithium hydroxide decomposition using deep potential molecular dynamics.

Chemical reactions and vapor-liquid equilibria for molten lithium hydroxide (LiOH) were studied using molecular dynamics simulations and a deep potential (DP) model. The neural network for the model was trained on quantum density functional theory data for a range of conditions. The DP model allows simulations over timescales of hundreds of ns, which provide equilibrium compositions for the systems of interest. Single-phase NPT simulations of the liquid show the decomposition of LiOH into lithium oxide (Li2O) and dissolved water (H2O). These DP results were validated by direct abinitio molecular dynamics simulations that confirmed the accuracy of the model with respect to reaction kinetics and equilibrium properties of the melt. The reactive vapor-liquid behavior of this system was subsequently studied using direct coexistence interfacial DP simulations. Partial pressures of H2O in the vapor are found to be in close agreement with available experimental measurements. By fitting temperature-dependent expressions for the reaction equilibrium and Henry's law constants, the equilibrium composition for any given initial composition and temperature can be quantitatively modeled. For high initial concentrations of Li2O or H2O, mixtures of LiOH + Li2O/H2O are found to undergo phase separation. The present study illustrates how DP-based molecular dynamics simulations can be used for quantitative modeling of multiphase reactive behavior with the accuracy of the underlying abinitio quantum chemical methods.

Molecular dynamics simulations of the shear and tensile mechanical properties of rare-earth metal erbium based on deep-learning potential

To gain atomic insights into the physical and mechanical properties of rare-earth metal erbium (Er), performing molecular dynamics (MD) simulations is highly advantageous but has been constrained for lacking of Er interatomic potential. In this work, the essential Er potential for MD simulations was developed by using the deep-potential (DP) method based on first-principles calculations. By systematically comparing the DP-predicated physical properties (melting and solidifying points, elastic properties, etc.) with the results of density functional theory (DFT), experimental or MEAM, we demonstrated that the developed DP model of Er exhibits satisfactory generalization ability and reasonable DFT accuracy on predicting these properties. From the DP-predicted results, we confirmed that the HCP-Er is mechanically stable. The melting point of HCP-Er is 1847 K, while the solidifying point is 1105 K at the cooling rate of 1×1011 K/s. Moreover, we found that the prismatic unstable stacking fault energy of HCP-Er is lower than the basal one, indicating that the Shockley partial dislocation along prismatic planes is easier to slip. The basal/prismatic and prismatic/basal interfaces were discovered during the tensile deformation of HCP-Er single-crystal along the [0001] direction, signifying the occurrence of the parent-to-‘twin’ lattice reorientation. The yield strength of HCP-Er decreases from 5.41 to 5.21 GPa with rising the temperature from 150 to 500 K. The results would be helpful for better understanding the mechanical behaviors of metal Er and further developing the binary or multinary Er-containing DP models.

Melting temperature of iron under the Earth’s inner core condition from deep machine learning

Constraining the melting temperature of iron under Earth’s inner core conditions is crucial for understanding core dynamics and planetary evolution. Here, we develop a deep potential (DP) model for iron that explicitly incorporates electronic entropy contributions governing thermodynamics under Earth’s core conditions. Extensive benchmarking demonstrates the DP’s high fidelity across relevant iron phases and extreme pressure and temperature conditions. Through thermodynamic integration and direct solid–liquid coexistence simulations, the DP predicts melting temperatures for iron at the inner core boundary, consistent with previous ab initio results. This resolves the previous discrepancy of iron’s melting temperature at ICB between the DP model and ab initio calculation and suggests the crucial contribution of electronic entropy. Our work provides insights into machine learning melting behavior of iron under core conditions and provides the basis for future development of binary or ternary DP models for iron and other elements in the core.

An accurate and transferable machine learning interatomic potential for nickel

Nickel (Ni) is a magnetic transition metal with two allotropic phases, stable face-centered cubic (FCC) and metastable hexagonal close-packed (HCP), widely used in structural applications. Magnetism affects many mechanical and defect properties, but spin-polarized density functional theory (DFT) calculations are computationally inefficient for studying material behavior requiring large system sizes and/or long simulation times. Here we develop a “magnetism-hidden” machine-learning Deep Potential (DP) model for Ni without a descriptor for magnetic moments, using training datasets derived from spin-polarized DFT calculations. The DP-Ni model exhibits excellent transferability and representability for a wide-range of FCC and HCP properties, including (finite-temperature) lattice parameters, elastic constants, phonon spectra, and many defects. As an example of its applicability, we investigate the Ni FCC-HCP allotropic phase transition under (high-stress) uniaxial tensile loading. The high accurate DP model for magnetic Ni facilitates accurate large-scale atomistic simulations for complex phase transformation behavior and may serve as a foundation for developing interatomic potentials for Ni-based superalloys and other multi-principal component alloys.

Investigation of the Degradation of LiPF6- in Polar Solvents through Deep Potential Molecular Dynamics.

The nonaqueous electrolyte based on lithium hexafluorophosphate (LiPF6) is the dominant liquid electrolyte in lithium-ion batteries (LIBs). However, trace protic impurities, including H3O+, alcohols, and hydrofluoric acid (HF), can trigger a series of side reactions that lead to rapid capacity fading in high energy density LIBs. It is worth noting that this degradation process is highly dependent on the polarity of the solvents. In this work, a deep potential (DP) model is trained with a certain commercial electrolyte formula through a machine learning method. H3O+ is anchored with polar solvents, making it difficult to approach the PF6-, and suppressing the degradation process quickly at room temperature. Control experiments and simulations at different temperatures or concentrations are also performed to verify it. This work proposes a precise model to describe the solvation structure quantitatively and offers a new perspective on the degradation mechanism of PF6- in polar solvents.

Properties of radiation defects and threshold energy of displacement in zirconium hydride obtained by new deep-learning potential

Abstract Zirconium hydride (ZrH2) is an ideal neutron moderator material. However, radiation effect significantly changes its properties, which affect its behavior and the lifespan of the reactor. The threshold energy of displacement is an important quantity of the number of radiation defects produced, which helps us to predict the evolution of radiation defects in ZrH2. Molecular dynamics (MD) and ab initio molecular dynamics (AIMD) are two main methods of calculating the threshold energy of displacement. The MD simulations with empirical potentials often cannot accurately depict the transitional states that lattice atoms must surpass to reach an interstitial state. Additionally, the AIMD method is unable to perform large-scale calculation, which poses a computational challenge beyond the simulation range of density functional theory. Machine learning potentials are renowned for their high accuracy and efficiency, making them an increasingly preferred choice for molecular dynamics simulations. In this work, we develop an accurate potential energy model for the ZrH2 system by using the deep-potential (DP) method. The DP model has a high degree of agreement with first-principles calculations for the typical defect energy and mechanical properties of the ZrH2 system, including the basic bulk properties, formation energy of point defects, as well as diffusion behavior of hydrogen and zirconium. By integrating the DP model with Ziegler–Biersack–Littmark (ZBL) potential, we can predict the threshold energy of displacement of zirconium and hydrogen in ε-ZrH2.

Modelling infrared spectra of the O-H stretches in liquid H2O based on a deep learning potential, the importance of nuclear quantum effects

ABSTRACT In this study, we have trained a deep learning (DL) potential for water using training datasets obtained from the DPLibrary (https://dplibrary.deepmd.net/). Subsequently, we conducted classical molecular dynamics simulation (DeePMD) and path-integral MD simulation (PI-DeePMD) of liquid water based on this deep potential (DP). Using the velocity-velocity auto-correlation function (VVAF) formula, we constructed infrared (IR) spectra for the O-H stretching mode based on the DeePMD simulation trajectories. Our results showed that the DeePMD/VVAF approach accurately captured the experimental result for O-H stretching vibration, with the O-H vibrational peak located at 3400 cm−1. Additionally, the PI-DeePMD approach successfully predicted the red-shift and broadening of the O-H stretching band of water, emphasising the importance of nuclear quantum effects (NQEs). In particular, the PI-DeePMD simulation correctly reproduced the shoulder located at 3250 cm−1, which was underestimated by classical DeePMD simulation. The success of the PI-DeePMD/VVAF approach can be attributed to the following reasons: (1) the DeePMD simulation improves the accuracy of calculating atomic velocities due to the DFT-level accuracy of the DP model; (2) the PI-DeePMD simulation takes into account the contribution from nuclear quantum effects; (3) the non-Condon effect is considered in the VVAF formalism.

Deep Potential Molecular Dynamics Study of Propane Oxidative Dehydrogenation.

Oxidative dehydrogenation (ODH) of light alkanes is a key process in the oxidative conversion of alkanes to alkenes, oxygenated hydrocarbons, and COx (x = 1,2). Understanding the underlying mechanisms extensively is crucial to keep the ODH under control for target products, e.g., alkenes rather than COx, with minimal energy consumption, e.g., during the alkene production or maximal energy release, e.g., during combustion. In this work, deep potential (DP), a neural network atomic potential developed in recent years, was employed to conduct large-scale accurate reactive dynamic simulations. The model was trained on a sufficient data set obtained at the density functional theory level. The intricate reaction network was elucidated and organized in the form of a hierarchical network to demonstrate the key features of the ODH mechanisms, including the activation of propane and oxygen, the influence of propyl reaction pathways on the propene selectivity, and the role of rapid H2O2 decomposition for sustainable and efficient ODH reactions. The results indicate the more complex reaction mechanism of propane ODH than that of ethane ODH and are expected to provide insights in the ODH catalyst optimization. In addition, this work represents the first application of deep potential in the ODH mechanistic study and demonstrates the ample advantages of DP in the study of mechanism and dynamics of complex systems.

Investigating the interfacial charge transfer between electrodeposited BiVO4 and pulsed laser-deposited Co3O4 p-n junction photoanode in photoelectrocatalytic water splitting

The formation of a p-n junction consisting small-sized, and homogeneous material over the porous semiconductor is an effective strategy for improved photoelectrocatalytic (PEC) water oxidation. Here, the facile pulsed laser deposition (PLD) method was used to load small-sized Co3O4 on BiVO4. The BiVO4/Co3O4 (30 s) photoanode exhibits a higher photocurrent density of 4.66 mA cm−2 @ +1.23 VRHE which is ∼ 4-fold higher than pristine BiVO4. This improved PEC performance is due to the availability of more active sites, improved charge separation, rapid interfacial charge transfer process, higher injection ability, and higher water oxidation kinetics. The higher open circuit voltage (VOC) of BiVO4/Co3O4 offers the greater driving force for charge separation. On the other hand, the density functional theory (DFT) investigations were carried out for further understanding of the facile interfacial charge transfer process. The electrostatic plots from the DFT studies reveals that Co3O4 has a deeper potential than BiVO4 and this potential difference can induce a strong internal electric field across the junction which promotes facile charge transfer from BiVO4 to Co3O4 until equilibration. Under illumination, BiVO4 and Co3O4 act electron acceptor and hole acceptor, respectively. Hence, the hole accumulated water oxidation is taken place in the valence band maximum (VBM) of Co3O4 for an enhanced PEC performance of the p-n junction photoanode.

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.

Determining the thermal conductivity and phonon behavior of SiC materials with quantum accuracy via deep learning interatomic potential model

SiC is essential for next-generation semiconductors and nuclear plant components. Its performance is strongly influenced by its thermal conductivity, which is highly sensitive to its microstructure. Molecular dynamics (MD) simulation is one of the most reliable methods for studying thermal transportation mechanisms in devices with nano-scale microstructures. Nevertheless, owing to inaccurate interatomic potentials, the implementation of MD for studying SiC still presents limitations. This study used the deep potential (DP) methodology to develop two interatomic potential (DP-IAPs) models for studying SiC, based on two adaptively generated datasets within the density functional approximations at the local density and generalized gradient levels. Combined with the LD and MD simulations, the thermal transport and mechanical properties of SiC were systematically investigated. The proposed DP-IAPs can accurately reproduce the structural properties, phonon behaviors, and thermal properties of various SiC polytypes. The two DP-IAPs exhibited extraordinary speed with high accuracy in both simulating the lattice dynamics (LD) and analyzing the scattering rate of phonon transportation. Our proposed methodology paves the way for a systematic approach to model heat transport in SiC-based devices and nuclear grade SiC components using multiscale modeling.

Compositional transferability of deep potential in molten LiF-BeF2 and LaF3 mixtures: prediction of density, viscosity, and local structure.

The accumulation of lanthanide fission products carries the risk of altering the structure and properties of the nuclear fuel carrier salt LiF-BeF2 (Flibe), thereby downgrading the operating efficiency and safety of the molten salt reactor. However, the condition-limited experimental measurements, spatiotemporal-limited first-principles calculations, and accuracy-limited classical dynamic simulations are unable to capture the precise local structure and reliable thermophysical properties of heterogeneous molten salts. Therefore, the deep potential (DP) of LaF3 and Flibe molten mixtures is developed here, and DP molecular dynamics simulations are performed to systemically study the densities, diffusion coefficients, viscosities, radial distribution functions and coordination numbers of multiple molten Flibe + xLaF3, the quantitative relationships between these properties and LaF3 concentration are investigated, and the potential structure-property relationships are analyzed. Eventually, the transferability of DP on molten Flibe + LaF3 with different formulations as well as the predictability of structures and properties are achieved at the nanometer spatial scale and the nanosecond timescale.

Hierarchical structures and magnetism of Co clusters: a perspective from integration of deep learning and a hybrid differential evolution algorithm.

Theoretically determining the lowest-energy structure of a cluster has been a persistent challenge due to the inherent difficulty in accurate description of its potential energy surface (PES) and the exponentially increasing number of local minima on the PES with the cluster size. In this work, density-functional theory (DFT) calculations of Co clusters were performed to construct a dataset for training deep neural networks to deduce a deep potential (DP) model with near-DFT accuracy while significantly reducing computational consumption comparable to classic empirical potentials. Leveraging the DP model, a high-efficiency hybrid differential evolution (HDE) algorithm was employed to search for the lowest-energy structures of CoN (N = 11-50) clusters. Our results revealed 38 of these clusters superior to those recorded in the Cambridge Cluster Database and identified diverse architectures of the clusters, evolving from layered structures for N = 11-27 to Marks decahedron-like structures for N = 28-42 and to icosahedron-like structures for N = 43-50. Subsequent analyses of the atomic arrangement, structural similarity, and growth pattern further verified their hierarchical structures. Meanwhile, several highly stable clusters, i.e., Co13, Co19, Co22, Co39, and Co43, were discovered by the energetic analyses. Furthermore, the magnetic stability of the clusters was verified, and a competition between the coordination number and bond length in affecting the magnetic moment was observed. Our study provides high-accuracy and high-efficiency prediction of the optimal structures of clusters and sheds light on the growth trend of Co clusters containing tens of atoms, contributing to advancing the global optimization algorithms for effective determination of cluster structures.

Deep learning interatomic potential for thermal and defect behaviour of aluminum nitride with quantum accuracy

Due to its exceptional physical properties, such as high thermal conductivity and mechanical strength, AlN has been widely used in high-power, high-temperature electronic, and optoelectronic devices. Molecular dynamics simulation is a powerful tool to study its thermal and defect properties. The selection of interatomic potentials plays an important role in the accuracy of calculation results. However, molecular dynamics simulations with various interatomic potentials have yielded different results when investigating the thermal and defect properties of AlN over the last few decades. In this paper, an interatomic potential (DP-IAP) model is developed using a deep potential (DP) methodology for AlN, with the training model's datasets derived from density functional theory (DFT) calculations. The DP-IAP demonstrates quantum-level accuracy in the calculation of the mechanical properties, thermal transport properties, and the defects formation and defects migration for AlN. The developed DP model paves the way for modeling thermal transport and defect evolution in AlN-based devices.

Machine-learning-driven simulations on microstructure, thermodynamic properties, and transport properties of LiCl-KCl-LiF molten salt

The thermodynamic and transport properties of high-temperature chloride molten salt systems are of great significance for spent fuel reprocessing in the field of nuclear energy engineering. Here, by using machine learning based deep potential (DP) method, we train a high-precision force field model for the LiCl-KCl-LiF system. During force field training, adding new dataset through multiple iterations improves the accuracy of the force field model and its applicability to more configurations. The comparison of density functional theory (DFT) and DP results for the test dataset indicates that our trained DP model has the same accuracy as DFT. Then, we comprehensively investigate the local structure, thermophysical properties, and transport properties of the LiCl-KCl and LiCl-KCl-LiF molten salt systems using the trained DP model. The effects of temperature and LiF concentration on the above properties are analyzed. This work provides guidance for the training of machine learning force fields in molten salt systems and the study of basic physical properties of high-temperature chloride molten salt systems.

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 abinitio 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 ∼238.8meV 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/m2K, smaller than ∼13.17 × 109 W/m2K 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.

Interfacial heat and mass transfer at silica/binary molten salt interface from deep potential molecular dynamics

Interfacial heat and mass transfer properties at molten salt/solid interfaces are crucial for the study of heat storage/transfer properties of molten salt nanocomposite materials as well as the microscopic mechanism of thermophysical property enhancement, but accurate force field parameters for describing molten salt-solid interactions are still lacking. This study has utilized a workflow that could meet the demand of high accuracy and efficiency in molecular dynamics (MD) simulations of molten salt/solid interface with the deep potentials (DPs) trained by deep learning (DL), using SiO2/LiCl-KCl interface as a model system. In terms of the short-ranged polarizability and long-ranged correlations of ions, DPs can give accurate description of potential energy surface over wide temperature range at the level of ab initio calculations. Further analysis on interfacial thermal resistance (ITR) and thermal conductivity shows that the slowing down of heat transfer is related to the disordered microstructure of molten salt ions near the SiO2 surfaces, which also leads to larger ITR. For the mass transfer of molten salt ions on the SiO2 surfaces, the more active ionic diffusion and permeation through the solid can be observed due to the weaker adsorption between them, which is ascribed primarily to the high temperature. The workflow, of which the feasibility has been verified for molten salt/solid interfaces in this work with rigorous modeling, will be used for building accurate interatomic interaction models and calculating thermophysical properties for various complex interfacial systems containing molten salts. The influence of interfacial microstructure on heat and mass transfer will provide theoretical support for the application of molten salts in energy industry.

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.