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In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN.
Program summary
Program Title: DP-GEN
Program Files doi: http://dx.doi.org/10.17632/sxybkgc5xc.1
Licensing provisions: LGPL
Programming language: Python
Nature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost.
Solution method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.

To read the full-text of this research,

you can request a copy directly from the authors.

... 80 Compared to its initial release, 29 DeePMD-kit has evolved significantly, with the current version (v2.2.1) offering an extensive range of features. These include DeepPot-SE, attentionbased, and hybrid descriptors, 10,50,51,53 the ability to fit tensorial properties, 105,106 type embedding, model deviation, 103,107 Deep Potential-Range Correction (DPRc), 52,75 Deep Potential Long Range (DPLR), 53 graphics processing unit (GPU) support for customized operators, 108 model compression, 109 non-von Neumann molecular dynamics (NVNMD), 110 and various usability improvements, such as documentation, compiled binary packages, graphical user interfaces (GUIs), and application programming interfaces (APIs). This article provides an overview of the current major version of the DeePMD-kit, highlighting its features and technical details, presenting a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarking the accuracy and efficiency of different models, and discussing ongoing developments. ...

... The maximum model deviation of forces ϵF,max in a frame was found to be the best error indicator in a concurrent or active learning algorithm. 103,107 ...

... The C++, C, or headeronly C++ API has also been integrated into several third-party MD packages, such as LAMMPS, 140,150 i-PI, 151 GROMACS, 152 AMBER, 52,54,141 OpenMM, 153,154 and ABACUS. 155 Moreover, the CLI is called by various third-party workflow packages, such as DP-GEN 107 and MLatom. 34 While the ASE calculator, the LAMMPS plugin, the i-PI driver, and the GROMACS patch are developed within the DeePMD-kit code, others are distributed separately. ...

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 tensorial 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.

... Compared to its initial release 19 , DeePMD-kit has evolved significantly, with the current version (v2.2.1) offering an extensive range of features. These include DeepPot-SE, attentionbased, and hybrid descriptors 10,41,42,44 , the ability to fit tensorial properties 97,98 , type embedding, model deviation 99,100 , Deep Potential -Range Correction (DPRc) 43,81 , Deep Potential Long Range (DPLR) 44 , graphics processing unit (GPU) support for customized operators 101 , model compression 102 , non-von Neumann molecular dynamics (NVNMD) 103 , and various usability improvements such as documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article provides an overview of the current major additions to the DeePMD-kit, highlighting its features and technical details, benchmarking the accuracy and efficiency of different models, and dis- cussing ongoing developments. ...

... DeePMD 1. Deep Potential GENerator (DP-GEN) 100 is a package that implements the concurrent learning procedure 99 and is capable of generating uniformly accurate DP models with minimal human intervention and computational cost. DP-GEN2 is the next generation of this package, built on the workflow platform Dflow. ...

... In all models, we set r s to 0.5Å, M < to 16, and L a to 2, if applicable. We used (25,50,100) We used the LAMMPS package 136 to perform MD simulations for water, Cu, and HEA with as many atoms as possible. We compared the performance of compressed models with that of the original model where applicable. ...

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) 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, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments.

... The neural network potential models are well trained based on datasets generated by Density Function Theory (DFT) calculation without sacrificing accuracy compared with that of AIMD, which has been specially validated as shown in Supplementary Table 7. Consequently, MD with deep-learning potential runs 100-1000 times faster than AIMD while system size is also ten times larger than that of AIMD. The details of computational methods, model training, MD simulation settings (Supplementary Tables 8 and 9) and software packages [39][40][41][42] used in this work are summarized in Supplementary Materials. ...

... The pristine structure, LASI, is trained individually and all other doped structures, including LASI-25Si, LASI-50Si and LASI-80Si, are trained together based on another model. As similar with the workflow introduced in previous works 41,76 , some short Ab initio molecular dynamics (AIMD) trajectories are pre-calculated. For each structure, AIMD simulations at 600, 800, and 1000 K are performed with a duration of 4 ps and a timestep of 2 fs. ...

Inorganic sulfide solid-state electrolytes, especially Li6PS5X (X = Cl, Br, I), are considered viable materials for developing all-solid-state batteries because of their high ionic conductivity and low cost. However, this class of solid-state electrolytes suffers from structural and chemical instability in humid air environments and a lack of compatibility with layered oxide positive electrode active materials. To circumvent these issues, here, we propose Li6+xMxAs1-xS5I (M=Si, Sn) as sulfide solid electrolytes. When the Li6+xSixAs1-xS5I (x = 0.8) is tested in combination with a Li-In negative electrode and Ti2S-based positive electrode at 30 °C and 30 MPa, the Li-ion lab-scale Swagelok cells demonstrate long cycle life of almost 62500 cycles at 2.44 mA cm⁻², decent power performance (up to 24.45 mA cm⁻²) and areal capacity of 9.26 mAh cm⁻² at 0.53 mA cm⁻².

... This was measured by σ (ref. 66), defined as the maximal standard deviation of the atomic forces predicted by these four NN potentials: ...

Ammonia decomposition on lithium imide surfaces has been intensively investigated owing to its potential role in a sustainable hydrogen-based economy. Here, through advanced molecular dynamics simulations of ab initio accuracy, we show that the surface structure of the catalyst changes on exposure to the reactants and a dynamic state is activated. It is this highly fluctuating state that is responsible for catalysis and not a well-defined static catalytic centre. In this activated environment, a series of reactions that eventually leads to the release of N2 and H2 molecules becomes possible. Once the flow of reagent is terminated, the imide surface returns to its pristine state. We suggest that by properly engineering this dynamic interfacial state one can design improved catalytic systems.

... 11 The detailed configuration is explained in the supplementary material. [19][20][21] The most widely used structural analysis method at the atomic scale is Voronoi polyhedron (VP) analysis. 22,23 It uses Voronoi tessellation to describe the local environment of the given atom. ...

The phase selection mechanism within undercooled liquid Nb90Si10 hypoeutectic alloy was investigated by electrostatic levitation technique combined with deep neural network molecular dynamics. A stepwise-solidification procedure was conducted, where the primary phase and eutectic microstructure successively solidified from undercooled liquid alloy and undercooled residual liquid, respectively. The intermetallic phase of the eutectic structure transfers from Nb3Si to βNb5Si3 and finally into αNb5Si3 compound with the increase in liquid undercooling. The deep neural network molecular dynamic simulations have shown that the phase selection between Nb3Si and Nb5Si3 is mainly controlled by the short-range order of residual liquid, considering that the predominant short-range configuration transforms from Nb3Si-like to Nb5Si3-like structures. The αNb5Si3-like medium-range order, which is characterized by vertex-connected ⟨0,2,8,4⟩ clusters, is shown to significantly influence the competitive nucleation of the αNb5Si3 and βNb5Si3 phases. The residual liquid favors the αNb5Si3-like medium-range order rather than βNb5Si3 at large undercoolings, which explains the transformation from βNb5Si3 to αNb5Si3.

... The DP models are trained using highly accurate DFT datasets constructed by the concurrent learning scheme as implemented in the Deep-Potential Generator (DP-GEN) 43 . The DP-GEN 43 is an efficient tool to construct the most compact and adequate dataset for a DP model. ...

Lithium (Li) is a prototypical simple metal at ambient conditions, but exhibits remarkable changes in structural and electronic properties under compression. There has been intense debate about the structure of dense Li, and recent experiments offered fresh evidence for yet undetermined crystalline phases near the enigmatic melting minimum region in the pressure-temperature phase diagram of Li. Here, we report on an extensive exploration of the energy landscape of Li using an advanced crystal structure search method combined with a machine-learning approach, which greatly expands the scale of structure search, leading to the prediction of four complex Li crystal structures containing up to 192 atoms in the unit cell that are energetically competitive with known Li structures. These findings provide a viable solution to the observed yet unidentified crystalline phases of Li, and showcase the predictive power of the global structure search method for discovering complex crystal structures in conjunction with accurate machine learning potentials.

... 50 The training data sets are generated with open-source deep potential generator package. 47 Details on training and validation of the machine learning potentials are given in the SI. The step-free rutile TiO 2 (110) surface was modelled by a symmetric periodic slab of five O-T-O tri-layers with a 8 × 4 supercell, and the size of the supercell is 23.67 × 25.99 × 38.53 Å 3 . ...

Metal oxides are promising (photo)electrocatalysts for sustainable energy technologies due to their good activity and abundant resources. Their applications such as photocatalytic water splitting predominantly involve aqueous inter- faces at electrochemical conditions, but in situ probing oxide-water interfaces is proven to be extremely challenging. Here, we present an electrochemical scanning tunneling microscopy (EC-STM) study on the rutile TiO2(110)-water interface, and by tuning surface redox chemistry with careful potential control we are able to obtain high quality images of interfacial structures with atomic details. It is interesting to find that the interfacial water exhibits an unexpected double-row pattern that has never been observed. This finding is confirmed by performing a large scale simulation of a stepped interface model enabled by machine learning accelerated molecular dynamics (MLMD) at ab initio accuracy. Furthermore, we show that this pattern is induced by the steps present on the surface, which can propagate across the terraces by interfacial hydrogen bonds. Our work demonstrates that by combining EC-STM and MLMD we can obtain new atomic details of interfacial structures that are valuable to understand the activity of oxides at realistic conditions.

... The data used to train the potentials was generated using an active learning approach as implemented in the DPGen package (52). ...

The properties of lithium metal are key parameters in the design of lithium ion and lithium metal batteries. They are difficult to probe experimentally due to the high reactivity and low melting point of lithium as well as the microscopic scales at which lithium exists in batteries where it is found to have enhanced strength, with implications for dendrite suppression strategies. Computationally, there is a lack of empirical potentials that are consistently quantitatively accurate across all properties and ab-initio calculations are too costly. In this work, we train Machine Learning Interaction Potentials (MLIPs) on Density Functional Theory (DFT) data to state-of-the-art accuracy in reproducing experimental and ab-initio results across a wide range of simulations at large length and time scales. We accurately predict thermodynamic properties, phonon spectra, temperature dependence of elastic constants and various surface properties inaccessible using DFT. We establish that there exists a Bell-Evans-Polanyi relation correlating the self-adsorption energy and the minimum surface diffusion barrier for high Miller index facets.

Interphase boundaries are essential in the deformation and phase transformations in titanium (Ti) alloys. While static structures of semicoherent α/β interfaces in various Ti alloys have been carefully examined, their migration behavior at atomic scales is far less clear. In this study, we employed molecular dynamics simulations to investigate the migration of the semicoherent α/β interface in pure Ti. The interface migration behavior shows a shear-coupled feature with the interface dislocation glide and a macroscopic shear. The simulation reveals that both the glide direction of the dislocations with respect to the interface and the dislocation spacing strongly influence the migration rate, and the low-index glide plane of the interface dislocation plays a minor role. The dependence of interface mobility on temperatures confirms the critical role of thermal activation during the interface migration, especially for activating the interface dislocation glide. Furthermore, the shear-coupled interface migration driven by element partition is simulated using a newly developed Ti-Mo potential, consistent with the displacive-diffusional features previously observed in the surface precipitates. The simulated interface migration mode is validated by comparing it with the crystallography features of surface precipitates in a Ti-Cr alloy. The interface energy and mobility obtained from simulations further explain why the distinctive crystallographic features of the surface precipitates observed experimentally are favored over other candidate interfaces. The present study has explored an approach for systematically examining thermodynamic and kinetic factors governing the development of phase transformation crystallography at different temperatures and chemical driving forces.

Molecular dynamics (MD) simulations have become a powerful tool for investigating electrical double layers (EDLs), which play a crucial role in various electrochemical devices. In this Review, we provide a comprehensive overview of the techniques used in MD simulations for EDL studies, with a particular focus on methods for describing electrode polarization, and examine the principle behind these methods and their varying applicability. The applications of these approaches in supercapacitors, capacitive deionization, batteries, and electric double-layer transistors are explored, highlighting recent advancements and insights in each field. Finally, we emphasize the challenges and potential directions for future developments in MD simulations of EDLs, such as considering movable electrodes, improving electrode property representation, incorporating chemical reactions, and enhancing computational efficiency to deepen our understanding of complex electrochemical processes and contribute to the progress in the field involving EDLs.

Tungsten is a promising candidate for the plasma-facing material in fusion energy facilities, however, the low-energy, high-flux hydrogen plasma causes severe blistering in tungsten, which gives rise to safety concerns. By far, the formation mechanism of intragranular hydrogen blisters is still unclear. Large-scale atomistic simulations are crucial for improving the understanding, however, the available empirical interatomic potentials are mostly defective in predicting the formation of hydrogen self-clusters in tungsten, thus may lead to wrong blister formation mechanisms. In this work, we develop a machine-learning potential, DP-WH, for the tungsten-hydrogen binary system based on the Deep Potential method. We demonstrate that the DP-WH potential is able to describe, as accurately as ab initio calculations, the basic properties of bcc tungsten, the solute hydrogen properties in tungsten, adsorption and migration of hydrogen on tungsten free surfaces, interactions between hydrogen atoms and vacancy, dislocations, the interaction between neighboring interstitial hydrogen atoms, and the formation energy of H self-clusters. By using DP-WH, we perform nanosecond-long molecular dynamics simulations and report the formation of planar self-cluster of tetrahedral-interstitial-site hydrogen atoms normal to {001} tungsten planes at a hydrogen concentration of ≈10 at.%. This form of the H self-cluster is highly possible to be the early nucleates of the crack-shaped H blisters observed in recent experiments. The DP-WH is thus proven as a good candidate potential for the atomistic simulations to unveil the formation mechanisms of the intragranular hydrogen blisters in tungsten under the relevant working conditions.

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.

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.

The development of deep learning interatomic potentials has enabled efficient and accurate computations in quantum chemistry and materials science, circumventing computationally expensive ab initio calculations. However, the huge number of learnable parameters in deep learning models and their complex architectures hinder physical interpretability and affect the robustness of the derived potential. In this work, we propose graph-EAM, a lightweight graph neural network (GNN) inspired by the empirical embedded atom method to model the interatomic potential of single-element structures. Four material systems: platinum, niobium, silicon, and amorphous-carbon, for which quantum simulation data sets are publicly available, are examined to demonstrate that graph-EAM can achieve high energy and force prediction accuracy─comparable or better than existing state-of-the-art machine learning models─with much fewer parameters. It is also shown that the explicit inclusion of the angular information via three-body atomic density increases the prediction accuracy. The accuracy and efficiency of potentials obtained from graph-EAM can help accelerate the molecular dynamics simulation.

LaH10, as a member of hydrogen-rich superconductors, has a superconducting critical temperature of 250 K at high pressures, which exhibits the possibility of solving the long-term goal of room-temperature superconductivity. Considering the extreme pressure and low mass of hydrogen, the nuclear quantum effects in LaH10 should be significant and have an impact on its various physical properties. Here, we adopt the method that combines deep potential and quantum thermal bath, which was verified to be able to account for quantum effects in high-accuracy large-scale molecular dynamics simulations. Our method can actually reproduce pressure-temperature phase diagrams of LaH10 consistent with experimental and theoretical results. After incorporating quantum effects, the quantum fluctuation driven diffusion of protons is found even in the absence of thermal fluctuation near 0 K. The high mobility of protons is found to be compared to liquid, yet the structure of LaH10 is still rigid. These results would greatly enrich our vision to study quantum behavior of hydrogen-rich superconductors.

Boron phosphide (BP) is a (super)hard semiconductor constituted of light elements, which is promising for high demand applications at extreme conditions. The behaviour of BP at high temperatures and pressures is of special interest but is also poorly understood because both experimental and conventional ab initio methods are restricted to studying refractory covalent materials. The use of machine learning interatomic potentials is a revolutionary trend that gives a unique opportunity for high-temperature study of materials with ab initio accuracy. We develop a deep machine learning potential (DP) for accurate atomistic simulations of solid and liquid phases of BP as well as their transformations near the melting line. Our DP provides quantitative agreement with experimental and ab initio molecular dynamics data for structural and dynamic properties. DP-based simulations reveal that at ambient pressure tetrahedrally bonded cubic BP crystal melts into an open structure consisting of two interpenetrating sub-networks of boron and phosphorous with different structures. Structure transformations of BP melts under compressing are reflected by the evolution of low-pressure tetrahedral coordination to high-pressure octahedral coordination. The main contributions to structural changes at low pressures are made by the evolution of medium-range order in B-subnetwork and at high pressures by the change of short-range order in P-sub-network. Such transformations exhibit an anomalous behavior of structural characteristics in the range of 12-15 GPa. DP-based simulations reveal that Tm(P) curve develops a maximum at P ≈ 13 GPa, whereas experimental studies provide two separate branches of the melting curve, which demonstrate the opposite behaviour. Analysis of the results obtained raise open issues in developing machine learning potentials for covalent materials and stimulate further experimental and theoretical studies of melting behaviour in BP.

Ammonia decomposition on lithium imide surfaces has been intensively investigated owing to its potential role in a sustainable hydrogen-based economy. Through advanced molecular dynamics simulations of ab initio accuracy, we show that the surface structure of the catalyst changes upon exposure to the reactants, and a new dynamic state is activated. It is this highly fluctuating state that is responsible for catalysis and not a well defined static catalytic center. In this activated environment, a series of reactions that eventually leads to the release of N2 and H2 molecules become possible. Once the flow of reagent is terminated the imide surface returns to its pristine state. We suggest that by properly engineering this dynamic interfacial state one can design improved catalytic systems.

Machine learning potentials (MLPs) are poised to combine the accuracy of ab initio predictions with the computational efficiency of classical molecular dynamics (MD) simulation. While great progress has been made over the last two decades in developing MLPs, there is still much to be done to evaluate their model transferability and facilitate their development. In this work, we construct two deep potential (DP) models for liquid water near graphene surfaces, Model S and Model F, with the latter having more training data. A concurrent learning algorithm (DP-GEN) is adopted to explore the configurational space beyond the scope of conventional ab initio MD simulation. By examining the performance of Model S, we find that an accurate prediction of atomic force does not imply an accurate prediction of system energy. The deviation from the relative atomic force alone is insufficient to assess the accuracy of the DP models. Based on the performance of Model F, we propose that the relative magnitude of the model deviation and the corresponding root-mean-square error of the original test dataset, including energy and atomic force, can serve as an indicator for evaluating the accuracy of the model prediction for a given structure, which is particularly applicable for large systems where density functional theory calculations are infeasible. In addition to the prediction accuracy of the model described above, we also briefly discuss simulation stability and its relationship to the former. Both are important aspects in assessing the transferability of the MLP model.

Machine learning has seen increasing implementation as a predictive tool in the chemical and physical sciences in recent years. It offers a route to accelerate the process of scientific discovery through a computational data-driven approach. Whilst machine learning is well established in other fields, such as pharmaceutical research, it is still inits infancy in supercritical fluids research, but will likely accelerate dramatically in coming years. In this review,we present a basic introduction to machine learning and discuss its current uses by supercritical fluids researchers.In particular, we focus on the most common machine learning applications; including: (1) The estimation of the thermodynamic properties of supercritical fluids. (2) The estimation of solubilities, miscibilities, and extraction yields. (3) Chemical reaction optimization. (4) Materials synthesis optimization. (5) Supercritical power systems.(6) Fluid dynamics simulations of supercritical fluids. (7) Molecular simulation of supercritical fluids and (8) Geosequestration of CO2 using supercritical fluids.

The switching dynamics of ferroelectric materials is a crucial intrinsic property which directly affects the operation and performance of ferroelectric devices. In conventional ferroelectric materials, the typical ferroelectric switching mechanism is governed by a universal process of domain-wall motion. However, recent experiments indicate that van der Waals ferroelectric CuInP2S6 possesses anomalous polarization switching dynamics under an electric field. It is important to understand the switching dynamics, but it remains theoretically unexplored in CuInP2S6 due to the lack of description of its order-disorder phase transition characteristics by density functional theory. Here we employ a machine-learning potential trained from the first-principles density functional theory dataset to conduct large-scale atomistic simulations of temperature-driven order-disorder ferroelectric phase transition in CuInP2S6. Most importantly, it is found that the electric-field-driven polarization switching in CuInP2S6 is mediated by a single Cu dipole flip rather than a conventional domain-wall-motion mechanism. This intrinsic unconventional switching behavior can be attributed to the competition between the energy barrier of domain-wall motion and single-dipole flip.

So far, it has been a challenge for existing interatomic potentials to accurately describe a wide range of physical properties and maintain reasonable efficiency. In this work, we develop an interatomic potential for simulating radiation damage in body-centered cubic tungsten by employing deep potential, a neural network-based deep learning model for representing the potential energy surface. The resulting potential predicts a variety of physical properties consistent with first-principles calculations, including phonon spectrum, thermal expansion, generalized stacking fault energies, energetics of free surfaces, point defects, vacancy clusters, and prismatic dislocation loops. Specifically, we investigated the elasticity-related properties of prismatic dislocation loops, i.e., their dipole tensors, relaxation volumes, and elastic interaction energies. This potential is found to predict the maximal elastic interaction energy between two 1/2 \(\left\langle {1 \, 1 \, 1} \right\rangle\) loops better than previous potentials, with a relative error of only 7.6%. The predicted threshold displacement energies are in reasonable agreement with experimental results, with an average of 128 eV. The efficiency of the present potential is also comparable to the tabulated gaussian approximation potentials and modified embedded atom method potentials, meanwhile, can be further accelerated by graphical processing units. Extensive benchmark tests indicate that this potential has a relatively good balance between accuracy, transferability, and efficiency.

Machine learning atomistic potentials trained using density functional theory (DFT) datasets allow for the modeling of complex material properties with near-DFT accuracy while imposing a fraction of its computational cost. The curation of the DFT datasets can be extensive in size and time-consuming to train and refine. In this study, we focus on addressing these barriers by developing minimalistic and flexible datasets for many elements in the periodic table regardless of their mass, electronic configuration, and ground state lattice. These DFT datasets have, on average, ∼4000 different structures and 27 atoms per structure, which we found sufficient to maintain the predictive accuracy of DFT properties and notably with high transferability. We envision these highly curated training sets as starting points for the community to expand, modify, or use with other machine learning atomistic potential models, whatever may suit individual needs, further accelerating the utilization of machine learning as a tool for material design and discovery.

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xx operator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V^xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H2O)64 configurations (with densities spanning 0.4-1.7 g/cm3), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H2O)64 configurations. Using an out-of-sample set of (H2O)512 configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Molecular simulations, which simulate the motions of particles according to fundamental laws of physics, have been applied to a wide range of fields from physics and materials science to biochemistry and drug discovery. Developed for computationally intensive applications, most molecular simulation software involves significant use of hard-coded derivatives and code reuse across various programming languages. In this Review, we first align the relationship between molecular simulations and artificial intelligence (AI) and reveal the coherence between the two. We then discuss how the AI platform can create new possibilities and deliver new solutions to molecular simulations, from the perspective of algorithms, programming paradigms, and even hardware. Rather than focusing solely on increasingly complex neural network models, we introduce various concepts and techniques brought about by modern AI and explore how they can be transacted to molecular simulations. To this end, we summarized several representative applications of molecular simulations enhanced by AI, including from differentiable programming and high-throughput simulations. Finally, we look ahead to promising directions that may help address existing issues in the current framework of AI-enhanced molecular simulations.

MXenes are 2D materials with great potential in various applications. However, the degradation of MXenes in humid environments has become a main obstacle in their practical use. Here we combine deep neural networks and an active learning scheme to develop a neural network potential (NNP) for aqueous MXene systems with ab initio precision but low cost. The oxidation behaviors of super large aqueous MXene systems are investigated systematically at nanosecond timescales for the first time. The oxidation process of MXenes is clearly displayed at the atomic level. Free protons and oxides greatly inhibit subsequent oxidation reactions, leading to the degree of oxidation of MXenes to exponentially decay with time, which is consistent with the oxidation rate of MXenes measured experimentally. Importantly, this computational study represents the first exploration of the kinetic process of oxidation of super‐sized aqueous MXene systems. It opens a promising avenue for the future development of effective protection strategies aimed at controlling the stability of MXenes.

MXenes are two-dimensional (2D) materials with great potential in application to various fields. However, the degradation of MXenes in humid environments has become a main obstacle in their practical use. Here we combine deep neural networks and an active learning scheme to develop a neural network potential (NNP) for aqueous MXene systems with ab initio precision but the low cost. The oxidation behaviors of the super large MXenes aqueous system are investigated systematically at nanosecond timescales for the first time. The oxidation process of MXenes is clearly displayed at the atomic level. And free protons and oxides greatly inhibit subsequent oxidation reactions, leading to the degree of oxidation of MXenes to exponential decay with time, which is consistent with the oxidation rate of MXenes measured experimentally. Importantly, this computational study represents the first exploration of the kinetic process of oxidation reaction in the super-sized MXene aqueous system. This significant breakthrough opens a promising avenue for the future development of effective protection strategies aimed at controlling the stability of MXenes. Besides, the developed NNP could be used in other applications of complex aqueous MXene systems after adding new data.

Two-dimensional (2D) materials have been a research hot topic in the passed decades due to their unique and fascinating properties. Among them, mechanical properties play an important role in their application. However, there lacks an effective tool for high-throughput calculating, analyzing and visualizing the mechanical properties of 2D materials. In this work, we present the mech2d package, a highly automated toolkit for calculating and analyzing the second-order elastic constants (SOECs) tensor and relevant properties of 2D materials by considering their symmetry. In the mech2d, the SOECs can be fitted by both the strain–energy and stress–strain approaches, where the energy or strain can be calculated by a first-principles engine, such as VASP. As a key feature, the mech2d package can automatically submit and collect the tasks from a local or remote machine with robust fault-tolerant ability, making it suitable for high-throughput calculation. The present code has been validated by several common 2D materials, including graphene, black phosphorene, GeSe2 and so on.

Unraveling the reaction paths and structural evolutions during charging/discharging processes are critical for the development and tailoring of silicon anodes for high‐capacity batteries. However, a mechanistic understanding is still lacking due to the complex phase transformations between crystalline (c‐) and amorphous (a‐) phases involved in electrochemical cycles. In this study, by employing a newly developed machine learning potential, the key experimental phenomena not only reproduce, including voltage curves and structural evolution pathways, but also provide atomic scale mechanisms associated with these phenomena. The voltage plateaus of both the c‐Si and a‐Si lithiation processes are predicted with the plateau value difference close to experimental measurements, revealing the two‐phase reaction mechanism and reaction path differences. The observed voltage hysteresis between lithiation and delithiation mainly originates from the transformation between the c‐Li15‐δSi4 and a‐Li15‐δSi4 phases. Furthermore, stress accumulation is simulated along different reaction paths, indicating a better cycling stability of the a‐Si anode due to the lower stress concentration. Overall, the study provides a theoretical understanding of the thermodynamics of the complex structural evolutions in Si anodes during (de)lithiation processes, which may play a role in optimizations for battery performances.

Understanding the mechanism of the oxygen evolution reaction (OER) is essential to improve the efficiency of photocatalysis for TiO2. Previous studies have highlighted the importance of terminal hydroxide radical (TiOH•) in the OER. Ab initio molecular dynamics simulations (AIMD) with hybrid functional have revealed that this radical readily loses its proton, creating the key intermediate, oxygen radical anion (Ti5cO•–). Herein, we combine machine-learning-accelerated molecular dynamics with density functional theory calculations to demonstrate that the Ti5cO•– can alternatively be generated through the trapping of a hole in a terminal oxygen anion (Ti5cO2–) at rutile(110)–water interfaces. Further examination reveals that the Ti5cO2– results from the deprotonation of Ti5cOH– and remains stable at the charge-neutral interfaces for a transient time period of ca. 100 ps. The AIMD-based free energy perturbation method predicts that the acidity constant of Ti5cOH– is even smaller than that of Ti5cOH2, thereby rationalizing the stability of Ti5cO2–. Structural analyses show that this anomalous acidic tendency of terminal water originates from the decrease of Ti–O bond length and the transition of Titanium’s coordination from octahedral to pyramidal in Ti5cO2–. Our findings provide valuable insights into the surface acid–base chemistry and a potential explanation for the pH-dependent behavior of photogenerated holes for TiO2

The complex phase diagram and bonding nature of the TiAl system make it difficult to accurately describe its various properties and phases by traditional atomistic force fields. Here, we develop a machine learning interatomic potential with a deep neural network method for the TiAlNb ternary alloy based on a dataset built by first-principles calculations. The training set includes bulk elementary metals and intermetallic structures with slab and amorphous configurations. This potential is validated by comparing bulk properties—including lattice constant and elastic constants, surface energies, vacancy formation energies, and stacking fault energies—with their respective density functional theory values. Moreover, our potential could accurately predict the average formation energy and stacking fault energy of γ-TiAl doped with Nb. The tensile properties of γ-TiAl are simulated by our potential and verified by experiments. These results support the applicability of our potential under more practical conditions.

In this work, we construct distinct first-principles-based machine-learning models of CO2, reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN, and SCAN-rvv10 approximations of density functional theory. We employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid-phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for the liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that graphanol (hydroxylated graphane) will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy but requires a very small fraction of the computational cost. We used our DP to calculate proton self-diffusion coefficients as a function of temperature, to estimate the overall barrier to proton diffusion, and to characterize the impact of thermal fluctuations as a function of system size. We propose and test a detailed mechanism for proton conduction on the surface of graphanol. We show that protons can rapidly hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport only takes place as new Grotthuss chains are formed by rotation of one or more hydroxyl groups in the chain. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with even lower diffusion barriers.

One of the ultimate goals of chemistry is to understand and manipulate chemical reactions, which implies the ability to monitor the reaction and its underlying mechanism at an atomic scale....

Constructing an accurate atomistic model for the high-pressure phases of tin (Sn) is challenging because the properties of Sn are sensitive to pressures. We develop machine-learning-based deep potentials for Sn with pressures ranging from 0 to 50 GPa and temperatures ranging from 0 to 2000 K. In particular, we find the deep potential, which is obtained by training the ab initio data from density functional theory calculations with the state-of-the-art SCAN exchange-correlation functional, is suitable to characterize high-pressure phases of Sn. We systematically validate several structural and elastic properties of the α (diamond structure), β, bct, and bcc structures of Sn, as well as the structural and dynamic properties of liquid Sn. The thermodynamics integration method is further utilized to compute the free energies of the α, β, bct, and liquid phases, from which the deep potential successfully predicts the phase diagram of Sn including the existence of the triple-point that qualitatively agrees with the experiment.

Understanding the interaction mechanism between divalent metal ions with amino acids is of great significance to understand the interaction between metal ions with proteins. In this study, the interaction mechanisms of Mg2+, Ca2+, and Zn2+ with amino acid side chain analogs in water were systematically studied by combining neural network potential energy surface, molecular dynamics simulation and umbrella sampling. The calculated potential mean forces not only reveal the binding process of each ion and amino acid, the most stable coordination structure, but also show the difference between different ions. In addition, we also use the neural network based potential of mean force as a standard to benchmark classical force fields, which is also meaningful for the development of force fields targeting metal ions.

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology—a machine learning approach—to study this ubiquitous phase transition, starting from the phase diagram in the liquid–vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid–vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid–vapor coexistence and water cavitation.

In hybrid perovskites, the organic molecules and inorganic frameworks exhibit distinct static and dynamic characteristics. Their coupling will lead to fascinating phenomena, such as large polarons, dynamic Rashba–Dresselhaus effects, etc. In this paper, deep potential molecular dynamics (DPMD) is employed, a large‐scale MD simulation scheme with DFT accuracy, to study hybrid perovskites formamidinium lead iodide (FAPbI3) and methylamonium lead iodide (MAPbI3). A spontaneous hybrid nano‐domain behavior, namely multiple molecular rotation nano‐domains embedded into a single [PbI6]⁴⁻ octahedra rotation domain, is first discovered at low temperatures. The behavior originates from the interplay between the long range order of molecular rotation and local lattice deformation, and clarifies the puzzling structural features of FAPbI3 at low temperatures. The work provides new insights into the structural characteristics and stability of hybrid perovskite, as well as new ideas for the structural characterization of organic–inorganic coupled systems.

It has been studied whether machine learning interatomic potentials parameterized with only disordered configurations corresponding to liquid can describe the properties of crystalline phases and predict their structure. The study has been performed for a network-forming system SiO 2 , which has numerous polymorphic phases significantly different in structure and density. Using only high-temperature disordered configurations, a machine learning interatomic potential based on artificial neural networks (DeePMD model) has been parameterized. The potential reproduces well ab initio dependences of the energy on the volume and the vibrational density of states for all considered tetra- and octahedral crystalline phases of SiO 2 . Furthermore, the combination of the evolutionary algorithm and the developed DeePMD potential has made it possible to reproduce the really observed crystalline structures of SiO 2 . Such a good liquid–crystal portability of the machine learning interatomic potential opens prospects for the simulation of the structure and properties of new systems for which experimental information on crystalline phases is absent.

The multicomponent oxide solid solution is a versatile platform to tune the delicate balance between competing spin, charge, orbital, and lattice degrees of freedom for materials design and discovery. The development of compositionally complex oxides with superior functional properties has been largely empirical and serendipitous, in part due to the exceedingly complex chemistry and structure of solid solutions that span a range of length scales. The usage of classical molecular dynamics (MD), a powerful statistical method, in computer-aided materials design has not yet reached the same level of sophistication as that in computer-aided drug design because of the limited availability and accuracy of classical force fields for solids. Here, we introduce the strategy of “modular development of deep potential” (ModDP) that enables a systematic development and improvement of deep-neural-network-based model potential, termed as deep potential, for complex solid solutions with minimum human intervention. The converged training database associated with an end-member material is treated as an independent module and is reused to train the deep potential of solid solutions via a concurrent learning procedure. We apply ModDP to obtain classical force fields of two technologically important solid solutions, PbxSr1−xTiO3 and HfxZr1−xO2. For both materials' systems, a single model potential is capable of predicting various properties of solid solutions including temperature-driven and composition-driven phase transitions over a wide range of compositions. In particular, the deep potential of PbxSr1−xTiO3 reproduces a few known topological textures such as polar vortex lattice and electric dipole waves in PbTiO3/SrTiO3 superlattices, paving the way for MD investigations on the dynamics of topological structures in response to external stimuli. MD simulations of HfxZr1−xO2 reveal a substantial impact of composition variation on both the phase transition temperature and the nature of the high-temperature nonpolar phase.

The atomic cluster expansion (ACE) was proposed recently as a new class of data-driven interatomic potentials with a formally complete basis set. Since the development of any interatomic potential requires a careful selection of training data and thorough validation, an automation of the construction of the training dataset as well as an indication of a model's uncertainty are highly desirable. In this work, we compare the performance of two approaches for uncertainty indication of ACE models based on the D-optimality criterion and ensemble learning. While both approaches show comparable predictions, the extrapolation grade based on the D-optimality (MaxVol algorithm) is more computationally efficient. In addition, the extrapolation grade indicator enables an active exploration of new structures, opening the way to the automated discovery of rare-event configurations. We demonstrate that active learning is also applicable to explore local atomic environments from large-scale molecular-dynamics simulations.

An active learning procedure called deep potential generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg, and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data.

SchNetPack is a toolbox for the development and application of deep neural networks to the prediction of potential energy surfaces and other quantum-chemical properties of molecules and materials. It contains basic building blocks of atomistic neural networks, manages their training and provides simple access to common benchmark datasets. This allows for an easy implementation and evaluation of new models. For now, SchNetPack includes implementations of (weighted) atom-centered symmetry functions and the deep tensor neural network SchNet as well as ready-to-use scripts that allow to train these models on molecule and material datasets. Based upon the PyTorch deep learning framework, SchNetPack allows to efficiently apply the neural networks to large datasets with millions of reference calculations as well as parallelize the model across multiple GPUs. Finally, SchNetPack provides an interface to the Atomic Simulation Environment in order to make trained models easily accessible to researchers that are not yet familiar with neural networks.

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows our AL algorithm to automatically sample regions of chemical space where the machine learned potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach we develop the COMP6 benchmark (publicly available on GitHub), which contains a diverse set of organic molecules. We show the use of our proposed AL technique develops a universal ANI potential (ANI-1x), which provides very accurate energy and force predictions on the entire COMP6 benchmark. This universal potential achieves a level of accuracy on par with the best ML potentials for single molecule or materials while remaining applicable to the general class of organic molecules comprised of the elements CHNO.

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model.

Traditional force-fields cannot model chemical reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab-initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interatomic forces that have simple physical formulas. In this manuscript we construct a hybrid model chemistry consisting of a nearsighted Neural-Network potential with screened long-range electrostatic and Van-Der-Walls physics. This trained potential, simply dubbed "TensorMol-0.1", is offered in an open-source python package capable of many of the simulation types commonly used to study chemistry: Geometry optimizations, harmonic spectra, and open or periodic molecular dynamics, Monte Carlo, and nudged elastic band calculations. We describe the robustness and speed of the package, demonstrating millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating molecular dynamics of a protein. Our comparisons with electronic structure theory and experiment demonstrate that neural network molecular dynamics is poised to become an important tool for molecular simulation, lowering the resource barrier to simulate chemistry.

We introduce a new scheme for molecular simulations, based on a many-body potential and interatomic forces generated by a deep neural network trained with ab initio data. We show that the proposed scheme, which we call Deep Potential Molecular Dynamics (DeePMD), provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Moreover, in a few test cases, DeePMD shows good structural transferability to thermodynamic conditions not included in the original training data.

We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, whether empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and cost comparable to that of empirical potentials.

Phonon plays essential roles in dynamical behaviors and thermal properties,
which are central topics in fundamental issues of materials science. The
importance of first principles phonon calculations cannot be overly emphasized.
Phonopy is an open source code for such calculations launched by the present
authors, which has been world-widely used. Here we demonstrate phonon
properties with fundamental equations and show examples how the phonon
calculations are applied in materials science.

We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order N-atoms(3) operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ''metric'' and a special ''preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order N-atoms(2) scaling is found for systems up to 100 electrons. If we take into account that the number of k points can be implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.

We introduce a class of interatomic potential models that can be
automatically generated from data consisting of the energies and forces
experienced by atoms, derived from quantum mechanical calculations. The
resulting model does not have a fixed functional form and hence is capable of
modeling complex potential energy landscapes. It is systematically improvable
with more data. We apply the method to bulk carbon, silicon and germanium and
test it by calculating properties of the crystals at high temperatures. Using
the interatomic potential to generate the long molecular dynamics trajectories
required for such calculations saves orders of magnitude in computational cost.

TensorFlow [1] is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets up to large-scale distributed systems of hundreds of machines and thousands of computational devices such as GPU cards. The system is flexible and can be used to express a wide variety of algorithms, including training and inference algorithms for deep neural network models, and it has been used for conducting research and for deploying machine learning systems into production across more than a dozen areas of computer science and other fields, including speech recognition, computer vision, robotics, information retrieval, natural language processing, geographic information extraction, and computational drug discovery. This paper describes the TensorFlow interface and an implementation of that interface that we have built at Google. The TensorFlow API and a reference implementation were released as an open-source package under the Apache 2.0 license in November, 2015 and are available at www.tensorflow.org.

This paper introduces an active learning approach to the fitting of machine
learning interatomic potentials. Our approach is based on the D-optimality
criterion for selecting atomic configurations on which the potential is fitted.
It is shown that the proposed active learning approach is highly efficient in
training potentials on the fly, ensuring that no extrapolation is attempted and
leading to a completely reliable atomistic simulation without any significant
decrease in accuracy. We apply our approach to molecular dynamics and structure
relaxation, and we argue that it can be applied, in principle, to any other
type of atomistic simulation. The software, test cases, and examples of usage
are published at http://gitlab.skoltech.ru/shapeev/mlip/.

Machine learning interpolation of atomic potential energy surfaces enables the nearly automatic construction of highly accurate atomic interaction potentials. Here we discuss the Behler-Parrinello approach that is based on artificial neural networks (ANNs) and detail the implementation of the method in the free and open-source atomic energy network (ænet) package. The construction and application of ANN potentials using ænet is demonstrated at the example of titanium dioxide (TiO2), an industrially relevant and well-studied material. We show that the accuracy of lattice parameters, energies, and bulk moduli predicted by the resulting TiO2 ANN potential is excellent for the reference phases that were used in its construction (rutile, anatase, and brookite) and examine the potential's capabilities for the prediction of the high-pressure phases columbite (α-PbO2 structure) and baddeleyite (ZrO2 structure).

A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.

Computational science has seen in the last decades a spectacular rise in the
scope, breadth, and depth of its efforts. Notwithstanding this prevalence and
impact, it is often still performed using the renaissance model of individual
artisans gathered in a workshop, under the guidance of an established
practitioner. Great benefits could follow instead from adopting concepts and
tools coming from computer science to manage, preserve, and share these
computational efforts. We illustrate here our paradigm sustaining such vision,
based around the four pillars of Automation, Data, Environment, and Sharing,
and discuss its implementation in the open-source AiiDA platform
(http://www.aiida.net). The platform is tuned first to the demands of
computational materials science: coupling remote management with automatic data
generation; ensuring provenance, preservation, and searchability of
heterogeneous data through a design based on directed acyclic graphs; encoding
complex sequences of low-level codes into scientific workflows and turnkey
solutions to boost productivity and ensure reproducibility; and developing an
ecosystem that encourages the sharing and dissemination of codes, data, and
scientific workflows.

We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions. The method is straightforward to implement
and is based an adaptive estimates of lower-order moments of the gradients. The
method is computationally efficient, has little memory requirements and is well
suited for problems that are large in terms of data and/or parameters. The
method is also ap- propriate for non-stationary objectives and problems with
very noisy and/or sparse gradients. The method exhibits invariance to diagonal
rescaling of the gradients by adapting to the geometry of the objective
function. The hyper-parameters have intuitive interpretations and typically
require little tuning. Some connections to related algorithms, on which Adam
was inspired, are discussed. We also analyze the theoretical convergence
properties of the algorithm and provide a regret bound on the convergence rate
that is comparable to the best known results under the online convex
optimization framework. We demonstrate that Adam works well in practice when
experimentally compared to other stochastic optimization methods.

Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water.

cp 2 k has become a versatile open‐source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp 2 k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15–25. doi: 10.1002/wcms.1159
This article is categorized under: Software > Simulation Methods

Phonon frequencies for wave vectors along the principal symmetry directions in copper have been determined at 49 and 298\ifmmode^\circ\else\textdegree\fi{}K from neutron inelastic-scattering measurements. In general, the temperature dependences of the frequencies were found to be smaller for the higher-frequency modes. For the lower frequencies ($$\nu${}$\lesssim${}3\ifmmode\times\else\texttimes\fi{}{10}^{12}$ cps), the frequency changes measured are consistent with the 3-4% changes estimated from the isothermal elastic constants. For higher frequencies the relative changes are much smaller, often being 1% or less. Axially symmetric force models, which included interactions to the sixth nearest neighbors, were fitted to the data and have been used to calculate a frequency distribution function $g($\nu${})$ at each temperature. A comparison of the temperature dependences of the moments of these distributions with various Gr\"uneisen parameters leads to the conclusion that Cu does not satisfy the assumption of the quasiharmonic model. The Debye temperature ${$\Theta${}}_{C}$ versus temperature curve calculated with the 49\ifmmode^\circ\else\textdegree\fi{}K $g($\nu${})$ is in excellent agreement with results from specific-heat measurements in the entire 0 to 298\ifmmode^\circ\else\textdegree\fi{}K range. A fairly strong temperature dependence for the widths of some well-focused phonons was observed.

The weak beam technique is used to obtain a value for the stacking-fault energy of copper. The observed partial dislocation image spacings are compared with many-beam computational models and it is demonstrated that anisotropic elasticity theory breaks down for small partial dislocation spacings in copper.

The ultrasonic pulse technique has been used in conjunction with a specially devised cryogenic technique to measure the velocities of 10-Mc/sec acoustic waves in copper single crystals in the range from 4.2°K to 300°K. The values and the temperature variations of the elastic constants have been determined. The room temperature elastic constants were found to agree well with those of other experimental works. Fuchs' theoretical c44 at 0°K is 10 percent larger than our observed value but his theoretical c11, c12, K and (c11-c12) agree well with the observations. The isotropy, (c11-c12)2c44, was observed to remain practically constant from 4.2°K to 180°K, then to diminish gradually at higher temperatures. Some general features of the temperature variations of elastic constants are discussed.

Measurements of the peak counting rate in the angular correlation curve of positron annihilation radiation have been performed in the solid and liquid phase of indium, lead, and aluminum, and in the solid phase of magnesium, as a function of temperature. In the solid phase In, Pb, and Al show at low temperatures the thermal-expansion effect and at higher temperatures in addition the positron-trapping effect. At the melting point the peak counting rate increases abruptly and stays then constant with temperature. This behavior in the liquid phase is interpreted as "saturation trapping," i.e., all positrons annihilate from a trapping site and the thermal expansion of the lattice is not effective for these positrons. Trapped positrons are effectively "shielded" from the thermal expansion of the lattice. Therefore, it is possible to separate the thermal-expansion effect from the vacancy-trapping effect and very accurate values for the monovacancy formation energy can be obtained. A difference was found in the nature of trapping sites in solid and liquid aluminum. Magnesium shows only the thermal-expansion effect and no vacancy-trapping effect.

Predictions of observable properties by density-functional theory
calculations (DFT) are used increasingly often in experimental condensed-matter
physics and materials engineering as data. These predictions are used to
analyze recent measurements, or to plan future experiments. Increasingly more
experimental scientists in these fields therefore face the natural question:
what is the expected error for such an ab initio prediction? Information and
experience about this question is scattered over two decades of literature. The
present review aims to summarize and quantify this implicit knowledge. This
leads to a practical protocol that allows any scientist - experimental or
theoretical - to determine justifiable error estimates for many basic property
predictions, without having to perform additional DFT calculations. A central
role is played by a large and diverse test set of crystalline solids,
containing all ground-state elemental crystals (except most lanthanides). For
several properties of each crystal, the difference between DFT results and
experimental values is assessed. We discuss trends in these deviations and
review explanations suggested in the literature. A prerequisite for such an
error analysis is that different implementations of the same first-principles
formalism provide the same predictions. Therefore, the reproducibility of
predictions across several mainstream methods and codes is discussed too. A
quality factor Delta expresses the spread in predictions from two distinct DFT
implementations by a single number. To compare the PAW method to the highly
accurate APW+lo approach, a code assessment of VASP and GPAW with respect to
WIEN2k yields Delta values of 1.9 and 3.3 meV/atom, respectively. These
differences are an order of magnitude smaller than the typical difference with
experiment, and therefore predictions by APW+lo and PAW are for practical
purposes identical.

We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N-atoms(2) scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special 'preconditioning' optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package), The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

In a comprehensive study, the modified embedded-atom method is extended to a variety of cubic materials and impurities. In this extension, all functions are analytic and computationally simple. The basic equations of the method are developed and applied to 26 elements: ten fcc, ten bcc, three diamond cubic, and three gaseous materials. The materials modeled include metals, semiconductors, and diatomic gases, all of which exhibit different types of bonding. Properties of these materials, including equation of state, elastic moduli, structural energies and lattice constants, simple defects, and surfaces, are calculated. The formalism for applying the method to combinations of these elements is developed and applied to the calculation of dilute heats of solution. In all cases, comparison is made to experiment or higher-level calculations when possible.

We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.

Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}

The accurate description of chemical processes often requires the use of computationally demanding methods like density-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter--atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently --- those with short--range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed--memory parallel machine which allows for message--passing of data between independently executing processors. The algorithms are tested on a standard Lennard--Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers --- the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y--MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventi...

- W Kohn
- L J Sham

W. Kohn, L.J. Sham, Phys. Rev. 140 (4A) (1965) A1133.

- R Car
- M Parrinello

R. Car, M. Parrinello, Phys. Rev. Lett. 55 (22) (1985) 2471.

- J Han
- L Zhang
- R Car

J. Han, L. Zhang, R. Car, W. E, Commun. Comput. Phys. 23 (3) (2018)
629-639.

- L Zhang
- J Han
- H Wang
- R Car

L. Zhang, J. Han, H. Wang, R. Car, and W. E, Physical Review Letters
120, 143001 (2018).

- N Artrith
- A Urban

N. Artrith, A. Urban, Comput. Mater. Sci. 114 (2016) 135-150.

- H Wang
- L Zhang
- J Han

H. Wang, L. Zhang, J. Han, W. E., Comput. Phys. Comm. 228 (2018)
178-184.

- K Yao
- J E Herr
- D W Toth
- R Mckintyre
- J Parkhill

K. Yao, J.E. Herr, D.W. Toth, R. Mckintyre, J. Parkhill, Chem. Sci. 9 (8) (2018)
2261-2269.

- M Ceriotti
- J More
- D E Manolopoulos

M. Ceriotti, J. More, D.E. Manolopoulos, Comput. Phys. Comm. 185 (2014)
1019-1026.

- E V Podryabinkin
- A V Shapeev

E.V. Podryabinkin, A.V. Shapeev, Comput. Mater. Sci. 140 (2017) 171-180.

- L Zhang
- D.-Y Lin
- H Wang
- R Car

L. Zhang, D.-Y. Lin, H. Wang, R. Car, and W. E, Physical Review
Materials 3, 023804 (2019).

- P Giannozzi
- O Andreussi
- T Brumme
- O Bunau
- M B Nardelli
- M Calandra
- R Car
- C Cavazzoni
- D Ceresoli
- M Cococcioni

P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli,
M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al.,
Journal of Physics: Condensed Matter 29, 465901 (2017).

- J Hutter
- M Iannuzzi
- F Schiffmann
- J Vandevondele
- Wiley Interdiscip

J. Hutter, M. Iannuzzi, F. Schiffmann, J. Vandevondele, Wiley Interdiscip.
Rev. Comput. Mol. Sci. 4 (1) (2014) 15-25.

- H J Monkhorst
- J D Pack

H. J. Monkhorst and J. D. Pack, Physical Review B 13, 5188 (1976).

- K Lejaeghere
- V Van Speybroeck
- G Van Oost
- S Cottenier

K. Lejaeghere, V. Van Speybroeck, G. Van Oost, S. Cottenier, Crit. Rev. Solid
State Mater. Sci. 39 (1) (2014) 1-24.

- W Overton
- J Gaffney

W. Overton Jr and J. Gaffney, Physical Review 98, 969 (1955).

- W Stobbs

W. Stobbs, C. Sworn, Phil. Mag. 24 (192) (1971) 1365-1381.

- A Togo
- I Tanaka

A. Togo and I. Tanaka, Scr. Mater. 108, 1 (2015).

- R Nicklow
- G Gilat
- H Smith
- L Raubenheimer
- M Wilkinson

R. Nicklow, G. Gilat, H. Smith, L. Raubenheimer, and M. Wilkinson,
Physical Review 164, 922 (1967).