Machine Learning Interatomic Potentials Research Articles

Best practices for fitting machine learning interatomic potentials for molten salts: A case study using NaCl-MgCl2

In this work, we developed a compositionally transferable machine learning interatomic potential using atomic cluster expansion potential and PBE-D3 method for (NaCl)1-x(MgCl2)x molten salt and we showed that it is possible to fit a robust potential for this pseudo-binary system by only including data from x={0, 1/3, 2/3, 1}. We also assessed the performance of several DFT methods including PBE-D3, PBE-D4, R2SCAN-D4, and R2SCAN-rVV10 on unary NaCl and MgCl2 salts. Our results show that the R2SCAN-D4 method calculates the thermophysical properties of NaCl and MgCl2 with an overall modestly better accuracy compared to the other three methods.

Multikernel similarity‐based clustering of amorphous systems and machine‐learned interatomic potentials by active learning

AbstractWe present a hybrid similarity kernel that exemplifies the integration of short‐ and long‐range descriptors via the use of an average kernel approach. This technique allows for a direct measure of the similarity between amorphous configurations, and when combined with an active learning (AL) spectral clustering approach, it leads to a classification of the amorphous configurations into uncorrelated clusters. Subsequently, a minimum size database is built by considering a small fraction of configurations belonging to each cluster and a machine learning interatomic potential (MLIP), within the Gaussian approximation scheme, is fitted by relying on a Bayesian optimization of the potential hyperparameters. This step is embedded within an AL loop that allows to sequentially increase the size of the learning database whenever the MLIP fails to meet a predefined energy convergence threshold. As such, MLIP are fitted in an almost fully automatized fashion. This approach is tested on two diverse amorphous systems that were previously generated using first‐principles molecular dynamics. Accurate potentials with less than 2 meV/atom root mean square energy error compared to the reference data are obtained. This accuracy is achieved with only 175 configurations sampling the studied systems at various temperatures. The robustness of these potentials is then confirmed by producing models with several thousands of atoms featuring a good agreement with reference ab initio and experimental data.

A Molecular View of Methane Activation on Ni(111) through Enhanced Sampling and Machine Learning.

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a data set constructed via ab initio molecular dynamics simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that upon incorporation of collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting density functional theory-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression toward the transition state involves a CH4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C-H bond. This leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

A unified moment tensor potential for silicon, oxygen, and silica

Si and its oxides have been extensively explored in theoretical research due to their technological importance. Simultaneously describing interatomic interactions within both Si and SiO2 without the use of ab initio methods is considered challenging, given the charge transfers involved. Herein, this challenge is overcome by developing a unified machine learning interatomic potentials describing the Si/SiO2/O system, based on the moment tensor potential (MTP) framework. This MTP is trained using a comprehensive database generated using density functional theory simulations, encompassing diverse crystal structures, point defects, extended defects, and disordered structure. Extensive testing of the MTP is performed, indicating it can describe static and dynamic features of very diverse Si, O, and SiO2 atomic structures with a degree of fidelity approaching that of DFT.

Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets.

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

TH-graphyne: a new porous bidimensional carbon allotrope.

Graphyne and two-dimensional porous carbon-based materials have garnered significant attention due to their interesting structural characteristics and essential properties for new technological applications. Within this scope, this work investigates the structural, thermal, electronic, optical, and mechanical properties of a novel two-dimensional allotrope that combines triangular (T) and hexagonal (H) rings, connected by acetylenic linkages (graphyne-like), thus named TH-graphyne (TH-GY). This study comprehensively characterizes the proposed system's behavior using density functional theory, ab initio molecular dynamics, and classical reactive molecular dynamics simulations. Our results confirm the structural stability of TH-GY. AIMD simulations demonstrate the material's thermal stability at elevated temperatures, while phonon dispersions indicate its dynamical stability. Electronic band structure calculations show that the system is metallic. The analysis of optical properties reveals intense activity in the visible and UV regions, with pronounced anisotropy. A machine learning interatomic potentials model was developed for TH-GY and used to determine the mechanical behavior of the system, which exhibits Young's modulus ranging from 263 to 356 GPa, highlighting its flexibility. Classical reactive MD simulations elucidate the fracture behavior of TH-GY, revealing distinct fracture patterns and mechanical anisotropy.

Review of External Field Effects on Electrocatalysis: Machine Learning Guided Design

AbstractExternal field‐enhanced electrocatalysis is a novel and promising approach for boosting the efficiency of electrocatalytic reactions, potentially achieving significant enhancement without altering the composition and structure of electrocatalysts. In addition, the scaling relations of electrocatalysis typically lead to similar variations of initial‐state and transition‐state (TS) energy, which minimally impacts the reaction energy barrier. A sophisticated design of the external field effects shall break these scaling relations. This review provides a comprehensive overview of current research on the effect of mechanical, electric, and magnetic fields on electrocatalysis. It meticulously details the mechanisms underlying activity enhancement based on external field regulations, spanning from the synthesis of electrocatalytic materials to their behavior during the reaction process and modulation of the electrolyte environment. Additionally, the applications of emerging machine learning (ML) technologies in electrocatalysis design, including machine learning interatomic potentials (MLIPs) to simulate large‐scale and dynamic chemical reaction processes, data‐driven design and optimization of electrocatalysis performance, are briefly reviewed. In addition, the significant potential of ML technologies in conjunction with external field regulation, envisioning them as effective tools for optimizing or reverse designing electrocatalysis, considering both thermodynamic and kinetic factors as well as the dynamic effect of electrocatalyst surfaces under extreme external fields, is highlighted.

A machine-learning interatomic potential to study dry/wet oxidation process of silicon

We developed an accurate and efficient machine learning potential with DFT accuracy and applied it to the silicon dry/wet oxidation process to investigate the underlying physics of thermal oxidation of silicon (001) surfaces. The accuracy of the potential was verified by comparing the melting point and structural properties of silicon, the structural properties of a-SiO2, and the adsorption properties on the silicon surface with experiment and DFT data. In subsequent thermal oxidation simulations, we successfully reproduced the accelerated growth phenomenon of the wet oxidation in the experiment, discussed the oxide growth process in detail, and elucidated that the accelerated growth is due to hydrogen in the system that both enhances the adsorption of oxygen on the silicon surface and promotes the migration of oxygen atoms. Finally, we annealed the oxidized structure, counted the defect information in the structure before and after annealing, and analyzed the defect evolution behavior during the annealing process.

Nitride Lithium-ion Conductors with Enhanced Oxidative Stability

It is desirable to develop solid electrolytes that have both excellent reductive stability against lithium metal and oxidative stability against high-voltage cathodes. However, no inorganic superionic conductors reported thus far satisfy these criteria. Nitrides exhibit intrinsically superior stability against reduction but are often readily oxidized at voltages as low as 0.6 V. In this article, we investigated all nitride-based compounds to search for materials with improved oxidative stabilities over 2.0 V while retaining their intrinsic stability against Li metal. We found two compounds, LiPN2 and Li2CN2, with high oxidative stability > 2.0 V and low vacancy migration energies. Using fine-tuned CHGNet machine-learning interatomic potential, we found that upon introducing aliovalent dopants to introduce vacancies in Li2CN2, the dopant and vacancy strongly anchor with each other to result in trapped vacancies, which lowers ionic conductivity. In contrast, vacancies and dopants have minimal interactions in LiPN2, resulting in a high ionic conductivity. These two compounds were synthesized, but their ionic conductivities were not successfully measured because of the challenges in densification. With improved processing conditions, these compounds may serve as anode-side separators in dual-separator-type all-solid-state batteries or anode buffer layer materials interfaced with lithium metal.

Equivariant tensor network potentials

Abstract Machine-learning interatomic potentials (MLIPs) have made a significant contribution to the recent progress in the fields of computational materials and chemistry due to the MLIPs’ ability of accurately approximating energy landscapes of quantum-mechanical models while being orders of magnitude more computationally efficient. However, the computational cost and number of parameters of many state-of-the-art MLIPs increases exponentially with the number of atomic features. Tensor (non-neural) networks, based on low-rank representations of high-dimensional tensors, have been a way to reduce the number of parameters in approximating multidimensional functions, however, it is often not easy to encode the model symmetries into them. In this work we develop a formalism for rank-efficient equivariant tensor networks (ETNs), i.e. tensor networks that remain invariant under actions of SO(3) upon contraction. All the key algorithms of tensor networks like orthogonalization of cores and DMRG-based algorithms carry over to our equivariant case. Moreover, we show that many elements of modern neural network architectures like message passing, pulling, or attention mechanisms, can in some form be implemented into the ETNs. Based on ETNs, we develop a new class of polynomial-based MLIPs that demonstrate superior performance over existing MLIPs for multicomponent systems.

Construction of Machine Learning Interatomic Potentials for Metals

Construction of Machine Learning Interatomic Potentials for Metals

Dual-Vacancy-Engineered ZnIn2S4 Nanosheets for Harnessing Low-Frequency Vibration Induced Piezoelectric Polarization Coupled with Static Dipole Field to Enhance Photocatalytic H2 Evolution.

This study investigates the impact of In- and S-vacancy concentrations on the photocatalytic activity of non-centrosymmetric zinc indium sulfide (ZIS) nanosheets for the hydrogen evolution reaction (HER). A positive correlation between the concentrations of dual In and S vacancies and the photocatalytic HER rate over ZIS nanosheets is observed. The piezoelectric polarization, stimulated by low-frequency vortex vibration to ensure the well-dispersion of ZIS nanosheets in solution, plays a crucial role in enhancing photocatalytic HER over the dual-vacancy engineered ZIS nanosheets. The piezoelectric characteristic of the defective ZIS nanosheets is confirmed through the piezopotential response measured using piezoelectric force microscopy. Piezophotocatalytic H2 evolution over the ZIS nanosheets is boosted under accelerated vortex vibrations. The research explores how vacancies alter ZIS's dipole moment and piezoelectric properties, thereby increasing electric potential gradient and improving charge-separation efficiency, through multi-scale simulations, including Density Functional Theory and Finite Element Analysis, and a machine-learning interatomic potential for defect identification. Increased In and S vacancies lead to higher electric potential gradients in ZIS along [100] and [010] directions, attributing to dipole moment and the piezoelectric effect. This research provides a comprehensive exploration of vacancy engineering in ZIS nanosheets, leveraging the piezopotential and dipole field to enhance photocatalytic performances.

Fitting to magnetic forces improves the reliability of magnetic Moment Tensor Potentials

We developed a method for fitting machine-learning interatomic potentials with magnetic degrees of freedom, namely, magnetic Moment Tensor Potentials (mMTP). The main feature of our method consists in fitting mMTP to magnetic forces (negative derivatives of energies with respect to magnetic moments) as obtained spin-polarized density functional theory calculations. We test our method on the bcc Fe–Al system with different compositions. Specifically, we calculate formation energies, equilibrium lattice parameter, and total cell magnetization. Our findings demonstrate an accurate correspondence between the values calculated with mMTP and those obtained by DFT at zero temperature. Additionally, using molecular dynamics, we estimate the finite-temperature lattice parameter and capture the cell expansion as was previously revealed in experiment. Furthermore, we demonstrate that fitting to magnetic forces increases the reliability of structure relaxation (or, equilibration), in the sense of ensuring that every relaxation run ends up with a successfully relaxed structure (the failure may otherwise be caused by falsely driving a configuration away from the region covered in the training set).

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions.

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. This study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure-temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

Thermal conductivity calculation using homogeneous non-equilibrium molecular dynamics simulation with Allegro

In this study, we derive the heat flux formula for the Allegro model, one of machine-learning interatomic potentials using the equivariant deep neural network, to calculate lattice thermal conductivity using the homogeneous non-equilibrium molecular dynamics (HNEMD) method based on the Green-Kubo formula. Allegro can construct more advanced atomic descriptors than conventional ones, and can be applied to multicomponent and large-scale systems, providing a significant advantage in estimating the thermal conductivity of anharmonic materials, such as thermoelectric materials. In addition, the spectral heat current (SHC) method, recently developed for the HNEMD framework (HNEMD-SHC), allows the calculation of not only the total thermal conductivity but also its frequency components. The verification of the heat flux and the demonstration of HNEMD-SHC method are performed for the extremely anharmonic low-temperature phase of Ag2Se.

Molecular dynamics of liquid-electrode interface by integrating Coulomb interaction into universal neural network potential.

Computational understanding of the liquid-electrode interface faces challenges in efficiently incorporating reactive force fields and electrostatic potentials within reasonable computational costs. Although universal neural network potentials (UNNPs), representing pretrained machine learning interatomic potentials, are emerging, current UNNP models lack explicit treatment of Coulomb potentials, and methods for integrating additional charges on the electrode remain to be established. We propose a method to analyze liquid-electrode interfaces by integrating a UNNP, known as the preferred potential, with Coulomb potentials using the ONIOM method. This approach extends the applicability of UNNPs to electrode-liquid interface systems. Through molecular dynamics simulations of graphene-water and graphene oxide (GO)-water interfaces, we demonstrate the effectiveness of our method. Our findings emphasize the necessity of incorporating long-range Coulomb potentials into the water potential to accurately describe water polarization at the interface. Furthermore, we observe that functional groups on the GO electrode influence both polarization and capacitance.

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.

Benchmarking machine learning interatomic potentials via phonon anharmonicity

Abstract Machine learning approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, machine learning interatomic potentials (MLIPs) can accurately reproduce first-principles data at a cost similar to that of conventional interatomic potential approaches. While MLIPs have been extensively tested across various classes of materials and molecules, a clear characterization of the anharmonic terms encoded in the MLIPs is lacking. Here, we benchmark popular MLIPs using the anharmonic vibrational Hamiltonian of ThO2 in the fluorite crystal structure, which was constructed from density functional theory (DFT) using our highly accurate and efficient irreducible derivative methods. The anharmonic Hamiltonian was used to generate molecular dynamics (MD) trajectories, which were used to train three classes of MLIPs: Gaussian approximation potentials, artificial neural networks (ANN), and graph neural networks (GNN). The results were assessed by directly comparing phonons and their interactions, as well as phonon linewidths, phonon lineshifts, and thermal conductivity. The models were also trained on a DFT MD dataset, demonstrating good agreement up to fifth-order for the ANN and GNN. Our analysis demonstrates that MLIPs have great potential for accurately characterizing anharmonicity in materials systems at a fraction of the cost of conventional first principles-based approaches.

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

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

Atomic cluster expansion potential for large scale simulations of hydrocarbons under shock compression.

We present an Atomic Cluster Expansion (ACE) machine learned potential developed for high-fidelity atomistic simulations of hydrocarbons, targeting pressures and temperatures near and above supercritical fluid regimes for molecular fluids. A diverse set of stoichiometries were covered in training, including 1:0 (pure carbon), 1:4 (methane), and 1:1 (benzene), and rich bonding environments sampled at supercritical temperatures, hydrogen rich, reactive mixtures where metastable stoichiometries arise, including 1:2 (ethylene) and 1:3 (ethane). A high-fidelity training database was constructed by performing large-scale quantum molecular dynamic simulations [density functional theory (DFT) MD] of diamond, graphite, methane, and benzene. A novel approach to selecting structures from DFT MD is also presented, which allows for the rapid selection of unique DFT MD frames from complex trajectories. Comparisons to DFT and experimental data demonstrate that the presented ACE potential accurately reproduces isotherms, carbon melting curves, radial distribution functions, and shock Hugoniots for carbon and hydrocarbon systems for pressures up to 100GPa and temperatures up to 6000K for hydrocarbon systems and up to 9000K for pure carbon systems. This work delivers a potential that can be used for accurate, large-scale simulations of shocked hydrocarbons and demonstrates a methodology for fitting and validating machine learning interatomic potentials to complex molecular environments, which can be applied to energetic materials in future works.