Machine Learning Force Fields Research Articles

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields.

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope.

As the sophistication of machine learning force fields (MLFF) increases to match the complexity of extended molecules and materials, so does the need for tools to properly analyze and assess the practical performance of MLFFs. To go beyond average error metrics and into a complete picture of a model's applicability and limitations, we developed FFAST (force field analysis software and tools): a cross-platform software package designed to gain detailed insights into a model's performance and limitations, complete with an easy-to-use graphical user interface. The software allows the user to gauge the performance of any molecular force field,─such as popular state-of-the-art MLFF models, ─ on various popular data set types, providing general prediction error overviews, outlier detection mechanisms, atom-projected errors, and more. It has a 3D visualizer to find and picture problematic configurations, atoms, or clusters in a large data set. In this paper, the example of the MACE and NequIP models is used on two data sets of interest [stachyose and docosahexaenoic acid (DHA)]─to illustrate the use cases of the software. With this, it was found that carbons and oxygens involved in or near glycosidic bonds inside the stachyose molecule present increased prediction errors. In addition, prediction errors on DHA rise as the molecule folds, especially for the carboxylic group at the edge of the molecule. We emphasize the need for a systematic assessment of MLFF models for ensuring their successful application to the study of dynamics of molecules and materials.

Calibration of uncertainty in the active learning of machine learning force fields

FFLUX is a machine learning force field that uses the maximum expected prediction error (MEPE) active learning algorithm to improve the efficiency of model training. MEPE uses the predictive uncertainty of a Gaussian process (GP) to balance exploration and exploitation when selecting the next training sample. However, the predictive uncertainty of a GP is unlikely to be accurate or precise immediately after training. We hypothesize that calibrating the uncertainty quantification within MEPE will improve active learning performance. We develop and test two methods to improve uncertainty estimates: post-hoc calibration of predictive uncertainty using the CRUDE algorithm, and replacing the GP with a student-t process. We investigate the impact of these methods on MEPE for single sample and batch sample active learning. Our findings suggest that post-hoc calibration does not improve the performance of active learning using the MEPE method. However, we do find that the student-t process can outperform active learning strategies and random sampling using a GP if the training set is sufficiently large.

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

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

Phase Transitions, Dielectric Response, and Nonlinear Optical Properties of Aziridinium Lead Halide Perovskites.

Hybrid organic-inorganic lead halide perovskites are promising candidates for next-generation solar cells, light-emitting diodes, photodetectors, and lasers. The structural, dynamic, and phase-transition properties play a key role in the performance of these materials. In this work, we use a multitechnique experimental (thermal, X-ray diffraction, Raman scattering, dielectric, nonlinear optical) and theoretical (machine-learning force field) approach to map the phase diagrams and obtain information on molecular dynamics and mechanism of the structural phase transitions in novel 3D AZRPbX3 perovskites (AZR = aziridinium; X = Cl, Br, I). Our work reveals that all perovskites undergo order-disorder phase transitions at low temperatures, which significantly affect the structural, dielectric, phonon, and nonlinear optical properties of these compounds. The desirable cubic phases of AZRPbX3 remain stable at lower temperatures (132, 145, and 162 K for I, Br, and Cl) compared to the methylammonium and formamidinium analogues. Similar to other 3D-connected hybrid perovskites, the dielectric response reveals a rather high dielectric permittivity, an important feature for defect tolerance. We further show that AZRPbBr3 and AZRPbI3 exhibit strong nonlinear optical absorption. The high two-photon brightness of AZRPbI3 emission stands out among lead perovskites emitting in the near-infrared region.

Physics infused machine learning force fields for 2D materials monolayers

Large-scale atomistic simulations of two-dimensional (2D) materials rely on highly accurate and efficient force fields. Here, we present a physics-infused machine learning framework that enables the efficient development and interpretability of interatomic interaction models for 2D materials. By considering the characteristics of chemical bonds and structural topology, we have devised a set of efficient descriptors. This enables accurate force field training using a small dataset. The machine learning force fields show great success in describing the phase transformation and domain switching behaviors of monolayer Group IV monochalcogenides, e.g., GeSe and PbTe. Notably, this type of force field can be readily extended to other non-transition 2D systems, such as hexagonal boron nitride (h BN), leveraging their structural similarity. Our work provides a straightforward but accurate extension of simulation time and length scales for 2D materials.

Modelling electrified microporous carbon/electrolyte electrochemical interface and unraveling charge storage mechanism by machine learning accelerated molecular dynamics

Ion storage in electric double layer (EDL) of microporous carbon (< 1 nm) has been demonstrated to be a partially desolvated structure, leading to a capacitance increase. Due to the relevance of the interface structure to capacitance behavior and charge storage mechanism, it is critical to give a deep insight into the micropore/electrolyte interface at the molecular scale. Ab initio molecular dynamics (AIMD) simulation can describe the electronic structure and dynamic properties of the EDL. However, the complex EDL is hard to be well equilibrated at the limited time scale of the AIMD simulation. Here, we have performed machine learning force field accelerated molecular dynamics (MLMD) to construct the EDL of microporous carbon at different electrode potentials with a much lower cost while keeping ab initio accuracy. Based on the MLMD with a longer time scale, we have clarified the microscopic information of the interface, such as the distributions of ions and water molecules. By simulating the Na+ intercalation process, the critical role of the electrode potential on ion storage in pore is clarified. In addition, according to the MLMD simulation on micropore/electrolyte EDLs with different pore sizes, the pore size of ∼0.65 nm is appropriate for desolvation effect due to the match between the pore size and the solvated ion size. These theoretical results provide a way for studying micropore/electrolyte EDL by MLMD and improving the electrochemical performance of microporous carbon electrodes.

Modeling Exchange Reactions in Covalent Adaptable Networks with Machine Learning Force Fields

Modeling Exchange Reactions in Covalent Adaptable Networks with Machine Learning Force Fields

Accurate energy barriers for catalytic reaction pathways: an automatic training protocol for machine learning force fields

We introduce a training protocol for developing machine learning force fields (MLFFs), capable of accurately determining energy barriers in catalytic reaction pathways. The protocol is validated on the extensively explored hydrogenation of carbon dioxide to methanol over indium oxide. With the help of active learning, the final force field obtains energy barriers within 0.05 eV of Density Functional Theory. Thanks to the computational speedup, not only do we reduce the cost of routine in-silico catalytic tasks, but also find an alternative path for the previously established rate-limiting step, with a 40% reduction in activation energy. Furthermore, we illustrate the importance of finite temperature effects and compute free energy barriers. The transferability of the protocol is demonstrated on the experimentally relevant, yet unexplored, top-layer reduced indium oxide surface. The ability of MLFFs to enhance our understanding of extensively studied catalysts underscores the need for fast and accurate alternatives to direct ab-initio simulations.

Mobile dislocation mediated Hall-Petch and inverse Hall-Petch behaviors in nanocrystalline Al-doped boron carbide

The Hall-Petch and inverse Hall-Petch behaviors in nanocrystalline ceramics are not well understood because dislocation activities, which are important in metals, are usually limited in these materials. In this study, we use molecular dynamics simulations with a machine-learning force field to investigate the shear deformation behaviors of nanocrystalline Al-doped boron carbide (n-B12-CAlC) as the grain size varies. We find a transition from the Hall-Petch to inverse Hall-Petch behavior in n-B12-CAlC when the grain size reaches its critical value of 6.09 nm, with a maximum shear strength of 14.93 GPa. Interestingly, mobile dislocation nucleated from grain boundaries (GBs) is activated in n-B12-CAlC due to the breakage of weakened C-Al chain bonds, which plays a significant role in its Hall-Petch behaviors. As the grain size decreases, the increasing GB regions homogenize the shear stress, which suppresses dislocation nucleation from GBs and strengthens the material, as observed in the conventional Hall-Petch relationship. However, with a further decrease in the grain size (< ∼ 6 nm), the increasing GB regions provide more favorable sites and a higher possibility for dislocation nucleation, reducing the shear strength and triggering a transition into the inverse Hall-Petch behavior. These findings shed light on deformation behaviors and mechanisms of nanocrystalline ceramics and provide an explanation for the transition from Hall-Petch to inverse Hall-Petch behaviors.

Dynamic Local Structure in Caesium Lead Iodide: Spatial Correlation and Transient Domains.

Metal halide perovskites are multifunctional semiconductors with tunable structures and properties. They are highly dynamic crystals with complex octahedral tilting patterns and strongly anharmonic atomic behavior. In the higher temperature, higher symmetry phases of these materials, several complex structural features are observed. The local structure can differ greatly from the average structure and there is evidence that dynamic 2D structures of correlated octahedral motion form. An understanding of the underlying complex atomistic dynamics is, however, still lacking. In this work, the local structure of the inorganic perovskite CsPbI3 is investigated using a new machine learning force field based on the atomic cluster expansion framework. Through analysis of the temporal and spatial correlation observed during large-scale simulations, it is revealed that the low frequency motion of octahedral tilts implies a double-well effective potential landscape, even well into the cubic phase. Moreover, dynamic local regions of lower symmetry are present within both higher symmetry phases. These regions are planar and the length and timescales of the motion are reported. Finally, the spatial arrangement of these features and their interactions are investigated and visualized, providing a comprehensive picture of local structure in the higher symmetryphases.

A Set of Moment Tensor Potentials for Zirconium with Increasing Complexity.

Machine learning force fields (MLFFs) are an increasingly popular choice for atomistic simulations due to their high fidelity and improvable nature. Here we propose a hybrid small-cell approach that combines attributes of both offline and active learning to systematically expand a quantum-mechanical (QM) database while constructing MLFFs with increasing model complexity. Our MLFFs employ the moment tensor potential formalism. During this process, we quantitatively assessed the structural properties, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, free surface energies, and generalized stacking fault (GSF) energies of Zr as predicted by our MLFFs. Unsurprisingly, the model complexity has a positive correlation with prediction accuracy. We also find that the MLFFs were able to predict the properties of out-of-sample configurations without directly including these specific configurations in the training dataset. Additionally, we generated 100 MLFFs of high complexity (1513 parameters each) that reached different local optima during training. Their predictions cluster around the benchmark DFT values, but subtle physical features such as the location of local minima on the GSF energy surface are washed out by statistical noise.

Molecular dynamics simulations for liquid electrolytes of propylene carbonate with LiTFSI, LiPF6, and LiBF4 salts

Understanding the role that molecular interactions play on physicochemical properties of ionic solutions is of fundamental importance to design novel electrolytes used in devices to storage energy, such as lithium ion batteries. Several salts containing propylene carbonate are studied. The propylene carbonate and TFSI− anion force fields were previously parametrized by our group. Those of lithium (Li+), hexafluorophosphate (PF6−) and tetrafluoroborate (BF4−) are developed in this work with ions carrying a charge of ±1e. The calculated properties are liquid density, dielectric constant, self-diffusion coefficient and viscosity. The results are in excellent agreement with experimental data at different salt concentrations and temperatures. The dielectric constant of PC/LiBF4 is greater than that of the other two electrolytes because the ions form large clusters and the solvent molecules behave as a pure liquid. The predictions with the new parameters improve those from a polarizable model for PC/LiTFSI and those from a machine learning force field for PC/LiPF6.

Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics.

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

Deciphering the Atomistic Mechanism of Si(111)-7 × 7 Surface Reconstruction Using a Machine-Learning Force Field.

While the complex 7 × 7 structure that arises upon annealing the Si(111) surface is well-known, the mechanism underlying this unusual surface reconstruction has remained a mystery. Here, we report molecular dynamics simulations using a machine-learning force field for Si to investigate the Si(111)-7 × 7 surface reconstruction from the melt. We find that there are two possible pathways for the formation of the 7 × 7 structure. The first path arises from the growth of a faulted half domain from the metastable 5 × 5 phase to the final 7 × 7 structure, while the second path involves the direct formation of the 7 × 7 reconstruction. Both pathways involve the creation of dimers and bridged five-membered rings, followed by the formation of additional dimers and the stabilization of the triangular halves of the unit cell. The corner hole is formed from the joining of several five-member rings. The insertion of atoms below the adatoms to form a dumbbell configuration involves extra atom diffusion or rearrangement during the evolution of triangular halves and dimer formation along the unit cell boundary. Our findings may provide insights for manipulating the surface structure by introducing other atomic species.

Accuracy evaluation of different machine learning force field features

Predicting energies and forces using machine learning force field (MLFF) depends on accurate descriptions (features) of chemical environment. Despite the numerous features proposed, there is a lack of controlled comparison among them for their universality and accuracy. In this work, we compared several commonly used feature types for their ability to describe physical systems. These different feature types include cosine feature, Gaussian feature, moment tensor potential (MTP) feature, spectral neighbor analysis potential feature, simplified smooth deep potential with Chebyshev polynomials feature and Gaussian polynomials feature, and atomic cluster expansion feature. We evaluated the training root mean square error (RMSE) for the atomic group energy, total energy, and force using linear regression model regarding to the density functional theory results. We applied these MLFF models to an amorphous sulfur system and carbon systems, and the fitting results show that MTP feature can yield the smallest RMSE results compared with other feature types for either sulfur system or carbon system in the disordered atomic configurations. Moreover, as an extending test of other systems, the MTP feature combined with linear regression model can also reproduce similar quantities along the ab initio molecular dynamics trajectory as represented by Cu systems. Our results are helpful in selecting the proper features for the MLFF development.

Structural Dynamics Descriptors for Metal Halide Perovskites.

Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature. Understanding the local and average structures continues to be challenging for both modeling and experiments. Here, we report the quantitative analysis of structural dynamics in time and space from molecular dynamics simulations of perovskite crystals. The compact descriptors provided cover a wide variety of structural properties, including octahedral tilting and distortion, local lattice parameters, molecular orientations, as well as their spatial correlation. To validate our methods, we have trained a machine learning force field (MLFF) for methylammonium lead bromide (CH3NH3PbBr3) using an on-the-fly training approach with Gaussian process regression. The known stable phases are reproduced, and we find an additional symmetry-breaking effect in the cubic and tetragonal phases close to the phase-transition temperature. To test the implementation for large trajectories, we also apply it to 69,120 atom simulations for CsPbI3 based on an MLFF developed using the atomic cluster expansion formalism. The structural dynamics descriptors and Python toolkit are general to perovskites and readily transferable to more complex compositions.

Insights into Electrolyte Reactivity and Solid Electrolyte Interphase Formation at the Li Metal Anode Surface from DFT Simulations

Solid electrolyte interphase (SEI) is a critical component of lithium ion batteries, yet is poorly characterized and not well understood. We use plane wave density functional theory simulations to perform a comprehensive study of the degradation reaction mechanisms of four electrolyte solvents and additives, ethylene carbonate (EC), propylene carbonate (PC), fluoroethylene carbonate (FEC), and vinylene carbonate (VC), at the Li (001) metal anode surface. The calculations provide fundamental insights into electrolyte decomposition and spontaneous SEI formation. Utilizing automated workflows implemented in the Schrödinger Materials Science Suite, we compute the adsorption energies and calculate the reaction energies for each decomposition pathway. Furthermore, we employ nudged elastic band calculations to compute the decomposition reaction barriers and provide mechanistic insights into the onset of SEI formation. We analyze trends in decomposition reaction energies and the relationships between the reaction energies and the activation barriers for the various electrolyte molecules as a function of applied bias potential. We find that the preferred decomposition pathways are different for the solvent molecules (EC and PC) than for the additives (FEC and VC). Calculations also suggest that applied bias reduces decomposition reaction barriers thus enhancing SEI formation. Such a comprehensive dataset of reaction energies and activation barriers provides useful benchmarks for the development and validation of reactive machine learned force fields for modeling advanced battery chemistries at a larger scale.

Atom-centered machine-learning force field package

In recent years, machine learning algorithms have been widely used for constructing force fields with an accuracy of ab initio methods and the efficiency of classical force fields. Here, we developed a python-based atom-centered machine-learning force field (PyAMFF) package to provide a simple and efficient platform for fitting and using machine learning force fields by implementing an atom-centered neural-network algorithm with Behler-Parrinello symmetry functions as structural fingerprints. The following three features are included in PyAMFF: (1) integrated Fortran modules for fast fingerprint calculations and Python modules for user-friendly integration through scripts and facile extension of future algorithms; (2) a pure Fortran backend to interface with the software, including the long-timescale dynamic simulation package EON, enabling both molecular dynamic simulations and adaptive kinetic Monte Carlo simulations with machine-learning force fields; and (3) integration with the Atomic Simulation Environment package for active learning and ML-based algorithm development. Here, we demonstrate an efficient parallelization of PyAMFF in terms of CPU and memory usage and show that the Fortran-based PyAMFF calculator exhibits a linear scaling relationship with the number of symmetry functions and the system size. Program summaryProgram title: python-based atom-centered machine-learning force field (PyAMFF)CPC Library link to program files:https://doi.org/10.17632/fsn6dkcvrv.1Developer's repository link:https://gitlab.com/pyamff/pyamffLicensing provisions: Apache License, 2.0Nature of problem: Determine an approximate (surrogate) model based upon atomic forces and energies from density functional theory (DFT). With a surrogate model that is less computationally expensive to evaluate than DFT, there can be a rapid exploration of the potential energy surface, accelerated optimization to minima and saddle points, and ultimately, accelerated design of active materials where the kinetics are key to the material function.Solution method: The atomic environments of training data are calculated in terms of Behler-Parrinello fingerprints. These fingerprints are passed to a neural network which is trained to reproduce the energy and force of the training data. A parallel implementation and Fortran backend allow for efficient training and calculation of the resulting surrogate model. Examples of long-time simulations of materials on the surrogate model surfaces are provided.

Machine learning force fields for molecular liquids: Ethylene Carbonate/Ethyl Methyl Carbonate binary solvent

Highly accurate ab initio molecular dynamics (MD) methods are the gold standard for studying molecular mechanisms in the condensed phase, however, they are too expensive to capture many key properties that converge slowly with respect to simulation length and time scales. Machine learning (ML) approaches which reach the accuracy of ab initio simulation, and which are, at the same time, sufficiently affordable hold the key to bridging this gap. In this work we present a robust ML potential for the EC:EMC binary solvent, a key component of liquid electrolytes in rechargeable Li-ion batteries. We identify the necessary ingredients needed to successfully model this liquid mixture of organic molecules. In particular, we address the challenge posed by the separation of scale between intra- and inter-molecular interactions, which is a general issue in all condensed phase molecular systems.