Machine Learning Force Fields Research Articles

Atomic diffusion in liquid gallium and gallium-nickel alloys probed by quasielastic neutron scattering and molecular dynamic simulations

The atomic mobility in liquid pure gallium and a gallium-nickel alloy with 2 at% of nickel is studied experimentally by incoherent quasielastic neutron scattering. The integral diffusion coefficients for all-atom diffusion are derived from the experimental data at different temperatures. DFT-based ab-initio molecular dynamics (MD) is used to find numerically the diffusion coefficient of liquid gallium at different temperatures, and numerical theory results well agree with the experimental findings at temperatures below 500 K. Machine learning force fields derived from ab-initio molecular dynamics (AIMD) overestimate within a small 6% error the diffusion coefficient of pure gallium within the genuine AIMD. However, they better agree with experiment for pure gallium and enable the numerical finding of the diffusion coefficient of nickel in the considered melted alloy along with the diffusion coefficient of gallium and integral diffusion coefficient, that agrees with the corresponding experimental values within the error bars. The temperature dependence of the gallium diffusion coefficient DGa(T) follows the Arrhenius law experimentally for all studied temperatures and below 500 K also in the numerical simulations. However, DGa(T) can be well described alternatively by an Einstein–Stokes dependence with the metallic liquid viscosity following the Arrhenius law, especially for the MD simulation results at all studied temperatures. Moreover, a novel variant of the excess entropy scaling theory rationalized our findings for gallium diffusion. Obtained values of the Arrhenius activation energies are profoundly different in the competing theoretical descriptions, which is explained by different temperature-dependent prefactors in the corresponding theories. The diffusion coefficient of gallium is significantly reduced (at the same temperature) in a melted alloy with natural nickel, even at a tiny 2 at% concentration of nickel, as compared with its pure gallium value. This highly surprising behavior contradicts the existing excess entropy scaling theories and opens a venue for further research.

Development of machine learning force field for thermal conductivity analysis in MoAlB: Insights into anisotropic heat transfer mechanisms

The MAB phases have garnered significant attention as a new generation high-temperature structural materials due to their outstanding high-temperature mechanical properties, resistance to oxidation at elevated temperatures, low-temperature synthesis, and machining capabilities. The chemically anisotropic bonding within MAB phases leads to unique anisotropic elastic properties, oxidation behavior, and electrical characteristics, posing challenges in understanding the structure-property relationships.To address this challenge, we leveraged recent advances in machine learning force fields based on quantum mechanics methods. Using ab initio molecular dynamics simulations, we constructed a comprehensive dataset and developed an accurate machine learning force field for the Mo–Cr–Al–B system based on deep neural network. We then employed non-equilibrium molecular dynamics simulations to calculate the phonon thermal conductivity of MoAlB, investigating its temperature dependence and anisotropy. Our analysis includes phonon density of states, phonon participation ratio, and spectral heat flux analysis, shedding light on the temperature-dependent anisotropy of phonon thermal conductivity in MoAlB. This work not only provides a reliable force field for large-scale molecular dynamics simulations but also advances our understanding of the composition-structure-performance relationship in MAB phases.

Machine learned force-fields for an Ab-initio quality description of metal-organic frameworks

Metal-organic frameworks (MOFs) are an incredibly diverse group of highly porous hybrid materials, which are interesting for a wide range of possible applications. For a meaningful theoretical description of many of their properties accurate and computationally highly efficient methods are in high demand. These would avoid compromises regarding either the quality of modelling results or the level of complexity of the calculated properties. With the advent of machine learning approaches, it is now possible to generate such approaches with relatively little human effort. Here, we build on existing types of machine-learned force fields belonging to the moment-tensor and kernel-based potential families to develop a recipe for their efficient parametrization. This yields exceptionally accurate and computationally highly efficient force fields. The parametrization relies on reference configurations generated during molecular dynamics based, active learning runs. The performance of the potentials is benchmarked for a representative selection of commonly studied MOFs revealing a close to DFT accuracy in predicting forces and structural parameters for a set of validation structures. The same applies to elastic constants and phonon band structures. Additionally, for MOF-5 the thermal conductivity is obtained with full quantitative agreement to single-crystal experiments. All this is possible while maintaining a very high degree of computational efficiency. The exceptional accuracy of the parameterized force field potentials combined with their computational efficiency has the potential of lifting the computational modelling of MOFs to the next level.

Bromination of 2D materials

The adsorption, reaction and thermal stability of bromine on Rh(111)-supported hexagonal boron nitride (h-BN) and graphene were investigated. Synchrotron radiation-based high-resolution x-ray photoelectron spectroscopy (XPS) and temperature-programmed XPS allowed us to follow the adsorption process and the thermal evolution in situ on the molecular scale. On h-BN/Rh(111), bromine adsorbs exclusively in the pores of the nanomesh while we observe no such selectivity for graphene/Rh(111). Upon heating, bromine undergoes an on-surface reaction on h-BN to form polybromides (170–240 K), which subsequently decompose to bromide (240–640 K). The high thermal stability of Br/h-BN/Rh(111) suggests strong/covalent bonding. Bromine on graphene/Rh(111), on the other hand, reveals no distinct reactivity except for intercalation of small amounts of bromine underneath the 2D layer at high temperatures. In both cases, adsorption is reversible upon heating. Our experiments are supported by a comprehensive theoretical study. DFT calculations were used to describe the nature of the h-BN nanomesh and the graphene moiré in detail and to study the adsorption energetics and substrate interaction of bromine. In addition, the adsorption of bromine on h-BN/Rh(111) was simulated by molecular dynamics using a machine-learning force field.

Segregation of Phosphorus and Silicon at the Grain Boundary in Bcc Iron via Machine-Learned Force Fields

The study of the effects of impurity on grain boundaries is a critical aspect of materials science, particularly when it comes to understanding and controlling the properties of materials for specific applications. One of the related key issues is the segregation preference of impurity atoms in the grain boundary region. In this paper, we employed the on-the-fly machine learning to generate force fields, which were subsequently used to calculate the segregation energies of phosphorus and silicon in bcc iron containing the ∑5(310)[001] grain boundary. The generated force fields were successfully benchmarked using ab initio data. Our further calculations considered impurity atoms at a number of possible interstitial and substitutional segregation sites. Our predictions of the preferred sites agree with the experimental observations. Planar concentration of impurity atoms affects the segregation energy and, moreover, can change the preferred segregation sites.

First principles molecular dynamics simulation and thermal decomposition kinetics study of CL-20.

2,4,6,8,10, 12-hexanitro-2,4,6,8,10, 12-hexazepane (CL-20) is a new energetic material with high performance and low sensitivity. In-depth study of the thermal decomposition mechanism of CL-20 is a necessary condition to improve its performance, ensure its safety, and optimize its application. On the basis of a large number of empirical force fields used in molecular dynamics simulation in the past, the machine learning augmented first-principles molecular dynamics method was used for the first time to simulate the thermal decomposition reaction of CL-20 at 2200 K, 2500 K, 2800 K, and 3000 K isothermal temperature. The main stable resulting compounds are N2, CO2, CO, H2O, andH2, where CO2 and H2O continue to decompose at higher temperatures. The initial decomposition pathways are denitration by N-N fracture, ring-opening by C-N bond fracture, and redox reaction involving NO2 and CL-20. After ring opening, two main compounds, fused tricyclic pyrazine and azadicyclic, were formed, which were decomposed continuously to form monocyclic pyrazine and pyrazole ring structures. The most common fragments formed during decomposition are those containing two, three, four, and six carbons. The formation rule and quantity of main small molecule intermediates and resulting stable products under different simulated temperatures were analyzed. Based on ab initio Bayesian active learning algorithm, efficient and accurate prediction of CL-20 is made using the dynamic machine learning function of Vienna Ab-Initio Simulation Package (VASP), which constructs the energy potential surface by learning a large number of data based on AIMD calculations. The result is a machine learning force field (MLFF). Then the molecular dynamics of CL-20 was simulated using the trained MLFF model. PAW pseudopotentials and generalized gradient approximation (GGA), namely, Perdew-Burke-Ernzerhof (PBE) functional, are used in the calculation. The plane wave truncation energy (ENCUT) is set to 550 eV, and using the Gaussian broadening, the thermal broadening size of the single-electron orbital is 0.05 eV. A van der Waals revision of the system with Grimme Version 3. The energy convergence accuracy (EDIFF) of electron self-consistent iteration is set to 1E-5 eV and 1E-6 eV, respectively. The two-step structure optimization is carried out using 1'1'1 k point grid and conjugate gradient method. The ENCUT was changed to 500 eV and EDIFF to 1E-5 eV, and NVT integration (ISIF = 2) of Langevin thermostat was used for machine learning force field training and AIMD simulation of the system.

The emergence of machine learning force fields in drug design.

In the field of molecular simulation for drug design, traditional molecular mechanic force fields and quantum chemical theories have been instrumental but limited in terms of scalability and computational efficiency. To overcome these limitations, machine learning force fields (MLFFs) have emerged as a powerful tool capable of balancing accuracy with efficiency. MLFFs rely on the relationship between molecular structures and potential energy, bypassing the need for a preconceived notion of interaction representations. Their accuracy depends on the machine learning models used, and the quality and volume of training data sets. With recent advances in equivariant neural networks and high-quality datasets, MLFFs have significantly improved their performance. This review explores MLFFs, emphasizing their potential in drug design. It elucidates MLFF principles, provides development and validation guidelines, and highlights successful MLFF implementations. It also addresses potential challenges in developing and applying MLFFs. The review concludes by illuminating the path ahead for MLFFs, outlining the challenges to be overcome and the opportunities to be harnessed. This inspires researchers to embrace MLFFs in their investigations as a new tool to perform molecular simulations in drug design.

A Machine Learning Force Field for Bio-Macromolecular Modeling Based on Quantum Chemistry-Calculated Interaction Energy Datasets.

Accurate energy data from noncovalent interactions are essential for constructing force fields for molecular dynamics simulations of bio-macromolecular systems. There are two important practical issues in the construction of a reliable force field with the hope of balancing the desired chemical accuracy and working efficiency. One is to determine a suitable quantum chemistry level of theory for calculating interaction energies. The other is to use a suitable continuous energy function to model the quantum chemical energy data. For the first issue, we have recently calculated the intermolecular interaction energies using the SAPT0 level of theory, and we have systematically organized these energies into the ab initio SOFG-31 (homodimer) and SOFG-31-heterodimer datasets. In this work, we re-calculate these interaction energies by using the more advanced SAPT2 level of theory with a wider series of basis sets. Our purpose is to determine the SAPT level of theory proper for interaction energies with respect to the CCSD(T)/CBS benchmark chemical accuracy. Next, to utilize these energy datasets, we employ one of the well-developed machine learning techniques, called the CLIFF scheme, to construct a general-purpose force field for biomolecular dynamics simulations. Here we use the SOFG-31 dataset and the SOFG-31-heterodimer dataset as the training and test sets, respectively. Our results demonstrate that using the CLIFF scheme can reproduce a diverse range of dimeric interaction energy patterns with only a small training set. The overall errors for each SAPT energy component, as well as the SAPT total energy, are all well below the desired chemical accuracy of ~1 kcal/mol.

Hydrogen diffusion in zirconium hydrides from on-the-fly machine learning molecular dynamics

Reactor pressure vessels and fuel cladding tubes have repeatedly failed due to zirconium hydrides. Zirconium hydride precipitation and growth are directly affected by hydrogen atom transport properties, which would make nuclear fuel storage less safe over long periods of time. Herein, we employ first-principles calculations to investigate the hydrogen diffusion mechanism in zirconium hydrides, utilizing on-the-fly machine learning force field molecular dynamics. It is verified that the machine learning force field can accurately describe the hydrogen atomic diffusion properties in zirconium hydrides at several temperatures and compositions. The atomic migration paths of hydrogen in zirconium hydrides as well as their barriers and pre-factors are also calculated. According to our results, the temperature and composition of zirconium hydrides affect the microscopic dynamical behavior of hydrogen.

A first-principles machine-learning force field for heterogeneous ice nucleation on microcline feldspar.

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water under deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high-fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. Our training set includes configurations of bulk supercooled water, hexagonal and cubic ice, microcline, and fully-hydroxylated feldspar surfaces exposed to a vacuum, liquid water, and ice. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to a vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in a vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 10 Å from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30 000 atoms. Future work will be directed towards the calculation of nucleation free-energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces in ice nucleation.

Dynamic Monkey Bar Mechanism of Superionic Li‐ion Transport in LiTaCl6

AbstractThe LiTaCl6 solid electrolyte has the lowest activation energy of ionic conduction at ambient conditions (0.165 eV), with a record high ionic conductivity for a ternary compound (11 mS cm−1). However, the mechanism has been unclear. We train machine‐learning force fields (MLFF) on ab initio molecular dynamics (AIMD) data on‐the‐fly and perform MLFF MD simulations of AIMD quality up to the nanosecond scale at the experimental temperatures, which allows us to predict accurate activation energy for Li‐ion diffusion (at 0.164 eV). Detailed analyses of trajectories and vibrational density of states show that the large‐amplitude vibrations of Cl− ions in TaCl6− enable the fast Li‐ion transport by allowing dynamic breaking and reforming of Li−Cl bonds across the space in between the TaCl6− octahedra. We term this process the dynamic‐monkey‐bar mechanism of superionic Li+ transport which could aid the development of new solid electrolytes for all‐solid‐state lithium batteries.

Dynamic Monkey Bar Mechanism of Superionic Li-ion Transport in LiTaCl6.

The LiTaCl6 solid electrolyte has the lowest activation energy of ionic conduction at ambient conditions (0.165 eV), with a record high ionic conductivity for a ternary compound (11 mS cm-1 ). However, the mechanism has been unclear. We train machine-learning force fields (MLFF) on ab initio molecular dynamics (AIMD) data on-the-fly and perform MLFF MD simulations of AIMD quality up to the nanosecond scale at the experimental temperatures, which allows us to predict accurate activation energy for Li-ion diffusion (at 0.164 eV). Detailed analyses of trajectories and vibrational density of states show that the large-amplitude vibrations of Cl- ions in TaCl6 - enable the fast Li-ion transport by allowing dynamic breaking and reforming of Li-Cl bonds across the space in between the TaCl6 - octahedra. We term this process the dynamic-monkey-bar mechanism of superionic Li+ transport which could aid the development of new solid electrolytes for all-solid-state lithium batteries.

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.

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.