Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials

Rapid Characterization of Point Defects in Solid-State Ion Conductors Using Raman Spectroscopy, Machine-Learning Force Fields, and Atomic Raman Tensors

The successful design of solid-state photo- and electrochemical devices depends on the careful engineering of point defects in solid-state ion conductors. Characterization of point defects is critical to these efforts, but the best-developed techniques are difficult and time-consuming. Raman spectroscopy─with its exceptional speed, flexibility, and accessibility─is a promising alternative. Raman signatures arise from point defects due to local symmetry breaking and structural distortions. Unfortunately, the assignment of these signatures is often hampered by a shortage of reference compounds and corresponding reference spectra. This issue can be circumvented by calculation of defect-induced Raman signatures from first principles, but this is computationally demanding. Here, we introduce an efficient computational procedure for the prediction of point defect Raman signatures in solid-state ion conductors. Our method leverages machine-learning force fields and "atomic Raman tensors", i.e., polarizability fluctuations due to motions of individual atoms. We find that our procedure reduces computational cost by up to 80% compared to existing first-principles frozen-phonon approaches. These efficiency gains enable synergistic computational-experimental investigations, in our case allowing us to precisely interpret the Raman spectra of Sr(Ti0.94Ni0.06)O3-δ, a model oxygen ion conductor. By predicting Raman signatures of specific point defects, we determine the nature of dominant defects and unravel impacts of temperature and quenching on in situ and ex situ Raman spectra. Specifically, our findings reveal the temperature-dependent distribution and association behavior of oxygen vacancies and nickel substitutional defects. Overall, our approach enables rapid Raman-based characterization of point defects to support defect engineering in novel solid-state ion conductors.

Going beyond the Ordered Bulk: A Perspective on the Use of the Cambridge Structural Database for Predictive Materials Design

When Olga Kennard founded the Cambridge Crystallographic Data Centre in 1965, the Cambridge Structural Database was a pioneering attempt to collect scientific data in a standard format. Since then, it has evolved into an indispensable resource in contemporary molecular materials science, with over 1.25 million structures and comprehensive software tools for searching, visualizing and analyzing the data. In this perspective, we discuss the use of the CSD and CCDC tools to address the multiscale challenge of predictive materials design. We provide an overview of the core capabilities of the CSD and CCDC software and demonstrate their application to a range of materials design problems with recent case studies drawn from topical research areas, focusing in particular on the use of data mining and machine learning techniques. We also identify several challenges that can be addressed with existing capabilities or through new capabilities with varying levels of development effort.

COSMOPharm: Drug-Polymer Compatibility of Pharmaceutical Amorphous Solid Dispersions from COSMO-SAC

The quantum mechanics-aided COSMO-SAC activity coefficient model is applied and systematically examined for predicting the thermodynamic compatibility of drugs and polymers. The drug-polymer compatibility is a key aspect in the rational selection of optimal polymeric carriers for pharmaceutical amorphous solid dispersions (ASD) that enhance drug bioavailability. The drug-polymer compatibility is evaluated in terms of both solubility and miscibility, calculated using standard thermodynamic equilibrium relations based on the activity coefficients predicted by COSMO-SAC. As inherent to COSMO-SAC, our approach relies only on quantum-mechanically derived σ-profiles of the considered molecular species and involves no parameter fitting to experimental data. All σ-profiles used were determined in this work, with those of the polymers being derived from their shorter oligomers by replicating the properties of their central monomer unit(s). Quantitatively, COSMO-SAC achieved an overall average absolute deviation of 13% in weight fraction drug solubility predictions compared to experimental data. Qualitatively, COSMO-SAC correctly categorized different polymer types in terms of their compatibility with drugs and provided meaningful estimations of the amorphous-amorphous phase separation. Furthermore, we analyzed the sensitivity of the COSMO-SAC results for ASD to different model configurations and σ-profiles of polymers. In general, while the free volume and dispersion terms exerted a limited effect on predictions, the structures of oligomers used to produce σ-profiles of polymers appeared to be more important, especially in the case of strongly interacting polymers. Explanations for these observations are provided. COSMO-SAC proved to be an efficient method for compatibility prediction and polymer screening in ASD, particularly in terms of its performance-cost ratio, as it relies only on first-principles calculations for the considered molecular species. The open-source nature of both COSMO-SAC and the Python-based tool COSMOPharm, developed in this work for predicting the API-polymer thermodynamic compatibility, invites interested readers to explore and utilize this method for further research or assistance in the design of pharmaceutical formulations.

Derivative learning of tensorial quantities-Predicting finite temperature infrared spectra from first principles

We develop a strategy that integrates machine learning and first-principles calculations to achieve technically accurate predictions of infrared spectra. In particular, the methodology allows one to predict infrared spectra for complex systems at finite temperatures. The method's effectiveness is demonstrated in challenging scenarios, such as the analysis of water and the organic-inorganic halide perovskite MAPbI3, where our results consistently align with experimental data. A distinctive feature of the methodology is the incorporation of derivative learning, which proves indispensable for obtaining accurate polarization data in bulk materials and facilitates the training of a machine learning surrogate model of the polarization adapted to rotational and translational symmetries. We achieve polarization prediction accuracies of about 1% for the water dimer by training only on the predicted Born effective charges.

On-the-Fly Machine Learning Force Field Study of Liquid-Al/Solid-TiB2 Interfaces

Using the on-the-fly machine learning force field, simulations were performed to study the atomic structure evolution of the liquid-Al/solid-TiB2 interface with two different terminations, aiming to deepen the understanding of the mechanism of TiB2 as nucleating particles in an aluminum alloy. We conducted simulations using MLFF for up to 100 ps, enabling us to observe the interfacial properties from a deeper and more comprehensive perspective. The nucleation potential of TiB2 particles is determined by the formation of various ordered structures at the interface, which is significantly influenced by the termination of the TiB2 (0001) surface. The evolution of the interface during heterogeneous nucleation processes with different terminations is described using structural information and dynamic characteristics. The Ti-terminated surface is more prone to forming quasi-solid regions compared to the B-termination. Analysis of mean square displacement and vibrational density of states indicates that the liquid layer at the Ti-terminated interface is closer in characteristics to a solid compared to the B-terminated interface. We also found that on the TiB2 (0001) surface different terminations give rise to distinct ordered structures at the interfaces, which is ascribed to their different diffusion abilities.

Designing Accurate Moment Tensor Potentials for Phonon-Related Properties of Crystalline Polymers

The phonon-related properties of crystalline polymers are highly relevant for various applications. Their simulation is, however, particularly challenging, as the systems that need to be modeled are often too extended to be treated by ab initio methods, while classical force fields are too inaccurate. Machine-learned potentials parametrized against material-specific ab initio data hold the promise of being extremely accurate and also highly efficient. Still, for their successful application, protocols for their parametrization need to be established to ensure an optimal performance, and the resulting potentials need to be thoroughly benchmarked. These tasks are tackled in the current manuscript, where we devise a protocol for parametrizing moment tensor potentials (MTPs) to describe the structural properties, phonon band structures, elastic constants, and forces in molecular dynamics simulations for three prototypical crystalline polymers: polyethylene (PE), polythiophene (PT), and poly-3-hexylthiophene (P3HT). For PE, the thermal conductivity and thermal expansion are also simulated and compared to experiments. A central element of the approach is to choose training data in view of the considered use case of the MTPs. This not only yields a massive speedup for complex calculations while essentially maintaining DFT accuracy, but also enables the reliable simulation of properties that, so far, have been entirely out of reach.

A solution for 4-propylguaiacol hydrodeoxygenation without ring saturation

We investigate solvent effects in the hydrodeoxygenation of 4-propylguaiacol (4PG, 166 amu), a key lignin-derived monomer, over Ru/C catalyst by combined operando synchrotron photoelectron photoion coincidence (PEPICO) spectroscopy and molecular dynamics simulations. With and without isooctane co-feeding, ring-hydrogenated 2-methoxy-4-propylcyclohexanol (172 amu) is the first product, due to the favorable flat adsorption configuration of 4PG on the catalyst surface. In contrast, tetrahydrofuran (THF)-a polar aprotic solvent that is representative of those used for lignin solubilization and upgrading-strongly coordinates to the catalyst surface at the oxygen atom. This induces a local steric hindrance, blocking the flat adsorption of 4PG more effectively, as it needs more Ru sites than the tilted adsorption configuration revealed by molecular dynamics simulations. Therefore, THF suppresses benzene ring hydrogenation, favoring a demethoxylation route that yields 4-propylphenol (136 amu), followed by dehydroxylation to propylbenzene (120 amu). Solvent selection may provide new avenues for controlling catalytic selectivity.

Screening and Mechanism Exploration of Non-Noble Metal Ni3M Catalysts for Propane Dehydrogenation: The Excellence of Synergistic Effects

The development of cost-effective and anti-coking catalysts for propane dehydrogenation (PDH) is crucial. Here, non-noble metal-incorporated Ni-based catalysts (Ni3M, M = Sc, Ti, V, Mn, Fe, Co, Cu, Zn, Ga, Zr, Nb, Mo, In, Sn) were employed in the PDH process. The introduction of V, Nb, and Mo, with their strong carbon binding ability, created unique Ni-M cooperative sites, enhancing the catalytic performance. Other non-noble metals influenced the electronic structure of Ni, affecting the overall catalytic behavior. V and Nb exhibited a balanced combination of activity, selectivity, and stability, making them potential catalyst candidates. Microkinetic simulations revealed that Ni3V and Ni3Nb displayed high selectivity toward olefins with low apparent activation energies. This study emphasizes the significance of bimetallic synergy in enhancing PDH performance and provides new directions for the development of efficient alkane dehydrogenation catalyst development.

Layer-by-layer phase transformation in Ti3O5 revealed by machine-learning molecular dynamics simulations

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive phase transitions are usually slow due to the large energy barrier. Nevertheless, the reconstructive phase transformation from β- to λ-Ti3O5 exhibits an ultrafast and reversible behavior. Despite extensive studies, the underlying microscopic mechanism remains unclear. Here, we discover a kinetically favorable in-plane nucleated layer-by-layer transformation mechanism through metadynamics and large-scale molecular dynamics simulations. This is enabled by developing an efficient machine learning potential with near first-principles accuracy through an on-the-fly active learning method and an advanced sampling technique. Our results reveal that the β-λ phase transformation initiates with the formation of two-dimensional nuclei in the ab-plane and then proceeds layer-by-layer through a multistep barrier-lowering kinetic process via intermediate metastable phases. Our work not only provides important insight into the ultrafast and reversible nature of the β-λ transition, but also presents useful strategies and methods for tackling other complex structural phase transitions.

Temperature-transferable tight-binding model using a hybrid-orbital basis

Finite-temperature calculations are relevant for rationalizing material properties, yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many explicit first-principles calculations, tight-binding and machine-learning models for the electronic structure emerged as promising alternatives, but transferability of such methods to elevated temperatures in a data-efficient way remains a great challenge. In this work, we suggest a tight-binding model for efficient and accurate calculations of temperature-dependent properties of semiconductors. Our approach utilizes physics-informed modeling of the electronic structure in the form of hybrid-orbital basis functions and numerically integrating atomic orbitals for the distance dependence of matrix elements. We show that these design choices lead to a tight-binding model with a minimal amount of parameters that are straightforwardly optimized using density functional theory or alternative electronic-structure methods. The temperature transferability of our model is tested by applying it to existing molecular-dynamics trajectories without explicitly fitting temperature-dependent data and comparison with density functional theory. We utilize it together with machine-learning molecular dynamics and hybrid density functional theory for the prototypical semiconductor gallium arsenide. We find that including the effects of thermal expansion on the onsite terms of the tight-binding model is important in order to accurately describe electronic properties at elevated temperatures in comparison with experiment.

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

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.

Experimental Realization of Monolayer α-Tellurene

2D materials emerge as a versatile platform for developing next-generation devices. The experimental realization of novel artificial 2D atomic crystals, which does not have bulk counterparts in nature, is still challenging and always requires new physical or chemical processes. Monolayer α-tellurene is predicted to be a stable 2D allotrope of tellurium (Te), which has great potential for applications in high-performance field-effect transistors. However, the synthesis of monolayer α-tellurene remains elusive because of its complex lattice configuration, in which the Te atoms are stacked in tri-layers in an octahedral fashion. Here, a self-assemble approach, using three atom-long Te chains derived from the dynamic non-equilibrium growth of an a-Si:Te alloy as building blocks, is reported for the epitaxial growth of monolayer α-tellurene on a Sb2 Te3 substrate. By combining scanning tunneling microscopy/spectroscopy with density functional theory calculations, the surface morphology and electronic structure of monolayer α-tellurene are revealed and the underlying growth mechanism is determined. The successful synthesis of monolayer α-tellurene opens up the possibility for the application of this new single-element 2D material in advanced electronic devices.

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-basedab-initiomolecular 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 fromab-initiomolecular 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 coefficientDGa(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.

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 evolutionin situon the molecular scale. Onh-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 onh-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 theh-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 onh-BN/Rh(111) was simulated by molecular dynamics using a machine-learning force field.

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

CONTEXT

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.

METHODS

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.

Tunable and parabolic piezoelectricity in hafnia under epitaxial strain

Piezoelectrics are a class of functional materials that have been extensively used for application in modern electro-mechanical and mechatronics technologies. The sign of longitudinal piezoelectric coefficients is typically positive but recently a few ferroelectrics, such as ferroelectric polymer poly(vinylidene fluoride) and van der Waals ferroelectric CuInP2S6, were experimentally found to have negative piezoelectricity. Here, using first-principles calculation and measurements, we show that the sign of the longitudinal linear piezoelectric coefficient of HfO2 can be tuned from positive to negative via epitaxial strain. Nonlinear and even parabolic piezoelectric behaviors are further found at tensile epitaxial strain. This parabolic piezoelectric behavior implies that the polarization decreases when increasing the magnitude of either compressive or tensile longitudinal strain, or, equivalently, that the strain increases when increasing the magnitude of electric field being either parallel or antiparallel to the direction of polarization. The unusual piezoelectric effects are from the chemical coordination of the active oxygen atoms. These striking piezoelectric features of positive and negative sign, as well as linear and parabolical behaviors, expand the current knowledge in piezoelectricity and broaden the potential of piezoelectric applications towards electro-mechanical and communications technology.

Investigating the role of dispersion corrections and anharmonic effects on the phase transition in SrZrS3: A systematic analysis from AIMD free energy calculations

A thermally driven needle-like (NL) to distorted perovskite (DP) phase transition in SrZrS3 was investigated by means of ab initio free energy calculations accelerated by machine learning. As a first step, a systematic screening of the methods to include long-range interactions in semilocal density functional theory Perdew-Burke-Ernzerhof calculations was performed. Out of the ten correction schemes tested, the Tkatchenko-Scheffler method with iterative Hirshfeld partitioning method was found to yield the best match between calculated and experimental lattice geometries, while predicting the correct order of stability of NL and DP phases at zero temperature. This method was then used in free energy calculations, performed using several approaches, so as to determine the effect of various anharmonicity contributions, such as the anisotropic thermal lattice expansion or the thermally induced internal structure changes, on the phase transition temperature (TNP→DP). Accounting for the full anharmonicity by combining the NPT molecular dynamics data with thermodynamic integration with harmonic reference provided our best estimate of TNL→DP = 867 K. Although this result is ∼150 K lower than the experimental value, it still provides an improvement by nearly 300 K compared to the previous theoretical report by Koocher et al. [Inorg. Chem. 62, 11134-11141 (2023)].

Machine Learning Density Functionals from the Random-Phase Approximation

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

DFT-assisted low-dimensional carbon-based electrocatalysts design and mechanism study: a review

Low-dimensional carbon-based (LDC) materials have attracted extensive research attention in electrocatalysis because of their unique advantages such as structural diversity, low cost, and chemical tolerance. They have been widely used in a broad range of electrochemical reactions to relieve environmental pollution and energy crisis. Typical examples include hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), carbon dioxide reduction reaction (CO2RR), and nitrogen reduction reaction (NRR). Traditional "trial and error" strategies greatly slowed down the rational design of electrocatalysts for these important applications. Recent studies show that the combination of density functional theory (DFT) calculations and experimental research is capable of accurately predicting the structures of electrocatalysts, thus revealing the catalytic mechanisms. Herein, current well-recognized collaboration methods of theory and practice are reviewed. The commonly used calculation methods and the basic functionals are briefly summarized. Special attention is paid to descriptors that are widely accepted as a bridge linking the structure and activity and the breakthroughs for high-volume accurate prediction of electrocatalysts. Importantly, correlated multiple descriptors are used to systematically describe the complicated interfacial electrocatalytic processes of LDC catalysts. Furthermore, machine learning and high-throughput simulations are crucial in assisting the discovery of new multiple descriptors and reaction mechanisms. This review will guide the further development of LDC electrocatalysts for extended applications from the aspect of DFT computations.

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on ab initio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated ab initio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

Free and internal energies for the adsorption of short alkanes into the zeolite SSZ-13 from ab initio molecular dynamics simulations

Electronic structure calculations have become a valuable tool in understanding chemical reactions of hydrocarbons in zeolite pores. However, commonly applied approaches to calculate free energies based on static electronic structure calculations significantly overestimate the entropic penalty for molecular adsorption into zeolite pores. Here, we use ab initio molecular dynamics (AIMD) simulations to model the adsorption of methane, ethane, and propane to purely siliceous and protonated SSZ-13. In our analyses we focus on the internal and Helmholtz free energies of adsorption of each molecule and compare our results to various approaches for the calculation of free energies based on static calculations. We find that only an approach that retains two thirds of the translational entropy of the adsorbate upon adsorption compares favorably with AIMD simulations. However, comparison to experimental measurements of Gibbs free energies of adsorption reported in the literature implies that we might not have captured the full complexity of alkane adsorption in our model. We expect that results in this work will help to develop a better understanding of alkane adsorption in zeolites, and that the provided data will serve as a benchmark for free energy calculations of alkane adsorption in zeolites in the future.

How the Temperature and Composition Govern the Structure and Band Gap of Zr-Based Chalcogenide Perovskites: Insights from ML Accelerated AIMD

The effects of temperature and composition on the structural and electronic properties of chalcogenide perovskite (CP) materials AZrX3 (A = Ba, Sr, Ca; X = S, Se) in the distorted perovskite (DP) phase are investigated using ab initio molecular dynamics (AIMD) accelerated by machine-learned force fields. Long-range van der Waals (vdW) interactions, incorporated into the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional using the DFT-D3 scheme, are found to be crucial for achieving correct predictions of structural parameters. Our calculations show that the distortion of the DP structure with respect to the parent cubic (C) phase, realized in the form of interoctahedral tilting, decreases with the increasing size of the A cations. The tendency for a gradual transformation of the DP-to-C phase with increasing temperature is shown to be strongly composition-dependent. The transformation temperature decreases with the size of cation A and increases with the size of anion X. Thus, within the range of the temperatures considered here (300-1200 K), a complete transformation is observed only for BaZrS3 (∼600 K) and BaZrSe3 (∼900 K). The computed band gap of CPs is shown to monotonically decrease with increasing temperature, and the magnitude of this decrease is found to be proportional to the extent of the thermally induced changes in the internal structure. Diverse factors affecting the magnitude of band gaps of CP materials are analyzed.

Machine-learned acceleration for molecular dynamics in CASTEP

Machine learning (ML) methods are of rapidly growing interest for materials modeling, and yet, the use of ML interatomic potentials for new systems is often more demanding than that of established density-functional theory (DFT) packages. Here, we describe computational methodology to combine the CASTEP first-principles simulation software with the on-the-fly fitting and evaluation of ML interatomic potential models. Our approach is based on regular checking against DFT reference data, which provides a direct measure of the accuracy of the evolving ML model. We discuss the general framework and the specific solutions implemented, and we present an example application to high-temperature molecular-dynamics simulations of carbon nanostructures. The code is freely available for academic research.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Addressing the Conflict between Mobility and Stability in Oxide Thin-film Transistors

Amorphous oxide semiconductor thin-film transistors (AOS TFTs) are ever-increasingly utilized in displays. However, to bring high mobility and excellent stability together is a daunting challenge. Here, the carrier transport/relaxation bilayer stacked AOS TFTs are investigated to solve the mobility-stability conflict. The charge transport layer (CTL) is made of amorphous In-rich InSnZnO, which favors big average effective coordination number for all cations and more edge-shared structures for better charge transport. Praseodymium-doped InSnZnO is used as the charge relaxation layer (CRL), which substantially shortens the photoelectron lifetime as revealed by femtosecond transient absorption spectroscopy. The CTL and CRL with the thickness suitable for industrial production respectively afford minute potential barrier fluctuation for charge transport and fast relaxation for photo-generated carriers, resulting in transistors with an ultrahigh mobility (75.5 cm² V^-1 s^-1 ) and small negative-bias-illumination-stress/positive-bias-temperature-stress voltage shifts (-1.64/0.76 V). The design concept provides a promising route to address the mobility-stability conflict for high-end displays.

Proton Transport in Perfluorinated Ionomer Simulated by Machine-Learned Interatomic Potential

Polymers are a class of materials that are highly challenging to deal with using first-principles methods. Here, we present an application of machine-learned interatomic potentials to predict structural and dynamical properties of dry and hydrated perfluorinated ionomers. An improved active-learning algorithm using a small number of descriptors allows to efficiently construct an accurate and transferable model for this multielemental amorphous polymer. Molecular dynamics simulations accelerated by the machine-learned potentials accurately reproduce the heterogeneous hydrophilic and hydrophobic domains formed in this material as well as proton and water diffusion coefficients under a variety of humidity conditions. Our results reveal pronounced contributions of Grotthuss chains consisting of two to three water molecules to the high proton mobility under strongly humidified conditions.

Do Machine-Learning Atomic Descriptors and Order Parameters Tell the Same Story? The Case of Liquid Water

Machine-learning (ML) has become a key workhorse in molecular simulations. Building an ML model in this context involves encoding the information on chemical environments using local atomic descriptors. In this work, we focus on the Smooth Overlap of Atomic Positions (SOAP) and their application in studying the properties of liquid water both in the bulk and at the hydrophobic air-water interface. By using a statistical test aimed at assessing the relative information content of different distance measures defined on the same data space, we investigate if these descriptors provide the same information as some of the common order parameters that are used to characterize local water structure such as hydrogen bonding, density, or tetrahedrality to name a few. Our analysis suggests that the ML description and the standard order parameters of the local water structure are not equivalent. In particular, a combination of these order parameters probing local water environments can predict SOAP similarity only approximately, and vice versa, the environments that are similar according to SOAP are not necessarily similar according to the standard order parameters. We also elucidate the role of some of the metaparameters in the SOAP definition in encoding chemical information.

Combining Machine Learning and Many-Body Calculations: Coverage-Dependent Adsorption of CO on Rh(111)

Adsorption of carbon monoxide (CO) on transition-metal surfaces is a prototypical process in surface sciences and catalysis. Despite its simplicity, it has posed great challenges to theoretical modeling. Pretty much all existing density functionals fail to accurately describe surface energies and CO adsorption site preference as well as adsorption energies simultaneously. Although the random phase approximation (RPA) cures these density functional theory failures, its large computational cost makes it prohibitive to study the CO adsorption for any but the simplest ordered cases. Here, we address these challenges by developing a machine-learned force field (MLFF) with near RPA accuracy for the prediction of coverage-dependent adsorption of CO on the Rh(111) surface through an efficient on-the-fly active learning procedure and a Δ-machine learning approach. We show that the RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy and CO adsorption site preference as well as adsorption energies at different coverages that are all in good agreement with experiments. Moreover, the coverage-dependent ground-state adsorption patterns and adsorption saturation coverage are identified.

Investigation of PbSnTeSe High-Entropy Thermoelectric Alloy: A DFT Approach

Thermoelectric materials have attracted extensive attention because they can directly convert waste heat into electric energy. As a brand-new method of alloying, high-entropy alloys (HEAs) have attracted much attention in the fields of materials science and engineering. Recent researches have found that HEAs could be potentially good thermoelectric (TE) materials. In this study, special quasi-random structures (SQS) of PbSnTeSe high-entropy alloys consisting of 64 atoms have been generated. The thermoelectric transport properties of the highest-entropy PbSnTeSe-optimized structure were investigated by combining calculations from first-principles density-functional theory and on-the-fly machine learning with the semiclassical Boltzmann transport theory and Green-Kubo theory. The results demonstrate that PbSnTeSe HEA has a very low lattice thermal conductivity. The electrical conductivity, thermal electronic conductivity and Seebeck coefficient have been evaluated for both n-type and p-type doping. N-type PbSnTeSe exhibits better power factor (PF = S²σ) than p-type PbSnTeSe because of larger electrical conductivity for n-type doping. Despite high electrical thermal conductivities, the calculated ZT are satisfactory. The maximum ZT (about 1.1) is found at 500 K for n-type doping. These results confirm that PbSnTeSe HEA is a promising thermoelectric material.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Molecular dynamics simulations of proton conducting mediums containing phosphoric acid

An anhydrous proton conducting electrolyte is a key material to realise medium-temperature fuel cells that can drastically simplify heat radiation systems in transportation applications. However, practical applications are limited by...

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Strategies for the construction of machine-learning potentials for accurate and efficient atomic-scale simulations

Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum-mechanics based methods. At the same time, the construction of new machine-learning potentials can seem a daunting task, as it involves data-science techniques that are not yet common in chemistry and materials science. Here, we provide a tutorial-style overview of strategies and best practices for the construction of artificial neural network (ANN) potentials. We illustrate the most important aspects of (a) data collection, (b) model selection, (c) training and validation, and (d) testing and refinement of ANN potentials on the basis of practical examples. Current research in the areas of active learning and delta learning are also discussed in the context of ANN potentials. This tutorial review aims at equipping computational chemists and materials scientists with the required background knowledge for ANN potential construction and application, with the intention to accelerate the adoption of the method, so that it can facilitate exciting research that would otherwise be challenging with conventional strategies.

Compact atomic descriptors enable accurate predictions via linear models

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.

Machine learning meets chemical physics

Over recent years, the use of statistical learning techniques applied to chemical problems has gained substantial momentum. This is particularly apparent in the realm of physical chemistry, where the balance between empiricism and physics-based theory has traditionally been rather in favor of the latter. In this guest Editorial for the special topic issue on "Machine Learning Meets Chemical Physics," a brief rationale is provided, followed by an overview of the topics covered. We conclude by making some general remarks.

First-principles hydration free energies of oxygenated species at water-platinum interfaces

The hydration free energy of atoms and molecules adsorbed at liquid-solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from well-defined non-interacting species to the fully interacting ones. The atomistic interactions are described by a machine-learned inter-atomic potential trained on first-principles data. The free energy calculated by the machine-learned potential is further corrected by using thermodynamic perturbation theory to provide the first-principles free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.

Machine Learning in Computational Surface Science and Catalysis: Case Studies on Water and Metal-Oxide Interfaces

The goal of many computational physicists and chemists is the ability to bridge the gap between atomistic length scales of about a few multiples of an Ångström (Å), i. e., 10⁻¹⁰ m, and meso- or macroscopic length scales by virtue of simulations. The same applies to timescales. Machine learning techniques appear to bring this goal into reach. This work applies the recently published on-the-fly machine-learned force field techniques using a variant of the Gaussian approximation potentials combined with Bayesian regression and molecular dynamics as efficiently implemented in the Vienna ab initio simulation package, VASP. The generation of these force fields follows active-learning schemes. We apply these force fields to simple oxides such as MgO and more complex reducible oxides such as iron oxide, examine their generalizability, and further increase complexity by studying water adsorption on these metal oxide surfaces. We successfully examined surface properties of pristine and reconstructed MgO and Fe₃O₄ surfaces. However, the accurate description of water–oxide interfaces by machine-learned force fields, especially for iron oxides, remains a field offering plenty of research opportunities.

Multi-scale approach for the prediction of atomic scale properties

Electronic nearsightedness is one of the fundamental principles that governs the behavior of condensed matter and supports its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables - such as the cohesive energy, the electron density, or a variety of response properties - as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

Recursive evaluation and iterative contraction of N-body equivariant features

Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible N-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different order (generalizations of N-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically improvable, symmetry adapted representations for atomistic machine learning.

On-the-Fly Active Learning of Interatomic Potentials for Large-Scale Atomistic Simulations

The on-the-fly generation of machine-learning force fields by active-learning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to self-learn an interatomic potential and construct machine-learned models on the fly during simulations. State-of-the-art query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are first-principles calculations carried out. Otherwise, the yet available machine-learned model is used to update the atomic positions. In this manner, most of the first-principles calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost first-principles accuracy. In this Perspective, after describing essential components of the active-learning algorithms, we demonstrate the power of the schemes by presenting recent applications.