Local-Softening Stochastic Surface Walking for Fast Exploration of Corrugated Potential Energy Surfaces

Global potential energy surface (PES) exploration provides a unique route to predict the thermodynamic and kinetic properties of unknown materials, but the task is highly challenging for systems with tight covalent bonds. Here, we develop the local-softening stochastic surface walking (LS-SSW) method for scanning corrugated PESs. LS-SSW transforms the vibrational mode space of a system by adding pairwise penalty potentials with a self-adaption mechanism, which helps to delocalize and soften the strong local modes. This allows the stochastic surface walking (SSW) method to capture more efficiently the correct local atomic movement toward nearby minima and simultaneously reduce the barrier height of reactions. As a result, the local trapping time in searching for the corrugated PES is greatly reduced. LS-SSW can be applied generally to the reaction pathway sampling and the global PES exploration of both clusters and crystals, the high efficiency of which is demonstrated in searching the reaction pathways between C4H6 isomers, finding the global minimum of carbon clusters up to 360 atoms, and constructing the global PES of Fe7C3 material.

LASP to the Future of Atomic Simulation: Intelligence and Automation

Atomic simulations aim to understand and predict complex physical phenomena, the success of which relies largely on the accuracy of the potential energy surface description and the efficiency to capture important rare events. LASP software (large-scale atomic simulation with a Neural Network Potential), released in 2018, incorporates the key ingredients to fulfill the ultimate goal of atomic simulations by combining advanced neural network potentials with efficient global optimization methods. This review introduces the recent development of the software along two main streams, namely, higher intelligence and more automation, to solve complex material and reaction problems. The latest version of LASP (LASP 3.7) features the global many-body function corrected neural network (G-MBNN) to improve the PES accuracy with low cost, which achieves a linear scaling efficiency for large-scale atomic simulations. The key functionalities of LASP are updated to incorporate (i) the ASOP and ML-interface methods for finding complex surface and interface structures under grand canonic conditions; (ii) the ML-TS and MMLPS methods to identify the lowest energy reaction pathway. With these powerful functionalities, LASP now serves as an intelligent data generator to create computational databases for end users. We exemplify the recent LASP database construction in zeolite and the metal-ligand properties for a new catalyst design.

An optimal Fe-C coordination ensemble for hydrocarbon chain growth: a full Fischer-Tropsch synthesis mechanism from machine learning

Fischer-Tropsch synthesis (FTS, CO + H2 → long-chain hydrocarbons) because of its great significance in industry has attracted huge attention since its discovery. For Fe-based catalysts, after decades of efforts, even the product distribution remains poorly understood due to the lack of information on the active site and the chain growth mechanism. Herein powered by a newly developed machine-learning-based transition state (ML-TS) exploration method to treat properly reaction-induced surface reconstruction, we are able to resolve where and how long-chain hydrocarbons grow on complex in situ-formed Fe-carbide (FeCx) surfaces from thousands of pathway candidates. Microkinetics simulations based on first-principles kinetics data further determine the rate-determining and the selectivity-controlling steps, and reveal the fine details of the product distribution in obeying and deviating from the Anderson-Schulz-Flory law. By showing that all FeCx phases can grow coherently upon each other, we demonstrate that the FTS active site, namely the A-P5 site present on reconstructed Fe3C(031), Fe5C2(510), Fe5C2(021), and Fe7C3(071) terrace surfaces, is not necessarily connected to any particular FeCx phase, rationalizing long-standing structure-activity puzzles. The optimal Fe-C coordination ensemble of the A-P5 site exhibits both Fe-carbide (Fe4C square) and metal Fe (Fe3 trimer) features.

ChecMatE: A workflow package to automatically generate machine learning potentials and phase diagrams for semiconductor alloys

Semiconductor alloy materials are highly versatile due to their adjustable properties; however, exploring their structural space is a challenging task that affects the control of their properties. Traditional methods rely on ad hoc design based on the understanding of known chemistry and crystallography, which have limitations in computational efficiency and search space. In this work, we present ChecMatE (Chemical Material Explorer), a software package that automatically generates machine learning potentials (MLPs) and uses global search algorithms to screen semiconductor alloy materials. Taking advantage of MLPs, ChecMatE enables a more efficient and cost-effective exploration of the structural space of materials and predicts their energy and relative stability with ab initio accuracy. We demonstrate the efficacy of ChecMatE through a case study of the InxGa1-xN system, where it accelerates structural exploration at reduced costs. Our automatic framework offers a promising solution to the challenging task of exploring the structural space of semiconductor alloy materials.

Silica-water superstructure and one-dimensional superionic conduit in Earth's mantle

Water in Earth's deep interior is predicted to be hydroxyl (OH-) stored in nominally anhydrous minerals, profoundly modulating both structure and dynamics of Earth's mantle. Here, we use a high-dimensional neuro-network potential and machine learning algorithm to investigate the weight percent water incorporation in stishovite, a main constituent of the subducted oceanic crust. We found that stishovite and water prefer forming medium- to long-range ordered superstructures, featuring one-dimensional (1D) water channels. Synthesizing single crystals of hydrous stishovite, we verified the ordering of OH- groups in the water channels through optical and nuclear magnetic resonance spectroscopy and found an average H-H distance of 2.05(3) Å, confirming simulation results. Upon heating, H atoms were predicted to behave fluid-like inside the channels, leading to an exotic 1D superionic state. Water-bearing stishovite could feature high ionic mobility and strong electrical anisotropy, manifesting as electrical heterogeneity in Earth's mantle.

Methanol Synthesis from CO2/CO Mixture on Cu-Zn Catalysts from Microkinetics-Guided Machine Learning Pathway Search

Methanol synthesis on industrial Cu/ZnO/Al₂O₃ catalysts via the hydrogenation of CO and CO₂ mixture, despite several decades of research, is still puzzling due to the nature of the active site and the role of CO₂ in the feed gas. Herein, with the large-scale machine learning atomic simulation, we develop a microkinetics-guided machine learning pathway search to explore thousands of reaction pathways for CO₂ and CO hydrogenations on thermodynamically favorable Cu-Zn surface structures, including Cu(111), Cu(211), and Zn-alloyed Cu(211) surfaces, from which the lowest energy pathways are identified. We find that Zn decorates at the step-edge at Cu(211) up to 0.22 ML under reaction conditions with the Zn-Zn dimeric sites being avoided. CO₂ and CO hydrogenations occur exclusively at the step-edge of the (211) surface with up to 0.11 ML Zn coverage, where the low coverage of Zn (0.11 ML) does not much affect the reaction kinetics, but the higher coverages of Zn (0.22 ML) poison the catalyst. It is CO₂ hydrogenation instead of CO hydrogenation that dominates methanol synthesis, agreeing with previous isotope experiments. While metallic steps are identified as the major active site, we show that the [-Zn-OH-Zn-] chains (cationic Zn) can grow on Cu(111) surfaces under reaction conditions, which suggests the critical role of CO in the mixed gas for reducing the cationic Zn and exposing metal sites for methanol synthesis. Our results provide a comprehensive picture on the dynamic coupling of the feed gas composition, the catalyst active site, and the reaction activity in this complex heterogeneous catalytic system.

In Situ Active Site for Fe-Catalyzed Fischer-Tropsch Synthesis: Recent Progress and Future Challenges

Fischer-Tropsch synthesis (FTS) that converts syngas into long-chain hydrocarbons is a key technology in the chemical industry. As one of the best catalysts for FTS, the Fe-based composite develops rich solid phases (metal, oxides, and carbides) in the catalytic reaction, which triggered the quest for the true active site in catalysis in the past century. Recent years have seen great advances in probing the active-site structure using modern experimental and theoretical tools. This Perspective serves to highlight these latest achievements, focusing on the geometrical structure and thermodynamic stability of Fe carbide bulk phases, the exposed surfaces, and their relationship to FTS activity. The current reaction mechanisms on CO activation and carbon chain growth are also discussed, in the context of theoretical models and experimental evidence. We also present the outlook regarding the current challenges in Fe-based FTS.

Stable All-Solid-State Lithium Metal Batteries Enabled by Machine Learning Simulation Designed Halide Electrolytes

Solid electrolytes (SEs) with superionic conductivity and interfacial stability are highly desirable for stable all-solid-state Li-metal batteries (ASSLMBs). Here, we employ neural network potential to simulate materials composed of Li, Zr/Hf, and Cl using stochastic surface walking method and identify two potential unique layered halide SEs, named Li₂ZrCl₆ and Li₂HfCl₆, for stable ASSLMBs. The predicted halide SEs possess high Li⁺ conductivity and outstanding compatibility with Li metal anodes. We synthesize these SEs and demonstrate their superior stability against Li metal anodes with a record performance of 4000 h of steady lithium plating/stripping. We further fabricate the prototype stable ASSLMBs using these halide SEs without any interfacial modifications, showing small internal cathode/SE resistance (19.48 Ω cm²), high average Coulombic efficiency (∼99.48%), good rate capability (63 mAh g^-1 at 1.5 C), and unprecedented cycling stability (87% capacity retention for 70 cycles at 0.5 C).

Pressure tuned incommensurability and guest structure transition in compressed scandium from machine learning atomic simulation

Scandium (Sc) is the lightest non-main-group element and transforms to a host-guest (H-G) incommensurate structure under gigapascal (GPa) pressures. While the host structure is stable over a wide pressure range, the guest structure may exist in multiple forms, featuring different incommensurate ratios, and mixing up to generate long-range "disordered" guest structures. Here, we employed the recently developed global neural network (g-NN) potential and the stochastic surface walking (SSW) global optimization algorithm to explore the global potential energy surface of Sc under various pressures. We probe the global minima structure in a system made of hundreds of atoms and revealed that the solid-phase transition between Sc-I and H-G Sc-II phases is fully reconstructive in nature. Above 62.5 GPa, the pressure will further destabilize the face-centered tetragonal (fct, Sc-IIa) guest structure to a body-centered tetragonal phase (bct, Sc-IIb), while sustaining the host structure. The structural transition mechanism of this work will shed light on the nature of the complex H-G structural modifications in compressed metals.

In Situ Active Site for CO Activation in Fe-Catalyzed Fischer-Tropsch Synthesis from Machine Learning

In situ-formed iron carbides (FeC_x) are the key components responsible for Fischer-Tropsch synthesis (FTS, CO + H₂ → long-chain hydrocarbons) on Fe-based catalysts in industry. The true active site is, however, highly controversial despite more than a century of study, which is largely due to the combined complexity in both FeC_x structures and mechanism of CO hydrogenation. Herein powered by machine learning simulation, millions of structure candidates for FeC_x bulk and surfaces are explored under FTS conditions, which leads to resolving the active site for CO activation. This is achieved without a priori input from experiment by first constructing the thermodynamics convex hull of bulk phases, followed by identifying the low surface energy surfaces and evaluating the adsorption ability of CO and H, and finally determining the lowest energy reaction pathway of CO activation. Rich information on FeC_x structures and CO hydrogenation pathways is gleaned: (i) Fe₅C₂, Fe₇C₃, and Fe₂C are the three stable bulk phases under FTS in producing olefins, where Fe₇C₃ and Fe₂C have multiple energetically nearly degenerate bulk crystal phases; (ii) only three low surface energy surfaces of these bulk phases, namely, χ-Fe₅C₂(510), χ-Fe₅C₂(111), and η-Fe₂C(111), expose the Fe sites that can adsorb H atoms exothermically, where the surface Fe:C ratio is 2, 1.75, and 2, respectively; (iii) CO activation via direct dissociation can occur at the surface C vacancies (e.g., with a barrier of 1.1 eV) that are created dynamically via hydrogenation. These atomic-level understandings facilitate the building of the structure-activity correlation and designing better FT catalysts.

The dome of gold nanolized for catalysis

Gold is noble in bulk but turns out to be a superior catalyst at the nanoscale when supported on oxides, in particular titania. The critical thickness for activity, namely two-layer gold particles on titania, observed two decades ago represents one of the most influential mysteries in the recent history of heterogeneous catalysis. By developing a Bayesian optimization controlled global potential energy surface exploration tool with machine learning potential, here we determine the atomic structures of gold particles within ∼2 nm on a TiO2 surface. We show that the smallest stable Au nanoparticle is Au24 which is pinned on the oxygen-rich TiO2 and exhibits an unprecedented dome architecture made by a single-layer Au sheet but with an apparent two-atomic-layer height. Importantly, this has the highest activity for CO oxidation at room temperature. The physical origin of the high activity is the outstanding electron storage ability of the nano-dome, which activates the lattice oxygen of the oxide. The determined CO oxidation mechanism, the simulated rate and the fitted apparent energy barrier are consistent with known experimental facts, providing key evidence for the presence of both the high-activity Au dome and the low-activity close-packed Au particles in real catalysts. The future direction for the preparation of active and stable Au-based catalysts is thus outlined.

Large-Scale Atomic Simulation via Machine Learning Potentials Constructed by Global Potential Energy Surface Exploration

Atomic simulations based on quantum mechanics (QM) calculations have entered into the tool box of chemists over the past few decades, facilitating an understanding of a wide range of chemistry problems, from structure characterization to reactivity determination. Due to the poor scaling and high computational cost intrinsic to QM calculations, one has to either sacrifice accuracy or time when performing large-scale atomic simulations. The battle to find a better compromise between accuracy and speed has been central to the development of new theoretical methods.The recent advances of machine-learning (ML)-based large-scale atomic simulations has shown great promise to the benefit of many branches of chemistry. Instead of solving the Schrödinger equation directly, ML-based simulations rely on a large data set of accurate potential energy surfaces (PESs) and complex numerical models to predict the total energy. These simulations feature both a high speed and a high accuracy for computing large systems. Due to the lack of a physical foundation in numerical models, ML models are often frustrated in their predictivity and robustness, which are key to applications. Focusing on these concerns, here we overview the recent advances in ML methodologies for atomic simulations on three key aspects. Namely, the generation of a representative data set, the extensity of ML models, and the continuity of data representation. While global optimization methods are the natural choice for building a representative data set, the stochastic surface walking method is shown to provide the desired PES sampling for both minima and transition regions on the PES. The current ML models generally utilize local geometrical descriptors as an input and consider the total energy as the sum of atomic energies. There are many flavors of data descriptors and ML models, but the applications for material and reaction predictions are still limited, not least because of the difficulty to train the associated vast global data sets. We show that our recently designed power-type structure descriptors together with a feed-forward neural network (NN) model are compatible with highly complex global PES data, which has led to a large family of global NN (G-NN) potentials.Two recent applications of G-NN potentials in material and reaction simulations are selected to illustrate how ML-based atomic simulations can help the discovery of new materials and reactions.

Computational searches for crystal structures of dioxides of group 14 elements (CO2, SiO2, GeO2) under ultrahigh pressure

In this study, we focused on the effect of pressure on the crystal structures of dioxides of group 14 elements, i.e. SiO₂, GeO₂, and CO₂.

Atomic structure of boron resolved using machine learning and global sampling

Boron crystals, despite their simple composition, must rank top for complexity: even the atomic structure of the ground state of β-B remains uncertain after 60 years' study. This makes it difficult to understand the many exotic photoelectric properties of boron. The presence of self-doping atoms in the crystal interstitial sites forms an astronomical configurational space, making the determination of the real configuration virtually impossible using current techniques. Here, by combining machine learning with the latest stochastic surface walking (SSW) global optimization, we explore for the first time the potential energy surface of β-B, revealing 15 293 distinct configurations out of the 2 × 105 minima visited, and reveal the key rules governing the filling of the interstitial sites. This advance is only allowed by the construction of an accurate and efficient neural network (NN) potential using a new series of structural descriptors that can sensitively discriminate the complex boron bonding environment. We show that, in contrast to the conventional views on the numerous energy-degenerate configurations, only 40 minima of β-B are identified to be within 7 meV per atom in energy above the global minimum of β-B, most of them having been discovered for the first time. These low energy structures are classified into three types of skeletons and six patterns of doping configurations, with a clear preference for a few characteristic interstitial sites. The observed β-B and its properties are influenced strongly by a particular doping site, the B19 site that neighbors the B18 site, which has an exceptionally large vibrational entropy. The configuration with this B19 occupancy, which ranks only 15th at 0 K, turns out to be dominant at high temperatures. Our results highlight the novel SSW-NN architecture as the leading problem solver for complex material phenomena, which would then expedite substantially the building of a material genome database.

Material discovery by combining stochastic surface walking global optimization with a neural network

While the underlying potential energy surface (PES) determines the structure and other properties of a material, it has been frustrating to predict new materials from theory even with the advent of supercomputing facilities. The accuracy of the PES and the efficiency of PES sampling are two major bottlenecks, not least because of the great complexity of the material PES. This work introduces a "Global-to-Global" approach for material discovery by combining for the first time a global optimization method with neural network (NN) techniques. The novel global optimization method, named the stochastic surface walking (SSW) method, is carried out massively in parallel for generating a global training data set, the fitting of which by the atom-centered NN produces a multi-dimensional global PES; the subsequent SSW exploration of large systems with the analytical NN PES can provide key information on the thermodynamics and kinetics stability of unknown phases identified from global PESs. We describe in detail the current implementation of the SSW-NN method with particular focuses on the size of the global data set and the simultaneous energy/force/stress NN training procedure. An important functional material, TiO2, is utilized as an example to demonstrate the automated global data set generation, the improved NN training procedure and the application in material discovery. Two new TiO2 porous crystal structures are identified, which have similar thermodynamics stability to the common TiO2 rutile phase and the kinetics stability for one of them is further proved from SSW pathway sampling. As a general tool for material simulation, the SSW-NN method provides an efficient and predictive platform for large-scale computational material screening.

Crystal phase transition of urea: what governs the reaction kinetics in molecular crystal phase transitions

The predominant type-I hydrogen-bonding network in urea crystals facilitates the solid-to-solid transformation between major crystal forms.