Constrained Broyden Minimization Combined with the Dimer Method for Locating Transition State of Complex Reactions

Fine-Tuned Global Neural Network Potentials for Global Potential Energy Surface Exploration at High Accuracy

Machine learning potential (MLP), by learning global potential energy surfaces (PES), has demonstrated its great value in finding unknown structures and reactions via global PES exploration. Due to the diversity and complexity of the global PES data set, an outstanding challenge emerges in achieving PES high accuracy (e.g., error <1 meV/atom), which is essential to determine the thermodynamics and kinetics properties. Here, we develop a lightweight fine-tuning MLP architecture, namely, AtomFT, that can explore PES globally and simultaneously describe the PES of a target system accurately. The AtomFT potential takes the pretrained many-body function corrected global neural network (MBNN) potential as the basis potential, exploits and iteratively updates the atomic features from the pretrained MBNN model, and finally generates the fine-tuning energy contribution. By implementing the AtomFT architecture on the commonly available CPU platform, we show the high efficiency of AtomFT potential in both training and inference and demonstrate the high performance in challenging PES problems, including the oxides with low defect content, molecular reactions, and molecular crystals─in all systems, the AtomFT potentials enhance significantly the PES prediction accuracy to 1 meV/atom.

Do Rh-Hydride Phases Contribute to the Catalytic Activity of Rh Catalysts under Reductive Conditions?

Rh-hydride phases were believed to be key causes of the exceptional catalytic ability of Rh catalysts under H2 reductive conditions. Here, we utilize the large-scale machine-learning-based global optimization to explore millions of Rh bulk, surface, and nanoparticle structures in contact with H2, which rules out the presence of subsurface/interstitial H in Rh and Rh-hydride phases as thermodynamically stable phases under ambient conditions. Instead, an exceptional Rh-H affinity is identified for surface Rh atoms in Rh nanoparticles that can accommodate a high concentration of adsorbed H, with the surface Rh to H ratio reaching ∼2.5, featuring stable six-H-coordinated Rh, [RhH6]. Such [RhH6] species forming at edged Rh sites are found to be the key intermediates in the electrochemical hydrogen evolution reaction (HER) on Rh. Guided by theory, our synthesized Rh concave nanocubes with a high density of edged Rh sites achieve a Tafel slope of 28.4 mV dec-1 and a low overpotential of 36.1 mV at jECSA = 1 mA cm-2, which outperforms commercial Pt/C and other morphologies of Rh catalysts. Our results clarify the active phase in Rh-H nanosystems and guide the catalyst design by precise morphology control of nanocatalysts.

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.

In Situ Surfaced Mn-Mn Dimeric Sites Dictate CO Hydrogenation Activity and C2 Selectivity over MnRh Binary Catalysts

Massive ethanol production has long been a dream of human society. Despite extensive research in past decades, only a few systems have the potential of industrialization: specifically, Mn-promoted Rh (MnRh) binary heterogeneous catalysts were shown to achieve up to 60% C2 oxygenates selectivity in converting syngas (CO/H2) to ethanol. However, the active site of the binary system has remained poorly characterized. Here, large-scale machine-learning global optimization is utilized to identify the most stable Mn phases on Rh metal surfaces under reaction conditions by exploring millions of likely structures. We demonstrate that Mn prefers the subsurface sites of Rh metal surfaces and is able to emerge onto the surface forming MnRh surface alloy once the oxidative O/OH adsorbates are present. Our machine-learning-based transition state exploration further helps to resolve automatedly the whole reaction network, including 74 elementary reactions on various MnRh surface sites, and reveals that the Mn-Mn dimeric site at the monatomic step edge is the true active site for C2 oxygenate formation. The turnover frequency of the C2 product on the Mn-Mn dimeric site at MnRh steps is at least 107 higher than that on pure Rh steps from our microkinetic simulations, with the selectivity to the C2 product being 52% at 523 K. Our results demonstrate the key catalytic role of Mn-Mn dimeric sites in allowing C-O bond cleavage and facilitating the hydrogenation of O-terminating C2 intermediates, and rule out Rh metal by itself as the active site for CO hydrogenation to C2 oxygenates.

Restructuring and Hydrogen Evolution on Sub-Nanosized PdxBy Clusters

As a Pt-group element, Pd has been regarded as one of the alternatives to Pt-based catalysts for the hydrogen evolution reaction (HER). Herein, we performed density functional theory (DFT) computations to explore the most stable structures of PdxBy (x = 6, 19, 44), revealed the in situ structural reconstruction of these clusters under acidic conditions, and evaluated their HER activity. We found that the presence of B can prevent underpotential hydrogen adsorption and activate the H atoms on the cluster surface for the HER. The theoretical calculations show that the reaction barrier for the HER on ~1 nm sized Pd44B4 can be as low as 0.36 eV, which is even lower than for the same-sized Pt and Pd2B nanoparticles. The ultra-high HER activity of sub-nanosized PdxBy clusters makes them a potential new and efficient HER electro-catalyst. This study provides new ideas for evaluating and designing novel nanocatalysts based on the structural reconstruction of small-sized nanoparticles in the future.

SCINE-Software for chemical interaction networks

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

A Q-learning method based on coarse-to-fine potential energy surface for locating transition state and reaction pathway

Transition state (TS) on the potential energy surface (PES) plays a key role in determining the kinetics and thermodynamics of chemical reactions. Inspired by the fact that the dynamics of complex systems are always driven by rare but significant transition events, we herein propose a TS search method in accordance with the Q-learning algorithm. Appropriate reward functions are set for a given PES to optimize the reaction pathway through continuous trial and error, and then the TS can be obtained from the optimized reaction pathway. The validity of this Q-learning method with reasonable settings of Q-value table including actions, states, learning rate, greedy rate, discount rate, and so on, is exemplified in 2 two-dimensional potential functions. In the applications of the Q-learning method to two chemical reactions, it is demonstrated that the Q-learning method can predict consistent TS and reaction pathway with those by ab initio calculations. Notably, the PES must be well prepared before using the Q-learning method, and a coarse-to-fine PES scanning scheme is thus introduced to save the computational time while maintaining the accuracy of the Q-learning prediction. This work offers a simple and reliable Q-learning method to search for all possible TS and reaction pathway of a chemical reaction, which may be a new option for effectively exploring the PES in an extensive search manner.

Global Neural Network Potential with Explicit Many-Body Functions for Improved Descriptions of Complex Potential Energy Surface

The high dimensional machine learning potential (MLP) that has developed rapidly in the past decade represents a giant step forward in large-scale atomic simulation for complex systems. The long-range interaction and the poor description of chemical reactions are typical problems of high dimensional MLP, which are mainly caused by the poor structure discrimination of the atom-centered ML model. Herein, we propose a low-cost neural-network-based MLP architecture for fitting global potential energy surface data, namely, G-MBNN, that can offer improved energy and force resolution on a complex potential energy surface. In G-MBNN, a set of many-body energy terms based on the local atomic environment are explicitly included in computing the total energy─the total energy of the system is written as the sum of atomic energy and many-body energy contributions. These extra many-body energy terms are computationally low-cost and, importantly, can provide easy access to delicate energy terms in complex systems such as very short repulsion, long-range attractions, and sensitive angular-dependent covalent interactions. We implement G-MBNN in the LASP code and demonstrate the improved accuracy of the new framework in representative systems, including ternary-element energy materials LiCoOx, TiO2 with defects, and a series of organic reactions.

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.

In Situ Structure of a Mo-Doped Pt-Ni Catalyst during Electrochemical Oxygen Reduction Resolved from Machine Learning-Based Grand Canonical Global Optimization

Pt-Ni alloy is by far the most active cathode material for oxygen reduction reaction (ORR) in the proton-exchange membrane fuel cell, and the addition of a tiny amount of a third-metal Mo can significantly improve the catalyst durability and activity. Here, by developing machine learning-based grand canonical global optimization, we are able to resolve the in situ structures of this important three-element alloy system under ORR conditions and identify their correlations with the enhanced ORR performance. We disclose the bulk phase diagram of Pt-Ni-Mo alloys and determine the surface structures under the ORR reaction conditions by exploring millions of likely structure candidates. The pristine Pt-Ni-Mo alloy surfaces are shown to undergo significant structure reconstruction under ORR reaction conditions, where a surface-adsorbed MoO₄ monomer or Mo₂O _x dimers cover the Pt-skin surface above 0.9 V vs RHE and protect the surface from Ni leaching. The physical origins are revealed by analyzing the electronic structure of O atoms in MoO₄ and on the Pt surface. In viewing the role of high-valence transition metal oxide clusters, we propose a set of quantitative measures for designing better catalysts and predict that six elements in the periodic table, namely, Mo, Tc, Os, Ta, Re, and W, can be good candidates for alloying with PtNi to improve the ORR catalytic performance. We demonstrate that machine learning-based grand canonical global optimization is a powerful and generic tool to reveal the catalyst dynamics behavior in contact with a complex reaction environment.

Unraveling different influences of the fraction of the tetragonal phase in oxide films on the corrosion resistance of Zr alloys from the phase transition mechanism

The mechanism of Sn and Nb influence on the fraction of tetragonal ZrO₂ in oxide films on Zr alloys and their influence mechanism on corrosion resistance of Zr alloys, despite decades of research, are ambiguous due to the lack of kinetic knowledge of phase evolution of ZrO₂ with doping. Using stochastic surface walking and density functional theory calculations, we investigate the influence of Nb and Sn on the stability of tetragonal (t) and monoclinic (m) ZrO₂, and t-m phase transition in oxide films. We found that though Nb and Sn result in similar apparent variation trends in the t-phase fraction in oxide films, their influences on t-m phase transition differ significantly, which is the underlying origin of different influences of the t-phase fraction in oxide films on the corrosion resistance of Zr alloys with Sn and Nb alloying. These results clarify an important aspect of the relationship between the microstructure and corrosion resistance of Zr alloys.

(2×1) Reconstruction Mechanism of Rutile TiO2(011) Surface

Understanding the reconstruction kinetics of solid surfaces involving an ensemble of atomic movements is practically important but challenging due to the complexity of high-dimensional potential energy surfaces. Herein, we develop a step-deciding technique incorporated with the nudged elastic band method, which enables multidirection pathway sampling and ensures the capture of a minimum energy path (MEP). Using this approach, the (2×1) reconstruction mechanism of a rutile-TiO₂(011) surface, a classic and long-standing open problem in the fields of surface science and heterogeneous catalysis, is quantified, and the MEP is explicitly identified and explained. Following the least-bond-breaking rule, it gives a stepwise Ti-O bond cleavage mechanism with a collection of decoupled local structural relaxation modes at an overall barrier of 1.25 eV critically affected by initial Ti-O bond opening, which is much lower than the common synergy mechanism. Moreover, the adsorption-induced reconstruction is rationalized considering practical reaction conditions, where H atom adsorbate is shown to effectively stabilize the labile one-fold O_1c intermediate and promote the reconstruction kinetics. This work reveals the reconstruction mechanism regarding multiatom movements and provides a general method for the structural exploration of other complicated systems.

Mechanical Understanding of Li-CO2 Batteries: The Critical Role of Forming Intermediate *Li2O

The emerging Li-CO₂ batteries are considered a promising next-generation power system because they can fix CO₂ while storing energy; however, their underlying mechanism remains elusive, impeding their efficient development. Meanwhile, apart from the conventional discharge product Li₂CO₃, the unexpected Li₂O species has also been detected, but its formation process is thus far undecided. Here, we report a new mechanism for Li-CO₂ batteries using first-principles calculations, which explains the long-standing puzzles. We show that such a process can be divided into two stages: (I) forming intermediate *Li₂C₂O₄ via surface lithiation and (II) generating -Li₂CO₃ and C through a *Li₂O-mediated pathway. We discover that the major kinetic barrier occurs in the coupling of *Li₂CO₂ and CO₂ in the first stage. Especially, in the second stage, *CO produced from *Li₂C₂O₄ decomposition is preferentially lithiated to *LiOC rather than disproportionated, and then *LiOC can be further lithiated to intermediate *Li₂O after C nucleation, which contributes to the final formation of Li₂CO₃ in the presence of sufficient CO₂.

A Theoretical Study of the In Situ Structural Reconstruction of Pdn (n = 6, 19, 44) Clusters for Catalytic Hydrogen Evolution

How in situ structural reconstructions affect the hydrogen evolution reaction (HER) activity of small Pd clusters is a long-standing problem in the field of heterogeneous catalysis. Herein, we reveal the structural evolution of Pdn (n = 6, 19, 44) clusters under the HER environment via stochastic global potential energy surface searching. We theoretically demonstrated that the HER activity of Pdn clusters first increases and then decreases under long-term working conditions. The intrinsic nature of these phenomenons includes interior H formations and structural reconstructions caused by the supersaturated adsorption of H atoms. This proves that carefully adjusting the hydrogenation degree of Pd clusters is a good strategy for improving the HER’s catalytic performance.

High-pressure phases of a Mn-N system

Highly compressed extended states of light elemental solids have emerged recently as a novel group of energetic materials. The application of these materials is seriously limited by the energy-safety contradiction, because the material with high energy density is highly metastable and can hardly be recovered under ambient conditions. Recently, it has been found that high-energy density transition metal polynitrides could be synthesized at ∼100 GPa and recovered at ∼20 GPa. Inspired by these findings, we have studied a high-pressure Mn-N system from the aspects of structure, stability, phase transition, energy density and electronic structure theoretically for the first time. The results reveal that MnN₄_P1̄ consisting of [N₄]_∞^2- is thermodynamically stable at 36.9-100 GPa, dynamically stable at 0 GPa and has a noticeably high volumetric energy density of 15.71 kJ cm^-3. Upon decompression, this structure will transform to MnN₄_C2/m with the transition barrier declining sharply at 5-10 GPa due to the switching of transition pathways. Hence, we propose MnN₄_P1̄ as a potential energetic material that is synthesizable above 40 GPa and recoverable until 10 GPa.

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.

Perspective on computational reaction prediction using machine learning methods in heterogeneous catalysis

Heterogeneous catalysis plays a significant role in the modern chemical industry. Towards the rational design of novel catalysts, understanding reactions over surfaces is the most essential aspect. Typical industrial catalytic processes such as syngas conversion and methane utilisation can generate a large reaction network comprising thousands of intermediates and reaction pairs. This complexity not only arises from the permutation of transformations between species but also from the extra reaction channels offered by distinct surface sites. Despite the success in investigating surface reactions at the atomic scale, the huge computational expense of ab initio methods hinders the exploration of such complicated reaction networks. With the proliferation of catalysis studies, machine learning as an emerging tool can take advantage of the accumulated reaction data to emulate the output of ab initio methods towards swift reaction prediction. Here, we briefly summarise the conventional workflow of reaction prediction, including reaction network generation, ab initio thermodynamics and microkinetic modelling. An overview of the frequently used regression models in machine learning is presented. As a promising alternative to full ab initio calculations, machine learning interatomic potentials are highlighted. Furthermore, we survey applications assisted by these methods for accelerating reaction prediction, exploring reaction networks, and computational catalyst design. Finally, we envisage future directions in computationally investigating reactions and implementing machine learning algorithms in heterogeneous catalysis.

In Situ Surface Structures of PdAg Catalyst and Their Influence on Acetylene Semihydrogenation Revealed by Machine Learning and Experiment

PdAg alloy is an industrial catalyst for acetylene-selective hydrogenation in excess ethene. While significant efforts have been devoted to increase the selectivity, there has been little progress in the catalyst performance at low temperatures. Here by combining a machine-learning atomic simulation and catalysis experiment, we clarify the surface status of PdAg alloy catalyst under the reaction conditions and screen out a rutile-TiO₂ supported Pd₁Ag₃ catalyst with high performance: i.e., 85% selectivity at >96% acetylene conversion over a 100 h period in an experiment. The machine-learning global potential energy surface exploration determines the Pd-Ag-H bulk and surface phase diagrams under the reaction conditions, which reveals two key bulk compositions, Pd₁Ag₁ (R3̅m) and Pd₁Ag₃ (Pm3̅m), and quantifies the surface structures with varied Pd:Ag ratios under the reaction conditions. We show that the catalyst activity is controlled by the PdAg patterns on the (111) surface that are variable under reaction conditions, but the selectivity is largely determined by the amount of Pd exposure on the (100) surface. These insights provide the fundamental basis for the rational design of a better catalyst via three measures: (i) controlling the Pd:Ag ratio at 1:3, (ii) reducing the nanoparticle size to limit PdAg local patterns, (iii) searching for active supports to terminate the (100) facets.

Reaction prediction via atomistic simulation: from quantum mechanics to machine learning

It is an ultimate goal in chemistry to predict reaction without recourse to experiment. Reaction prediction is not just the reaction rate determination of known reactions but, more broadly, the reaction exploration to identify new reaction routes. This review briefly overviews the theory on chemical reaction and the current methods for computing/estimating reaction rate and exploring reaction space. We particularly focus on the atomistic simulation methods for reaction exploration, which are benefited significantly by recently emerged machine learning potentials. We elaborate the stochastic surface walking global pathway sampling based on the global neural network (SSW-NN) potential, developed in our group since 2013, which can explore complex reactions systems unbiasedly and automatedly. Two examples, molecular reaction and heterogeneous catalytic reactions, are presented to illustrate the current status for reaction prediction using SSW-NN.

Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces. © 2019 Wiley Periodicals, Inc.

Group-VIII transition metal boride as promising hydrogen evolution reaction catalysts

A systematic bottom-up approach to search for acidic hydrogen evolution reaction (HER) catalyst with high thermodynamic stability and high HER activity.

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.

Anisotropic kinetics of solid phase transition from first principles: alpha-omega phase transformation of Zr

Structural inhomogeneity is ubiquitous in solid crystals and plays critical roles in phase nucleation and propagation. Here, we develop a heterogeneous solid-solid phase transition theory for predicting the prevailing heterophase junctions, the metastable states governing microstructure evolution in solids. Using this theory and first-principles pathway sampling simulation, we determine two types of heterophase junctions pertaining to metal α-ω phase transition at different pressures and predict the reversibility of transformation only at low pressures, i.e. below 7 GPa. The low-pressure transformation is dominated by displacive Martensitic mechanism, while the high-pressure one is controlled by the reconstructive mechanism. The mechanism of α-ω phase transition is thus highly pressure-sensitive, for which the traditional homogeneous model fails to explain the experimental observations. The results provide the first atomic-level evidence on the coexistence of two different solid phase transition mechanisms in one system.

Searching for new TiO₂ crystal phases with better photoactivity

Using the recently developed stochastic surface walking global optimization method, this work explores the potential energy surface of TiO2 crystals aiming to search for likely phases with higher photocatalytic activity. Five new phases of TiO2 are identified and the lowest energy phase transition pathways connecting to the most abundant phases (rutile and anatase) are determined. Theory shows that a high-pressure phase, α-PbO2-like form (TiO2II) acts as the key intermediate in between rutile and anatase. The phase transition of anatase to rutile belongs to the diffusionless Martensitic phase transition, occurring through a set of habit planes, rutile(101)//TiO2II(001), and TiO2II(100)//anatase(112). With regard to the photocatalytic activity, three pure phases (#110, pyrite and fluorite) are found to possess the band gap narrower than rutile, but they are unstable at the low-pressure condition. Instead, a mixed anatase-TiO2II phase is found to have good stability and narrower band gap than both parent phases. Because of the phase separation, the mixed phase is also expected to improve the photocatalytic performance by reducing the probability of the electron-hole pair recombination.

Restructuring and Hydrogen Evolution on Pt Nanoparticle

The restructuring of nanoparticles at the in situ condition is a common but complex phenomenon in nanoscience. Here, we present the first systematic survey on the structure dynamics and its catalytic consequence for hydrogen evolution reaction (HER) on Pt nanoparticles, as represented by a magic number Pt44 octahedron (∼1 nm size). Using a first principles calculation based global structure search method, we stepwise follow the significant nanoparticle restructuring under HER conditions as driven by thermodynamics to expose {100} facets, and reveal the consequent large activity enhancement due to the marked increase of the concentration of the active site, being identified to be apex atoms. The enhanced kinetics is thus a "byproduct" of the thermodynamical restructuring. Based on the results, the best Pt catalyst for HER is predicted to be ultrasmall Pt particles without core atoms, a size below ∼20 atoms.

Confined platinum nanoparticle in carbon nanotube: structure and oxidation

Confined metal particles show unexpected structural versatility, leading to higher stability and better catalytic performance, as predicted from first-principles-based global optimization methods.

Reaction sampling and reactivity prediction using the stochastic surface walking method

The new theoretical method demonstrates the ability of automated reaction sampling and activity prediction for complex organic reactions.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Electrocatalytic oxygen reduction kinetics on Fe-center of nitrogen-doped graphene

OOH dissociation is the key step in electrocatalytic oxygen reduction on Fe–N centers of graphite, as revealed from first principles.

Mechanism and active site of photocatalytic water splitting on titania in aqueous surroundings

Photocatalytic water oxidation is both phase and surface structure-sensitive due to the heat-driven first-step of O–H bond breaking.

Stochastic surface walking method for crystal structure and phase transition pathway prediction

SSW-crystal method for automated structure search and phase transition pathway sampling of crystals.