A genetic algorithm for first principles global structure optimization of supported nano structures

Determining the chemical ordering in nanoalloys by considering atomic coordination types

The energetically most favorable chemical ordering of bimetallic nanoparticles can be characterized by combining global optimization algorithms and surrogate energy models. The latter approximate the energy of nanoalloys relying on structural descriptors, training models, and data. Here, we systematically evaluate the performance of highly data-efficient topological descriptors [Kozlov et al., Chem. Sci. 6, 3868 (2015)] for predicting the energies of metal nanoalloys with different chemical orderings. We also introduce a new descriptor based on atomic coordination types, which results in a less data-efficient and interpretable approach, but improves the general accuracy and the quantification of orderings in the inner parts of nanoparticles. The capacity of both the original and new approaches in combination with a basin hopping algorithm is illustrated by generating convex hulls of PdZn nanoalloys and predicting the resulting active surface site distribution as a function of particle composition. Finally, we show how these approaches can be combined with machine-learning adsorption models in electrocatalysis studies for a fast evaluation of the reactivity landscape of targeted nanoalloys.

Tuning Reinforcement Learning Parameters for Cluster Selection to Enhance Evolutionary Algorithms

The ability to find optimal molecular structures with desired properties is a popular challenge, with applications in areas such as drug discovery. Genetic algorithms are a common approach to global minima molecular searches due to their ability to search large regions of the energy landscape and decrease computational time via parallelization. In order to decrease the amount of unstable intermediate structures being produced and increase the overall efficiency of an evolutionary algorithm, clustering was introduced in multiple instances. However, there is little literature detailing the effects of differentiating the selection frequencies between clusters. In order to find a balance between exploration and exploitation in our genetic algorithm, we propose a system of clustering the starting population and choosing clusters for an evolutionary algorithm run via a dynamic probability that is dependent on the fitness of molecules generated by each cluster. We define four parameters, MFavOvrAll-A, MFavClus-B, NoNewFavClus-C, and Select-D, that correspond to a reward for producing the best structure overall, a reward for producing the best structure in its own cluster, a penalty for not producing the best structure, and a penalty based on the selection ratio of the cluster, respectively. A reward increases the probability of a cluster's future selection, while a penalty decreases it. In order to optimize these four parameters, we used a Gaussian distribution to approximate the evolutionary algorithm performance of each cluster and performed a grid search for different parameter combinations. Results show parameter MFavOvrAll-A (rewarding clusters for producing the best structure overall) and parameter Select-D (appearance penalty) have a significantly larger effect than parameters MFavClus-B and NoNewFavClus-C. In order to produce the most successful models, a balance between MFavOvrAll-A and Select-D must be made that reflects the exploitation vs exploration trade-off often seen in reinforcement learning algorithms. Results show that our reinforcement-learning-based method for selecting clusters outperforms an unclustered evolutionary algorithm for quinoline-like structure searches.

Transferable, Living Data Sets for Predicting Global Minimum Energy Nanocluster Geometries

Modeling of nanocluster geometries is essential for studying the dependence of catalytic activity on the available active sites. In heterogeneous catalysis, the interfacial interaction of the support with the metal can result in modification of the structural and electronic properties of the clusters. To tackle the study of a diverse array of cluster shapes, data-driven methodologies are essential to circumvent prohibitive computational costs. At their core, these methods require large data sets in order to achieve the necessary accuracy to drive structural exploration. Given the similarity in binding character of the transition metals, cluster shapes encountered for various systems show a large amount of overlap. This overlap has been utilized to construct a living data set which may be carried over across multiple studies. Iterative refinement of this data set provides a low-cost pathway for initialization of cluster studies. It is shown that utilization of transferable structural information can reduce model construction costs by more than 90%. The benefits of this approach are particularly notable for alloy systems, which possess significantly larger configurational spaces compared to the pure-phase counterparts.

Active-learning for global optimization of Ni-Ceria nanoparticles: The case of Ce4-xNixO8- x (x = 1, 2, 3)

Ni-CeO2 nanoparticles (NPs) are promising nanocatalysts for water splitting and water gas shift reactions due to the ability of ceria to temporarily donate oxygen to the catalytic reaction and accept oxygen after the reaction is completed. Therefore, elucidating how different properties of the Ni-Ceria NPs relate to the activity and selectivity of the catalytic reaction, is of crucial importance for the development of novel catalysts. In this work the active learning (AL) method based on machine learning regression and its uncertainty is used for the global optimization of Ce(4-x)NixO(8-x) (x = 1, 2, 3) nanoparticles, employing density functional theory calculations. Additionally, further investigation of the NPs by mass-scaled parallel-tempering Born-Oppenheimer molecular dynamics resulted in the same putative global minimum structures found by AL, demonstrating the robustness of our AL search to learn from small datasets and assist in the global optimization of complex electronic structure systems.

Accelerating the prediction of inorganic surfaces with machine learning interatomic potentials

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the material's synthesis or operating conditions. These conditions dictate thermodynamic driving forces and kinetic rates responsible for yielding the observed surface structure and morphology. Computational surface science methods have long been applied to connect thermochemical conditions to surface phase stability, particularly in the heterogeneous catalysis and thin film growth communities. This review provides a brief introduction to first-principles approaches to compute surface phase diagrams before introducing emerging data-driven approaches. The remainder of the review focuses on the application of machine learning, predominantly in the form of learned interatomic potentials, to study complex surfaces. As machine learning algorithms and large datasets on which to train them become more commonplace in materials science, computational methods are poised to become even more predictive and powerful for modeling the complexities of inorganic surfaces at the nanoscale.

Accelerated Structural Optimization for the Supported Metal System Based on Hybrid Approach Combining Bayesian Optimization with Local Search

Numerous systematic methods have been developed to search for the global minimum of the potential energy surface, which corresponds to the optimal atomic structure. However, the majority of them still demand a substantial computing load due to the relaxation process that is embedded as an inner step inside the algorithm. Here, we propose a hybrid approach that combines Bayesian optimization (BO) and a local search that circumvents the relaxation step and efficiently finds the optimum structure, particularly in supported metal systems. The hybridization strategy combining the capabilities of BO's effective exploration and the local search's fast convergence expedites structural search. In addition, the formulation of physical constraints regarding the materials system and the feature of screening structure similarity enhance the computational efficiency of the proposed method. The proposed algorithm is demonstrated in two supported metal systems, showing the potential of the proposed method in the field of structural optimization.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Graph Neural Network-Accelerated Multitasking Genetic Algorithm for Optimizing PdxTi1-xHy Surfaces under Various CO2 Reduction Reaction Conditions

Palladium (Pd) hydride-based catalysts have been reported to have excellent performance in the CO2 reduction reaction (CO2RR) and hydrogen evolution reaction (HER). Our previous work on doped PdH and Pd alloy hydrides showed that Ti-doped and Ti-alloyed Pd hydrides could improve the performance of the CO2 reduction reaction compared with pure Pd hydride. Compositions and chemical orderings of the surfaces with only one adsorbate under certain reaction conditions are linked to their stability, activity, and selectivity toward the CO2RR and HER, as shown in our previous work. In fact, various coverages, types, and mixtures of the adsorbates, as well as state variables such as temperature, pressure, applied potential, and chemical potential, could impact their stability, activity, and selectivity. However, these factors are usually fixed at common values to reduce the complexity of the structures and the complexity of the reaction conditions in most theoretical work. To address the complexities above and the huge search space, we apply a deep learning-assisted multitasking genetic algorithm to screen for PdxTi1-xHy surfaces containing multiple adsorbates for CO2RR under different reaction conditions. The ensemble deep learning model can greatly speed up the structure relaxations and retain a high accuracy and low uncertainty of the energy and forces. The multitasking genetic algorithm simultaneously finds globally stable surface structures under each reaction condition. Finally, 23 stable structures are screened out under different reaction conditions. Among these, Pd0.56Ti0.44H1.06 + 25%CO, Pd0.31Ti0.69H1.25 + 50%CO, Pd0.31Ti0.69H1.25 + 25%CO, and Pd0.88Ti0.12H1.06 + 25%CO are found to be very active for CO2RR and suitable to generate syngas consisting of CO and H2.

QMLMaterial─A Quantum Machine Learning Software for Material Design and Discovery

Structural elucidation of chemical compounds is challenging experimentally, and theoretical chemistry methods have added important insight into molecules, nanoparticles, alloys, and materials geometries and properties. However, finding the optimum structures is a bottleneck due to the huge search space, and global search algorithms have been used successfully for this purpose. In this work, we present the quantum machine learning software/agent for materials design and discovery (QMLMaterial), intended for automatic structural determination in silico for several chemical systems: atomic clusters, atomic clusters and the spin multiplicity together, doping in clusters or solids, vacancies in clusters or solids, adsorption of molecules or adsorbents on surfaces, and finally atomic clusters on solid surfaces/materials or encapsulated in porous materials. QMLMaterial is an artificial intelligence (AI) software based on the active learning method, which uses machine learning regression algorithms and their uncertainties for decision making on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations as more data is obtained. The software has different acquisition functions for decision making (e.g., expected improvement and lower confidence bound). Also, the Gaussian process is available in the AI framework for regression, where the uncertainty is obtained analytically from Bayesian statistics. For the artificial neural network and support vector regressor algorithms, the uncertainty can be obtained by K-fold cross-validation or nonparametric bootstrap resampling methods. The software is interfaced with several quantum chemistry codes and atomic descriptors, such as the many-body tensor representation. QMLMaterial's capabilities are highlighted in the current work by its applications in the following systems: Na20, Mo6C3 (where the spin multiplicity was considered), H2O@CeNi3O5, Mg8@graphene, Na3Mg3@CNT (carbon nanotube).

Accessing complex reconstructed material structures with hybrid global optimization accelerated via on-the-fly machine learning

The complex reconstructed structure of materials can be revealed by global optimization. This paper describes a hybrid evolutionary algorithm (HEA) that combines differential evolution and genetic algorithms with a multi-tribe framework. An on-the-fly machine learning calculator is adopted to expedite the identification of low-lying structures. With a superior performance to other well-established methods, we further demonstrate its efficacy by optimizing the complex oxidized surface of Pt/Pd/Cu with different facets under (4 × 4) periodicity. The obtained structures are consistent with experimental results and are energetically lower than the previously presented model.

Amorphous nickel hydroxide shell tailors local chemical environment on platinum surface for alkaline hydrogen evolution reaction

In analogy to natural enzymes, an elaborated design of catalytic systems with a specifically tailored local chemical environment could substantially improve reaction kinetics, effectively combat catalyst poisoning effect and boost catalyst lifetime under unfavourable reaction conditions. Here we report a unique design of 'Ni(OH)2-clothed Pt-tetrapods' with an amorphous Ni(OH)2 shell as a water dissociation catalyst and a proton conductive encapsulation layer to isolate the Pt core from bulk alkaline electrolyte while ensuring efficient proton supply to the active Pt sites. This design creates a favourable local chemical environment to result in acidic-like hydrogen evolution reaction kinetics with a lowest Tafel slope of 27 mV per decade and a record-high specific activity and mass activity in alkaline electrolyte. The proton conductive Ni(OH)2 shell can also effectively reject impurity ions and retard the Oswald ripening, endowing a high tolerance to solution impurities and exceptional long-term durability that is difficult to achieve in the naked Pt catalysts. The markedly improved hydrogen evolution reaction activity and durability in an alkaline medium promise an attractive catalyst material for alkaline water electrolysers and renewable chemical fuel generation.

Heterogeneity of the vanadia phase dispersed on titania. Co-existence of distinct mono-oxo VOx sites

The structural and configurational characteristics of the species comprising the (VO_x)_n phase dispersed on TiO₂(P25) are studied under oxidative dehydration conditions by in situ molecular vibrational spectroscopy (Raman, FTIR) complemented by in situ Raman/¹⁸O isotope exchange and Raman spectroscopy under static equilibrium at temperatures of 175-430 °C and coverages in the 0.40-5.5 V nm^-2 range. It is found that the dispersed (VO_x)_n phase consists of distinct species with different configurations. At low coverages of 0.40 and 0.74 V nm^-2, isolated (monomeric) species prevail. Two distinct mono-oxo species are found: (i) a majority Species-I, presumably of distorted tetrahedral OV(-O-)₃ configuration with VO mode at 1022-1024 cm^-1 and (ii) a minority Species-II, presumably of distorted octahedral-like OV(-O-)₄ configuration with VO mode at 1013-1014 cm^-1. Cycling the catalysts in the 430 → 250 → 175 → 430 °C sequence results in temperature-dependent structural transformations. With decreasing temperature, a Species-II → Species-I transformation with concomitant surface hydroxylation takes place by means of a hydrolysis mechanism mediated by water molecules retained by the surface. A third species (Species-III, presumably of di-oxo configuration with ν_s/ν_as at ∼995/985 cm^-1) occurs in minority and its presence is increased when further lowering the temperature according to a Species-I → Species-III hydrolysis step. Species-II (OV(-O-)₄) shows the highest reactivity to water. For coverages above 1 V nm^-2, an association of VO_x units takes place leading to gradually larger polymeric domains when the coverage is increased in the 1.1-5.5 V nm^-2 range. Polymeric (VO_x)_n domains comprise building units that maintain the structural characteristics (termination configuration and V coordination number) of Species-I, Species-II, and Species-III. The terminal VO stretching modes are blue-shifted with increasing (VO_x)_n domain size. A lower extent of hydroxylation is evidenced under static equilibrium forced dehydrated conditions, thereby limiting the temperature dependent structural transformations and excluding the possibility of incoming water vapors as the cause for the temperature dependent effects observed in the in situ Raman/FTIR spectra. The results address open issues and offer new insight in the structural studies of VO_x/TiO₂ catalysts.

GAMaterial-A genetic-algorithm software for material design and discovery

Genetic algorithms (GAs) are stochastic global search methods inspired by biological evolution. They have been used extensively in chemistry and materials science coupled with theoretical methods, ranging from force-fields to high-throughput first-principles methods. The methodology allows an accurate and automated structural determination for molecules, atomic clusters, nanoparticles, and solid surfaces, fundamental to understanding chemical processes in catalysis and environmental sciences, for instance. In this work, we propose a new genetic algorithm software, GAMaterial, implemented in Python3.x, that performs global searches to elucidate the structures of atomic clusters, doped clusters or materials and atomic clusters on surfaces. For all these applications, it is possible to accelerate the GA search by using machine learning (ML), the ML@GA method, to build subsequent populations. Results for ML@GA applied for the dopant distributions in atomic clusters are presented. The GAMaterial software was applied for the automatic structural search for the Ti₆ O₁₂ cluster, doping Al in Si₁₁ (4Al@Si₁₁ ) and Na₁₀ supported on graphene (Na₁₀ @graphene), where DFTB calculations were used to sample the complex search surfaces with reasonably low computational cost. Finally, the global search by GA of the Mo₈ C₄ cluster was considered, where DFT calculations were made with the deMon2k code, which is interfaced with GAMaterial.

Data-Driven Machine Learning for Understanding Surface Structures of Heterogeneous Catalysts

The design of heterogeneous catalysts is necessarily surface-focused, generally achieved via optimization of adsorption energy and microkinetic modelling. A prerequisite is to ensure the adsorption energy is physically meaningful is the stable existence of the conceived active-site structure on the surface. The development of improved understanding of the catalyst surface, however, is challenging practically because of the complex nature of dynamic surface formation and evolution under in-situ reactions. We propose therefore data-driven machine-learning (ML) approaches as a solution. In this Minireview we summarize recent progress in using machine-learning to search and predict (meta)stable structures, assist operando simulation under reaction conditions and micro-environments, and critically analyze experimental characterization data. We conclude that ML will become the new norm to lower costs associated with discovery and design of optimal heterogeneous catalysts.

The Promoting Role of Ni on In2O3 for CO2 Hydrogenation to Methanol

Ni-promoted indium oxide (In2O3) is a promising catalyst for the selective hydrogenation of CO2 to CH3OH, but the nature of the active Ni sites remains unknown. By employing density functional theory and microkinetic modeling, we elucidate the promoting role of Ni in In2O3-catalyzed CO2 hydrogenation. Three representative models have been investigated: (i) a single Ni atom doped in the In2O3(111) surface, (ii) a Ni atom adsorbed on In2O3(111), and (iii) a small cluster of eight Ni atoms adsorbed on In2O3(111). Genetic algorithms (GAs) are used to identify the optimum structure of the Ni8 clusters on the In2O3 surface. Compared to the pristine In2O3(111) surface, the Ni8-cluster model offers a lower overall barrier to oxygen vacancy formation, whereas, on both single-atom models, higher overall barriers are found. Microkinetic simulations reveal that only the supported Ni8 cluster can lead to high methanol selectivity, whereas single Ni atoms either doped in or adsorbed on the In2O3 surface mainly catalyze CO formation. Hydride species obtained by facile H2 dissociation on the Ni8 cluster are involved in the hydrogenation of adsorbed CO2 to formate intermediates and methanol. At higher temperatures, the decreasing hydride coverage shifts the selectivity to CO. On the Ni8-cluster model, the formation of methane is inhibited by high barriers associated with either direct or H-assisted CO activation. A comparison with a smaller Ni6 cluster also obtained with GAs exhibits similar barriers for key rate-limiting steps for the formation of CO, CH4, and CH3OH. Further microkinetic simulations show that this model also has appreciable selectivity to methanol at low temperatures. The formation of CO over single Ni atoms either doped in or adsorbed on the In2O3 surface takes place via a redox pathway involving the formation of oxygen vacancies and direct CO2 dissociation.

Oxygen Healing and CO2 /H2 /Anisole Dissociation on Reduced Molybdenum Oxide Surfaces Studied by Density Functional Theory

Reduced molybdenum oxides are versatile catalysts for deoxygenation and hydrodeoxygenation reactions. In this work, we have performed spin-polarized DFT calculations to investigate oxygen healing energies on reduced molybdenum oxides (reduced α-MoO₃ , γ-Mo₄ O₁₁ and MoO₂ ). We find that Mo⁺⁴ on MoO₂ (100) is the most active for abstracting an oxygen from the oxygenated compounds. We further explored CO₂ adsorption and dissociation on reduced α-MoO₃ (010) and MoO₂ (100). In comparison to reduced α-MoO₃ (010), CO₂ adsorbs more strongly on MoO₂ (100). We find that CO₂ dissociates on MoO₂ (100) via a two-step process, the overall barrier for which is 0.6 eV. This barrier is 1.7 eV lower than that on reduced α-MoO₃ (010), suggesting a much higher activity for deoxygenation of CO₂ to CO. As H₂ dissociation is shown to be the rate-limiting step for hydrodeoxygenation reactions, we also studied activation barriers for H₂ chemisorption on MoO₂ (100). We find that the chemisorption barriers are 0.7 eV lower than that reported on reduced α-MoO₃ (010). Finally, we have studied the dissociation (C-O cleavage) of anisole (a lignin-based biofuel model compound) on MoO₂ (100). We find that anisole binds very strongly on MoO₂ (100) with an adsorption energy of -1.47 eV. According to Sabatier's principle, strongly adsorbing reactants poison the catalyst surface, which may explain the low activity of MoO₂ observed during experiments for hydrodeoxygenation of anisole.

Global optimization of extraframework ensembles in zeolites: structural analysis of extraframework aluminum species in MOR and MFI zeolites

Metal-modified zeolites are versatile catalytic materials with a wide range of industrial applications. Their catalytic behaviour is determined by the nature of externally introduced cationic species, i.e., its geometry, chemical composition, and location within the zeolite pores. Superior catalyst designs can be unlocked by understanding the confinement effect and spatial limitations of the zeolite framework and its influence on the geometry and location of such cationic active sites. In this study, we employ the genetic algorithm (GA) global optimization method to investigate extraframework aluminum species and their structural variations in different zeolite matrices. We focus on extraframework aluminum (EFAl) as a model system because it greatly influences the product selectivity and catalytic stability in several zeolite catalyzed processes. Specifically, the GA was used to investigate the configurational possibilities of EFAl within the mordenite (MOR) and ZSM-5 frameworks. The xTB semi-empirical method within the GA was employed for an automated sampling of the EFAl-zeolite space. Furthermore, geometry refinement at the density functional theory (DFT) level of theory allowed us to improve the most stable configurations obtained from the GA and elaborate on the limitations of the xTB method. A subsequent ab initio thermodynamics analysis (aiTA) was chosen to predict the most favourable EFAl structure(s) under the catalytically relevant operando conditions.

Hydrogen-Induced Restructuring of a Cu(100) Electrode in Electroreduction Conditions

The rearrangement of Cu surfaces under electrochemical conditions is known to play a key role in the surface activation for major electrocatalytic reactions. Despite the extensive experimental insights into such rearrangements, from surface-sensitive spectroscopy and microscopy, the spatial and temporal resolution of these methods is insufficient to provide an atomistic picture of the electrochemical interface. Theoretical characterization has also been challenged by the diversity of restructuring configurations, surface stoichiometry, adsorbate configurations, and the effect of the electrode potential. Here, atomistic insight into the restructuring of the electrochemical interface is gained from first principles. Cu(100) restructuring under varying applied potentials and adsorbate coverages is studied by grand canonical density functional theory and global optimization techniques, as well as ab initio molecular dynamics and mechanistic calculations. We show that electroreduction conditions cause the formation of a shifted-row reconstruction on Cu(100), induced by hydrogen adsorption. The reconstruction is initiated at 1/6 ML H coverage, when the Cu-H bonding sufficiently weakens the Cu-Cu bonds between the top- and sublayer, and further stabilized at 1/3 ML when H adsorbates fill all the created 3-fold hollow sites. The simulated scanning tunneling microscopy (STM) images of the calculated reconstructed interfaces agree with experimental in situ STM. However, compared to the thermodynamic prediction, the onsets of reconstruction events in the experiment occur at more negative applied voltages. This is attributed to kinetic effects in restructuring, which we describe via different statistical models, to produce the potential- and pH-dependent surface stability diagram. This manuscript provides rich atomistic insight into surface restructuring in electroreduction conditions, which is required for the understanding and design of Cu-based materials for electrocatalytic processes. It also offers the methodology to study the problem of in situ electrode reconstruction.

Neural-network-backed evolutionary search for SrTiO3(110) surface reconstructions

The determination of atomic structures in surface reconstructions has typically relied on structural models derived from intuition and domain knowledge. Evolutionary algorithms have emerged as powerful tools for such structure searches. However, when density functional theory is used to evaluate the energy the computational cost of a thorough exploration of the potential energy landscape is prohibitive. Here, we drive the exploration of the rich phase diagram of TiO x overlayer structures on SrTiO3(110) by combining the covariance matrix adaptation evolution strategy (CMA-ES) and a neural-network force field (NNFF) as a surrogate energy model. By training solely on SrTiO3(110) 4×1 overlayer structures and performing CMA-ES runs on 3×1, 4×1 and 5×1 overlayers, we verify the transferability of the NNFF. The speedup due to the surrogate model allows taking advantage of the stochastic nature of the CMA-ES to perform exhaustive sets of explorations and identify both known and new low-energy reconstructions.

Stability of oxidized states of free-standing and ceria-supported PtOx particles

Nanostructured materials based on CeO2 and Pt play a fundamental role in catalyst design. However, their characterization is often challenging due to their structural complexity and the tendency of the materials to change under reaction conditions. In this work, we combine calculations based on the density functional theory, a machine-learning assisted global optimization method (GOFEE), and ab initio thermodynamics to characterize stable oxidation states of ceria-supported PtyOx particles in different environments. The collection of global minima structures for different stoichiometries resulting from the global optimisation effort is used to assess the effect of temperature, oxygen pressure, and support interactions on the phase diagrams, oxidation states, and geometries of the PtyOx particles. We thus identify favoured structural motifs and O:Pt ratios, revealing that oxidized states of free-standing and ceria-supported platinum particles are more stable than reduced ones under a wide range of conditions. These results indicate that studies rationalizing activity of ceria-supported Pt clusters must consider oxidized states, and that previous understanding of such materials obtained only with fully reduced Pt clusters may be incomplete.

Fast atomic structure optimization with on-the-fly sparse Gaussian process potentials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022;34:344007. [PMID: 35675808 DOI: 10.1088/1361-648x/ac76ff]

We apply on-the-fly machine learning potentials (MLPs) using the sparse Gaussian process regression (SGPR) algorithm for fast optimization of atomic structures. Great acceleration is achieved even in the context of a single local optimization. Although for finding the exact local minimum, due to limited accuracy of MLPs, switching to another algorithm may be needed. For random gold clusters, the forces are reduced to ∼0.1 eV Å^-1within less than ten first-principles (FP) calculations. Because of highly transferable MLPs, this algorithm is specially suitable for global optimization methods such as random or evolutionary structure searching or basin hopping. This is demonstrated by sequential optimization of random gold clusters for which, after only a few optimizations, FP calculations were rarely needed.

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Modelling and understanding properties of materials from first principles require knowledge of the underlyingatomistic structure. This entails knowing the individual chemical identity and position of all atoms involved.Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, andbulk phases of amorphous and solid materials represents a difficult high-dimensional global optimizationproblem. The rise of machine learning techniques in materials science has, however, led to many compellingdevelopments that may speed up structure searches. The complexity of such new methods has prompted aneed for an efficient way of assembling them into global optimization algorithms that can be experimentedwith. In this paper, we introduce the Atomistic Global Optimization X (AGOX) framework and code, asa customizable approach that enables efficient building and testing of global optimization algorithms. Amodular way of expressing global optimization algorithms is described and modern programming practicesare used to enable that modularity in the freely available AGOX python package. A number of examplesof global optimization approaches are implemented and analyzed. This ranges from random search andbasin-hopping to machine learning aided approaches with on-the-fly learnt surrogate energy landscapes. Themethods are show-cased on problems ranging from supported clusters over surface reconstructions to largecarbon clusters and metal-nitride clusters incorporated into graphene sheets.

Structure of an Ultrathin Oxide on Pt3 Sn(111) Solved by Machine Learning Enhanced Global Optimization

Determination of the atomic structure of solid surfaces typically depends on comparison of measured properties with simulations based on hypothesized structural models. For simple structures, the models may be guessed, but for more complex structures there is a need for reliable theory-based search algorithms. So far, such methods have been limited by the combinatorial complexity and computational expense of sufficiently accurate energy estimation for surfaces. However, the introduction of machine learning methods has the potential to change this radically. Here, we demonstrate how an evolutionary algorithm, utilizing machine learning for accelerated energy estimation and diverse population generation, can be used to solve an unknown surface structure-the (4×4) surface oxide on Pt₃ Sn(111)-based on limited experimental input. The algorithm is efficient and robust, and should be broadly applicable in surface studies, where it can replace manual, intuition based model generation.

Structure of an Ultrathin Oxide on Pt3Sn(111) Solved by Machine Learning Enhanced Global Optimization

Determination of the atomic structure of solid surfaces typically depends on comparison of measured properties with simulations based on hypothesized structural models. For simple structures, the models may be guessed, but for more complex structures there is a need for reliable theory-based search algorithms. So far, such methods have been limited by the combinatorial complexity and computational expense of sufficiently accurate energy estimation for surfaces. However, the introduction of machine learning methods has the potential to change this radically. Here, we demonstrate how an evolutionary algorithm, utilizing machine learning for accelerated energy estimation and diverse population generation, can be used to solve an unknown surface structure-the (4×4) surface oxide on Pt3Sn(111)-based on limited experimental input. The algorithm is efficient and robust, and should be broadly applicable in surface studies, where it can replace manual, intuition based model generation.

Dimerization of dehydrogenated polycyclic aromatic hydrocarbons on graphene

Dimerization of polycyclic aromatic hydrocarbons (PAHs) is an important, yet poorly understood, step in the on-surface synthesis of graphene (nanoribbon), soot formation, and growth of carbonaceous dust grains in the interstellar medium (ISM). The on-surface synthesis of graphene and the growth of carbonaceous dust grains in the ISM require the chemical dimerization in which chemical bonds are formed between PAH monomers. An accurate and cheap method of exploring structure rearrangements is needed to reveal the mechanism of chemical dimerization on surfaces. This work has investigated the chemical dimerization of two dehydrogenated PAHs (coronene and pentacene) on graphene via an evolutionary algorithm augmented by machine learning surrogate potentials and a set of customized structure operators. Different dimer structures on surfaces have been successfully located by our structure search methods. Their binding energies are within the experimental errors of temperature programmed desorption measurements. The mechanism of coronene dimer formation on graphene is further studied and discussed.

Water Chemistry beneath Graphene: Condensation of a Dense OH-H2O Phase under Graphene

Room temperature oxygen hydrogenation below graphene flakes supported by Ir(111) is investigated through a combination of X-ray photoelectron spectroscopy, scanning tunneling microscopy, and density functional theory calculations using an evolutionary search algorithm. We demonstrate how the graphene cover and its doping level can be used to trap and characterize dense mixed O-OH-H₂O phases that otherwise would not exist. Our study of these graphene-stabilized phases and their response to oxygen or hydrogen exposure reveals that additional oxygen can be dissolved into them at room temperature creating mixed O-OH-H₂O phases with an increased areal coverage underneath graphene. In contrast, additional hydrogen exposure converts the mixed O-OH-H₂O phases back to pure OH-H₂O with a reduced areal coverage underneath graphene.

Automated search for optimal surface phases (ASOPs) in grand canonical ensemble powered by machine learning

The surface of a material often undergoes dramatic structure evolution under a chemical environment, which, in turn, helps determine the different properties of the material. Here, we develop a general-purpose method for the automated search of optimal surface phases (ASOPs) in the grand canonical ensemble, which is facilitated by the stochastic surface walking (SSW) global optimization based on global neural network (G-NN) potential. The ASOP simulation starts by enumerating a series of composition grids, then utilizes SSW-NN to explore the configuration and composition spaces of surface phases, and relies on the Monte Carlo scheme to focus on energetically favorable compositions. The method is applied to silver surface oxide formation under the catalytic ethene epoxidation conditions. The known phases of surface oxides on Ag(111) are reproduced, and new phases on Ag(100) are revealed, which exhibit novel structure features that could be critical for understanding ethene epoxidation. Our results demonstrate that the ASOP method provides an automated and efficient way for probing complex surface structures that are beneficial for designing new functional materials under working conditions.

High Stability of Methanol to Aromatic Conversion over Bimetallic Ca,Ga-Modified ZSM-5

The production of valuable aromatics and the rapid catalyst deactivation due to coking are intimately related in the zeolite-catalyzed aromatization reactions. Here, we demonstrate that these two processes can be decoupled by promoting the Ga/HZSM-5 aromatization catalyst with Ca. The resulting bimetallic catalysts combine high selectivity to light aromatics with extended catalyst lifetime in the methanol-to-aromatics process. Evaluation of the catalytic performance combined with detailed catalyst characterization suggests that the added Ca interacts with the Ga-LAS, with a strong effect on the aromatization processes. A genetic algorithm approach complemented by ab initio thermodynamic analysis is used to elucidate the possible structures of bimetallic extraframework species formed under reaction conditions. The promotion effect of minute amounts of Ca is attributed to the stabilization of the intra-zeolite extraframework gallium oxide clusters with moderated dehydrogenation activity.

Automatic structural elucidation of vacancies in materials by active learning

The artificial intelligence method based on active learning for the automatic structural elucidation of vacancies in materials. This is implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial).

Argyrodite configuration determination for DFT and AIMD calculations using an integrated optimization strategy

When constructing a partially occupied model structure for use in density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations, the selection of appropriate configurations has been a vexing issue. Random sampling and the ensuing low-Coulomb-energy entry selection have been routine. Here, we report a more efficient way of selecting low-Coulomb-energy configurations for a representative solid electrolyte, Li₆PS₅Cl. Metaheuristics (genetic algorithm, particle swarm optimization, cuckoo search, and harmony search), Bayesian optimization, and modified deep Q-learning are utilized to search the large configurational space. Ten configuration candidates that exhibit relatively low Coulomb energy values and thereby lead to more convincing DFT and AIMD calculation results are pinpointed along with computational cost savings by the assistance of the above-described optimization algorithms, which constitute an integrated optimization strategy. Consequently, the integrated optimization strategy outperforms the conventional random sampling-based selection strategy.

When constructing a partially occupied model structure for use in density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations, the selection of appropriate configurations has been a vexing issue. We suggest a reasonable strategy to sort out this issue.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

Structural characteristics of Al2O3 ultra-thin films supported on the NiAl(100) substrate from DFTB-aided global optimization

Surfaces of aluminum alloys are often coated with ultra-thin alumina films which form by self-limited selective oxidation. Although the presence of such films is of paramount importance in various applications, their structural and stability characteristics remain far from being known. In particular, on the NiAl(100) substrate, the observed structure has been tentatively assigned to a distorted θ-alumina polymorph, but the film stoichiometry, the nature of its surface and interface terminations, as well as the mechanisms that stabilize the θ phase remain unknown. Using a combined tight-binding/DFT genetic algorithm approach, we explicitly demonstrate that ultra-thin θ(100)-type films correspond to the structural ground state of alumina supported on the (2 × 1)-NiAl(100) substrate. Thus, experimentally observed θ-alumina films correspond to thermodynamic equilibrium, rather than being the result of kinetic effects involved in the alloy oxidation and film growth. They are favoured over other Al₂O₃ phases of dehydrated boehmite, pseudo-CaIrO₃, γ, or bixbyite structures, which have recently been identified among the most stable free-standing ultra-thin alumina polymorphs. Moreover, our results prove that nonstoichiometry can be easily accommodated by the supported θ(100) film structure via an excess or deficiency of oxygen atoms at the very interface with the metal substrate. Dedicated DFT analysis reveals that the oxide-metal interaction at stoichiometric interfaces depends surprisingly little on the composition of the NiAl surface. Conversely, at oxygen-rich/poor interfaces, the number of additional/missing Al-O bonds is directly responsible for their relative stability. Finally the comparison between the experimental and theoretical electronic characteristics (STM and XPS) of supported θ(100)-type films provides clues on the detailed structure of the experimentally observed films.

Atomic Structure Optimization with Machine-Learning Enabled Interpolation between Chemical Elements

We introduce a computational method for global optimization of structure and ordering in atomic systems. The method relies on interpolation between chemical elements, which is incorporated in a machine-learning structural fingerprint. The method is based on Bayesian optimization with Gaussian processes and is applied to the global optimization of Au-Cu bulk systems, Cu-Ni surfaces with CO adsorption, and Cu-Ni clusters. The method consistently identifies low-energy structures, which are likely to be the global minima of the energy. For the investigated systems with 23-66 atoms, the number of required energy and force calculations is in the range 3-75.

Combining artificial intelligence and physics-based modeling to directly assess atomic site stabilities: from sub-nanometer clusters to extended surfaces

The performance of functional materials is dictated by chemical and structural properties of individual atomic sites. In catalysts, for example, the thermodynamic stability of constituting atomic sites is a key descriptor from which more complex properties, such as molecular adsorption energies and reaction rates, can be derived. In this study, we present a widely applicable machine learning (ML) approach to instantaneously compute the stability of individual atomic sites in structurally and electronically complex nano-materials. Conventionally, we determine such site stabilities using computationally intensive first-principles calculations. With our approach, we predict the stability of atomic sites in sub-nanometer metal clusters of 3-55 atoms with mean absolute errors in the range of 0.11-0.14 eV. To extract physical insights from the ML model, we introduce a genetic algorithm (GA) for feature selection. This algorithm distills the key structural and chemical properties governing the stability of atomic sites in size-selected nanoparticles, allowing for physical interpretability of the models and revealing structure-property relationships. The results of the GA are generally model and materials specific. In the limit of large nanoparticles, the GA identifies features consistent with physics-based models for metal-metal interactions. By combining the ML model with the physics-based model, we predict atomic site stabilities in real time for structures ranging from sub-nanometer metal clusters (3-55 atom) to larger nanoparticles (147 to 309 atoms) to extended surfaces using a physically interpretable framework. Finally, we present a proof of principle showcasing how our approach can determine stable and active nanocatalysts across a generic materials space of structure and composition.

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.

Hydrogenation of C24 Carbon Clusters: Structural Diversity and Energetic Properties

This work aims at exploring the potential energy surfaces of C24Hn=0,6,12,18,24 using the genetic algorithm in combination with the density functional based tight binding potential. The structural diversity was analyzed using order parameters, in particular the sum of the numbers of 5- and 6-carbon rings R5/6. The most abundant and lowest energy population was designated as the flake population (isomers of variable shapes, large R5/6 values), characterized by an increasing number of spherical isomers when nH/nC increases. Simultaneously, the fraction of the pretzel population (spherical isomers, smaller R5/6 values) increases. The fraction of the cage population (largest R5/6 values) remains extremely minor while the branched population (smallest R5/6 values) remains the highest energy population for all nH/nC ratios. For all C24Hn=0,6,12,18,24 clusters, the evolution of the carbon ring size distribution with energy clearly shows the correlation between the stability and the number of 6-carbon rings. The average values of the ionization potentials of all populations were found to decrease when nH/nC increases, ranging from 7.9 down to 6.4 eV. This trend was correlated to geometric and electronic factors, in particular to carbon hybridization. These results are of astrophysical interest, especially regarding the role of carbon species in the gas ionization.

Development of a Structural Comparison Method to Promote Exploration of the Potential Energy Surface in the Global Optimization of Nanoclusters

A structural comparison method (SCM) was created to quantify the structural diversity of nanoclusters and was implemented into a global optimization algorithm to evaluate structural diversity between generated clusters on the fly and promote exploration of the potential energy surface. The SCM evaluated topological differences between clusters using the common neighbor analysis and provided a numerical measure of similarity between the two clusters. The SCM was implemented into a genetic algorithm by integrating it into a new structure + energy fitness operator such that structural diversity of clusters in the population and their energies were used to assign fitness values to clusters. The efficiency of the genetic algorithm with this new fitness operator was benchmarked against several Lennard-Jones clusters (LJ₃₈, LJ₇₅, and LJ₉₈) known to be difficult cases for global optimization algorithms. For LJ₃₈ and LJ₇₅, this new structure + energy fitness operator performed equally well or better than the energy fitness operator. However, the efficiency of locating the global minimum of LJ₉₈ decreased using this new structure + energy fitness operator. Further analysis of the genetic algorithm with this fitness operator showed that the algorithm did indeed promote exploration of the PES of LJ₉₈ as desired but hindered refinement of clusters, preventing it from locating the global minimum even if the energy funnel of the global minimum had been located.

Systematic Study of the Properties of CdS Clusters with Carboxylate Ligands Using a Deep Neural Network Potential Developed with Data from Density Functional Theory Calculations

Although structures of the inorganic core of CdS atomically precise quantum dots were reported, characterizing the nature of the metal-carboxylate coordination in these materials remains a challenge due to the large number of possible isomers. The computational cost imposed by first-principles methods is prohibitive for such a configurational search, and empirical potentials are not available. In this work, we applied deep neural network algorithms to train a potential for CdS clusters with carboxylate ligands using a database of energies and gradients obtained from density functional theory calculations. The derived potential provided energies and gradients based on a set of reference structures. Our trained potential was then used to accelerate genetic algorithm and molecular dynamics simulations searches of low-energy structures, which in turn, were used to compute the X-ray diffraction and electronic absorption spectra. Our results for CdS clusters with carboxylate ligands, analyzed and compared with experimental findings, demonstrated that the structure of a cluster whose properties agree better with experiment may deviate from the one previously assumed.