Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Surface phase diagrams from nested sampling

Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows for modeling phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. This work extends NS to calculate adsorbate phase diagrams, incorporating all relevant configurational contributions to the free energy. We apply NS to the adsorption of Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and construct the canonical partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and order parameters that characterize the structure of adsorbate phases. Key results include determining the nature of phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the effect of surface geometry on the presence of triple points in the phase diagrams. Overall, we demonstrate the ability and potential of NS for surface modeling.

A Data and DFT-Driven Framework for Predicting the Microstructure of Submonolayer Inverse Metal Oxide on Metal Catalysts

Metal oxides on metal (inverse) catalysts can selectively drive many important reactions. However, understanding the active site under experimentally relevant conditions is lacking. Herein, we introduce a computational framework for predicting atomic models of stable inverse catalysts and demonstrate it for WOx on Pt(553) and a Pt79 nanoparticle at variable WOx coverages. An evolutionary algorithm identifies a small (5%) subset of promising atomic configurations on which DFT simulations are performed. We predict a maximum coverage of ∼50% WOx on Pt(553), consisting of small clusters (tetramers and pentamers), which preferentially reside on the terrace, with their oxygen atoms interacting with the Pt step sites. Consistently, WOx does not lie on curved and undercoordinated metal sites of Pt nanoparticles. The oxide clusters prefer a partially reduced oxidation state. Theoretical EXAFS spectra for select configurations provide insights into interpreting experimental spectra of inverse catalysts. The framework applies to other catalysts.

Size-Dependent Dispersion of Rhodium Clusters into Isolated Single Atoms at Low Temperature and the Consequences for CO Oxidation Activity

Understanding the dynamic structural evolution of supported metal clusters under reaction conditions is crucial to develop structure reactivity relations. Here, we followed the structure of different size Rh clusters supported on Al2 O3 using in situ/operando spectroscopy and ex situ aberration-corrected electron microscopy. We report a dynamic evolution of rhodium clusters into thermally stable isolated single atoms upon exposure to oxygen and during CO oxidation. Rh clusters partially disperse into single atoms at room temperature and the extent of dispersion increases as the Rh size decreases and as the reaction temperature increases. A strong correlation is found between the extent of dispersion and the CO oxidation kinetics. More importantly, dispersing Rh clusters into single atoms increases the activity at room temperature by more than two orders of magnitude due to the much lower activation energy on single atoms (40 vs. 130 kJ/mol). This work demonstrates that the structure and reactivity of small Rh clusters are very sensitive to the reaction environment.

Machine Learning Design of Single-Atom Catalysts for Nitrogen Fixation

First-principles calculations have been combined with machine learning in the design of transition-metal single-atom catalysts. Readily available descriptors are selected to describe the nitrogen activation capability of metals and coordinating atoms. Thus, a series of V/Nb/Ta-Nx single-atom catalysts are screened out as promising structures upon considering the stability, activity, and selectivity investigated computationally. Furthermore, by using the gradient boosting regression algorithm, an accurate prediction of the hydrogenation barriers for the nitrogen reduction reaction (NRR) is achievable, with a root-mean-squared error of 0.07 eV. The integration of high-throughput computation and machine learning constitutes a powerful strategy for the acceleration of catalyst design. This approach facilitates the rapid and accurate prediction of the NRR performance of more than 1000 single-atom catalyst structures. Moreover, the current work provides further insights by elaborately correlating the structure and performance, which may be instructive for both the design and application of vanadium-group catalysts.

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.

Density functional theory based computational investigations on the stability of highly active trimetallic PtPdCu nanoalloys for electrochemical oxygen reduction

Activity, cost, and durability are the trinity of catalysis research for the electrochemical oxygen reduction reaction (ORR). While studies towards increasing activity and reducing cost of ORR catalysts have been carried out extensively, much effort is needed in durability investigation of highly active ORR catalysts. In this work, we examined the stability of a trimetallic PtPdCu catalyst that has demonstrated high activity and incredible durability during ORR using density functional theory (DFT) based computations. Specifically, we studied the processes of dissolution/deposition and diffusion between the surface and inner layer of Cu species of Pt₂₀Pd₂₀Cu₆₀ catalysts at electrode potentials up to 1.2 V to understand their role towards stabilizing Pt₂₀Pd₂₀Cu₆₀ catalysts. The results show there is a dynamic Cu surface composition range that is dictated by the interplay of the four processes, dissolution, deposition, diffusion from the surface to inner layer, and diffusion from the inner layer to the surface of Cu species, in the stability and observed oscillation of lattice constants of Cu-rich PtPdCu nanoalloys.

Boosting Benzene Oxidation with a Spin-State-Controlled Nuclearity Effect on Iron Sub-Nanocatalysts

A fundamental understanding of the nature of nuclearity effects is important for the rational design of superior sub-nanocatalysts with low nuclearity, but remains a long-standing challenge. Using atomic layer deposition, we precisely synthesized Fe sub-nanocatalysts with tunable nuclearity (Fe₁ -Fe₄ ) anchored on N,O-co-doped carbon nanorods (NOC). The electronic properties and spin configuration of the Fe sub-nanocatalysts were nuclearity dependent and dominated the H₂ O₂ activation modes and adsorption strength of active O species on Fe sites toward C-H oxidation. The Fe₁ -NOC single atom catalyst exhibits state-of-the-art activity for benzene oxidation to phenol, which is ascribed to its unique coordination environment (Fe₁ N₂ O₃ ) and medium spin state (t_2g ⁴ e_g ¹ ); turnover frequencies of 407 h^-1 at 25 °C and 1869 h^-1 at 60 °C were obtained, which is 3.4, 5.7, and 13.6 times higher than those of Fe dimer, trimer, and tetramer catalysts, respectively.

Exploring Structure-Sensitive Relations for Small Species Adsorption Using Machine Learning

Accurate prediction of adsorption energies on heterogeneous catalyst surfaces is crucial to predicting reactivity and screening materials. Adsorption linear scaling relations have been developed extensively but often lack accuracy and apply to one adsorbate and a single binding site type at a time. These facts undermine their ability to predict structure sensitivity and optimal catalyst structure. Using machine learning on nearly 300 density functional theory calculations, we demonstrate that generalized coordination number scaling relations hold well for oxygen- and high-valency carbon-binding species but fail for others. We reveal that the valency and the electronic coupling of a species with the surface, along with the site type and its coordination environment, are critical for small species adsorption. The model simultaneously predicts the adsorption energy and preferred site and significantly outperforms linear scalings in accuracy. It can expose the structure sensitivity of chemical reactions and enable enhanced catalyst activity via engineering particle shape and facet defects. The generality of our methodology is validated by training the model with transition metal data and transferring it to predict adsorption energies on single-atom alloys.

Psychological Stress Identification and Evaluation Method Based on Mobile Human-Computer Interaction Equipment

Since the 1980s, the research of artificial neural networks in the field of artificial intelligence has become more and more common. It accepts nonlinear parallel processing, has strong learning and flexibility, and can be used for influencing factor analysis. The ideal power values and triggers are obtained in the Hopfield network model using genetic algorithm, which best avoids the drawbacks of the Hopfield network model instillation learning method. Through the BP of mobile human-computer interaction equipment, hereditary, genetic algorithms, and Hi-PLS regression method in the artificial neural network, the psychological pressure of college students is identified, evaluated, and predicted from three dimensions such as learning, life, and personal events. This makes it possible to understand the current physical and mental conditions of the students in a timely manner, guide to relieve anxiety and fear, and reach a safe psychological level. The three test results are less than 1%, which has high research significance and value.

Pd Clusters on Schiff Base–Imidazole-Functionalized MOFs for Highly Efficient Catalytic Suzuki Coupling Reactions

Subnanometer noble metal clusters have attracted much attention because of abundant low-coordinated metal atoms that perform excellent catalytic activity in various catalytic processes. However, the surface free energy of metals increases significantly with decreasing size of the metal clusters, which accelerates the aggregation of small clusters. In this work, new Schiff base–imidazole-functionalized MOFs were successfully synthesized via the postsynthetic modification method. Highly dispersed Pd clusters with an average size of 1.5 nm were constructed on this functional MOFs and behaved excellent catalytic activity in the Suzuki coupling of phenyboronic acid and bromobenzene (yield of biaryl >99%) under mild reaction conditions. Moreover, the catalyst can be reused six times without loss of activity. Such catalytic behavior is found to closely related to the surface functional groups that promote the formation of small Pd⁰ clusters in the metallic state.

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.

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. We introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated and human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub.

Real-time dynamics and structures of supported subnanometer catalysts via multiscale simulations

Understanding the performance of subnanometer catalysts and how catalyst treatment and exposure to spectroscopic probe molecules change the structure requires accurate structure determination under working conditions. Experiments lack simultaneous temporal and spatial resolution and could alter the structure, and similar challenges hinder first-principles calculations from answering these questions. Here, we introduce a multiscale modeling framework to follow the evolution of subnanometer clusters at experimentally relevant time scales. We demonstrate its feasibility on Pd adsorbed on CeO2(111) at various catalyst loadings, temperatures, and exposures to CO. We show that sintering occurs in seconds even at room temperature and is mainly driven by free energy reduction. It leads to a kinetically (far from equilibrium) frozen ensemble of quasi-two-dimensional structures that CO chemisorption and infrared experiments probe. CO adsorption makes structures flatter and smaller. High temperatures drive very rapid sintering toward larger, stable/metastable equilibrium structures, where CO induces secondary structure changes only.