A review of multiscale modeling of metal-catalyzed reactions: Mechanism development for complexity and emergent behavior

Model-Based Design of Experiments for Temporal Analysis of Products (TAP): A Simulated Case Study in Oxidative Propane Dehydrogenation

Temporal analysis of products (TAP) reactors enable experiments that probe numerous kinetic processes within a single set of experimental data through variations in pulse intensity, delay, or temperature. Selecting additional TAP experiments often involves an arbitrary selection of reaction conditions or the use of chemical intuition. To make experiment selection in TAP more robust, we explore the efficacy of model-based design of experiments (MBDoE) for precision in TAP reactor kinetic modeling. We successfully applied this approach to a case study of synthetic oxidative propane dehydrogenation (OPDH) that involves pulses of propane and oxygen. We found that experiments identified as optimal through the MBDoE for precision generally reduce parameter uncertainties to a higher degree than alternative experiments. The performance of MBDoE for model divergence was also explored for OPDH, with the relevant active sites (catalyst structure) being unknown. An experiment that maximized the divergence between the three proposed mechanisms was identified and provided evidence that improved the mechanism discrimination. However, reoptimization of kinetic parameters eliminated the ability to discriminate between models. The findings yield insight into the prospects and limitations of MBDoE for TAP and transient kinetic experiments.

Reference-Quality Free Energy Barriers in Catalysis from Machine Learning Thermodynamic Perturbation Theory

For the first time, we report calculations of the free energies of activation of cracking and isomerization reactions of alkenes that combine several different electronic structure methods with molecular dynamics simulations. We demonstrate that the use of a high level of theory (here Random Phase Approximation-RPA) is necessary to bridge the gap between experimental and computed values. These transformations, catalyzed by zeolites and proceeding via cationic intermediates and transition states, are building blocks of many chemical transformations for valorization of long chain paraffins originating, e.g., from plastic waste, vegetable oils, Fischer-Tropsch waxes or crude oils. Compared with the free energy barriers computed at the PBE+D2 production level of theory via constrained ab initio molecular dynamics, the barriers computed at the RPA level by the application of Machine Learning thermodynamic Perturbation Theory (MLPT) show a significant decrease for isomerization reaction and an increase of a similar magnitude for cracking, yielding an unprecedented agreement with the results obtained by experiments and kinetic modeling.

Automated MUltiscale simulation environment

Multiscale techniques integrating detailed atomistic information on materials and reactions to predict the performance of heterogeneous catalytic full-scale reactors have been suggested but lack seamless implementation. The largest challenges in the multiscale modeling of reactors can be grouped into two main categories: catalytic complexity and the difference between time and length scales of chemical and transport phenomena. Here we introduce the Automated MUltiscale Simulation Environment AMUSE, a workflow that starts from Density Functional Theory (DFT) data, automates the analysis of the reaction networks through graph theory, prepares it for microkinetic modeling, and subsequently integrates the results into a standard open-source Computational Fluid Dynamics (CFD) code. We demonstrate the capabilities of AMUSE by applying it to the unimolecular iso-propanol dehydrogenation reaction and then, increasing the complexity, to the pre-commercial Pd/In2O3 catalyst employed for the CO2 hydrogenation to methanol. The results show that AMUSE allows the computational investigation of heterogeneous catalytic reactions in a comprehensive way, providing essential information for catalyst design from the atomistic to the reactor scale level.

Theoretical insights into the catalytic mechanism of propylene hydroformylation over Co-N-C materials

M-N-C was recently reported to be a high activity catalyst for hydroformylation compared with a metal nanocluster. However, the nature of M-N-C sites and the dominant path of propylene hydroformylation on M-N-C sites with different structures are poorly understood. In this work, five different Co-N-C models (Co-N3-C, Co-N4-C, 0N-bridged Co2-N6-C, 1N-bridged Co2-N7-C and 2N-bridged Co2-N6-C) were constructed to simulate the Co active sites with different coordination that may exist on the surface of MOF-derived Co-based carbon materials. DFT combined with kinetic Monte Carlo (kMC) methods were used to study the catalytic performance for hydroformylation of different Co-N-C models. The results of the DFT calculations show that the coordination number and mode of N atoms could regulate the electronic density of the Co sites. The electronic density of the Co sites further affects the catalytic activity. The higher the electronic density is, the lower the energy barrier for partial hydrogenation of propylene and CO insertion reactions. Besides, the catalytic activity is also affected by the strong interaction in closer neighboring Co atoms in some Co2-Nx-C models. The strong interaction affects the adsorption state and energy of species, which also reduces the overall reaction energy barrier. The kMC simulation results further showed that the dominant path of propylene hydroformylation was the n-butylaldehyde path for the 0N-bridged model, and the isobutylaldehyde path for Co-N3-C and 2N-bridged models.

Iterative multiscale and multi-physics computations for operando catalyst nanostructure elucidation and kinetic modeling

Modern heterogeneous catalysis has benefitted immensely from computational predictions of catalyst structure and its evolution under reaction conditions, first-principles mechanistic investigations, and detailed kinetic modeling, which are rungs on a multiscale workflow. Establishing connections across these rungs and integration with experiments have been challenging. Here, operando catalyst structure prediction techniques using density functional theory simulations and ab initio thermodynamics calculations, molecular dynamics, and machine learning techniques are presented. Surface structure characterization by computational spectroscopic and machine learning techniques is then discussed. Hierarchical approaches in kinetic parameter estimation involving semi-empirical, data-driven, and first-principles calculations and detailed kinetic modeling via mean-field microkinetic modeling and kinetic Monte Carlo simulations are discussed along with methods and the need for uncertainty quantification. With these as the background, this article proposes a bottom-up hierarchical and closed loop modeling framework incorporating consistency checks and iterative refinements at each level and across levels.

Nanostructured Materials for Photothermal Carbon Dioxide Hydrogenation: Regulating Solar Utilization and Catalytic Performance

Converting carbon dioxide (CO₂) into value-added fuels or chemicals through photothermal catalytic CO₂ hydrogenation is a promising approach to alleviate the energy shortage and global warming. Understanding the nanostructured material strategies in the photothermal catalytic CO₂ hydrogenation process is vital for designing photothermal devices and catalysts and maximizing the photothermal CO₂ hydrogenation performance. In this Perspective, we first describe several essential nanomaterial design concepts to enhance sunlight absorption and utilization in photothermal CO₂ hydrogenation. Subsequently, we review the latest progress in photothermal CO₂ hydrogenation into C₁ (e.g., CO, CH₄, and CH₃OH) and multicarbon hydrocarbon (C₂₊) products. Finally, the relevant challenges and opportunities in this exciting research realm are discussed. This perspective provides a comprehensive understanding for the light-heat synergy over nanomaterials and instruction for rational photothermal catalyst design for CO₂ utilization.

A probabilistic microkinetic modeling framework for catalytic surface reactions

We present a probabilistic microkinetic modeling (MKM) framework that incorporates the short-ranged order (SRO) evolution for adsorbed species (adspecies) on a catalyst surface. The resulting model consists of a system of ordinary differential equations. Adsorbate-adsorbate interactions, surface diffusion, adsorption, desorption, and catalytic reaction processes are included. Assuming that the adspecies ordering/arrangement is accurately described by the SRO parameters, we employ the reverse Monte Carlo (RMC) method to extract the relevant local environment probability distributions and pass them to the MKM. The reaction kinetics is faithfully captured as accurately as the kinetic Monte Carlo (KMC) method but with a computational time requirement of few seconds on a standard desktop computer. KMC, on the other hand, can require several days for the examples discussed. The framework presented here is expected to provide the basis for wider application of the RMC-MKM approach to problems in computational catalysis, electrocatalysis, and material science.

3D-printed heterogeneous Cu2O monoliths: Reusable supports for Antibiotic Treatmentantibiotic treatment of wastewater

In this study, surfactant stabilized dispersions of the Cu₂O microparticles in a commercially available photocurable resin were 3D printed into both porous and non-porous monoliths, and the heterogeneous Cu₂O catalytic monolith with improved mass transfer characteristics was applied for antibiotic wastewater treatment. The physicochemical properties of catalytic monoliths were characterized by scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy and thermogravimetric. Ten intermediates were analyzed and identified by GC-MS, and the corresponding degradation pathways were proposed. Both numerical simulation and degradation experiments were used to explore the mass transfer mechanism and catalytic performance of the monoliths. The results showed that the 3D-printed monolith with a well-defined porous network exhibited a high ofloxacin degradation efficiency (100%) based on the sulfate radical-based advanced oxidation processes. In addition, the catalytic monolith showed sustained high activity over 7 reusable cycles demonstrating its feasibility in removal of antibiotics from wastewater.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

Despite the success of multiscale modeling in science and engineering, embedding molecular-level information into nonlinear reactor design and control optimization problems remains challenging. In this work, we propose a computationally tractable scale-bridging approach that incorporates information from multi-product microkinetic (MK) models with thousands of rates and chemical species into nonlinear reactor design optimization problems. We demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. We assemble a library of six candidate ROK models based on literature and MK model structure. We find that three metrics—quality of fit (e.g., mean squared logarithmic error), thermodynamic consistency (e.g., low conversion of exothermic reactions at high temperatures), and model identifiability—are all necessary to train and select ROK models. The ROK models that closely mimic the structure of the MK model offer the best compromise to emulate the product distribution. Using the four best ROK models, we optimize the temperature profiles in staged reactors to maximize conversions to heavier oligomerization products. The optimal temperature starts at 630–900K and monotonically decreases to approximately 560 K in the final stage, depending on the choice of ROK model. For all models, staging increases heavier olefin production by 2.5% and there is minimal benefit to more than four stages. The choice of ROK model, i.e., model-form uncertainty, results in a 22% difference in the objective function, which is twice the impact of parametric uncertainty; we demonstrate sequential eigendecomposition of the Fisher information matrix to identify and fix sloppy model parameters, which allows for more reliable estimation of the covariance of the identifiable calibrated model parameters. First-order uncertainty propagation determines this parametric uncertainty induces less than a 10% variability in the reactor optimization objective function. This result highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multi-scale reactor and process design and optimization. Moreover, the fast dynamic optimization solution times suggest the ROK strategy is suitable for incorporating molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.

Challenges of modeling nanostructured materials for photocatalytic water splitting

Understanding the water splitting mechanism in photocatalysis is a rewarding goal as it will allow producing clean fuel for a sustainable life in the future. However, identifying the photocatalytic mechanisms by modeling photoactive nanoparticles requires sophisticated computational techniques based on multiscale modeling. In this review, we will survey the strengths and drawbacks of currently available theoretical methods at different length and accuracy scales. Understanding the surface-active site through Density Functional Theory (DFT) using new, more accurate exchange-correlation functionals plays a key role for surface engineering. Larger scale dynamics of the catalyst/electrolyte interface can be treated with Molecular Dynamics albeit there is a need for more generalizations of force fields. Monte Carlo and Continuum Modeling techniques are so far not the prominent path for modeling water splitting but interest is growing due to the lower computational cost and the feasibility to compare the modeling outcome directly to experimental data. The future challenges in modeling complex nano-photocatalysts involve combining different methods in a hierarchical way so that resources are spent wisely at each length scale, as well as accounting for excited states chemistry that is important for photocatalysis, a path that will bring devices closer to the theoretical limit of photocatalytic efficiency.

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

Catalytic resonance of ammonia synthesis by simulated dynamic ruthenium crystal strain

Ammonia affords dense storage for renewable energy as a fungible liquid fuel, provided it can be efficiently synthesized from hydrogen and nitrogen. In this work, the catalysis of ammonia synthesis was computationally explored beyond the Sabatier limit by dynamically straining a ruthenium crystal (±4%) at the resonant frequencies (10² to 10⁵⁺ Hz) of N₂ surface dissociation and hydrogenation. Density functional theory calculations at different strain conditions indicated that the energies of NH_x surface intermediates and transition states scale linearly, allowing the description of ammonia synthesis at a continuum of strain conditions. A microkinetic model including multiple sites and surface diffusion between step and Ru(0001) terrace sites of varying ratios for nanoparticles of differing size revealed that dynamic strain yields catalytic ammonia synthesis conversion and turnover frequency comparable to industrial reactors (400°C, 200 atm) but at lower temperature (320°C) and an order of magnitude lower pressure (20 atm).

Enhanced descriptor identification and mechanism understanding for catalytic activity using a data-driven framework: revealing the importance of interactions between elementary steps

A data-driven framework was developed which used ML surrogate model to extract activity controlling descriptors from kinetics dataset. It enhanced mechanic understanding and predicted catalytic activities more accurately than derivate-based method.

Effect of Potassium for Propylene Epoxidation on Cu2O(111) by Molecular Oxygen: A DFT Study

In the present work, spin-polarized density functional theory (DFT) calculations with a Hubbard U correction were employed to investigate the effect of potassium for propylene epoxidation on Cu2O(111) surface by...

Structure-Reactivity Relationship for Nano-Catalysts in the Hydrogenation/Dehydrogenation Controlled Reaction Systems

For the activity of a nano-catalyst, a general and quantitative solution to building direct structure-reactivity relationship has not yet been established. On top of the first-principle-based kinetic Monte Carlo (KMC) simulations, we developed a model to build the adsorption site dependence of the activity. We applied this model to study the nano effects of Cu catalysts in the water-gas shift reaction. By accumulating the activities of different adsorption sites, our model satisfactorily reproduced the experimental apparent activation energies for catalysts with sizes over hundreds of nanometers, which were out of reach for conventional KMC simulations. Our results disclose that, even for a cubic catalyst with size of 877 nm, its activity can still be closely related to the activity of edge sites, instead of only the exposed Cu(100) facets as might be expected. The present model is expected to be useful for systems that are controlled by the hydrogenation/dehydrogenation processes.

Quantifying the Impact of Parametric Uncertainty on Automatic Mechanism Generation for CO2 Hydrogenation on Ni(111)

Automatic mechanism generation is used to determine mechanisms for the CO2 hydrogenation on Ni(111) in a two-stage process while considering the correlated uncertainty in DFT-based energetic parameters systematically. In a coarse stage, all the possible chemistry is explored with gas-phase products down to the ppb level, while a refined stage discovers the core methanation submechanism. Five thousand unique mechanisms were generated, which contain minor perturbations in all parameters. Global uncertainty assessment, global sensitivity analysis, and degree of rate control analysis are performed to study the effect of this parametric uncertainty on the microkinetic model predictions. Comparison of the model predictions with experimental data on a Ni/SiO2 catalyst find a feasible set of microkinetic mechanisms within the correlated uncertainty space that are in quantitative agreement with the measured data, without relying on explicit parameter optimization. Global uncertainty and sensitivity analyses provide tools to determine the pathways and key factors that control the methanation activity within the parameter space. Together, these methods reveal that the degree of rate control approach can be misleading if parametric uncertainty is not considered. The procedure of considering uncertainties in the automated mechanism generation is not unique to CO2 methanation and can be easily extended to other challenging heterogeneously catalyzed reactions.

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.

Learning Chemistry of Complex Reaction Systems via a Python First-Principles Reaction Rule Stencil (pReSt) Generator

Complex reaction networks can be generated with automated network generators from initial reactants and reaction rules. Reaction rule specification is central to network generation. These reaction rules are, at present, user-defined based on (intuitive) expert knowledge of chemistry and are often transferred from gas-phase to surface processes. The catalyst active site geometry is usually left out but is often responsible for selectivity. We propose a first-principles-based reaction mechanism generation framework using density functional theory (DFT) data of published reaction mechanisms. The framework "learns the chemistry" from published mechanisms. It can generate reaction networks not studied before, "flag" reactions not seen before for further DFT convergence tests, and easily reconcile differences between catalysts and reactants that may introduce new pathways never seen before. As such, it can be a diagnostic tool for data (mechanism) quality assessment and novel pathway discovery to new molecules. A software, the Python Reaction Stencil (pReSt), was developed for this purpose to wrap around automatic mechanism generation software. Multiple catalytic chemistries are considered to show the efficacy of the proposed framework.

The role of oxygenated species in the catalytic self-coupling of MeOH on O pre-covered Au(111)

The oxidation of alcohols plays a central role in the valorisation of biomass, in particular when performed with a non-toxic oxidant such as O₂. Aerobic oxidation of methanol on gold has attracted attention lately and the main steps of its mechanism have been described experimentally. However, the exact role of O and OH on each elementary step and the effect of the interactions between adsorbates are still not completely understood. Here we investigate the mechanism of methanol oxidation to HCOOCH₃ and CO₂. We use Density Functional Theory (DFT) to assess the energetics of the underlying pathways, and subsequently build lattice kinetic Monte Carlo (kMC) models of increasing complexity, to elucidate the role of different oxygenates. Detailed comparisons of our simulation results with experimental temperature programmed desorption (TPD) spectra enable us to validate the mechanism and identify rate determining steps. Crucially, taking into account dispersion (van der Waals forces) and adsorbate-adsorbate lateral interactions are both important for reproducing the experimental data.

Enabling Circular Economy: The Overlooked Role of Inorganic Materials Chemistry

Circular economy is considered a new chance to build a more sustainable world from both the social and the economic point of view. In this Essay, the possible contribution of inorganic chemistry towards a smooth transition to circularity in inorganic materials design and production is discussed by adopting an interdisciplinary approach.

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

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

The first-principles-based microkinetic simulation of the dry reforming of methane over Ru(0001)

As the temperature was increased, the generation rate of H₂ and CO in the DRM reaction on Ru(0001) gradually increased along with the ratio of H₂/CO generation rate.

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.