Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling

Modeling Heterogeneous Catalysis Using Quantum Computers: An Academic and Industry Perspective

Heterogeneous catalysis plays a critical role in many industrial processes, including the production of fuels, chemicals, and pharmaceuticals, and research to improve current catalytic processes is important to make the chemical industry more sustainable. Despite its importance, the challenge of identifying optimal catalysts with the required activity and selectivity persists, demanding a detailed understanding of the complex interactions between catalysts and reactants at various length and time scales. Density functional theory (DFT) has been the workhorse in modeling heterogeneous catalysis for more than three decades. While DFT has been instrumental, this review explores the application of quantum computing algorithms in modeling heterogeneous catalysis, which could bring a paradigm shift in our approach to understanding catalytic interfaces. Bridging academic and industrial perspectives by focusing on emerging materials, such as multicomponent alloys, single-atom catalysts, and magnetic catalysts, we delve into the limitations of DFT in capturing strong correlation effects and spin-related phenomena. The review also presents important algorithms and their applications relevant to heterogeneous catalysis modeling to showcase advancements in the field. Additionally, the review explores embedding strategies where quantum computing algorithms handle strongly correlated regions, while traditional quantum chemistry algorithms address the remainder, thereby offering a promising approach for large-scale heterogeneous catalysis modeling. Looking forward, ongoing investments by academia and industry reflect a growing enthusiasm for quantum computing's potential in heterogeneous catalysis research. The review concludes by envisioning a future where quantum computing algorithms seamlessly integrate into research workflows, propelling us into a new era of computational chemistry and thereby reshaping the landscape of modeling heterogeneous catalysis.

Unifying thermochemistry concepts in computational heterogeneous catalysis

Thermophysical properties of adsorbates and gas-phase species define the free energy landscape of heterogeneously catalyzed processes and are pivotal for an atomistic understanding of the catalyst performance. These thermophysical properties, such as the free energy or the enthalpy, are typically derived from density functional theory (DFT) calculations. Enthalpies are species-interdependent properties that are only meaningful when referenced to other species. The widespread use of DFT has led to a proliferation of new energetic data in the literature and databases. However, there is a lack of consistency in how DFT data is referenced and how the associated enthalpies or free energies are stored and reported, leading to challenges in reproducing or utilizing the results of prior work. Additionally, DFT suffers from exchange-correlation errors that often require corrections to align the data with other global thermochemical networks, which are not always clearly documented or explained. In this review, we introduce a set of consistent terminology and definitions, review existing approaches, and unify the techniques using the framework of linear algebra. This set of terminology and tools facilitates the correction and alignment of energies between different data formats and sources, promoting the sharing and reuse of ab initio data. Standardization of thermochemistry concepts in computational heterogeneous catalysis reduces computational cost and enhances fundamental understanding of catalytic processes, which will accelerate the computational design of optimally performing catalysts.

Uncertainty Quantification of Linear Scaling, Machine Learning, and Density Functional Theory Derived Thermodynamics for the Catalytic Partial Oxidation of Methane on Rhodium

Accurate and complete microkinetic models (MKMs) are powerful for anticipating the behavior of complex chemical systems at different operating conditions. In heterogeneous catalysis, they can be further used for the rapid development and screening of new catalysts. Density functional theory (DFT) is often used to calculate the parameters used in MKMs with relatively high fidelity. However, given the high cost of DFT calculations for adsorbates in heterogeneous catalysis, linear scaling relations (LSRs) and machine learning (ML) models were developed to give rapid estimates of the parameters in MKM. Regardless of the method, few studies have attempted to quantify the uncertainty in catalytic MKMs, as the uncertainties are often orders of magnitude larger than those for gas phase models. This study explores uncertainty quantification and Bayesian Parameter Estimation for thermodynamic parameters calculated by DFT, LSRs, and GemNet-OC, a ML model developed under the Open Catalyst Project. A model for catalytic partial oxidation of methane (CPOX) on Rhodium was chosen as a case study, in which the model's thermodynamic parameters and their associated uncertainties were determined using DFT, LSR, and GemNet-OC. Markov Chain Monte Carlo coupled with Ensemble Slice Sampling was used to sample the highest probability density (HPD) region of the posterior and determine the maximum of the a posteriori (MAP) for each thermodynamic parameter included. The optimized microkinetic models for each of the three estimation methods had quite similar mechanisms and agreed well with the experimental data for gas phase mole fractions. Exploration of the HPD region of the posterior further revealed that adsorbed hydroxide and oxygen likely bind on facets other than Rhodium 111. The demonstrated workflow addresses the issue of inaccuracies arising from the integration of data from multiple sources by considering both experimental and computational uncertainties, and further reveals information about the active site that would not have been discovered without considering the posterior.

The Importance of Reaction Energy in Predicting Chemical Reaction Barriers with Machine Learning Models

Improving our fundamental understanding of complex heterocatalytic processes increasingly relies on electronic structure simulations and microkinetic models based on calculated energy differences. In particular, calculation of activation barriers, usually achieved through compute-intensive saddle point search routines, remains a serious bottleneck in understanding trends in catalytic activity for highly branched reaction networks. Although the well-known Brønsted-Evans-Polyani (BEP) scaling - a one-feature linear regression model - has been widely applied in such microkinetic models, they still rely on calculated reaction energies and may not generalize beyond a single facet on a single class of materials, e. g., a terrace sites on transition metals. For highly branched and energetically shallow reaction networks, such as electrochemical CO2 reduction or wastewater remediation, calculating even reaction energies on many surfaces can become computationally intractable due to the combinatorial explosion of states that must be considered. Here, we investigate the feasibility of activation barrier prediction without knowledge of the reaction energy using linear and nonlinear machine learning (ML) models trained on a new database of over 500 dehydrogenation activation barriers. We also find that inclusion of the reaction energy significantly improves both classes of ML models, but complex nonlinear models can achieve performance similar to the simplest BEP scaling when predicting activation barriers on new systems. Additionally, inclusion of the reaction energy significantly improves generalizability to new systems beyond the training set. Our results suggest that the reaction energy is a critical feature to consider when building models to predict activation barriers, indicating that efforts to reliably predict reaction energies through, e. g., the Open Catalyst Project and others, will be an important route to effective model development for more complex systems.

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.

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties

The study presents an ab-initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF-vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first-principles-based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange-correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT-constrained microkinetic model optimization for other heterogeneously catalyzed systems.

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.

Linking Experimental and Ab Initio Thermochemistry of Adsorbates with a Generalized Thermochemical Hierarchy

Enthalpies of formation of adsorbates are crucial parameters in the microkinetic modeling of heterogeneously catalyzed reactions since they quantify the stability of intermediates on the catalyst surface. This quantity is often computed using density functional theory (DFT), as more accurate methods are computationally still too expensive, which means that the derived enthalpies have a large uncertainty. In this study, we propose a new error cancellation method to compute the enthalpies of formation of adsorbates from DFT more accurately through a generalized connectivity-based hierarchy. The enthalpy of formation is determined through a hypothetical reaction that preserves atomistic and bonding environments. The method is applied to a data set of 60 adsorbates on Pt(111) with up to 4 heavy (non-hydrogen) atoms. Enthalpies of formation of the fragments required for the bond balancing reactions are based on experimental heats of adsorption for Pt(111). The comparison of enthalpies of formation derived from different DFT functionals using the isodesmic reactions shows that the effect of the functional is significantly reduced due to the error cancellation. Thus, the proposed methodology creates an interconnected thermochemical network of adsorbates that combines experimental with ab initio thermochemistry in a single and more accurate thermophysical database.

A Review on the Different Aspects and Challenges of the Dry Reforming of Methane (DRM) Reaction

The dry reforming of methane (DRM) reaction is among the most popular catalytic reactions for the production of syngas (H2/CO) with a H2:CO ratio favorable for the Fischer-Tropsch reaction; this makes the DRM reaction important from an industrial perspective, as unlimited possibilities for production of valuable products are presented by the FT process. At the same time, simultaneously tackling two major contributors to the greenhouse effect (CH4 and CO2) is an additional contribution of the DRM reaction. The main players in the DRM arena-Ni-supported catalysts-suffer from both coking and sintering, while the activation of the two reactants (CO2 and CH4) through different approaches merits further exploration, opening new pathways for innovation. In this review, different families of materials are explored and discussed, ranging from metal-supported catalysts, to layered materials, to organic frameworks. DRM catalyst design criteria-such as support basicity and surface area, bimetallic active sites and promoters, and metal-support interaction-are all discussed. To evaluate the reactivity of the surface and understand the energetics of the process, density-functional theory calculations are used as a unique tool.

Quantum effects in thermal reaction rates at metal surfaces

There is wide interest in developing accurate theories for predicting rates of chemical reactions that occur at metal surfaces, especially for applications in industrial catalysis. Conventional methods contain many approximations that lack experimental validation. In practice, there are few reactions where sufficiently accurate experimental data exist to even allow meaningful comparisons to theory. Here, we present experimentally derived thermal rate constants for hydrogen atom recombination on platinum single-crystal surfaces, which are accurate enough to test established theoretical approximations. A quantum rate model is also presented, making possible a direct evaluation of the accuracy of commonly used approximations to adsorbate entropy. We find that neglecting the wave nature of adsorbed hydrogen atoms and their electronic spin degeneracy leads to a 10× to 1000× overestimation of the rate constant for temperatures relevant to heterogeneous catalysis. These quantum effects are also found to be important for nanoparticle catalysts.

Predicting binding motifs of complex adsorbates using machine learning with a physics-inspired graph representation

Computational screening in heterogeneous catalysis relies increasingly on machine learning models for predicting key input parameters due to the high cost of computing these directly using first-principles methods. This becomes especially relevant when considering complex materials spaces such as alloys, or complex reaction mechanisms with adsorbates that may exhibit bi- or higher-dentate adsorption motifs. Here we present a data-efficient approach to the prediction of binding motifs and associated adsorption enthalpies of complex adsorbates at transition metals and their alloys based on a customized Wasserstein Weisfeiler-Lehman graph kernel and Gaussian process regression. The model shows good predictive performance, not only for the elemental transition metals on which it was trained, but also for an alloy based on these transition metals. Furthermore, incorporation of minimal new training data allows for predicting an out-of-domain transition metal. We believe the model may be useful in active learning approaches, for which we present an ensemble uncertainty estimation approach.

Automated exploitation of the big configuration space of large adsorbates on transition metals reveals chemistry feasibility

Mechanistic understanding of large molecule conversion and the discovery of suitable heterogeneous catalysts have been lagging due to the combinatorial inventory of intermediates and the inability of humans to enumerate all structures. Here, we introduce an automated framework to predict stable configurations on transition metal surfaces and demonstrate its validity for adsorbates with up to 6 carbon and oxygen atoms on 11 metals, enabling the exploration of ~10⁸ potential configurations. It combines a graph enumeration platform, force field, multi-fidelity DFT calculations, and first-principles trained machine learning. Clusters in the data reveal groups of catalysts stabilizing different structures and expose selective catalysts for showcase transformations, such as the ethylene epoxidation on Ag and Cu and the lack of C-C scission chemistry on Au. Deviations from the commonly assumed atom valency rule of small adsorbates are also manifested. This library can be leveraged to identify catalysts for converting large molecules computationally.

The discovery of heterogeneous catalysts for large molecule conversion has been lagging due to the combinatorial inventory of intermediates. Here, the author presents an automated framework to explore the chemical space of reaction intermediates.

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.

Multiscale kinetic analysis of proteins

The stochasticity of molecular motion results in the existence of multiple kinetically relevant pathways in many biomolecular mechanisms. Because it is highly demanding to characterize them for complex systems, mechanisms are often described with a single-pathway perspective. However, kinetic network analysis and sub-ensemble experimental insight are increasingly demonstrating not only the existence of competing pathways but also the importance of kinetic selection in biology. This review focuses on advances in multiscale kinetic analysis of proteins, which connects molecular level information from simulations to macroscopic data to characterize mechanistic reaction networks and the reactive flux through them. We describe a range of methods used and highlight several examples where kinetic modeling has revealed functional importance of pathway heterogeneity.

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

Autonomous computations that rely on automated reaction network elucidation algorithms may pave the way to make computational catalysis on a par with experimental research in the field. Several advantages of this approach are key to catalysis: (i) automation allows one to consider orders of magnitude more structures in a systematic and open-ended fashion than what would be accessible by manual inspection. Eventually, full resolution in terms of structural varieties and conformations as well as with respect to the type and number of potentially important elementary reaction steps (including decomposition reactions that determine turnover numbers) may be achieved. (ii) Fast electronic structure methods with uncertainty quantification warrant high efficiency and reliability in order to not only deliver results quickly, but also to allow for predictive work. (iii) A high degree of autonomy reduces the amount of manual human work, processing errors, and human bias. Although being inherently unbiased, it is still steerable with respect to specific regions of an emerging network and with respect to the addition of new reactant species. This allows for a high fidelity of the formalization of some catalytic process and for surprising in silico discoveries. In this work, we first review the state of the art in computational catalysis to embed autonomous explorations into the general field from which it draws its ingredients. We then elaborate on the specific conceptual issues that arise in the context of autonomous computational procedures, some of which we discuss at an example catalytic system.

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SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11244-021-01543-9.

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.

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.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

How a Quantum Computer Could Quantify Uncertainty in Microkinetic Models

A method of uncertainty quantification on a quantum circuit using three samples for the Rh(111)-catalyzed CO oxidation reaction is demonstrated. Three parametrized samples of a reduced, linearized microkinetic model populate a single block diagonal matrix for a quantum circuit. This approach leverages the logarithmic scaling of the number of qubits with respect to matrix size. The Harrow, Hassidim, and Lloyd (HHL) algorithm for solving linear systems is employed, and the results are compared with the classical results. This application area of uncertainty quantification in chemical kinetics can experience a quantum advantage using the method reported here, although issues related to larger systems are discussed.

Microkinetic Modeling: A Tool for Rational Catalyst Design

The design of heterogeneous catalysts relies on understanding the fundamental surface kinetics that controls catalyst performance, and microkinetic modeling is a tool that can help the researcher in streamlining the process of catalyst design. Microkinetic modeling is used to identify critical reaction intermediates and rate-determining elementary reactions, thereby providing vital information for designing an improved catalyst. In this review, we summarize general procedures for developing microkinetic models using reaction kinetics parameters obtained from experimental data, theoretical correlations, and quantum chemical calculations. We examine the methods required to ensure the thermodynamic consistency of the microkinetic model. We describe procedures required for parameter adjustments to account for the heterogeneity of the catalyst and the inherent errors in parameter estimation. We discuss the analysis of microkinetic models to determine the rate-determining reactions using the degree of rate control and reversibility of each elementary reaction. We introduce incorporation of Brønsted-Evans-Polanyi relations and scaling relations in microkinetic models and the effects of these relations on catalytic performance and formation of volcano curves are discussed. We review the analysis of reaction schemes in terms of the maximum rate of elementary reactions, and we outline a procedure to identify kinetically significant transition states and adsorbed intermediates. We explore the application of generalized rate expressions for the prediction of optimal binding energies of important surface intermediates and to estimate the extent of potential rate improvement. We also explore the application of microkinetic modeling in homogeneous catalysis, electro-catalysis, and transient reaction kinetics. We conclude by highlighting the challenges and opportunities in the application of microkinetic modeling for catalyst design.

Aqueous-phase effects on ethanol decomposition over Ru-based catalysts

Liquid water decelerates ethanol reforming over Ru(0001) but increases the H2 selectivity due to accelerated WGS and suppressed methanation.

Defect Electrocatalysts and Alkaline Electrolyte Membranes in Solid-State Zinc-Air Batteries: Recent Advances, Challenges, and Future Perspectives

Rechargeable zinc-air batteries (ZABs) have attracted much attention due to their promising capability for offering high energy density while maintaining a long operational lifetime. One of the biggest challenges in developing all-solid-state ZABs is to design suitable bifunctional air-electrodes, which can efficiently catalyze the key oxygen reduction reaction (ORR)/oxygen evolution reaction (OER) electrochemical processes. The other one is to develop robust electrolyte membranes with high ionic conductivity and superb water retention capability. In this review, an in-depth discussion of the challenges, mechanisms, and design strategies for the defect electrocatalyst and the electrolyte membrane in all-solid-state ZABs will be offered. In particular, the crucial defect engineering strategies to tune the ORR/OER catalysts are summarized, including direct controllable strategies: 1) atomically dispersed metal sites control, 2) vacancy defects control, and 3) lattice-strain control, and the indirect strategies: 4) crystallographic structure control and 5) metal-carbon support interaction control. Moreover, the most recent progress in designing electrolyte membranes, including polyvinyl alcohol-based membranes and gel polymer electrolyte membranes, is presented. Finally, the perspectives are proposed for rational design and fabrication of the desired air electrode and electrolyte membrane to improve the performance and prolong the lifetime of all-solid-state ZABs.

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.

Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences

Data science has primarily focused on big data, but for many physics, chemistry, and engineering applications, data are often small, correlated and, thus, low dimensional, and sourced from both computations and experiments with various levels of noise. Typical statistics and machine learning methods do not work for these cases. Expert knowledge is essential, but a systematic framework for incorporating it into physics-based models under uncertainty is lacking. Here, we develop a mathematical and computational framework for probabilistic artificial intelligence (AI)-based predictive modeling combining data, expert knowledge, multiscale models, and information theory through uncertainty quantification and probabilistic graphical models (PGMs). We apply PGMs to chemistry specifically and develop predictive guarantees for PGMs generally. Our proposed framework, combining AI and uncertainty quantification, provides explainable results leading to correctable and, eventually, trustworthy models. The proposed framework is demonstrated on a microkinetic model of the oxygen reduction reaction.

Data-powered augmented volcano plots for homogeneous catalysis

Given the computational resources available today, data-driven approaches can propel the next leap forward in catalyst design. Using a data-driven inspired workflow consisting of data generation, statistical analysis, and dimensionality reduction algorithms we explore trends surrounding the thermodynamics of a model hydroformylation reaction catalyzed by group 9 metals bearing phosphine ligands. Specifically, we introduce "augmented volcano plots" as a means to easily visualize the similarity of each catalyst's complete catalytic cycle energy profile to that of a hypothetical ideal reference profile without relying upon linear scaling relationships. In addition to quickly identifying catalysts that most closely match the ideal thermodynamic catalytic cycle energy profile, these maps also enable a more refined comparison of closely lying species in standard volcano plots. For the reaction studied here, they inherently uncover the presence of multiple sets of scaling relationships differentiated by metal type, where iridium catalysts follow distinct relationships from cobalt/rhodium catalysts and have profiles that more closely match the ideal thermodynamic profile. Reconstituted molecular volcano plots confirm the findings of the augmented volcanoes by showing that hydroformylation thermodynamics are governed by two distinct volcano shapes, one for iridium catalysts and a second for cobalt/rhodium species.

Combining Computational Modeling with Reaction Kinetics Experiments for Elucidating the In Situ Nature of the Active Site in Catalysis

Microkinetic modeling based on density functional theory (DFT) derived energetics is important for addressing fundamental questions in catalysis. The quantitative fidelity of microkinetic models (MKMs), however, is often insufficient to conclusively infer the mechanistic details of a specific catalytic system. This can be attributed to a number of factors such as an incorrect model of the active site for which DFT calculations are performed, deficiencies in the hypothesized reaction mechanism, inadequate consideration of the surface environment under reaction conditions, and intrinsic errors in the DFT exchange-correlation functional. Despite these limitations, we aim at developing a rigorous understanding of the reaction mechanism and of the nature of the active site for heterogeneous catalytic chemistries under reaction conditions. By achieving parity between experimental and modeling outcomes through robust parameter estimation and by ensuring coverage-consistency between DFT calculations and MKM predictions, it is possible to systematically refine the mechanistic model and, thereby, our understanding of the catalytic active site in situ.Our general approach consists of developing ab initio informed MKM for a given active site and then re-estimating the energies of the transition and intermediate states so that the model predictions match quantities measured in reaction kinetics experiments. If (i) model-experiment parity is high, (ii) the adjustments to the DFT-derived energetics for a given model of the active site are rationalized within the errors of standard DFT exchange-correlation functionals, and (iii) the resultant MKM predicts surface coverages that are consistent with those assumed in the DFT calculations used to initialize the MKM, we conclude that we have correctly identified the active site and the reaction mechanism. If one or more of these requirements are not met, we iteratively refine our model by updating our hypothesis for the structure of the active site and/or by incorporating coverage effects, until we obtain a high-fidelity coverage-self-consistent MKM whose final kinetic and thermodynamic parameters are within error of the values derived from DFT.Using the catalytic reaction of formic acid (FA, HCOOH) decomposition over transition-metal catalysts as an example, here we provide an account of how we applied this algorithm to study this chemistry on powder Au/SiC and Pt/C catalysts. For the case of Au catalysts, on which the FA decomposition occurred exclusively through the dehydrogenation reaction (HCOOH → CO₂+H₂), our approach was used to iteratively refine the model starting from the (111) facet until we found that specific ensembles of Au atoms present in sub-nanometer clusters can describe the active site for this catalysis. For the case of Pt catalysts, wherein both dehydrogenation (HCOOH → CO₂ + H₂) and dehydration (HCOOH → CO + H₂O) reactions were active, our approach identified that a partially CO*-covered (111) surface serves as the active site and that CO*-assisted steps contributed substantially to the overall FA decomposition activity. Finally, we suggest that once the active site and the mechanism are conclusively identified, the model can subsequently serve as a high-quality basis for designing specific goal-oriented experiments and improved catalysts.

Progress in Computational and Machine-Learning Methods for Heterogeneous Small-Molecule Activation

The chemical conversion of small molecules such as H₂ , H₂ O, O₂ , N₂ , CO₂ , and CH₄ to energy and chemicals is critical for a sustainable energy future. However, the high chemical stability of these molecules poses grand challenges to the practical implementation of these processes. In this regard, computational approaches such as density functional theory, microkinetic modeling, data science, and machine learning have guided the rational design of catalysts by elucidating mechanistic insights, identifying active sites, and predicting catalytic activity. Here, the theory and methodologies for heterogeneous catalysis and their applications for small-molecule activation are reviewed. An overview of fundamental theory and key computational methods for designing catalysts, including the emerging data science techniques in particular, is given. Applications of these methods for finding efficient heterogeneous catalysts for the activation of the aforementioned small molecules are then surveyed. Finally, promising directions of the computational catalysis field for further outlooks are discussed, focusing on the challenges and opportunities for new methods.

Graph Theory Model of Dry Reforming of Methane Using Rh(111)

The adsorption energies of intermediates of the dry reforming of methane reaction (DRM CH₄ + CO₂ ⇔ 2CO + 2H₂) using Rh(111) are approximated. Graph theory creates descriptors of the intermediates. The information recorded in these descriptors includes the elemental identities of each atom, its neighbors, and its next-nearest neighbors. Graph theory is employed because it is a rapid approximation of more expensive density functional theory (DFT) calculations and because the descriptors created by graph theory are both human and machine interpretable. DRM contains a significant number of adsorbates, and side reactions, including reverse water-gas shift, may occur simultaneously. Therefore, DRM is well-poised for analysis by a graph theory model to predict large numbers of adsorption energies. A portion of adsorbates were calculated with DFT. Then, predictions were reported for the remaining adsorption energies not calculated with DFT.

Exploring the origin of electrochemical performance of Cr-doped LiNi0.5Mn1.5O4

Discorded LiNi0.5Mn1.5O4 has become a promising candidate for Li ion batteries due to its high specific energy. However, its poor structural stability restricts its practical application. After extensive exploration, Cr-doped disordered LiNi0.5Mn1.5O4 demonstrates enhanced structural stability and electrochemical performance. Thus far, its origin at the electronic structural level remains elusive, which is important to further performance improvement. First-principles calculations disclose that a Cr atom prefers to substitute Ni rather than a Mn atom. The transferred charge from Cr to Mn induces the reduction of Mn ions and lengthens the Li-O bond distance, which are mainly responsible for the lower Li ion diffusion energy barrier and Li vacancy formation energy. The heavy oxidation of O ions is a main factor to induce the structural degeneration. In this case, the reduced Mn ion delays the oxidation of the O ion, enhancing the structural stability. In addition, Cr doping increases the thermodynamic stability of intermediate phases during delithiation, decreasing the structural strain in the delithiation process. Ordered and disordered LiNi0.5Mn1.5O4 are also included for comparison. Our work provides an opportunity to fully understand Cr-doped LiNi0.5Mn1.5O4 at the atomic scale.