Effect of errors in linear scaling relations and Brønsted–Evans–Polanyi relations on activity and selectivity maps

Mechanistic insights into CO2 hydrogenation to methanol on Cu(110): unveiling energy linear relationships and enhancing performance strategies

The study of energy correlations in catalytic reactions plays a pivotal role in guiding catalyst development. This paper focuses on the investigation of energy linear relationships in methanol synthesis from CO2 hydrogenation on copper surfaces, systematically exploring energy parameters including activation energy, reaction energy and adsorption energy. A comparative analysis of the adsorption characteristics and reaction parameters in the formate, formic acid and reverse water-gas shift pathways is conducted, laying the data foundation for subsequent linear studies. Then, descriptors are extracted from electronic, energetic and structural information and further integrated using the sure independence screening and sparsifying operator (SISSO) method to establish an energy description paradigm characterized by interpretability and accuracy. Additionally, reactions are further categorized based on hydrogenation types to mitigate the adverse effects of redundant data points. Finally, the summarized reaction descriptors are extended to Cu-based alloy systems to highlight the rationality and transferability of the developed descriptors.

Breaking the scaling relations of effective CO2 electrochemical reduction in diatomic catalysts by adjusting the flow direction of intermediate structures

The electrocatalytic carbon dioxide reduction reaction (CO2RR) is a promising approach to achieving a sustainable carbon cycle. Recently, diatomic catalysts (DACs) have demonstrated advantages in the CO2RR due to their complex and flexible active sites. However, our understanding of how DACs break the scaling relationship remains insufficient. Here, we investigate the CO2RR of 465 kinds of graphene-based DACs (M1M2-N6@Gra) formed from 30 metal atoms through high-throughput density functional theory (DFT) calculations. We find that the intermediates *COOH, *CO, and *CHO have multiple adsorption states, with 11 structural flow directions from *CO to *CHO. Four of these structural flow directions have catalysts that can break the linear scale relationship. Based on the adsorption energy relationship between *COOH, *CHO and *CO, we propose the concepts of linear scaling, moderate breaking, and severe deviation regions, leading to the establishment of new descriptors that identify 14 catalysts with potential superior performance. Among them, ZnRu-N6@Gra and CrNi-N6@Gra can reduce CO2 to CH4 at a low limiting potential. We also discovered that DACs have independent bidirectional electron transfer channels during the adsorption and activation of CO2, which can significantly improve the flexibility and efficiency of regulating the electronic structure. Furthermore, through machine learning (ML) analysis, we identify electronegativity, atomic number, and d electron count as key determinants of catalyst stability. This work provides new insights into the understanding of the DAC catalytic mechanism, as well as the design and screening of catalysts.

Structure Sensitivity of Metal Catalysts Revealed by Interpretable Machine Learning and First-Principles Calculations

The nature of the active sites and their structure sensitivity are the keys to rational design of efficient catalysts but have been debated for almost one century in heterogeneous catalysis. Though the Brønsted-Evans-Polanyi (BEP) relationship along with linear scaling relation has long been used to study the reactivity, explicit geometry, and composition properties are absent in this relationship, a fact that prevents its exploration in structure sensitivity of supported catalysts. In this work, based on interpretable multitask symbolic regression and a comprehensive first-principles data set, we discovered a structure descriptor, the topological under-coordinated number mediated by number of valence electrons and the lattice constant, to successfully address the structure sensitivity of metal catalysts. The database used for training, testing, and transferability investigation includes bond-breaking barriers of 20 distinct chemical bonds over 10 transition metals, two metal crystallographic phases, and 17 different facets. The resulting 2D descriptor composing the structure term and the reaction energy term shows great accuracy to predict the reaction barriers and generalizability over the data set with diverse chemical bonds in symmetry, bond order, and steric hindrance. The theory is physical and concise, providing a constructive strategy not only to understand the structure sensitivity but also to decipher the entangled geometric and electronic effects of metal catalysts. The insights revealed are valuable for the rational design of the site-specific metal catalysts.

A comparative study on the linear scaling relations for the diffusion of S-vacancies on MoS2 and WS2

This work uses density functional theory (DFT) calculations and kinetic Monte Carlo (kMC) simulations to compare the diffusion of S-vacancies on defective MoS2 and WS2, two structures that are often discussed as catalysts. Similar to what has been discussed for MoS2, the vacancy diffusion barriers on WS2 also follow Brønsted-Evans-Polanyi (BEP) type linear scaling relations. The vacancy diffusion kinetics is discussed at the example of a large vacancy cluster consisting of 37 unoccupied sites in direct vicinity and how its structure changes with time. Using barriers estimated via linear scaling relations as input for the kMC simulations yields results that qualitatively agree with results calculated self-consistently at DFT level. As the diffusion barriers for WS2 are significantly higher than those for MoS2, the vacancy diffusion on WS2 is poorly described by the linear scaling relations derived from MoS2 and vice versa. This work further shows that one needs DFT level barriers of about 40% of all S-vacancy diffusion processes on a material to derive sufficiently reliable linear scaling relations. This means that computational costs for future studies may be reduced by only explicitly computing one fraction of the diffusion barriers while estimating the remaining ones via linear scaling. However, in this case, one would lack information about the partition function of the transition states, which are needed for calculating the rate constants. Thus, we have also proposed a scheme to estimate the contribution of the partition functions based only on the initial state's vibrational modes.

Topology-Determined Structural Genes Enable Data-Driven Discovery and Intelligent Design of Potential Metal Oxides for Inert C-H Bond Activation

The identification of appropriate structural genes that influence the active-site configuration for a given reaction is critical for discovering potential catalysts with reduced reaction barriers. In this study, we introduce bulk-phase topology-derived tetrahedral descriptors as a means of expressing a catalyst's "material structural genes". We combine this approach with an interpretable machine learning model to accurately and efficiently predict the effective barrier associated with methane C-H bond cleavage across a wide range of metal oxides (MOs). These structural genes enable high-throughput catalyst screening for low-temperature methane activation and ultimately identify 13 candidate catalysts from a pool of 9095 MOs that are recommended for experimental synthesis. The topology-based method that we describe can also be extended to facilitate high-throughput catalyst screening and design for other dehydrogenation reactions.

Linear Scaling Relationships for Furan Hydrodeoxygenation over Transition Metal and Bimetallic Surfaces

Brønsted-Evans-Polanyi (BEP) and transition-state-scaling (TSS) relationships have become valuable tools for the rational design of catalysts for complex reactions like hydrodeoxygenation (HDO) of bio-oil (containing heterocyclic and homocyclic molecules). In this work, BEP and TSS relationships are developed for all the elementary steps of furan activation (C and O hydrogenation and CHx -OHy scission, for both ring and open-ring intermediates) to oxygenates, ring-saturated compounds and deoxygenated products on the most stable facets of Ni, Co, Rh, Ru, Pt, Pd, Fe and Ir surfaces using Density Functional Theory (DFT) calculations. Furan ring opening barriers were found to be facile and strongly dependent on carbon and oxygen binding strength on the investigated surfaces. Our calculations suggest linear chain oxygenates form on Ir, Pt, Pd and Rh surfaces due to their low hydrogenation and high CHx -OHy scission barriers, while deoxygenated linear products are favoured on Fe and Ni surfaces due to their low CHx -OHy scission and moderate hydrogenation barriers. Bimetallic alloy catalysts were also screened for their potential HDO activity and PtFe catalysts were found to significantly lower the ring opening and deoxygenation barriers relative to the corresponding pure metals. The developed BEPs for monometallic surfaces can be extended to estimate the barriers on bimetallic surfaces for ring opening and ring hydrogenation reactions but fails to predict the barriers for open-ring activation reactions due to the change in transition state binding sites on the bimetallic surface. The obtained BEP and TSS relationships can be used to develop microkinetic models for facilitating accelerated catalyst discovery for HDO.

Successes and challenges in using machine-learned activation energies in kinetic simulations

The prediction of the thermodynamic and kinetic properties of chemical reactions is increasingly being addressed by machine-learning (ML) methods such as artificial neural networks (ANNs). While a number of recent studies have reported success in predicting chemical reaction activation energies, less attention has focused on how the accuracy of ML predictions filter through to predictions of macroscopic observables. Here, we consider the impact of the uncertainty associated with ML prediction of activation energies on observable properties of chemical reaction networks, as given by microkinetics simulations based on ML-predicted reaction rates. After training an ANN to predict activation energies given standard molecular descriptors for reactants and products alone, we performed microkinetics simulations of three different prototypical reaction networks: formamide decomposition, aldol reactions and decomposition of 3-hydroperoxypropanal. We find that the kinetic modelling predictions can be in excellent agreement with corresponding simulations performed with ab initio calculations, but this is dependent on the inherent energetic landscape of the networks. We use these simulations to suggest some guidelines for when ML-based activation energies can be reliable, and when one should take more care in applications to kinetics modelling.

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.

Towards the object-oriented design of active hydrogen evolution catalysts on single-atom alloys

Given a desired property, locating relevant materials is always highly desired but very challenging in a range of areas, including heterogeneous catalysis. Obviously, object-oriented design/screening is an ideal solution to this problem. Herein, we develop an inverse catalyst design workflow in Python (CATIDPy) that utilizes a genetic-algorithm-based global optimization method to guide on-the-fly density functional theory calculations, successfully realizing the highly accelerated location of active single-atom alloy (SAA) catalysts for the hydrogen evolution reaction (HER). 70 binary and 752 ternary SAA candidate catalysts are identified for the HER. Furthermore, via considering the segregation stability and cost of materials, we extracted 6 binary and 142 ternary SAA candidate catalysts that are recommended for experimental synthesis. Remarkably, guided by these theoretical identifications, homogeneously dispersed Ni-based bimetallic catalysts (e.g., NiMo, NiAl, Ni₃Al, NiGa, and NiIn) were synthesized experimentally to test the reliability of the CATIDPy workflow, and they showed superior HER performance to bare Ni foam, indicating huge potential for use in real-world water electrolysis techniques. Perhaps more importantly, these results demonstrate the capacity of such a proposed approach for investigating unexplored chemical spaces to efficiently design promising catalysts without knowledge from the expert domain, which has far-reaching implications.

An inverse catalyst design workflow in Python (CATIDPy) for discovering unexplored chemical spaces successfully realized the highly accelerated location of active single-atom alloy (SAA) catalysts for the hydrogen evolution reaction (HER).

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.

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.

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.

Catalytic resonance theory: superVolcanoes, catalytic molecular pumps, and oscillatory steady state

Catalytic reactions on surfaces with forced oscillations in physical or electronic properties undergo controlled acceleration consistent with the selected parameters of frequency, amplitude, and external stimulus waveform.

Towards rational catalyst design: boosting the rapid prediction of transition-metal activity by improved scaling relations

The improved UBI-QEP+BEP are utilized to rapidly estimate surface energetics, which satisfactorily fit the DFT (BEEF-vdW) values. These energetics are then applied in microkinetic modeling to predict catalyst activity and perform catalyst screening.

Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes

For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present in all but the simplest chemical processes, approximate quantum chemical methods are required that allow for fast evaluations of the relative energies but at the expense of accuracy. Despite the plethora of benchmark studies, the accuracy of a quantum chemical method is often difficult to assess. Moreover, a significant improvement of a method's accuracy (e.g., through reparameterization or systematic model extension) is rarely possible. Here, we present a new approach that allows for the systematic, problem-oriented, and rolling improvement of quantum chemical results through the application of Gaussian processes. Due to its Bayesian nature, reliable error estimates are provided for each prediction. A reference method of high accuracy can be employed if the uncertainty associated with a particular calculation is above a given threshold. The new data point is then added to a growing data set in order to continuously improve the model and, as a result, all subsequent predictions. Previous predictions are validated by the updated model to ensure that uncertainties remain within the given confidence bound, which we call backtracking. We demonstrate our approach with the example of a complex chemical reaction network.

Thermochemistry of gas-phase and surface species via LASSO-assisted subgraph selection

Graph theory-based regression techniques, such as group additivity, have widely been implemented for fast estimation of thermochemistry of large molecules.

Escaping the trap of complication and complexity in multiscale microkinetic modelling of heterogeneous catalytic processes

In this feature article, the development of methods to enable a hierarchical multiscale approach to the microkinetic analysis of heterogeneous catalytic processes is reviewed. This methodology is an effective route to escape the trap of complication and complexity in multiscale microkinetic modelling. On the one hand, the complication of the problem is related to the fact that the observed catalyst functionality is inherently a multiscale property of the reacting system and its analysis requires bridging the phenomena at different time and length scales. On the other hand, the complexity of the problem derives from the system dimension of the chemical systems, which typically results in a number of elementary steps and species, that are beyond the limit of accessibility of present-day computational power even for the most efficient implementation of atomistic first-principles simulations. The main idea behind the hierarchical approach is to tackle the problem with methods of increasing accuracy in a dual feed-back loop between theory and experiments. The potential of the methodology is shown in the context of unravelling the WGS and r-WGS catalytic mechanisms on Rh catalysts. As a perspective, the extension to structure-dependent microkinetic modelling is discussed.