Degree of Rate Control: How Much the Energies of Intermediates and Transition States Control Rates

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.

Identifying the Critical Surface Descriptors for the Negative Slopes in the Adsorption Energy Scaling Relationships via Density Functional Theory and Compressed Sensing

Adsorption energy scaling relationships have progressed beyond their original form, which was primarily focused on optimizing catalytic sites and lowering computational costs in simulations. The recent rise in interest in adsorption energy scaling relations is to investigate surfaces other than transition metals (TMs) as well as interactions involving complex compounds. In this work, we report our extensive study on the scaling relation (SR) between oxygen (O), with elements of neighboring groups such as boron (B), aluminum (Al), carbon (C), silicon (Si), nitrogen (N), phosphorus (P), and fluorine (F) on magnetic bimetallic surfaces. We observed that only O versus N and F seems to have a positive slope; the other slopes are negative. We present new theoretical model in terms of multiple surface descriptors using density functional theory and compressed sensing, whereas the original scaling theory was based on a single adsorbate descriptor: adsorbate valency.

Theoretical study of gas-phase detoxication of DMMP and DMPT using ammonia-borane and its analogous compound

The detoxication of DMMP (Dimethyl methylphosphonate) and DMPT (O, S-dimethyl methylphosphonothiolate) via hydrogenation have been investigated computationally employing density functional theory (DFT). In this present study, we aim to explore the direct molecular H₂ assisted as well as ammonia-borane (NH₃BH₃) and 3-methyl-1,2-BN-cyclopentane (denoted as cy-AB) assisted hydrogenation pathways of DMMP and DMPT in order to detoxify them. The detoxication of DMMP has been carried out by successive elimination of two -OMe groups. However, in the case of DMPT, two possibilities have been identified because of two different substituents, -OMe and -SMe. In possibility-I, the elimination of the -OMe group occurs at the beginning, followed by the -SMe group, whereas in possibility-II, the reverse order of elimination occurs for -OMe and -SMe groups. During the detoxication of DMMP using both NH₃BH₃ and cy-AB as the assisting reagents, the first step has been identified as the rate-determining step (RDS) in which the hydrogens attached to the N- and B-centers of NH₃BH₃ are transferred to the O-center of PO and P-center, respectively. In harmony with DMMP detoxication, for DMPT also, analyzing the activation barriers, it can be articulated that for both NH₃BH₃ and cy-AB assisted pathways, both the possibilities are equally feasible as in both the possibilities the common first step is the RDS. Therefore, our computational study is designed to explore the assisting efficiency of NH₃BH₃ and its cyclic analogue for detoxifying the OPCs.

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.

Unveiling Potential Dependence in NO Electroreduction to Ammonia

Recently, electrochemical NO reduction (eNORR) to ammonia has attracted enormous research interests due to the dual benefits in ammonia synthesis and denitrification fields. Herein, taking Ag as a model catalyst, we have developed a microkinetic model to rationalize the general selectivity trend of eNORR with varying potential, which has been observed widely in experiments, but not understood well. The model reproduces experiments well, quantitatively describing the selectivity turnover from N₂O to NH₃ and from NH₃ to H₂ with more negative potential. The first turnover of selectivity is due to the thermochemical coupling of two NO* limiting the N₂O production. The second turnover is attributed to the larger transfer coefficient (β) of HER than NH₃ production. This work reveals how electrode potential regulate the selectivity of eNORR, which is also beneficial to understand the commonly increasing HER selectivity with the decrease of potential in some other electroreduction reactions such as CO₂ reduction.

Kinetic description of site ensembles on catalytic surfaces

We demonstrate that the Langmuir-Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A₂ The Hinshelwood assumption results in miscounting of site pairs (e.g., A*-A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir-Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method-with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir-Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step-including adsorbate diffusion-traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

Oriented Electrostatic Effects on O2 and CO2 Reduction by a Polycationic Iron Porphyrin

Next-generation energy technologies require improved methods for rapid and efficient chemical-to-electrical energy transformations. One new approach has been to include atomically positioned, electrostatic motifs in molecular catalysts to stabilize high-energy, charged intermediates. For example, an iron porphyrin bearing four cationic, o-N,N,N-trimethylanilinium groups (o-[N(CH₃)₃]⁺) has recently been used to catalyze the complex, multistep O₂ and CO₂ reduction reactions (ORR and CO₂RR) with fast rates and at low overpotentials. The success of this catalyst is attributed, at least in part, to specific charge-charge interactions between the atomically positioned o-[N(CH₃)₃]⁺ groups and the bound substrate. However, by nature of the mono-ortho substitution pattern, there are four possible atropisomers of this metalloporphyrin and thus four unique electrostatic environments. This work reports that each of the four individual atropisomers catalyzes both the ORR and CO₂RR with fast rates and low overpotentials. The maximum turnover frequencies vary among the atropisomers, by a factor of 60 for the ORR and a factor of 5 for CO₂RR. For the ORR, the αβαβ isomer is the fastest and has the highest overpotential, while for the CO₂RR the αααα isomer is the fastest and has the highest overpotential. The role of charge positioning is complex and can affect more than a single step such as CO₂ binding. These data offer a first-of-a-kind perspective on atomically positioned charge and highlight the significance of high charge density, rather than orientation, on the thermodynamics and kinetics of multistep molecular electrochemical transformations.

Performance of Made Simple Meta-GGA Functionals with rVV10 Nonlocal Correlation for H2 + Cu(111), D2 + Ag(111), H2 + Au(111), and D2 + Pt(111)

Accurately modeling heterogeneous catalysis requires accurate descriptions of rate-controlling elementary reactions of molecules on metal surfaces, but standard density functionals (DFs) are not accurate enough for this. The problem can be solved with the specific reaction parameter approach to density functional theory (SRP-DFT), but the transferability of SRP DFs among chemically related systems is limited. We combine the MS-PBEl, MS-B86bl, and MS-RPBEl semilocal made simple (MS) meta-generalized gradient approximation (GGA) (mGGA) DFs with rVV10 nonlocal correlation, and we evaluate their performance for the hydrogen (H2) + Cu(111), deuterium (D2) + Ag(111), H2 + Au(111), and D2 + Pt(111) gas-surface systems. The three MS mGGA DFs that have been combined with rVV10 nonlocal correlation were not fitted to reproduce particular experiments, nor has the b parameter present in rVV10 been reoptimized. Of the three DFs obtained the MS-PBEl-rVV10 DF yields an excellent description of van der Waals well geometries. The three original MS mGGA DFs gave a highly accurate description of the metals, which was comparable in quality to that obtained with the PBEsol DF. Here, we find that combining the three original MS mGGA DFs with rVV10 nonlocal correlation comes at the cost of a slightly less accurate description of the metal. However, the description of the metal obtained in this way is still better than the descriptions obtained with SRP DFs specifically optimized for individual systems. Using the Born-Oppenheimer static surface (BOSS) model, simulations of molecular beam dissociative chemisorption experiments yield chemical accuracy for the D2 + Ag(111) and D2 + Pt(111) systems. A comparison between calculated and measured E 1/2(ν, J) parameters describing associative desorption suggests chemical accuracy for the associative desorption of H2 from Au(111) as well. Our results suggest that ascending Jacob's ladder to the mGGA rung yields increasingly more accurate results for gas-surface reactions of H2 (D2) interacting with late transition metals.

Reversible catalysis

We describe as 'reversible' a bidirectional catalyst that allows a reaction to proceed at a significant rate in response to even a small departure from equilibrium, resulting in fast and energy-efficient chemical transformation. Examining the relation between reaction rate and thermodynamic driving force is the basis of electrochemical investigations of redox reactions, which can be catalysed by metallic surfaces and biological or synthetic molecular catalysts. This relation has also been discussed in the context of biological energy transduction, regarding the function of biological molecular machines that harness chemical reactions to do mechanical work. This Perspective describes mean-field kinetic modelling of these three types of systems - surface catalysts, molecular catalysts of redox reactions and molecular machines - with the goal of unifying concepts in these different fields. We emphasize that reversibility should be distinguished from other figures of merit, such as rate or directionality, before its design principles can be identified and used to engineer synthetic catalysts.

Synergetic effect dependence on activated oxygen in the interface of NiOx-modified Pt nanoparticles for the CO oxidation from first-principles

CO oxidation on NiO_x-modified Pt nanoparticles (NPs) was investigated by first-principles calculations and microkinetic methods. The binding energies of O₂ and CO on NiO_x/Pt suggest that CO adsorption is dominant and the CO oxidation mainly follows the Mars-van Krevelen (M-vK) mechanism. It was found that the interfacial O of NiO_x/Pt played a key role in the combination of adsorbed CO to O, as well as the O₂ dissociation. With a lower O vacancy formation energy, NiO_x/Pt_edge shows about four orders higher reaction rates than NiO_x/Pt₍₁₀₀₎. Microkinetic analysis suggests that the rate-determining step also depends on the active O at the interface. The calculations highlight the synergetic effect difference of NiO_x selectively deposited on the different sites of Pt NPs on the CO oxidation from the atomic reaction mechanism, and throws light on the high activity of CO oxidation on partially covered NiO_x/Pt_edge nanoparticles.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Kinetic effects of molecular clustering and solvation by extended networks in zeolite acid catalysis

Reactions catalyzed within porous inorganic and organic materials and at electrochemical interfaces commonly occur at high coverage and in condensed media, causing turnover rates to depend strongly on interfacial structure and composition, collectively referred to as "solvent effects". Transition state theory treatments define how solvation phenomena enter kinetic rate expressions, and identify two distinct types of solvent effects that originate from molecular clustering and from the solvation of such clusters by extended solvent networks. We review examples from the recent literature that investigate reactions within microporous zeolite catalysts to illustrate these concepts, and provide a critical appraisal of open questions in the field where future research can aid in developing new chemistry and catalyst design principles.

CATKINAS: A large-scale catalytic microkinetic analysis software for mechanism auto-analysis and catalyst screening

As an effective method to analyze complex catalytic reaction networks, microkinetic modeling is gaining increasing popularity in the catalytic activity evaluation and rational design of heterogeneous catalysts. An automated simulator with stable and reliable performance is especially useful and in great request. Here we introduce the CATKINAS package developed for large-scale microkinetic modeling and analysis. Featuring with a multilevel solver and a multifunctional analyzer, CATKINAS can provide both accurate solutions and various quantitative and automatic analysis for a wide range of catalytic systems. The structure and the basic workflow are overviewed with the multilevel solver particularly illustrated. Also, we take the CO methanation reaction as an example to illustrate the application and efficiency of the CATKINAS package.

A DFT-based microkinetic study on methanol synthesis from CO2 hydrogenation over the In2O3 catalyst

In this work, we performed density functional theory (DFT)-based microkinetic simulations to elucidate the reaction mechanism of methanol synthesis on two of the most stable facets of the cubic In2O3 (c-In2O3) catalyst, namely the (111) and (110) surfaces. Our DFT calculations show that for both surfaces, it is difficult for the H atom adsorbed at the remaining surface O atom around the O vacancy (Ov) active site to migrate to an O adsorbed at the Ov due to the very high energy barrier involved. In addition, we also find that the C-O bond in the bt-CO2* chemisorption structure can directly break to form CO with a lower energy barrier than that in its hydrogenation to the COOH* intermediate in the COOH route. However, our microkinetic simulations suggest that for both surfaces, CO2 deoxygenation to form CO in both pathways, namely the COOH and CO-O routes, are kinetically slower than methanol formation under typical steady state conditions assuming a CO2 conversion of 10% and a CO selectivity of 1%. Although these results agree with previous experimental observations at relatively low reaction temperature, where methanol formation dominates, they cannot explain the predominant formation of CO at relatively high reaction temperature. We tentatively attribute this to the simplicity of our microkinetic model as well as possible structural changes of the catalyst at relatively high reaction temperature. Furthermore, although the rate-determining step (RDS) from the degree of rate control (DRC) analysis is usually consistent with that judged from the DFT calculated energy barriers, for CO2 hydrogenation to methanol over the (111) surface, our DRC analysis suggests homolytic H2 dissociation to be the rate-controlling step, which is not apparent from the DFT-calculated energy barriers. This indicates that CO2 conversion and methanol selectivity over the (111) surface can be further enhanced if homolytic H2 dissociation can be accelerated for instance by introducing transition metal dopants as already shown by some experimental observations.

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.

SSIA: A sensitivity-supervised interlock algorithm for high-performance microkinetic solving

Microkinetic modeling has drawn increasing attention for quantitatively analyzing catalytic networks in recent decades, in which the speed and stability of the solver play a crucial role. However, for the multi-step complex systems with a wide variation of rate constants, the often encountered stiff problem leads to the low success rate and high computational cost in the numerical solution. Here, we report a new efficient sensitivity-supervised interlock algorithm (SSIA), which enables us to solve the steady state of heterogeneous catalytic systems in the microkinetic modeling with a 100% success rate. In SSIA, we introduce the coverage sensitivity of surface intermediates to monitor the low-precision time-integration of ordinary differential equations, through which a quasi-steady-state is located. Further optimized by the high-precision damped Newton's method, this quasi-steady-state can converge with a low computational cost. Besides, to simulate the large differences (usually by orders of magnitude) among the practical coverages of different intermediates, we propose the initial coverages in SSIA to be generated in exponential space, which allows a larger and more realistic search scope. On examining three representative catalytic models, we demonstrate that SSIA is superior in both speed and robustness compared with its traditional counterparts. This efficient algorithm can be promisingly applied in existing microkinetic solvers to achieve large-scale modeling of stiff catalytic networks.

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.

Rational catalyst design for CO oxidation: a gradient-based optimization strategy

In this work, we proposed a gradient-based optimization strategy for rational catalyst design.

Ethanol steam reforming on Rh: microkinetic analyses on the complex reaction network

Reaction networks were generated for ethanol steam reforming to CO and CO2. After the pruning of the networks, the preferred reaction pathways of the CO and CO2 production on Rh(111) were identified and detailed kinetic information was analyzed.

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.

The catalytic decomposition of nitrous oxide and the NO + CO reaction over Ni/Cu dilute and single atom alloy surfaces: first-principles microkinetic modelling

Density functional theory calculations and microkinetic modelling reveal that well-engineered Ni/Cu dilute alloys are promising for the catalytic reduction of NO by CO.

Surface reaction kinetics of the methanol synthesis and the water gas shift reaction on Cu/ZnO/Al2O3

Detailed modeling of the methanol synthesis combining theoretical surface kinetics, catalyst structural changes, and a broad experimental validation.

A synergetic effect between a single Cu site and S vacancy on an MoS2 basal plane for methanol synthesis from syngas

Compared to MoS₂(001), the synergetic effect between the single Cu site and S vacancy on Cu/MoS₂(001) destabilizes O, which not only increases the CO hydrogenation rate by 5 orders of magnitude, but leads to the selectivity switch from CH₄ to CH₃OH.

Kinetic modeling of nitrous oxide decomposition on Fe-ZSM-5 in the presence of nitric oxide based on parameters obtained from first-principles calculations

A variety of experiments for the N₂O decomposition over Fe-ZSM-5 catalysts have been simulated in the presence and absence of small amounts of nitric oxide and water vapor.

Active Reaction Control of Cu Redox State Based on Real-Time Feedback from In Situ Synchrotron Measurements

We achieve a target material state by using a recursive algorithm to control the material reaction based on real-time feedback on the system chemistry from in situ X-ray absorption spectroscopy. Without human intervention, the algorithm controlled O₂:H₂ gas partial pressures to approach a target average Cu oxidation state of 1+ for γ-Al₂O₃-supported Cu. This approach represents a new paradigm in autonomation for materials discovery and synthesis optimization; instead of iterating the parameters following the conclusion of each of a series of reactions, the iteration cycle has been scaled down to time points during an individual reaction. Application of the proof-of-concept illustrated here, using a feedback loop to couple in situ material characterization and the reaction conditions via a decision-making algorithm, can be readily envisaged in optimizing and understanding a broad range of systems including catalysis.