Discerning complex reaction networks using automated generators

Reaction Networks Resemble Low-Dimensional Regular Lattices

The computational exploration, manipulation, and design of complex chemical reactions face fundamental challenges related to the high-dimensional nature of potential energy surfaces (PESs) that govern reactivity. Accurately modeling complex reactions is crucial for understanding the chemical processes involved in, for example, organocatalysis, autocatalytic cycles, and one-pot molecular assembly. Our prior research demonstrated that discretizing PESs using heuristics based on bond breaking and bond formation produces a reaction network representation with a low-dimensional structure (metric space). We now find that these stoichiometry-preserving reaction networks possess additional, though approximate, structure and resemble low-dimensional regular lattices with a small amount of random edge rewiring. The heuristics-based discretization thus generates a nonlinear dimensionality reduction by a factor of 10 with an a posteriori error measure (probability of random rewiring). The structure becomes evident through a comparative analysis of CHNO reaction networks of varying stoichiometries against a panel of size-matched generative network models, taking into account their local, metric, and global properties. The generative models include random networks (Erdős-Rényi and bipartite random networks), regular lattices (periodic and nonperiodic), and network models with a tunable level of "randomness" (Watts-Strogatz graphs and regular lattices with random rewiring). The CHNO networks are simultaneously closely matched in all these properties by 3-4-dimensional regular lattices with 10% or less of edges randomly rewired. The effective dimensionality reduction is found to be independent of the system size, stoichiometry, and ruleset, suggesting that search and sampling algorithms for PESs of complex chemical reactions can be effectively leveraged.

Graph to Activation Energy Models Easily Reach Irreducible Errors but Show Limited Transferability

Activation energy characterization of competing reactions is a costly but crucial step for understanding the kinetic relevance of distinct reaction pathways, product yields, and myriad other properties of reacting systems. The standard methodology for activation energy characterization has historically been a transition state search using the highest level of theory that can be afforded. However, recently, several groups have popularized the idea of predicting activation energies directly based on nothing more than the reactant and product graphs, a sufficiently complex neural network, and a broad enough data set. Here, we have revisited this task using the recently developed Reaction Graph Depth 1 (RGD1) transition state data set and several newly developed graph attention architectures. All of these new architectures achieve similar state-of-the-art results of ∼4 kcal/mol mean absolute error on withheld testing sets of reactions but poor performance on external testing sets composed of reactions with differing mechanisms, reaction molecularity, or reactant size distribution. Limited transferability is also shown to be shared by other contemporary graph to activation energy architectures through a series of case studies. We conclude that an array of standard graph architectures can already achieve results comparable to the irreducible error of available reaction data sets but that out-of-distribution performance remains poor.

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.

ReNeGate: A Reaction Network Graph-Theoretical Tool for Automated Mechanistic Studies in Computational Homogeneous Catalysis

Exploration of the chemical reaction space of chemical transformations in multicomponent mixtures is one of the main challenges in contemporary computational chemistry. To remove expert bias from mechanistic studies and to discover new chemistries, an automated graph-theoretical methodology is proposed, which puts forward a network formalism of homogeneous catalysis reactions and utilizes a network analysis tool for mechanistic studies. The method can be used for analyzing trajectories with single and multiple catalytic species and can provide unique conformers of catalysts including multinuclear catalyst clusters along with other catalytic mixture components. The presented three-step approach has the integrated ability to handle multicomponent catalytic systems of arbitrary complexity (mixtures of reactants, catalyst precursors, ligands, additives, and solvents). It is not limited to predefined chemical rules, does not require prealignment of reaction mixture components consistent with a reaction coordinate, and is not agnostic to the chemical nature of transformations. Conformer exploration, reactive event identification, and reaction network analysis are the main steps taken for identifying the pathways in catalytic systems given the starting precatalytic reaction mixture as the input. Such a methodology allows us to efficiently explore catalytic systems in realistic conditions for either previously observed or completely unknown reactive events in the context of a network representing different intermediates. Our workflow for the catalytic reaction space exploration exclusively focuses on the identification of thermodynamically feasible conversion channels, representative of the (secondary) catalyst deactivation or inhibition paths, which are usually most difficult to anticipate based solely on expert chemical knowledge. Thus, the expert bias is sought to be removed at all steps, and the chemical intuition is limited to the choice of the thermodynamic constraint imposed by the applicable experimental conditions in terms of threshold energy values for allowed transformations. The capabilities of the proposed methodology have been tested by exploring the reactivity of Mn complexes relevant for catalytic hydrogenation chemistry to verify previously postulated activation mechanisms and unravel unexpected reaction channels relevant to rare deactivation events.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

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

Catalytic Conversion of Alkenes on Acidic Zeolites: Automated Generation of Reaction Mechanisms and Lumping Technique

Acid-catalyzed hydrocarbon transformations are essential for industrial processes, including oligomerization, cracking, alkylation, and aromatization. However, these chemistries are extremely complex, and computational (automatic) reaction network generation is required to capture these intricacies. The approach relies on the concept that underlying mechanisms for the transformations can be described by a limited number of reaction families applied to various species, with both gaseous and protonated intermediate species tracked. Detailed reaction networks can then be tailored to each industrially relevant process for better understanding or for application in kinetic modeling, which is demonstrated here. However, we show that these networks can grow very large (thousands of species) when they are bound by typical carbon number and rank criteria, and lumping strategies are required to decrease computational expense. For acid-catalyzed hydrocarbon transformations, we propose lumping isomers based on carbon number, branch number, and ion position to reach high carbon limits while maintaining the high resolution of species. Two case studies on propene oligomerization verified the lumping technique in matching a fully detailed model as well as experimental data.

Data-driven learning how oncogenic gene expression locally alters heterocellular networks

Developing drugs increasingly relies on mechanistic modeling and simulation. Models that capture causal relations among genetic drivers of oncogenesis, functional plasticity, and host immunity complement wet experiments. Unfortunately, formulating such mechanistic cell-level models currently relies on hand curation, which can bias how data is interpreted or the priority of drug targets. In modeling molecular-level networks, rules and algorithms are employed to limit a priori biases in formulating mechanistic models. Here we combine digital cytometry with Bayesian network inference to generate causal models of cell-level networks linking an increase in gene expression associated with oncogenesis with alterations in stromal and immune cell subsets from bulk transcriptomic datasets. We predict how increased Cell Communication Network factor 4, a secreted matricellular protein, alters the tumor microenvironment using data from patients diagnosed with breast cancer and melanoma. Predictions are then tested using two immunocompetent mouse models for melanoma, which provide consistent experimental results.

While mechanistic models play increasing roles in immuno-oncology, hand network curation is current practice. Here the authors use a Bayesian data-driven approach to infer how expression of a secreted oncogene alters the cellular landscape within the tumor.

Concluding Remarks on Faraday Discussion on Unimolecular Reactions

This Faraday Discussion, marking the centenary of Lindemann’s explanation of the pressure-dependence of unimolecular reactions, presented recent advances in measuring and computing collisional energy transfer efficiencies, microcanonical rate coefficients, pressure-dependent...

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.

A quantitative multiscale perspective on primary olefin formation from methanol

The formation of the first C-C bond and primary olefins from methanol over zeolite and zeotype catalysts has been studied for over 40 years. Over 20 mechanisms have been proposed for the formation of the first C-C bond. In this quantitative multiscale perspective, we decouple the adsorption, desorption, mobility, and surface reactions of early species through a combination of vacuum and sub-vacuum studies using temporal analysis of products (TAP) reactor systems, and through studies with atmospheric fixed bed reactors. These results are supplemented with density functional theory calculations and data-driven physical models, using partial differential equations, that describe the temporal and spatial evolution of species. We consider the effects of steam, early degradation species, and product masking due to the inherent autocatalytic nature of the process, which all complicate the observation of the primary olefin(s). Although quantitative spectroscopic determination of the lifetimes, surface mobility, and reactivity of adspecies is still lacking in the literature, we observe that reaction barriers are competitive with adsorption enthalpies and/or activation energies of desorption, while facile diffusion occurs in the porous structures of the zeolite/zeotype catalysts. Understanding the various processes allows for quantitative evaluation of their competing energetics, which leads to molecular insights as to what governs the catalytic activity during the conversion of methanol to primary olefins over zeolite/zeotype catalysts.

Simultaneously improving reaction coverage and computational cost in automated reaction prediction tasks

Automated reaction prediction has the potential to elucidate complex reaction networks for applications ranging from combustion to materials degradation, but computational cost and inconsistent reaction coverage are still obstacles to exploring deep reaction networks. Here we show that cost can be reduced and reaction coverage can be increased simultaneously by relatively straightforward modifications of the reaction enumeration, geometry initialization and transition state convergence algorithms that are common to many prediction methodologies. These components are implemented in the context of yet another reaction program (YARP), our reaction prediction package with which we report reaction discovery benchmarks for organic single-step reactions, thermal degradation of a γ-ketohydroperoxide, and competing ring-closures in a large organic molecule. Compared with recent benchmarks, YARP (re)discovers both established and unreported reaction pathways and products while simultaneously reducing the cost of reaction characterization by nearly 100-fold and increasing convergence of transition states. This combination of ultra-low cost and high reaction coverage creates opportunities to explore the reactivity of larger systems and more complex reaction networks for applications such as chemical degradation, where computational cost is a bottleneck.

Perspective on computational reaction prediction using machine learning methods in heterogeneous catalysis

Heterogeneous catalysis plays a significant role in the modern chemical industry. Towards the rational design of novel catalysts, understanding reactions over surfaces is the most essential aspect. Typical industrial catalytic processes such as syngas conversion and methane utilisation can generate a large reaction network comprising thousands of intermediates and reaction pairs. This complexity not only arises from the permutation of transformations between species but also from the extra reaction channels offered by distinct surface sites. Despite the success in investigating surface reactions at the atomic scale, the huge computational expense of ab initio methods hinders the exploration of such complicated reaction networks. With the proliferation of catalysis studies, machine learning as an emerging tool can take advantage of the accumulated reaction data to emulate the output of ab initio methods towards swift reaction prediction. Here, we briefly summarise the conventional workflow of reaction prediction, including reaction network generation, ab initio thermodynamics and microkinetic modelling. An overview of the frequently used regression models in machine learning is presented. As a promising alternative to full ab initio calculations, machine learning interatomic potentials are highlighted. Furthermore, we survey applications assisted by these methods for accelerating reaction prediction, exploring reaction networks, and computational catalyst design. Finally, we envisage future directions in computationally investigating reactions and implementing machine learning algorithms in heterogeneous catalysis.

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.

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.

Role of External Field in Polymerization: Mechanism and Kinetics

The past decades have witnessed an increasing interest in developing advanced polymerization techniques subjected to external fields. Various physical modulations, such as temperature, light, electricity, magnetic field, ultrasound, and microwave irradiation, are noninvasive means, having superb but distinct abilities to regulate polymerizations in terms of process intensification and spatial and temporal controls. Gas as an emerging regulator plays a distinctive role in controlling polymerization and resembles a physical regulator in some cases. This review provides a systematic overview of seven types of external-field-regulated polymerizations, ranging from chain-growth to step-growth polymerization. A detailed account of the relevant mechanism and kinetics is provided to better understand the role of each external field in polymerization. In addition, given the crucial role of modeling and simulation in mechanisms and kinetics investigation, an overview of model construction and typical numerical methods used in this field as well as highlights of the interaction between experiment and simulation toward kinetics in the existing systems are given. At the end, limitations and future perspectives for this field are critically discussed. This state-of-the-art research progress not only provides the fundamental principles underlying external-field-regulated polymerizations but also stimulates new development of advanced polymerization methods.