On the Generality of Molecular Volcano Plots

Automated de Novo Design of Olefin Metathesis Catalysts: Computational and Experimental Analysis of a Simple Thermodynamic Design Criterion

Methods for computational de novo design of inorganic molecules have paved the way for automated design of homogeneous catalysts. Such studies have so far relied on correlation-based prediction models as fitness functions (figures of merit), but the soundness of these approaches has yet to be tested by experimental verification of de novo-designed catalysts. Here, a previously developed criterion for the optimization of dative ligands L in ruthenium-based olefin metathesis catalysts RuCl2(L)(L')(═CHAr), where Ar is an aryl group and L' is a phosphine ligand dissociating to activate the catalyst, was used in de novo design experiments. These experiments predicted catalysts bearing an N-heterocyclic carbene (L = 9) substituted by two N-bound mesityls and two tert-butyl groups at the imidazolidin-2-ylidene backbone to be promising. Whereas the phosphine-stabilized precursor assumed by the prediction model could not be made, a pyridine-stabilized ruthenium alkylidene complex (17) bearing carbene 9 was less active than a known leading pyridine-stabilized Grubbs-type catalyst (18, L = H2IMes). A density functional theory-based analysis showed that the unsubstituted metallacyclobutane (MCB) intermediate generated in the presence of ethylene is the likely resting state of both 17 and 18. Whereas the design criterion via its correlation between the stability of the MCB and the rate-determining barrier indeed seeks to stabilize the MCB, it relies on RuCl2(L)(L')(═CH2) adducts as resting states. The change in resting state explains the discrepancy between the prediction and the actual performance of catalyst 17. To avoid such discrepancies and better address the multifaceted challenges of predicting catalytic performance, future de novo catalyst design studies should explore and test design criteria incorporating information from more than a single relative energy or intermediate.

Zeolite encapsulated organometallic complexes as model catalysts

Heterogeneities in the structure of active centers in metal-containing porous materials are unavoidable and complicate the description of chemical events occurring along reaction coordinates at the atomic level. Metal containing zeolites include sites of varied local coordination and secondary confining environments, requiring careful titration protocols to quantify the predominant active sites. Hybrid organometallic-zeolite catalysts are useful well-defined platform materials for spectroscopic, kinetic, and computational studies of heterogeneous catalysis that avoid the complications of conventional metal-containing porous materials. Such materials have been synthesized and studied previously, but catalytic applications were mostly limited to liquid-phase oxidation and electrochemical reactions. The hydrothermal stability, time-on-stream stability, and utility of these materials in gas-phase oxidation reactions are under-studied. The potential applications for single-site heterogeneous catalysts in fundamental research are abundant and motivate future synthetic, spectroscopic, kinetic, and computational studies.

Tetraphenylporphyrin electrocatalysts for the hydrogen evolution reaction: applicability of molecular volcano plots to experimental operating conditions

Recent years have seen an increasing interest in molecular electrocatalysts for the hydrogen evolution reaction (HER). Efficient hydrogen evolution would play an important role in a sustainable fuel economy, and molecular systems could serve as highly specific and tunable alternatives to traditional noble metal surface catalysts. However, molecular catalysts are currently mostly used in homogeneous setups, where quantitative evaluation of catalytic activity is non-standardized and cumbersome, in particular for multistep, multielectron processes. The molecular design community would therefore be well served by a straightforward model for prediction and comparison of the efficiency of molecular catalysts. Recent developments in this area include attempts at applying the Sabatier principle and the volcano plot concept - popular tools for comparing metal surface catalysts - to molecular catalysis. In this work, we evaluate the predictive power of these tools in the context of experimental operating conditions, by applying them to a series of tetraphenylporphyrins employed as molecular electrocatalysts of the HER. We show that the binding energy of H and the redox chemistry of the porphyrins depend solely on the electron withdrawing ability of the central metal ion, and that the thermodynamics of the catalytic cycle follow a simple linear free energy relation. We also find that the catalytic efficiency of the porphyrins is almost exclusively determined by reaction kinetics and therefore cannot be explained by thermodynamics alone. We conclude that the Sabatier principle, linear free energy relations and molecular volcano plots are insufficient tools for predicting and comparing activity of molecular catalysts, and that experimentally useful information of catalytic performance can still only be obtained through detailed knowledge of the catalytic pathway for each individual system.

Materials Screening by the Descriptor G max(η): The Free-Energy Span Model in Electrocatalysis

To move from fossil-based energy resources to a society based on renewables, electrode materials free of precious noble metals are required to efficiently catalyze electrochemical processes in fuel cells, batteries, or electrolyzers. Materials screening operating at minimal computational cost is a powerful method to assess the performance of potential electrode compositions based on heuristic concepts. While the thermodynamic overpotential in combination with the volcano concept refers to the most popular descriptor-based analysis in the literature, this notion cannot reproduce experimental trends reasonably well. About two years ago, the concept of G _max(η), based on the idea of the free-energy span model, has been proposed as a universal approach for the screening of electrocatalysts. In contrast to other available descriptor-based methods, G _max(η) factors overpotential and kinetic effects by a dedicated evacuation scheme of adsorption free energies into an analysis of trends. In the present perspective, we discuss the application of G _max(η) to different electrocatalytic processes, including the oxygen evolution and reduction reactions, the nitrogen reduction reaction, and the selectivity problem of the competing oxygen evolution and peroxide formation reactions, and we outline the advantages of this screening approach over previous investigations.

Constructing and interpreting volcano plots and activity maps to navigate homogeneous catalyst landscapes

Volcano plots and activity maps are powerful tools for studying homogeneous catalysis. Once constructed, they can be used to estimate and predict the performance of a catalyst from one or more descriptor variables. The relevance and utility of these tools has been demonstrated in several areas of catalysis, with recent applications to homogeneous catalysts having been pioneered by our research group. Both volcano plots and activity maps are built from linear free energy scaling relationships that connect the value of a descriptor variable(s) with the relative energies of other catalytic cycle intermediates/transition states. These relationships must be both constructed and postprocessed appropriately to obtain the resulting plots/maps; this process requires careful execution to obtain meaningful results. In this protocol, we provide a step-by-step guide to building volcano plots and activity maps using curated reaction profile data. The reaction profile data are obtained using density functional theory computations to model the catalytic cycle. In addition, we provide volcanic, a Python code that automates the steps of the process following data acquisition. Unlike the computation of individual reaction energy profiles, our tools lead to a holistic view of homogeneous catalyst performance that can be broadly applied for both explanatory and screening purposes.

Mapping Catalyst–Solvent Interplay in Competing Carboamination/Cyclopropanation Reactions

Group 9 metals, in particular Rh^III complexes with cyclopentadienyl ligands, are competent C−H activation catalysts. Recently, a Cp*Rh^III‐catalyzed reaction of alkenes with N‐enoxyphthalimides showed divergent outcome based on the solvent, with carboamination favored in methanol and cyclopropanation in 2,2,2‐trifluoroethanol (TFE). Here, we create selectivity and activity maps capable of unravelling the catalyst‐solvent interplay on the outcome of these competing reactions by analyzing 42 cyclopentadienyl metal catalysts, Cp^XM^III (M=Co, Rh, Ir). These maps not only can be used to rationalize previously reported experimental results, but also capably predict the behavior of untested catalyst/solvent combinations as well as aid in identifying experimental protocols that simultaneously optimize both catalytic activity and selectivity (solutions in the Pareto front). In this regard, we demonstrate how and why the experimentally employed Cp*Rh^III catalyst represents an ideal choice to invoke a solvent‐induced change in reactivity. Additionally, the maps reveal the degree to which even perceived minor changes in the solvent (e. g., replacing methanol with ethanol) influence the ratio of carboamination and cyclopropanation products. Overall, the selectivity and activity maps presented here provide a generalizable tool to create global pictures of anticipated reaction outcome that can be used to develop new experimental protocols spanning metal, ligand, and solvent space.

Metal-Free Catalytic Hydrogenolysis of Silyl Triflates and Halides into Hydrosilanes

The metal-free catalytic hydrogenolysis of silyl triflates and halides (I, Br) to hydrosilanes is unlocked by using arylborane Lewis acids as catalysts. In the presence of a nitrogen base, the catalyst acts as a Frustrated Lewis Pair (FLP) able to split H₂ and generate a boron hydride intermediate capable of reducing (pseudo)halosilanes. This metal-free organocatalytic system is competitive with metal-based catalysts and enables the formation of a variety of hydrosilanes at room temperature in high yields (>85 %) under a low pressure of H₂ (≤10 bar).

New Strategies for Direct Methane-to-Methanol Conversion from Active Learning Exploration of 16 Million Catalysts

Despite decades of effort, no earth-abundant homogeneous catalysts have been discovered that can selectively oxidize methane to methanol. We exploit active learning to simultaneously optimize methane activation and methanol release calculated with machine learning-accelerated density functional theory in a space of 16 M candidate catalysts including novel macrocycles. By constructing macrocycles from fragments inspired by synthesized compounds, we ensure synthetic realism in our computational search. Our large-scale search reveals that low-spin Fe(II) compounds paired with strong-field (e.g., P or S-coordinating) ligands have among the best energetic tradeoffs between hydrogen atom transfer (HAT) and methanol release. This observation contrasts with prior efforts that have focused on high-spin Fe(II) with weak-field ligands. By decoupling equatorial and axial ligand effects, we determine that negatively charged axial ligands are critical for more rapid release of methanol and that higher-valency metals [i.e., M(III) vs M(II)] are likely to be rate-limited by slow methanol release. With full characterization of barrier heights, we confirm that optimizing for HAT does not lead to large oxo formation barriers. Energetic span analysis reveals designs for an intermediate-spin Mn(II) catalyst and a low-spin Fe(II) catalyst that are predicted to have good turnover frequencies. Our active learning approach to optimize two distinct reaction energies with efficient global optimization is expected to be beneficial for the search of large catalyst spaces where no prior designs have been identified and where linear scaling relationships between reaction energies or barriers may be limited or unknown.

Trends in computational molecular catalyst design

Computational methods have emerged as a powerful tool to augment traditional experimental molecular catalyst design by providing useful predictions of catalyst performance and decreasing the time needed for catalyst screening. In this perspective, we discuss three approaches for computational molecular catalyst design: (i) the reaction mechanism-based approach that calculates all relevant elementary steps, finds the rate and selectivity determining steps, and ultimately makes predictions on catalyst performance based on kinetic analysis, (ii) the descriptor-based approach where physical/chemical considerations are used to find molecular properties as predictors of catalyst performance, and (iii) the data-driven approach where statistical analysis as well as machine learning (ML) methods are used to obtain relationships between available data/features and catalyst performance. Following an introduction to these approaches, we cover their strengths and weaknesses and highlight some recent key applications. Furthermore, we present an outlook on how the currently applied approaches may evolve in the near future by addressing how recent developments in building automated computational workflows and implementing advanced ML models hold promise for reducing human workload, eliminating human bias, and speeding up computational catalyst design at the same time. Finally, we provide our viewpoint on how some of the challenges associated with the up-and-coming approaches driven by automation and ML may be resolved.

The Genesis of Molecular Volcano Plots

ConspectusFor the past two decades, linear free energy scaling relationships and volcano plots have seen frequent use as computational tools that aid in understanding and predicting the catalytic behavior of heterogeneous and electrocatalysts. Based on Sabatier's principle, which states that a catalyst should bind a substrate neither too strongly nor too weakly, volcano plots provide an estimate of catalytic performance (e.g., overpotential, catalytic cycle thermodynamics/kinetics, etc.) through knowledge of a descriptor variable. By the use of linear free energy scaling relationships, the value of this descriptor is employed to estimate the relative energies of other catalytic cycle intermediates/transition states. Postprocessing of these relationships leads to a volcano curve that reveals the anticipated performance of each catalyst, with the best species appearing on or near the peak or plateau. While the origin of volcanoes is undoubtedly rooted in examining heterogeneously catalyzed reactions, only recently has this concept been transferred to the realm of homogeneous catalysis. This Account summarizes the work done by our group in implementing and refining "molecular volcano plots" for use in analyzing and predicting the behavior of homogeneous catalysts.We begin by taking the reader through the initial proof-of-principle study that transferred the model from heterogeneous to homogeneous catalysis by examining thermodynamic aspects of a Suzuki-Miyaura cross-coupling reaction. By establishing linear free energy scaling relationships and reproducing the volcano shape, we definitively showed that volcano plots are also valid for homogeneous systems. On the basis of this key finding, we further illustrate how unified pictures of C-C cross-coupling thermodynamics were created using three-dimensional molecular volcanoes.The second section highlights an important transformation from "thermodynamic" to "kinetic" volcanoes by using the descriptor variable to directly estimate transition state barriers. Taking this idea further, we demonstrate how volcanoes can be used to directly predict an experimental observable, the turnover frequency. Discussion is also provided on how different flavors of molecular volcanoes can be used to analyze aspects of homogeneous catalysis of interest to experimentalists, such as determining the product selectivity and probing the substrate scope.The third section focuses on incorporating machine learning approaches into molecular volcanoes and invoking big-data-type approaches in the analysis of catalytic behavior. Specifically, we illustrate how machine learning can be used to predict the value of the descriptor variable, which facilitates nearly instantaneous screening of thousands of catalysts. With the large amount of data created from the machine learning/volcano plot tandem, we show how the resulting database can be mined to garner an enhanced understanding of catalytic processes. Emphasis is also placed on the latest generation of augmented volcano plots, which differ fundamentally from earlier volcanoes by elimination of the use of linear free energy scaling relationships and by assessment of the similarity of the complete catalytic cycle energy profile to that for an ideal reference species that is used to discriminate catalytic performance.We conclude by examining a handful of applications of molecular volcano plots to interesting problems in homogeneous catalysis and offering thoughts on the future prospects and uses of this new set of tools.

Scaling Relationships and Volcano Plots in Homogeneous Catalysis

Scaling relations and volcano plots are widely used in heterogeneous catalysis. In this Perspective, we discuss the prospects and challenges associated with the application of similar concepts in homogeneous catalysis using examples from the literature that have appeared recently.

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.

Scaling relationships and volcano plots of homogeneous transition metal catalysis

This Frontier article highlights the recent applications of linear scaling relationships and volcano plots in homogeneous transition metal catalysis.

Machine learning meets volcano plots: computational discovery of cross-coupling catalysts

The application of modern machine learning to challenges in atomistic simulation is gaining attraction.

The application of modern machine learning to challenges in atomistic simulation is gaining attraction. We present new machine learning models that can predict the energy of the oxidative addition process between a transition metal complex and a substrate for C–C cross-coupling reactions. In turn, this quantity can be used as a descriptor to estimate the activity of homogeneous catalysts using molecular volcano plots. The versatility of this approach is illustrated for vast libraries of organometallic catalysts based on Pt, Pd, Ni, Cu, Ag, and Au combined with 91 ligands. Out-of-sample machine learning predictions were made on a total of 18 062 compounds leading to 557 catalyst candidates falling into the ideal thermodynamic window. This number was further refined by searching for candidates with an estimated price lower than 10 US$ per mmol. The 37 catalyst finalists are dominated by palladium phosphine ligand combinations but also include the earth abundant transition metal (Cu) with less common ligands. Our results indicate that modern statistical learning techniques can be applied to the computational discovery of readily available and promising catalyst candidates.