Scaling Relationships and Volcano Plots in Homogeneous Catalysis

Proton-Coupled Electron Transfer Mechanisms for CO2 Reduction to Methanol Catalyzed by Surface-Immobilized Cobalt Phthalocyanine

Immobilized cobalt phthalocyanine (CoPc) is a highly promising architecture for the six-proton, six-electron reduction of CO2 to methanol. This electroreduction process relies on proton-coupled electron transfer (PCET) reactions that can occur by sequential or concerted mechanisms. Immobilization on a conductive support such as carbon nanotubes or graphitic flakes can fundamentally alter the PCET mechanisms. We use density functional theory (DFT) calculations of CoPc adsorbed on an explicit graphitic surface model to investigate intermediates in the electroreduction of CO2 to methanol. Our calculations show that the alignment of the CoPc and graphitic electronic states influences the reductive chemistry. These calculations also distinguish between charging the graphitic surface and reducing the CoPc and adsorbed intermediates as electrons are added to the system. This analysis allows us to identify the chemical transformations that are likely to be concerted PCET, defined for these systems as the mechanism in which protonation of a CO2 reduction intermediate is accompanied by electron abstraction from the graphitic surface to the adsorbate without thermodynamically stable intermediates. This work establishes a mechanistic pathway for methanol production that is consistent with experimental observations and provides fundamental insight into how immobilization of the CoPc impacts its CO2 reduction chemistry.

Microkinetic Molecular Volcano Plots for Enhanced Catalyst Selectivity and Activity Predictions

Molecular volcano plots, which facilitate the rapid prediction of the activity and selectivity of prospective catalysts, have emerged as powerful tools for computational catalysis. Here, we integrate microkinetic modeling into the volcano plot framework to develop "microkinetic molecular volcano plots". The resulting unified computational framework allows the influence of important reaction parameters, including temperature, reaction time, and concentration, to be quickly incorporated and more complex situations, such as off-cycle resting states and coupled catalytic cycles, to be tackled. Compared to previous generations of molecular volcanoes, these microkinetic counterparts offer a more comprehensive understanding of catalytic behavior, in which selectivity and product ratios can be explicitly determined by tracking the evolution of each product concentration over time. This is demonstrated by examining two case studies, rhodium-catalyzed hydroformylation and metal-catalyzed hydrosilylation, in which the unique insights provided by microkinetic modeling, as well as the ability to simultaneously screen catalysts and reaction conditions, are highlighted. To facilitate the construction of these plots/maps, we introduce mikimo, a Python program that seamlessly integrates with our previously developed automated volcano builder, volcanic.

Modeling Heterogeneous Catalysis and Electrocatalysis

With this special collection of articles with contributions from friends, former colleagues, collaborators, students, and postdocs, we celebrate Jens K. Nørskov′s belated 70th birthday. The studies reported here highlight just a small portion of the breadth and depth of Jens Nørskov's 40 years of influence in modeling heterogeneous catalysis and electrocatalysis. Many challenges remain in enabling in silico catalyst design, and the contributions in this special collection highlight the growing importance of machine learning approaches towards solving these challenges.

Machine Learning-Accelerated High-Throughput Computational Screening: Unveiling Bimetallic Nanoparticles with Peroxidase-Like Activity

Bimetallic nanoparticles (NPs) with peroxidase-like (POD-like) activity play a crucial role in biosensing, disease treatment, environmental management, and other fields. However, their development is impeded by a vast range of tunable properties in components and structures, making the establishment of structure-effect relationships and the discovery of active materials challenging. Addressing this, we established robust scaling relationships by meticulously analyzing the catalytic reaction networks of pure metal NPs, which laid the volcano-shaped correlation between the activity and O* adsorption energy. Utilizing these relationships, we introduced an innovative and versatile descriptor of the NPs, which was then integrated into a machine learning-accelerated high-throughput computational workflow, significantly boosting the predictive accuracy for the POD-like activity of bimetallic NPs. Our methodological approach enabled the successful prediction of activities for 1260 bimetallic NPs, leading to the identification of several highly effective catalysts. Furthermore, we distilled several strategies for designing efficient bimetallic NPs based on our screening results.

Thermodynamic and Kinetic Activity Descriptors for the Catalytic Hydrogenation of Ketones

Activity descriptors are a powerful tool for the design of catalysts that can efficiently utilize H2 with minimal energy losses. In this study, we develop the use of hydricity and H- self-exchange rates as thermodynamic and kinetic descriptors for the hydrogenation of ketones by molecular catalysts. Two complexes with known hydricity, HRh(dmpe)2 and HCo(dmpe)2, were investigated for the catalytic hydrogenation of ketones under mild conditions (1.5 atm and 25 °C). The rhodium catalyst proved to be an efficient catalyst for a wide range of ketones, whereas the cobalt catalyst could only hydrogenate electron-deficient ketones. Using a combination of experiment and electronic structure theory, thermodynamic hydricity values were established for 46 alkoxide/ketone pairs in both acetonitrile and tetrahydrofuran solvents. Through comparison of the hydricities of the catalysts and substrates, it was determined that catalysis was observed only for catalyst/ketone pairs with an exergonic H- transfer step. Mechanistic studies revealed that H- transfer was the rate-limiting step for catalysis, allowing for the experimental and computation construction of linear free-energy relationships (LFERs) for H- transfer. Further analysis revealed that the LFERs could be reproduced using Marcus theory, in which the H- self-exchange rates for the HRh/Rh+ and ketone/alkoxide pairs were used to predict the experimentally measured catalytic barriers within 2 kcal mol-1. These studies significantly expand the scope of catalytic reactions that can be analyzed with a thermodynamic hydricity descriptor and firmly establish Marcus theory as a valid approach to develop kinetic descriptors for designing catalysts for H- transfer reactions.

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.

Toward the Rational Design of More Efficient Mo2C Catalysts for Hydrodeoxygenation-Mechanism and Descriptor Identification

Viable alternatives to scarce and expensive noble-metal-based catalysts are transition-metal carbides such as Mo and W carbides. It has been shown that these are active and selective catalysts in the hydrodeoxygenation of renewable lipid-based feedstocks. However, the reaction mechanism and the structure-activity relationship of these transition-metal carbides have not yet been fully clarified. In this work, the reaction mechanism of butyric acid hydrodeoxygenation (HDO) over molybdenum carbide (Mo2C) has been studied comprehensively by means of density functional theory coupled with microkinetic modeling. We identified the rate-determining step to be butanol dissociation: C4H9*OH + * → C4H9* + *OH. Then we further explored the possibility to facilitate this step upon heteroatom doping and found that Zr- and Nb-doped Mo2C are the most promising catalysts with enhanced HDO catalytic activity. Linear-scaling relationships were established between the electronic and geometrical descriptors of the dopants and the catalytic performance of various doped Mo2C catalysts. It was demonstrated that descriptors such as dopants' d-band filling and atomic radius play key roles in governing the catalytic activity. This fundamental understanding delivers practical strategies for the rational design of Mo2C-based transition-metal carbide catalysts with improved HDO performance.

Reactivity Prediction of Cu-Catalyzed Halogen Atom Transfer Reactions Using Data-Driven Techniques

In catalysis, linear free energy relationships (LFERs) are commonly used to identify reaction descriptors that enable the prediction of outcomes and the design of more effective catalysts. Herein, LFERs are established for the reductive cleavage of the C(sp3)-X bond in alkyl halides (RX) by Cu complexes. This reaction represents the activation step in atom transfer radical polymerization and atom transfer radical addition/cyclization. The values of the activation rate constant, kact, for 107 Cu complex/RX couples in 5 different solvents spanning over 13 orders of magnitude were effectively interpolated by the equation: log kact = sC(I + C + S), where I, C, and S are, respectively, the initiator, catalyst, and solvent parameters, and sC is the catalyst-specific sensitivity parameter. Furthermore, each of these parameters was correlated to relevant descriptors, which included the bond dissociation free energy of RX and its Tolman cone angle θ, the electron affinity of X, the radical stabilization energy, the standard reduction potential of the Cu complex, the polarizability parameter π* of the solvent, and the distortion energy of the complex in its transition state. This set of descriptors establishes the fundamental properties of Cu complexes and RX that determine their reactivity and that need to be considered when designing novel systems for atom transfer radical reactions. Finally, a multivariate linear regression (MLR) approach was adopted to develop an objective model that surpassed the predictive capability of the LFER equation. Thus, the MLR model was employed to predict kact values for >2000 Cu complex/RX pairs.

Dynamic evolution of the active center driven by hemilabile coordination in Cu/CeO2 single-atom catalyst

Hemilability is an important concept in homogeneous catalysis where both the reactant activation and the product formation can occur simultaneously through a reversible opening and closing of the metal-ligand coordination sphere. However, this effect has rarely been discussed in heterogeneous catalysis. Here, by employing a theoretical study on CO oxidation over substituted Cu₁/CeO₂ single atom catalysts, we show that dynamic evolution of metal-support coordination can significantly change the electronic structure of the active center. The evolution of the active center is shown to either strengthen or weaken the metal-adsorbate bonding as the reaction proceeds from reactants, through intermediates, to products. As a result, the activity of the catalyst can be increased. We explain our observations by extending hemilability effects to single atom heterogenous catalysts and anticipate that introducing this concept can offer a new insight into the important role active site dynamics have in catalysis toward the rational design of more sophisticated single atom catalyst materials.

Analyzing Structure-Activity Variations for Mn-Carbonyl Complexes in the Reduction of CO2 to CO

Contemporary electrocatalysts for the reduction of CO₂ often suffer from low stability, activity, and selectivity, or a combination thereof. Mn-carbonyl complexes represent a promising class of molecular electrocatalysts for the reduction of CO₂ to CO as they are able to promote this reaction at relatively mild overpotentials, whereby rare-earth metals are not required. The electronic and geometric structure of the reaction center of these molecular electrocatalysts is precisely known and can be tuned via ligand modifications. However, ligand characteristics that are required to achieve high catalytic turnover at minimal overpotential remain unclear. We consider 55 Mn-carbonyl complexes, which have previously been synthesized and characterized experimentally. Four intermediates were identified that are common across all catalytic mechanisms proposed for Mn-carbonyl complexes, and their structures were used to calculate descriptors for each of the 55 Mn-carbonyl complexes. These electronic-structure-based descriptors encompass the binding energies, the highest occupied and lowest unoccupied molecular orbitals, and partial charges. Trends in turnover frequency and overpotential with these descriptors were analyzed to afford meaningful physical insights into what ligand characteristics lead to good catalytic performance, and how this is affected by the reaction conditions. These insights can be expected to significantly contribute to the rational design of more active Mn-carbonyl electrocatalysts.

Clear-Box Machine Learning for Virtual Screening of 2D Nanozymes to Target Tumor Hydrogen Peroxide

Targeting tumor hydrogen peroxide (H₂ O₂ ) with catalytic materials has provided a novel chemotherapy strategy against solid tumors. Because numerous materials have been fabricated so far, there is an urgent need for an efficient in silico method, which can automatically screen out appropriate candidates from materials libraries for further therapeutic evaluation. In this work, adsorption-energy-based descriptors and criteria are developed for the catalase-like activities of materials surfaces. The result enables a comprehensive prediction of H₂ O₂ -targeted catalytic activities of materials by density functional theory (DFT) calculations. To expedite the prediction, machine learning models, which efficiently calculate the adsorption energies for 2D materials without DFT, are further developed. The finally obtained method takes advantage of both interpretability of physics model and high efficiency of machine learning. It provides an efficient approach for in silico screening of 2D materials toward tumor catalytic therapy, and it will greatly promote the development of catalytic nanomaterials for medical applications.

The Sabatier principle as a tool for discovery and engineering of industrial enzymes

The recent breakthrough in all-atom, protein structure prediction opens new avenues for a range of computational approaches in enzyme design. These new approaches could become instrumental for the development of technical biocatalysts, and hence our transition toward more sustainable industries. Here, we discuss one approach, which is well-known within inorganic catalysis, but essentially unexploited in biotechnology. Specifically, we review examples of linear free-energy relationships (LFERs) for enzyme reactions and discuss how LFERs and the associated Sabatier Principle may be implemented in algorithms that estimate kinetic parameters and enzyme performance based on model structures.

Breaking the Volcano-Shaped Relationship for Highly Efficient Electrocatalytic Nitrogen Reduction: A Computational Guideline

The volcano-shaped relationship is very common in electrocatalytic nitrogen reduction reaction (e-NRR) and is usually caused by the competition between the first and last hydrogenation steps. How to break such a relationship to further improve the catalytic performance remains a great challenge. Herein, using first-principles calculations, we investigate a range of transition-metal (TM)-doped Cu-based single-atom alloys (TM₁-Cu(111)) as catalysts for e-NRR. When the adsorption of N₂ on the catalysts is strong enough, the inert N₂ molecules can be effectively activated for the first hydrogenation step. Meanwhile, the last hydrogenation step is not affected by the scaling relationship and remains easy on all of the catalysts due to the unstable top-site adsorption of NH₂, resulting in the break of the volcano-shaped relationship in e-NRR. Thus, only the first hydrogenation step is identified as the potential determining step. Four TM₁-Cu(111) catalysts (TM = Re, W, Tc, and Mo) are selected as promising catalysts with limiting potential ranging from -0.38 to -0.56 V, showing outstanding e-NRR activity. Besides, the four catalysts also inhibit the competing hydrogen evolution reaction and long-term stability. Our work provides a guideline for breaking the volcano-shaped relationship in e-NRR and significant in the rational design of highly efficient electrocatalysts.

Design of Single-Atom Catalysts and Tracking Their Fate Using Operando and Advanced X-ray Spectroscopic Tools

The potential of operando X-ray techniques for following the structure, fate, and active site of single-atom catalysts (SACs) is highlighted with emphasis on a synergetic approach of both topics. X-ray absorption spectroscopy (XAS) and related X-ray techniques have become fascinating tools to characterize solids and they can be applied to almost all the transition metals deriving information about the symmetry, oxidation state, local coordination, and many more structural and electronic properties. SACs, a newly coined concept, recently gained much attention in the field of heterogeneous catalysis. In this way, one can achieve a minimum use of the metal, theoretically highest efficiency, and the design of only one active site-so-called single site catalysts. While single sites are not easy to characterize especially under operating conditions, XAS as local probe together with complementary methods (infrared spectroscopy, electron microscopy) is ideal in this research area to prove the structure of these sites and the dynamic changes during reaction. In this review, starting from their fundamentals, various techniques related to conventional XAS and X-ray photon in/out techniques applied to single sites are discussed with detailed mechanistic and in situ/operando studies. We systematically summarize the design strategies of SACs and outline their exploration with XAS supported by density functional theory (DFT) calculations and recent machine learning tools.

A predictive journey towards trans-thioamides/amides

The cis-trans isomerization of (thio)amides was studied by DFT calculations to get the model for the higher preference for the cis conformation by guided predictive chemistry, suggesting how to select the alkyl/aryl substituents on the C/N atoms that lead to the trans isomer. Multilinear analysis, together with cross-validation analysis, helped to select the best fitting parameters to achieve the energy barriers of the cis to trans interconversion, as well as the relative stability between both isomers. Double experimental check led to the synthesis of the best trans candidate with sterically demanding t-butyl substituents, confirming the utility of predictive chemistry, bridging organic and computational chemistry.

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 Active Site Geometry to Activity in Immobilized Frustrated Lewis Pair Catalysts

The immobilization of molecular catalysts imposes spatial constraints on their active site. We reveal that in bifunctional catalysis such constraints can also be utilized as an appealing handle to boost intrinsic activity through judicious control of the active site geometry. To demonstrate this, we develop a pragmatic approach, based on nonlinear scaling relationships, to map the spatial arrangements of the acid–base components of frustrated Lewis pairs (FLPs) to their performance in the catalytic hydrogenation of CO₂. The resulting activity map shows that fixing the donor–acceptor centers at specific distances and locking them into appropriate orientations leads to an unforeseen many‐fold increase in the catalytic activity of FLPs compared to their unconstrained counterparts.

Inverse molecular design of alkoxides and phenoxides for aqueous direct air capture of CO2

Aqueous direct air capture (DAC) is a key technology toward a carbon negative infrastructure. Developing sorbent molecules with water and oxygen tolerance and high CO₂ binding capacity is therefore highly desired. We analyze the CO₂ absorption chemistries on amines, alkoxides, and phenoxides with density functional theory calculations, and perform inverse molecular design of the optimal sorbent. The alkoxides and phenoxides are found to be more suitable for aqueous DAC than amines thanks to their water tolerance (lower pK_a prevents protonation by water) and capture stoichiometry of 1:1 (2:1 for amines). All three molecular systems are found to generally obey the same linear scaling relationship (LSR) between [Formula: see text] and [Formula: see text], since both CO₂ and proton are bonded to the nucleophilic (alkoxy or amine) binding site through a majorly [Formula: see text] bonding orbital. Several high-performance alkoxides are proposed from the computational screening. Phenoxides have comparatively poorer correlation between [Formula: see text] and [Formula: see text], showing promise for optimization. We apply a genetic algorithm to search the chemical space of substituted phenoxides for the optimal sorbent. Several promising off-LSR candidates are discovered. The most promising one features bulky ortho substituents forcing the CO₂ adduct into a perpendicular configuration with respect to the aromatic ring. In this configuration, the phenoxide binds CO₂ and a proton using different molecular orbitals, thereby decoupling the [Formula: see text] and [Formula: see text]. The [Formula: see text] trend and off-LSR behaviors are then confirmed by experiments, validating the inverse molecular design framework. This work not only extensively studies the chemistry of the aqueous DAC, but also presents a transferrable computational workflow for understanding and optimization of other functional molecules.

A framework for constructing linear free energy relationships to design molecular transition metal catalysts

A computational framework for ligand-driven design of transition metal complexes is presented in this work. We propose a general procedure for the construction of active site-specific linear free energy relationships (LFERs), which are inspired from Hammett and Taft correlations in organic chemistry and grounded in the activation strain model (ASM). Ligand effects are isolated and quantified in terms of their contribution to interaction and strain energy components of ASM. Scalar descriptors that are easily obtainable are then employed to construct the complete LFER. We successfully demonstrate proof-of-concept by constructing and applying an LFER to CH activation with enzyme-inspired [Cu2O2]2+ complexes. The key benefit of using ASM is a built-in compensation or error cancellation between LFER prediction of interaction and strain terms, resulting in accurate barrier predictions for 37 of the 47 catalysts examined in this study. The LFER is also transferable with respect to level of theory and flexible towards the choice of reference system. The absence of interaction-strain compensation or poor model performance for the remaining systems is a consequence of the approximate nature of the chosen interaction energy descriptor and LFER construction of the strain term, which focuses largely on trends in substrate and not catalyst strain.

Physical constraints and functional plasticity of cellulases

Enzyme reactions, both in Nature and technical applications, commonly occur at the interface of immiscible phases. Nevertheless, stringent descriptions of interfacial enzyme catalysis remain sparse, and this is partly due to a shortage of coherent experimental data to guide and assess such work. In this work, we produced and kinetically characterized 83 cellulases, which revealed a conspicuous linear free energy relationship (LFER) between the substrate binding strength and the activation barrier. The scaling occurred despite the investigated enzymes being structurally and mechanistically diverse. We suggest that the scaling reflects basic physical restrictions of the hydrolytic process and that evolutionary selection has condensed cellulase phenotypes near the line. One consequence of the LFER is that the activity of a cellulase can be estimated from its substrate binding strength, irrespectively of structural and mechanistic details, and this appears promising for in silico selection and design within this industrially important group of enzymes.

A computational approach to understand the role of metals and axial ligands in artificial heme enzyme catalyzed C-H insertion

Engineered heme enzymes such as myoglobin and cytochrome P450s metalloproteins are gaining widespread importance due to their efficiency in catalyzing non-natural reactions. In a recent strategy, the naturally occurring Fe metal in the heme unit was replaced with non-native metals such as Ir, Rh, Co, Cu, etc., and axial ligands to generate artificial metalloenzymes. Determining the best metal-ligand for a chemical transformation is not a trivial task. Here we demonstrate how computational approaches can be used in deciding the best metal-ligand combination which would be highly beneficial in designing new enzymes as well as small molecule catalysts. We have used Density Functional Theory (DFT) to shed light on the enhanced reactivity of an Ir system with varying axial ligands. We look at the insertion of a carbene group generated from diazo precursors via N2 extrusion into a C-H bond. For both Ir(Me) and Fe systems, the first step, i.e., N2 extrusion is the rate determining step. Strikingly, neither the better ligand overlap with 5d orbitals on Ir nor the electrophilicity on the carbene centre play a significant role. A comparison of Fe and Ir systems reveals that a lower distortion in the Ir(Me)-porphyrin on moving from the reactant to the transition state renders it catalytically more active. We notice that for both metal porphyrins, the free energy barriers are affected by axial ligand substitution. Further, for Fe porphyrin, the axial ligand also changes the preferred spin state. We show that for the carbene insertion into the C-H bond, Fe porphyrin systems undergo a stepwise HAT (hydrogen atom transfer) instead of a concerted hydride transfer process. Importantly, we find that the substitution of the axial Me ligand on Ir to imidazole or chloride, or without an axial substitution changes the rate determining step of the reaction. Therefore, an optimum ligand that can balance the barriers for both steps of the catalytic cycle is essential. We subsequently used the QM cluster approach to delineate the protein environment's role and mutations in improving the catalytic activity of the Ir(Me) system.

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.