Scaling Relationships for Binding Energies of Transition Metal Complexes

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.

Chemical Looping Technology in Mild-Condition Ammonia Production: A Comprehensive Review and Analysis

Ammonia is an efficient and clean hydrogen carrier that promises to tackle the increasing energy and environmental problems. However, more than 90% of ammonia is produced by the Haber-Bosch process, and its enormous energy consumption and CO2 emissions require the development of novel alternatives. Chemical looping technology can decouple the one-step ammonia synthesis reaction into separated nitridation and hydrogenation processes at atmospheric pressure, thereby achieving the mild ammonia synthesis based on renewable energy. The strategy of stepwise reactions circumvents the problem of competing adsorption of N2 and H2 /H2 O at the active sites and provides additive freedom for optimal regulation of sub-reactions. This review introduces the concept and mechanism of chemical looping ammonia production (CLAP), and comprehensively summarizes the state-of-art research from the perspective of reaction pathways and nitrogen carriers. The challenges faced by CLAP and strategies to address them in terms of nitrogen carriers, methods, equipment, and technological processes are also proposed.

Benchmark Study of Density Functional Theory Methods in Geometry Optimization of Transition Metal-Dinitrogen Complexes

The current benchmark study is focused on determining the most precise theoretical method for optimizing the geometry of transition metal-dinitrogen complexes. To accomplish this goal, seven density functional (DF) methods from five distinct classes of density functional theory (DFT) have been selected, including B3LYP-D3(BJ), BP86-D3(BJ), PBE0-D3(BJ), ωB97X-D, M06, M06-L, and TPSSh-D3(BJ). These DFs will be utilized with the Karlsruhe basis set (def2-SVP). To carry out this benchmark study, a total of forty-two structurally diverse transition metal-dinitrogen compounds with experimentally known X-ray data have been selected from the Cambridge Crystallographic Data Centre (CCDC). Based on a comparison of the theoretical data with experimental values (X-ray) of the selected transition metal-dinitrogen compounds, statistical parameters such as root-mean-square deviation (RMSD) and N-N and M-N bond lengths are obtained to evaluate the performance of the seven chosen DFs. According to the obtained results, among all DFT methods used in the study, Minnesota functionals (M06 and M06-L) and TPSSh-D3(BJ) show good performance, with lower RMSD values. This suggests that these three methods are the most reliable for optimizing the geometry of transition metal-dinitrogen complexes. Based on the absolute errors of the N-N and M-N bond lengths relative to the X-ray data, further analysis is conducted, and it is determined that M06-L is the best functional for optimizing the geometry of transition metal-dinitrogen compounds. Additionally, the influence of using a high-level basis set (def2-TZVP) compared to def2-SVP on the calculated RMSD among the seven chosen methods is found to be negligible.

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.

Tandem electrocatalytic N2 fixation via proton-coupled electron transfer

New electrochemical ammonia (NH3) synthesis technologies are of interest as a complementary route to the Haber-Bosch process for distributed fertilizer generation, and towards exploiting ammonia as a zero-carbon fuel produced via renewably sourced electricity1. Apropos of these goals is a surge of fundamental research targeting heterogeneous materials as electrocatalysts for the nitrogen reduction reaction (N2RR)2. These systems generally suffer from poor stability and NH3 selectivity; the hydrogen evolution reaction (HER) outcompetes N2RR3. Molecular catalyst systems can be exquisitely tuned and offer an alternative strategy4, but progress has been thwarted by the same selectivity issue; HER dominates. Here we describe a tandem catalysis strategy that offers a solution to this puzzle. A molecular complex that can mediate an N2 reduction cycle is partnered with a co-catalyst that interfaces the electrode and an acid to mediate proton-coupled electron transfer steps, facilitating N-H bond formation at a favourable applied potential (-1.2 V versus Fc+/0) and overall thermodynamic efficiency. Certain intermediates of the N2RR cycle would be otherwise unreactive via uncoupled electron transfer or proton transfer steps. Structurally diverse complexes of several metals (W, Mo, Os, Fe) also mediate N2RR electrocatalysis at the same potential in the presence of the mediator, pointing to the generality of this tandem approach.

Comprehensive insights into synthetic nitrogen fixation assisted by molecular catalysts under ambient or mild conditions

N2 is fixed as NH3 industrially by the Haber-Bosch process under harsh conditions, whereas biological nitrogen fixation is achieved under ambient conditions, which has prompted development of alternative methods to fix N2 catalyzed by transition metal molecular complexes. Since the early 21st century, catalytic conversion of N2 into NH3 under ambient conditions has been achieved by using molecular catalysts, and now H2O has been utilized as a proton source with turnover frequencies reaching the values found for biological nitrogen fixation. In this review, recent advances in the development of molecular catalysts for synthetic N2 fixation under ambient or mild conditions are summarized, and potential directions for future research are also discussed.

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.

Catalytic N2-to-NH3 (or -N2H4) Conversion by Well-Defined Molecular Coordination Complexes

Nitrogen fixation, the six-electron/six-proton reduction of N₂, to give NH₃, is one of the most challenging and important chemical transformations. Notwithstanding the barriers associated with this reaction, significant progress has been made in developing molecular complexes that reduce N₂ into its bioavailable form, NH₃. This progress is driven by the dual aims of better understanding biological nitrogenases and improving upon industrial nitrogen fixation. In this review, we highlight both mechanistic understanding of nitrogen fixation that has been developed, as well as advances in yields, efficiencies, and rates that make molecular alternatives to nitrogen fixation increasingly appealing. We begin with a historical discussion of N₂ functionalization chemistry that traverses a timeline of events leading up to the discovery of the first bona fide molecular catalyst system and follow with a comprehensive overview of d-block compounds that have been targeted as catalysts up to and including 2019. We end with a summary of lessons learned from this significant research effort and last offer a discussion of key remaining challenges in the field.

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.

Accessing and predicting the kinetic profiles of homogeneous catalysts from volcano plots

Volcano plots, which generally describe only thermodynamics, are expanded to include kinetics that markedly influence the performance of homogeneous catalysts.

Volcano plots are frequently used as aids in the search for new heterogeneous and electrochemical catalysts. These tools successfully predict catalytic processes based solely on thermodynamic descriptions, which also capably describe many aspects of the catalytic cycles of homogeneous species. However, homogeneous catalysts also frequently depend upon the kinetic influences brought about by steric interactions to promote or prevent specific chemical reactions. Here, a prototypical transformation facilitated by a homogeneous catalysis, the hydroformylation of an olefin using CO and H₂, is examined to establish the viability of creating kinetic volcano plots and to determine their ability to ascertain the influences steric bulk plays on catalytic cycle energetics. Similar to their thermodynamic counterparts, kinetic volcanoes successfully reproduce many experimentally known facets of the hydroformylation reaction. In contrast to thermodynamic volcanoes, kinetic volcanoes emphasize changes in the height of the different activation barriers brought about by steric interactions. This crucial information, however, comes with considerable computational cost, since the transition states of catalysts bearing large bulky ligands must be identified and characterized. To overcome this drawback, a procedure is proposed that relates a simple steric parameter, the Tolman cone angle, with the descriptors used to create the kinetic volcano plots. In this way, the activation barriers of bulky catalysts can be estimated without requiring expensive transition state computations. These newly derived structure–activity relationship volcano plots represent useful tools for identifying new homogeneous catalysts.

Polarization-driven catalysis via ferroelectric oxide surfaces

Ferroelectric polarization can tune the surface chemistry: enhancing technologically important catalytic reactions such as NO_x direct decomposition and SO₂ oxidation.