Machine Learning Accelerates the Discovery of Design Rules and Exceptions in Stable Metal–Oxo Intermediate Formation

Leveraging natural language processing to curate the tmCAT, tmPHOTO, tmBIO, and tmSCO datasets of functional transition metal complexes

The breadth of transition metal chemical space covered by databases such as the Cambridge Structural Database and the derived computational database tmQM is not conducive to application-specific modeling and the development of structure-property relationships. Here, we employ both supervised and unsupervised natural language processing (NLP) techniques to link experimentally synthesized compounds in the tmQM database to their respective applications. Leveraging NLP models, we curate four distinct datasets: tmCAT for catalysis, tmPHOTO for photophysical activity, tmBIO for biological relevance, and tmSCO for magnetism. Analyzing the chemical substructures within each dataset reveals common chemical motifs in each of the designated applications. We then use these common chemical structures to augment our initial datasets for each application, yielding a total of 21 631 compounds in tmCAT, 4599 in tmPHOTO, 2782 in tmBIO, and 983 in tmSCO. These datasets are expected to accelerate the more targeted computational screening and development of refined structure-property relationships with machine learning.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Computational Discovery of Stable Metal-Organic Frameworks for Methane-to-Methanol Catalysis

The challenge of direct partial oxidation of methane to methanol has motivated the targeted search of metal-organic frameworks (MOFs) as a promising class of materials for this transformation because of their site-isolated metals with tunable ligand environments. Thousands of MOFs have been synthesized, yet relatively few have been screened for their promise in methane conversion. We developed a high-throughput virtual screening workflow that identifies MOFs from a diverse space of experimental MOFs that have not been studied for catalysis, yet are thermally stable, synthesizable, and have promising unsaturated metal sites for C-H activation via a terminal metal-oxo species. We carried out density functional theory calculations of the radical rebound mechanism for methane-to-methanol conversion on models of the secondary building units (SBUs) from 87 selected MOFs. While we showed that oxo formation favorability decreases with increasing 3d filling, consistent with prior work, previously observed scaling relations between oxo formation and hydrogen atom transfer (HAT) are disrupted by the greater diversity in our MOF set. Accordingly, we focused on Mn MOFs, which favor oxo intermediates without disfavoring HAT or leading to high methanol release energies─a key feature for methane hydroxylation activity. We identified three Mn MOFs comprising unsaturated Mn centers bound to weak-field carboxylate ligands in planar or bent geometries with promising methane-to-methanol kinetics and thermodynamics. The energetic spans of these MOFs are indicative of promising turnover frequencies for methane to methanol that warrant further experimental catalytic studies.

Computational Screening of Supported Metal Oxide Nanoclusters for Methane Activation: Insights into Homolytic versus Heterolytic C-H Bond Dissociation

Since its discovery in zeolites, the [CuOCu]²⁺ motif has played an important role in our understanding of selective methane activation over supported metal oxide nanoclusters. Although there are two known C-H bond dissociation mechanisms, namely, homolytic and heterolytic cleavage, most computational studies on optimizing metal oxide nanoclusters for improved methane activation reactivity have focused only on the homolytic mechanism. In this work, both mechanisms were examined for a set of 21 mixed metal oxide complexes of the form of [M₁OM₂]²⁺ (M₁ and M₂ = Mn, Fe, Co, Ni, Cu, and Zn). Except for pure copper, heterolytic cleavage was found to be the dominant C-H bond activation pathway for all systems. Furthermore, mixed systems including [CuOMn]²⁺, [CuONi]²⁺, and [CuOZn]²⁺ are predicted to possess methane activation activity similar to pure [CuOCu]²⁺. These results suggest that both homolytic and heterolytic mechanisms should be considered in computing methane activation energies on supported metal oxide nanoclusters.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Low-cost machine learning prediction of excited state properties of iridium-centered phosphors

Prediction of the excited state properties of photoactive iridium complexes challenges ab initio methods such as time-dependent density functional theory (TDDFT) both from the perspective of accuracy and of computational cost, complicating high-throughput virtual screening (HTVS). We instead leverage low-cost machine learning (ML) models and experimental data for 1380 iridium complexes to perform these prediction tasks. We find the best-performing and most transferable models to be those trained on electronic structure features from low-cost density functional tight binding calculations. Using artificial neural network (ANN) models, we predict the mean emission energy of phosphorescence, the excited state lifetime, and the emission spectral integral for iridium complexes with accuracy competitive with or superseding that of TDDFT. We conduct feature importance analysis to determine that high cyclometalating ligand ionization potential correlates to high mean emission energy, while high ancillary ligand ionization potential correlates to low lifetime and low spectral integral. As a demonstration of how our ML models can be used for HTVS and the acceleration of chemical discovery, we curate a set of novel hypothetical iridium complexes and use uncertainty-controlled predictions to identify promising ligands for the design of new phosphors while retaining confidence in the quality of the ANN predictions.

High-throughput computational workflow for ligand discovery in catalysis with the CSD

A novel semi-automated, high-throughput computational workflow for ligand/catalyst discovery based on the Cambridge Structural Database is reported.

OSCAR: an extensive repository of chemically and functionally diverse organocatalysts

The automated construction of datasets has become increasingly relevant in computational chemistry. While transition-metal catalysis has greatly benefitted from bottom-up or top-down strategies for the curation of organometallic complexes libraries, the field of organocatalysis is mostly dominated by case-by-case studies, with a lack of transferable data-driven tools that facilitate both the exploration of a wider range of catalyst space and the optimization of reaction properties. For these reasons, we introduce OSCAR, a repository of 4000 experimentally derived organocatalysts along with their corresponding building blocks and combinatorially enriched structures. We outline the fragment-based approach used for database generation and showcase the chemical diversity, in terms of functions and molecular properties, covered in OSCAR. The structures and corresponding stereoelectronic properties are publicly available (https://archive.materialscloud.org/record/2022.106) and constitute the starting point to build generative and predictive models for organocatalyst performance.

Machine Learning Models Predict Calculation Outcomes with the Transferability Necessary for Computational Catalysis

Virtual high-throughput screening (VHTS) and machine learning (ML) have greatly accelerated the design of single-site transition-metal catalysts. VHTS of catalysts, however, is often accompanied with a high calculation failure rate and wasted computational resources due to the difficulty of simultaneously converging all mechanistically relevant reactive intermediates to expected geometries and electronic states. We demonstrate a dynamic classifier approach, i.e., a convolutional neural network that monitors geometry optimizations on the fly, and exploit its good performance and transferability in identifying geometry optimization failures for catalyst design. We show that the dynamic classifier performs well on all reactive intermediates in the representative catalytic cycle of the radical rebound mechanism for the conversion of methane to methanol despite being trained on only one reactive intermediate. The dynamic classifier also generalizes to chemically distinct intermediates and metal centers absent from the training data without loss of accuracy or model confidence. We rationalize this superior model transferability as arising from the use of electronic structure and geometric information generated on-the-fly from density functional theory calculations and the convolutional layer in the dynamic classifier. When used in combination with uncertainty quantification, the dynamic classifier saves more than half of the computational resources that would have been wasted on unsuccessful calculations for all reactive intermediates being considered.

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.

A rapid feature selection method for catalyst design: Iterative Bayesian additive regression trees (iBART)

Feature selection (FS) methods often are used to develop data-driven descriptors (i.e., features) for rapidly predicting the functional properties of a physical or chemical system based on its composition and structure. FS algorithms identify descriptors from a candidate pool (i.e., feature space) built by feature engineering (FE) steps that construct complex features from the system's fundamental physical properties. Recursive FE, which involves repeated FE operations on the feature space, is necessary to build features with sufficient complexity to capture the physical behavior of a system. However, this approach creates a highly correlated feature space that contains millions or billions of candidate features. Such feature spaces are computationally demanding to process using traditional FS approaches that often struggle with strong collinearity. Herein, we address this shortcoming by developing a new method that interleaves the FE and FS steps to progressively build and select powerful descriptors with reduced computational demand. We call this method iterative Bayesian additive regression trees (iBART), as it iterates between FE with unary/binary operators and FS with Bayesian additive regression trees (BART). The capabilities of iBART are illustrated by extracting descriptors for predicting metal-support interactions in catalysis, which we compare to those predicted in our previous work using other state-of-the-art FS methods (i.e., least absolute shrinkage and selection operator + l0, sure independence screening and sparsifying operator, and Bayesian FS). iBART matches the performance of these methods yet uses a fraction of the computational resources because it generates a maximum feature space of size O(102), as opposed to O(106) generated by one-shot FE/FS methods.

Machine Learning for the Discovery, Design, and Engineering of Materials

Machine learning (ML) has become a part of the fabric of high-throughput screening and computational discovery of materials. Despite its increasingly central role, challenges remain in fully realizing the promise of ML. This is especially true for the practical acceleration of the engineering of robust materials and the development of design strategies that surpass trial and error or high-throughput screening alone. Depending on the quantity being predicted and the experimental data available, ML can either outperform physics-based modes, be used to accelerate such models, or be integrated with them to improve their performance. We cover recent advances in algorithms and in their application that are starting to make inroads toward (a) the discovery of new materials through large-scale enumerative screening, (b) the design of materials through identification of rules and principles that govern materials properties, and (c) the engineering of practical materials by satisfying multiple objectives. We conclude with opportunities for further advancement to realize ML as a widespread tool for practical computational materials design. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Computational Scaling Relationships Predict Experimental Activity and Rate-Limiting Behavior in Homogeneous Water Oxidation

While computational screening with first-principles density functional theory (DFT) is essential for evaluating candidate catalysts, limitations in accuracy typically prevent the prediction of experimentally relevant activities. Exemplary of these challenges are homogeneous water oxidation catalysts (WOCs) where differences in experimental conditions or small changes in ligand structure can alter rate constants by over an order of magnitude. Here, we compute mechanistically relevant electronic and energetic properties for 19 mononuclear Ru transition-metal complexes (TMCs) from three experimental water oxidation catalysis studies. We discover that 15 of these TMCs have experimental activities that correlate with a single property, the ionization potential of the Ru(II)-O₂ catalytic intermediate. This scaling parameter allows the quantitative understanding of activity trends and provides insight into the rate-limiting behavior. We use this approach to rationalize differences in activity with different experimental conditions, and we qualitatively analyze the source of distinct behavior for different electronic states in the other four catalysts. Comparison to closely related single-atom catalysts and modified WOCs enables rationalization of the source of rate enhancement in these WOCs.

Machine learning reveals key ion selectivity mechanisms in polymeric membranes with subnanometer pores

Designing single-species selective membranes for high-precision separations requires a fundamental understanding of the molecular interactions governing solute transport. Here, we comprehensively assess molecular-level features that influence the separation of 18 different anions by nanoporous cellulose acetate membranes. Our analysis identifies the limitations of bulk solvation characteristics to explain ion transport, highlighted by the poor correlation between hydration energy and the measured permselectivity (R² = 0.37). Entropy-enthalpy compensation, spanning 40 kilojoules per mole, leads to a free-energy barrier (∆G^‡) variation of only ~8 kilojoules per mole across all anions. We apply machine learning to elucidate descriptors for energetic barriers from a set of 126 collected features. Notably, electrostatic features account for 75% of the overall features used to describe ∆G^‡, despite the relatively uncharged state of cellulose acetate. Our work presents an approach for studying ion transport across nanoporous membranes that could enable the design of ion-selective membranes.

Electronic Structure of RhO2+, Its Ammoniated Complexes (NH3)1-5RhO2+, and Mechanistic Exploration of CH4 Activation by Them

High-level electronic structure calculations are initially performed to investigate the electronic structure of RhO²⁺. The construction of potential energy curves for the ground and low-lying excited states allowed the calculation of spectroscopic constants, including harmonic and anharmonic vibrational frequencies, bond lengths, spin-orbit constants, and excitation energies. The equilibrium electronic configurations were used for the interpretation of the chemical bonding. We further monitored how the Rh-O bonding scheme changes with the gradual addition of ammonia ligands. The nature of this bond remains unaffected up to four ammonia ligands but adopts a different electronic configuration in the pseudo-octahedral geometry of (NH₃)₅RhO²⁺. This has consequences in the activation mechanism of the C-H bond of methane by these complexes, especially (NH₃)₄RhO²⁺. We show that the [2 + 2] mechanism in the (NH₃)₄RhO²⁺ case has a very low energy barrier comparable to that of a radical mechanism. We also demonstrate that methane can coordinate to the metal in a similar fashion to ammonia and that knowledge of the electronic structure of the pure ammonia complexes provides qualitative insights into the optimal reaction mechanism.

Applying Active Learning to the Screening of Molecular Oxygen Evolution Catalysts

The oxygen evolution reaction (OER) can enable green hydrogen production; however, the state-of-the-art catalysts for this reaction are composed of prohibitively expensive materials. In addition, cheap catalysts have associated overpotentials that render the reaction inefficient. This impels the search to discover novel catalysts for this reaction computationally. In this communication, we present machine learning algorithms to enhance the hypothetical screening of molecular OER catalysts. By predicting calculated binding energies using Gaussian process regression (GPR) models and applying active learning schemes, we provide evidence that our algorithm can improve computational efficiency by guiding simulations towards candidates with promising OER descriptor values. Furthermore, we derive an acquisition function that, when maximized, can identify catalysts that can exhibit theoretical overpotentials that circumvent the constraints imposed by linear scaling relations by attempting to enforce a specific mechanism. Finally, we provide a brief perspective on the appropriate sets of molecules to consider when screening complexes that could be stable and active for this reaction.

Deciphering Cryptic Behavior in Bimetallic Transition-Metal Complexes with Machine Learning

We demonstrate an alternative, data-driven approach to uncovering structure-property relationships for the rational design of heterobimetallic transition-metal complexes that exhibit metal-metal bonding. We tailor graph-based representations of the metal-local environment for these complexes for use in multiple linear regression and kernel ridge regression (KRR) models. We curate a set of 28 experimentally characterized complexes to develop a multiple linear regression model for oxidation potentials. We achieve good accuracy (mean absolute error of 0.25 V) and preserve transferability to unseen experimental data with a new ligand structure. We also train a KRR model on a subset of 330 structurally characterized heterobimetallics to predict the degree of metal-metal bonding. This KRR model predicts relative metal-metal bond lengths in the test set to within 5%, and analysis of key features reveals the fundamental atomic contributions (e.g., the valence electron configuration) that most strongly influence the behavior of these complexes. Our work provides guidance for rational bimetallic design, suggesting that properties, including the formal shortness ratio, should be transferable from one period to another.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Combining artificial intelligence and physics-based modeling to directly assess atomic site stabilities: from sub-nanometer clusters to extended surfaces

The performance of functional materials is dictated by chemical and structural properties of individual atomic sites. In catalysts, for example, the thermodynamic stability of constituting atomic sites is a key descriptor from which more complex properties, such as molecular adsorption energies and reaction rates, can be derived. In this study, we present a widely applicable machine learning (ML) approach to instantaneously compute the stability of individual atomic sites in structurally and electronically complex nano-materials. Conventionally, we determine such site stabilities using computationally intensive first-principles calculations. With our approach, we predict the stability of atomic sites in sub-nanometer metal clusters of 3-55 atoms with mean absolute errors in the range of 0.11-0.14 eV. To extract physical insights from the ML model, we introduce a genetic algorithm (GA) for feature selection. This algorithm distills the key structural and chemical properties governing the stability of atomic sites in size-selected nanoparticles, allowing for physical interpretability of the models and revealing structure-property relationships. The results of the GA are generally model and materials specific. In the limit of large nanoparticles, the GA identifies features consistent with physics-based models for metal-metal interactions. By combining the ML model with the physics-based model, we predict atomic site stabilities in real time for structures ranging from sub-nanometer metal clusters (3-55 atom) to larger nanoparticles (147 to 309 atoms) to extended surfaces using a physically interpretable framework. Finally, we present a proof of principle showcasing how our approach can determine stable and active nanocatalysts across a generic materials space of structure and composition.

Electronic structure of the dicationic first row transition metal oxides

Multi-reference electronic structure calculations combined with large basis sets are performed to investigate the electronic structure of the ground and low-lying electronic states of the MO²⁺ diatomic species with M = Ti-Cu. These systems have shown high efficiency in the activation of the C-H of saturated hydrocarbons. This study is the first systematic and accurate work for these systems and our results and discussion provides insights into the reactivity and stability of MO²⁺ units. We find that they can be divided in three groups. The early transition metals (Ti, V, Cr) have very stable and well separated oxo (M⁴⁺O^2-) character ground states, the middle transition metals (Mn, Fe) have oxyl (M³⁺O˙^-) ground states with low-lying oxo excited states, and the late transition metals (Co, Ni, Cu) have well separated oxyl states. The reported spectroscopic constants will aid future experimental investigations, which are sparse in the literature. Periodic trends for the bond lengths, energetics, excitation energies, and wavefunction composition are discussed in detail. Complete basis set limit results indicate the high accuracy of the quintuple-ζ basis sets.

σ-Donation and π-Backdonation Effects in Dative Bonds of Main-Group Elements

The nature of donor-acceptor interactions is important for the understanding of dative bonding and can provide vital insights into many chemical processes. Here, we have performed a computational study to elucidate substantial differences between different types of dative interactions. For this purpose, a data set of 20 molecular complexes stabilized by dative bonds was developed (DAT20). A benchmark study that considers many popular density functionals with respect to accurate quantum chemical interaction energies and geometries revealed two different trends between the complexes of DAT20. This behavior was further explored by means of frontier molecular orbitals, extended-transition-state natural orbitals for chemical valence (ETS-NOCV), and natural energy decomposition analysis (NEDA). These methods revealed the extent of the forward and backdonation between the donor and acceptor molecules and how they influence the total interaction energies and molecular geometries. A new classification of dative bonds is suggested.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Dreams, False Starts, Dead Ends, and Redemption: A Chronicle of the Evolution of a Chemoinformatic Workflow for the Optimization of Enantioselective Catalysts

Catalyst design in enantioselective catalysis has historically been driven by empiricism. In this endeavor, experimentalists attempt to qualitatively identify trends in structure that lead to a desired catalyst function. In this body of work, we lay the groundwork for an improved, alternative workflow that uses quantitative methods to inform decision making at every step of the process. At the outset, we define a library of synthetically accessible permutations of a catalyst scaffold with the philosophy that the library contains every potential catalyst we are willing to make. To represent these chiral molecules, we have developed general 3D representations, which can be calculated for tens of thousands of structures. This defines the total chemical space of a given catalyst scaffold; it is constructed on the basis of catalyst structure only without regard to a specific reaction or mechanism. As such, any algorithmic subset selection method, which is unsupervised (i.e., only considers catalyst structure), should provide an ideal initial screening set for any new reaction that can be catalyzed by that scaffold. Notably, because this design strategy, the same set of catalysts can be used for any reaction that can be catalyzed with that parent catalyst scaffold. These are tested experimentally, and statistical learning tools can be used to create a model relating catalyst structure to catalyst function. Further, this model can be used to predict the performance of each catalyst candidate in the greater database of virtual catalyst candidates. In this way, it is possible estimate the performance of tens of thousands of catalysts by experimentally testing a smaller subset. Using error assessment metrics, it is possible to understand the confidence in new predictions. An experimentalist using this tool can balance the predicted results (reward) with the prediction confidence (risk) when deciding which catalysts to synthesize next in an optimization campaign. These catalysts are synthesized and tested experimentally. At this stage, either the optimization is a success or the predicted values were incorrect and further optimization is required. In the case of the latter, the information can be fed back into the statistical learning model to refine the model, and this iterative process can be used to determine the optimal catalyst. In this body of work, we not only establish this workflow but quantitatively establish how best to execute each step. Herein, we evaluate several 3D molecular representations to determine how best to represent molecules. Several selection protocols are examined to best decide which set of molecules can be used to represent the library of interest. In addition, the number of reactions needed to make accurate, statistical learning models is evaluated. Taken together these components establish a tool ready to progress from the development stage to the utility stage. As such, current research endeavors focus on applying these tools to optimize new reactions.

Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design

The variability of chemical bonding in open-shell transition-metal complexes not only motivates their study as functional materials and catalysts but also challenges conventional computational modeling tools. Here, tailoring ligand chemistry can alter preferred spin or oxidation states as well as electronic structure properties and reactivity, creating vast regions of chemical space to explore when designing new materials atom by atom. Although first-principles density functional theory (DFT) remains the workhorse of computational chemistry in mechanism deduction and property prediction, it is of limited use here. DFT is both far too computationally costly for widespread exploration of transition-metal chemical space and also prone to inaccuracies that limit its predictive performance for localized d electrons in transition-metal complexes. These challenges starkly contrast with the well-trodden regions of small-organic-molecule chemical space, where the analytical forms of molecular mechanics force fields and semiempirical theories have for decades accelerated the discovery of new molecules, accurate DFT functional performance has been demonstrated, and gold-standard methods from correlated wavefunction theory can predict experimental results to chemical accuracy.The combined promise of transition-metal chemical space exploration and lack of established tools has mandated a distinct approach. In this Account, we outline the path we charted in exploration of transition-metal chemical space starting from the first machine learning (ML) models (i.e., artificial neural network and kernel ridge regression) and representations for the prediction of open-shell transition-metal complex properties. The distinct importance of the immediate coordination environment of the metal center as well as the lack of low-level methods to accurately predict structural properties in this coordination environment first motivated and then benefited from these ML models and representations. Once developed, the recipe for prediction of geometric, spin state, and redox potential properties was straightforwardly extended to a diverse range of other properties, including in catalysis, computational "feasibility", and the gas separation properties of periodic metal-organic frameworks. Interpretation of selected features most important for model prediction revealed new ways to encapsulate design rules and confirmed that models were robustly mapping essential structure-property relationships. Encountering the special challenge of ensuring that good model performance could generalize to new discovery targets motivated investigation of how to best carry out model uncertainty quantification. Distance-based approaches, whether in model latent space or in carefully engineered feature space, provided intuitive measures of the domain of applicability. With all of these pieces together, ML can be harnessed as an engine to tackle the large-scale exploration of transition-metal chemical space needed to satisfy multiple objectives using efficient global optimization methods. In practical terms, bringing these artificial intelligence tools to bear on the problems of transition-metal chemical space exploration has resulted in ML-model assessments of large, multimillion compound spaces in minutes and validated new design leads in weeks instead of decades.

Molecular and heterogeneous water oxidation catalysts: recent progress and joint perspectives

The recent synthetic and mechanistic progress in molecular and heterogeneous water oxidation catalysts highlights the new, overarching strategies for knowledge transfer and unifying design concepts.

Computational methods for training set selection and error assessment applied to catalyst design: guidelines for deciding which reactions to run first and which to run next

Different subset selection methods are examined to guide catalyst selection in optimization campaigns. Error assessment methods are used to quantitatively inform selection of new catalyst candidates from in silico libraries of catalyst structures.

A data-driven perspective on the colours of metal-organic frameworks

Colour is at the core of chemistry and has been fascinating humans since ancient times. It is also a key descriptor of optoelectronic properties of materials and is often used to assess the success of a synthesis. However, predicting the colour of a material based on its structure is challenging. In this work, we leverage subjective and categorical human assignments of colours to build a model that can predict the colour of compounds on a continuous scale. In the process of developing the model, we also uncover inadequacies in current reporting mechanisms. For example, we show that the majority of colour assignments are subject to perceptive spread that would not comply with common printing standards. To remedy this, we suggest and implement an alternative way of reporting colour—and chemical data in general. All data is captured in an objective, and standardised, form in an electronic lab notebook and subsequently automatically exported to a repository in open formats, from where it can be interactively explored by other researchers. We envision this to be key for a data-driven approach to chemical research.

Colour is at the core of chemistry and has been fascinating humans since ancient times.

Composition- and Condition-Dependent Kinetics of Homogeneous Ester Hydrogenation by a Mn-Based Catalyst

The reaction medium and conditions are the key parameters defining the efficiency and performance of a homogeneous catalyst. In the state-of-the-art molecular descriptions of catalytic systems by density functional theory (DFT) calculations, the reaction medium is commonly reduced to an infinitely diluted ideal solution model. In this work, we carry out a detailed operando computational modeling analysis of the condition dependencies and nonideal solution effects on the mechanism and kinetics of a model ester hydrogenation reaction by a homogeneous Mn(I)-P,N catalyst. By combining DFT calculations, COSMO-RS solvent model, and the microkinetic modeling approach, the kinetic behavior of the multicomponent homogeneous catalyst system under realistic reaction conditions was investigated in detail. The effects of the reaction medium and its dynamic evolution in the course of the reaction were analyzed by comparing the results obtained for the model methyl acetate hydrogenation reaction in a THF solution and under solvent-free neat reaction conditions. The dynamic representations of the reaction medium give rise to strongly nonlinear effects in the kinetic models. The nonideal representation of the reaction medium results in pronounced condition dependencies of the computed energetics of the elementary reaction steps and the computed kinetic profiles but affects only slightly such experimentally accessible kinetic descriptors as the apparent activation energy and the degree of rate control.

The Role of Machine Learning in the Understanding and Design of Materials

Developing algorithmic approaches for the rational design and discovery of materials can enable us to systematically find novel materials, which can have huge technological and social impact. However, such rational design requires a holistic perspective over the full multistage design process, which involves exploring immense materials spaces, their properties, and process design and engineering as well as a techno-economic assessment. The complexity of exploring all of these options using conventional scientific approaches seems intractable. Instead, novel tools from the field of machine learning can potentially solve some of our challenges on the way to rational materials design. Here we review some of the chief advancements of these methods and their applications in rational materials design, followed by a discussion on some of the main challenges and opportunities we currently face together with our perspective on the future of rational materials design and discovery.

Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening

Despite its widespread use in chemical discovery, approximate density functional theory (DFT) is poorly suited to many targets, such as those containing open-shell, 3d transition metals that can be expected to have strong multireference (MR) character. For discovery workflows to be predictive, we need automated, low-cost methods that can distinguish the regions of chemical space where DFT should be applied from those where it should not. We curate more than 4800 open-shell transition-metal complexes up to hundreds of atoms in size from prior high-throughput DFT studies and evaluate affordable, finite-temperature DFT fractional occupation number (FON)-based MR diagnostics. We show that intuitive measures of strong correlation (i.e., the HOMO-LUMO gap) are not predictive of MR character as judged by FON-based diagnostics. Analysis of independently trained machine learning (ML) models to predict HOMO-LUMO gaps and FON-based diagnostics reveals differences in the metal and ligand sensitivity of the two quantities. We use our trained ML models to rapidly evaluate MR character over a space of ∼187000 theoretical complexes, identifying large-scale trends in spin-state-dependent MR character and finding small HOMO-LUMO gap complexes while ensuring low MR character.

Progress in Computational and Machine-Learning Methods for Heterogeneous Small-Molecule Activation

The chemical conversion of small molecules such as H₂ , H₂ O, O₂ , N₂ , CO₂ , and CH₄ to energy and chemicals is critical for a sustainable energy future. However, the high chemical stability of these molecules poses grand challenges to the practical implementation of these processes. In this regard, computational approaches such as density functional theory, microkinetic modeling, data science, and machine learning have guided the rational design of catalysts by elucidating mechanistic insights, identifying active sites, and predicting catalytic activity. Here, the theory and methodologies for heterogeneous catalysis and their applications for small-molecule activation are reviewed. An overview of fundamental theory and key computational methods for designing catalysts, including the emerging data science techniques in particular, is given. Applications of these methods for finding efficient heterogeneous catalysts for the activation of the aforementioned small molecules are then surveyed. Finally, promising directions of the computational catalysis field for further outlooks are discussed, focusing on the challenges and opportunities for new methods.

Big-Data Science in Porous Materials: Materials Genomics and Machine Learning

By combining metal nodes with organic linkers we can potentially synthesize millions of possible metal-organic frameworks (MOFs). The fact that we have so many materials opens many exciting avenues but also create new challenges. We simply have too many materials to be processed using conventional, brute force, methods. In this review, we show that having so many materials allows us to use big-data methods as a powerful technique to study these materials and to discover complex correlations. The first part of the review gives an introduction to the principles of big-data science. We show how to select appropriate training sets, survey approaches that are used to represent these materials in feature space, and review different learning architectures, as well as evaluation and interpretation strategies. In the second part, we review how the different approaches of machine learning have been applied to porous materials. In particular, we discuss applications in the field of gas storage and separation, the stability of these materials, their electronic properties, and their synthesis. Given the increasing interest of the scientific community in machine learning, we expect this list to rapidly expand in the coming years.

Quantum-mechanical transition-state model combined with machine learning provides catalyst design features for selective Cr olefin oligomerization

The use of data science tools to provide the emergence of non-trivial chemical features for catalyst design is an important goal in catalysis science. Additionally, there is currently no general strategy for computational homogeneous, molecular catalyst design. Here, we report the unique combination of an experimentally verified DFT-transition-state model with a random forest machine learning model in a campaign to design new molecular Cr phosphine imine (Cr(P,N)) catalysts for selective ethylene oligomerization, specifically to increase 1-octene selectivity. This involved the calculation of 1-hexene : 1-octene transition-state selectivity for 105 (P,N) ligands and the harvesting of 14 descriptors, which were then used to build a random forest regression model. This model showed the emergence of several key design features, such as Cr-N distance, Cr-α distance, and Cr distance out of pocket, which were then used to rapidly design a new generation of Cr(P,N) catalyst ligands that are predicted to give >95% selectivity for 1-octene.

Accurate Multiobjective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization

The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. The multidimensional nature of the search necessitates exploration of multimillion compound libraries over which even density functional theory (DFT) screening is intractable. Machine learning (e.g., artificial neural network, ANN, or Gaussian process, GP) models for this task are limited by training data availability and predictive uncertainty quantification (UQ). We overcome such limitations by using efficient global optimization (EGO) with the multidimensional expected improvement (EI) criterion. EGO balances exploitation of a trained model with acquisition of new DFT data at the Pareto front, the region of chemical space that contains the optimal trade-off between multiple design criteria. We demonstrate this approach for the simultaneous optimization of redox potential and solubility in candidate M(II)/M(III) redox couples for redox flow batteries from a space of 2.8 M transition metal complexes designed for stability in practical redox flow battery (RFB) applications. We show that a multitask ANN with latent-distance-based UQ surpasses the generalization performance of a GP in this space. With this approach, ANN prediction and EI scoring of the full space are achieved in minutes. Starting from ca. 100 representative points, EGO improves both properties by over 3 standard deviations in only five generations. Analysis of lookahead errors confirms rapid ANN model improvement during the EGO process, achieving suitable accuracy for predictive design in the space of transition metal complexes. The ANN-driven EI approach achieves at least 500-fold acceleration over random search, identifying a Pareto-optimal design in around 5 weeks instead of 50 years.

Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins of open-shell transition-metal complexes is critical to understanding catalytic and materials properties but also challenging with approximate electronic structure methods. As an alternative approach, we demonstrate how structure alone can be used to guide assignment of ground-state spin from experimentally determined crystal structures of transition-metal complexes. We first identify the limits of distance-based heuristics from distributions of metal–ligand bond lengths of over 2000 unique mononuclear Fe(II)/Fe(III) transition-metal complexes. To overcome these limits, we employ artificial neural networks (ANNs) to predict spin-state-dependent metal–ligand bond lengths and classify experimental ground-state spins based on agreement of experimental structures with the ANN predictions. Although the ANN is trained on hybrid density functional theory data, we exploit the method-insensitivity of geometric properties to enable assignment of ground states for the majority (ca. 80–90%) of structures. We demonstrate the utility of the ANN by data-mining the literature for spin-crossover (SCO) complexes, which have experimentally observed temperature-dependent geometric structure changes, by correctly assigning almost all (>95%) spin states in the 46 Fe(II) SCO complex set. This approach represents a promising complement to more conventional energy-based spin-state assignment from electronic structure theory at the low cost of a machine learning model.

Reaction mechanisms at the homogeneous–heterogeneous frontier: insights from first-principles studies on ligand-decorated metal nanoparticles

The frontiers between homogeneous and heterogeneous catalysis are progressively disappearing.