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

Force-Activated Spin-Crossover in Fe2+ and Co2+ Transition Metal Mechanophores

Transition metal mechanophores exhibiting force-activated spin-crossover are attractive design targets, yet large-scale discovery of them has not been pursued due in large part to the time-consuming nature of trial-and-error experiments. Instead, we leverage density functional theory (DFT) and external force explicitly included (EFEI) modeling to study a set of 395 feasible Fe2+ and Co2+ mechanophore candidates with tridentate ligands that we curate from the Cambridge Structural Database. Among nitrogen-coordinating low-spin complexes, we observe the prevalence of spin crossover at moderate force, and we identify 155 Fe2+ and Co2+ spin-crossover mechanophores and derive their threshold force for low-spin to high-spin transition (FSCO). The calculations reveal strong correlations of FSCO with spin-splitting energies and coordination bond lengths, facilitating rapid prediction of FSCO using force-free DFT calculations. Then, among all Fe2+ and Co2+ spin-crossover mechanophores, we further identity 11 mechanophores that combine labile spin-crossover and good mechanical robustness that are thus predicted to be the most versatile for force-probing applications. We discover two classes of mer-symmetric complexes comprising specific heteroaromatic rings within extended π-conjugation that give rise to Fe2+ mechanophores with these characteristics. We expect the set of spin-crossover mechanophores, the design principles, and the computational approach to be useful in guiding the high-throughput discovery of transition metal mechanophores with diverse functionalities and broad applications, including mechanically activated catalysis.

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.

Catalysing (organo-)catalysis: Trends in the application of machine learning to enantioselective organocatalysis

Organocatalysis has established itself as a third pillar of homogeneous catalysis, besides transition metal catalysis and biocatalysis, as its use for enantioselective reactions has gathered significant interest over the last decades. Concurrent to this development, machine learning (ML) has been increasingly applied in the chemical domain to efficiently uncover hidden patterns in data and accelerate scientific discovery. While the uptake of ML in organocatalysis has been comparably slow, the last two decades have showed an increased interest from the community. This review gives an overview of the work in the field of ML in organocatalysis. The review starts by giving a short primer on ML for experimental chemists, before discussing its application for predicting the selectivity of organocatalytic transformations. Subsequently, we review ML employed for privileged catalysts, before focusing on its application for catalyst and reaction design. Concluding, we give our view on current challenges and future directions for this field, drawing inspiration from the application of ML to other scientific domains.

Automated prediction of ground state spin for transition metal complexes

Exploiting crystallographic data repositories for large-scale quantum chemical computations requires the rapid and accurate extraction of the molecular structure, charge and spin from the crystallographic information file. Here, we develop a general approach to assign the ground state spin of transition metal complexes, in complement to our previous efforts on determining metal oxidation states and bond order within the cell2mol software. Starting from a database of 31k transition metal complexes extracted from the Cambridge Structural Database with cell2mol, we construct the TM-GSspin dataset, which contains 2063 mononuclear first row transition metal complexes and their computed ground state spins. TM-GSspin is highly diverse in terms of metals, metal oxidation states, coordination geometries, and coordination sphere compositions. Based on TM-GSspin, we identify correlations between structural and electronic features of the complexes and their ground state spins to develop a rule-based spin state assignment model. Leveraging this knowledge, we construct interpretable descriptors and build a statistical model achieving 98% cross-validated accuracy in predicting the ground state spin across the board. Our approach provides a practical way to determine the ground state spin of transition metal complexes directly from crystal structures without additional computations, thus enabling the automated use of crystallographic data for large-scale computations involving transition metal complexes.

Computational Screening of Putative Catalyst Transition Metal Complexes as Guests in a Ga4L612- Nanocage

Metal-organic cages form well-defined microenvironments that can enhance the catalytic proficiency of encapsulated transition metal complexes (TMCs). We introduce a screening protocol to efficiently identify TMCs that are promising candidates for encapsulation in the Ga4L612- nanocage. We obtain TMCs from the Cambridge Structural Database with geometric and electronic characteristics amenable to encapsulation and mine the text of associated manuscripts to curate TMCs with documented catalytic functionality. By docking candidate TMCs inside the nanocage cavity and carrying out electronic structure calculations, we identify a subset of successfully optimized candidates (TMC-34) and observe that encapsulated guests occupy an average of 60% of the cavity volume, in line with previous observations. Notably, some guests occupy as much as 72% of the cavity as a result of linker rotation. Encapsulation has a universal effect on the electrostatic potential (ESP), systematically decreasing the ESP at the metal center of each TMC in the TMC-34 data set, while minimally altering TMC metal partial charges. Collectively these observations support geometry-based screening of potential guests and suggest that encapsulation in Ga4L612- cages could electrostatically stabilize diverse cationic or electropositive intermediates. We highlight candidate guests with associated known reactivity and solubility most amenable for encapsulation in experimental follow-up studies.

Modeling Fe(II) Complexes Using Neural Networks

We report a Fe(II) data set of more than 23000 conformers in both low-spin (LS) and high-spin (HS) states. This data set was generated to develop a neural network model that is capable of predicting the energy and the energy splitting as a function of the conformation of a Fe(II) organometallic complex. In order to achieve this, we propose a type of scaled electronic embedding to cover the long-range interactions implicitly in our neural network describing the Fe(II) organometallic complexes. For the total energy prediction, the lowest MAE is 0.037 eV, while the lowest MAE of the splitting energy is 0.030 eV. Compared to baseline models, which only incorporate short-range interactions, our scaled electronic embeddings improve the accuracy by over 70% for the prediction of the total energy and the splitting energy. With regard to semiempirical methods, our proposed models reduce the MAE, with respect to these methods, by 2 orders of magnitude.

Protein3D: Enabling analysis and extraction of metal-containing sites from the Protein Data Bank with molSimplify

Metalloenzymes catalyze a wide range of chemical transformations, with the active site residues playing a key role in modulating chemical reactivity and selectivity. Unlike smaller synthetic catalysts, a metalloenzyme active site is embedded in a larger protein, which makes interrogation of electronic properties and geometric features with quantum mechanical calculations challenging. Here we implement the ability to fetch crystallographic structures from the Protein Data Bank and analyze the metal binding sites in the program molSimplify. We show the usefulness of the newly created protein3D class to extract the local environment around non-heme iron enzymes containing a two histidine motif and prepare 372 structures for quantum mechanical calculations. Our implementation of protein3D serves to expand the range of systems molSimplify can be used to analyze and will enable high-throughput study of metal-containing active sites in proteins.

Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) complexes are materials that exhibit changes in the spin state in response to external stimuli, with potential applications in molecular electronics. It is challenging to know a priori how to design ligands to achieve the delicate balance of entropic and enthalpic contributions needed to tailor a transition temperature close to room temperature. We leverage the SCO complexes from the previously curated SCO-95 data set [Vennelakanti et al. J. Chem. Phys. 159, 024120 (2023)] to train three machine learning (ML) models for transition temperature (T1/2) prediction using graph-based revised autocorrelations as features. We perform feature selection using random forest-ranked recursive feature addition (RF-RFA) to identify the features essential to model transferability. Of the ML models considered, the full feature set RF and recursive feature addition RF models perform best, achieving moderate correlation to experimental T1/2 values. We then compare ML T1/2 predictions to those from three previously identified best-performing density functional approximations (DFAs) which accurately predict SCO behavior across SCO-95, finding that the ML models predict T1/2 more accurately than the best-performing DFAs. In addition, we study ML model predictions for a set of 18 SCO complexes for which only estimated T1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T1/2 values with a Pearson's r of 0.82. In contrast, DFA-predicted T1/2 values have large errors and show no correlation to estimated T1/2 values over the same set of complexes. Overall, our study demonstrates slightly superior performance of ML models in comparison with some of the best-performing DFAs, and we expect ML models to improve further as larger data sets of SCO complexes are curated and become available for model training.

Classification of Hemilabile Ligands Using Machine Learning

Hemilabile ligands have the capacity to partially disengage from a metal center, providing a strategy to balance stability and reactivity in catalysis, but they are not straightforward to identify. We identify ligands in the Cambridge Structural Database that have been crystallized with distinct denticities and are thus identifiable as hemilabile ligands. We implement a semi-supervised learning approach using a label-spreading algorithm to augment a small negative set that is supported by heuristic rules of ligand and metal co-occurrence. We show that a heuristic based on coordinating atom identity alone is not sufficient to identify whether a ligand is hemilabile, and our trained machine-learning classification models are instead needed to predict whether a bi-, tri-, or tetradentate ligand is hemilabile with high accuracy and precision. Feature importance analysis of our models shows that the second, third, and fourth coordination spheres all play important roles in ligand hemilability.

Discovering Molecular Coordination Environment Trends for Selective Ion Binding to Molecular Complexes Using Machine Learning

The design of ion-selective materials with improved separation efficacy and efficiency is paramount, as current technologies fail to meet real-world deployment challenges. Selectivity in these materials can be informed by local ion binding in confined membrane ion channels. In this study, we utilize a data-driven approach to investigate design features in small molecular complexes coordinating ions as simplified models of ion channels. We curate a data set of 563 alkali metal coordinating molecular complexes (i.e., with Li+, Na+, or K+) from the Cambridge Structural Database and calculate differential ion binding energies using density functional theory. Using this information, we probe when and why structures favor exchange with alternate ions. Our analysis reveals that energetic preferences are related to ion size but are largely due to chemical interactions rather than structural reorganization. We identify unique trends in the selectivity for Li+ over other alkali ions, including the presence of N coordination atoms, planar coordination geometry, and small coordinating ring sizes. We use machine learning models to identify the key contributions of both geometric and electronic features in predicting selective ion binding. These physical insights offer preliminary guidance into the design of optimal membranes for ion selectivity.

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.

Architector for high-throughput cross-periodic table 3D complex building

Rare-earth and actinide complexes are critical for a wealth of clean-energy applications. Three-dimensional (3D) structural generation and prediction for these organometallic systems remains a challenge, limiting opportunities for computational chemical discovery. Here, we introduce Architector, a high-throughput in-silico synthesis code for s-, p-, d-, and f-block mononuclear organometallic complexes capable of capturing nearly the full diversity of the known experimental chemical space. Beyond known chemical space, Architector performs in-silico design of new complexes including any chemically accessible metal-ligand combinations. Architector leverages metal-center symmetry, interatomic force fields, and tight binding methods to build many possible 3D conformers from minimal 2D inputs including metal oxidation and spin state. Over a set of more than 6,000 x-ray diffraction (XRD)-determined complexes spanning the periodic table, we demonstrate quantitative agreement between Architector-predicted and experimentally observed structures. Further, we demonstrate out-of-the box conformer generation and energetic rankings of non-minimum energy conformers produced from Architector, which are critical for exploring potential energy surfaces and training force fields. Overall, Architector represents a transformative step towards cross-periodic table computational design of metal complex chemistry.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

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.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

MOFSimplify, machine learning models with extracted stability data of three thousand metal-organic frameworks

We report a workflow and the output of a natural language processing (NLP)-based procedure to mine the extant metal–organic framework (MOF) literature describing structurally characterized MOFs and their solvent removal and thermal stabilities. We obtain over 2,000 solvent removal stability measures from text mining and 3,000 thermal decomposition temperatures from thermogravimetric analysis data. We assess the validity of our NLP methods and the accuracy of our extracted data by comparing to a hand-labeled subset. Machine learning (ML, i.e. artificial neural network) models trained on this data using graph- and pore-geometry-based representations enable prediction of stability on new MOFs with quantified uncertainty. Our web interface, MOFSimplify, provides users access to our curated data and enables them to harness that data for predictions on new MOFs. MOFSimplify also encourages community feedback on existing data and on ML model predictions for community-based active learning for improved MOF stability models.

Measurement(s)	thermal decomposition
Technology Type(s)	thermogravimetry

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.

Ligand Optimization of Exchange Interaction in Co(II) Dimer Single Molecule Magnet by Machine Learning

Designing single-molecule magnets (SMMs) for potential applications in quantum computing and high-density data storage requires tuning their magnetic properties, especially the strength of the magnetic interaction. These properties can be characterized by first-principles calculations based on density functional theory (DFT). In this work, we study the experimentally synthesized Co(II) dimer (Co₂(C₅NH₅)₄(μ-PO₂(CH₂C₆H₅)₂)₃) SMM with the goal to control the exchange energy, ΔE_J, between the Co atoms through tuning of the capping ligands. The experimentally synthesized Co(II) dimer molecule has a very small ΔE_J < 1 meV. We assemble a DFT data set of 1081 ligand substitutions for the Co(II) dimer. The ligand exchange provides a broad range of exchange energies, ΔE_J, from +50 to -200 meV, with 80% of the ligands yielding a small ΔE_J < 10 meV. We identify descriptors for the classification and regression of ΔE_J using gradient boosting machine learning models. We compare one-hot encoded, structure-based, and chemical descriptors consisting of the HOMO/LUMO energies of the individual ligands and the maximum electronegativity difference and bond order for the ligand atom connecting to Co. We observe a similar overall performance with the chemical descriptors outperforming the other descriptors. We show that the exchange coupling, ΔE_J, is correlated to the difference in the average bridging angle between the ferromagnetic and antiferromagnetic states, similar to the Goodenough-Kanamori rules.

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.

Electronic Structures of Cr(III) and V(II) Polypyridyl Systems: Undertones in an Isoelectronic Analogy

A recently reported description of the photophysical properties of V²⁺ polypyridyl systems has highlighted several distinctions between isoelectronic, d³, Cr³⁺, and V²⁺ tris-homoleptic polypyridyl complexes of 2,2'-bipyridine (bpy) and 1,10-phenanthroline (phen). Here, we combine theory and experimental data to elucidate the differences in electronic structures. We provide the first crystallographic structures of the V²⁺ complexes [V(bpy)₃](BPh₄)₂ (V-1B) and [V(phen)₃](OTf)₂ (V2) and observe pronounced trigonal distortion relative to analogous Cr³⁺ complexes. We use electronic absorption spectroscopy in tandem with TD-DFT computations to assign metal-ligand charge transfer (MLCT) properties of V-1B and V2 that are unique from the intraligand transitions, ⁴(³IL), solely observed in Cr³⁺ analogues. Our newly developed natural transition spin density (NTρ^α,β) plots characterize both the Cr³⁺ and V²⁺ absorbance properties. A multideterminant approach to DFT assigns the energy of the ²E state of V-1B as stabilized through electron delocalization. We find that the profound differences in excited state lifetimes for Cr³⁺ and V²⁺ polypyridyls arise from differences in the characters of their lowest doublet states and pathways for intersystem crossing, both of which stem from trigonal structural distortion and metal-ligand π-covalency.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

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.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Trends in computational molecular catalyst design

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

Palladium Goes First: A Neutral Asymmetric Heteroditopic N,P Ligand Forming Pd-3d Heterobimetallic Complexes

A facile two-step synthesis of bis(1-methylhydrazinyl)pyrimidine from pyridine-2-carbaldehyde and 2-diphenylphosphanylbenzaldehyde gave access to the new asymmetric ligand 1. The phosphane selectively guides Pd^II into the softer tridentate N,N,P pocket, yielding monometallic complex 2. A second reaction with a 3d transition metal complex precursor (groups 7 to 12) fills the vacant N,N,N pocket and thus provides a variety of heterobimetallic complexes of the type Pd^II/M^II (M = Mn (3), Fe (4), Co (5), Ni (6), Cu (7), Zn (8)). Single-crystal X-ray diffraction studies were performed for all complexes. The assembly of μ₂-chlorido-bridged dimers was observed for complexes 5-7 in the solid state, while DOSY NMR experiments have shown that 5-7 are unbridged monomers in solution. As an exception, Fe^II prefers to form the homoleptic meridional complex [Fe{PdCl(1)}₂](OTf)₄ (4). The electrochemical behavior and the effective magnetic moment in solution were investigated for all complexes by cyclic voltammetry and Evans method, respectively. Experimental UV/vis results were interpreted by performing TD-DFT calculations on 1, 2, and 3.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.

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.

Predicting oxidation and spin states by high-dimensional neural networks: Applications to lithium manganese oxide spinels

Lithium ion batteries often contain transition metal oxides such as Li_xMn₂O₄ (0 ≤ x ≤ 2). Depending on the Li content, different ratios of Mn^III to Mn^IV ions are present. In combination with electron hopping, the Jahn-Teller distortions of the Mn^IIIO₆ octahedra can give rise to complex phenomena such as structural transitions and conductance. While for small model systems oxidation and spin states can be determined using density functional theory (DFT), the investigation of dynamical phenomena by DFT is too demanding. Previously, we have shown that a high-dimensional neural network potential can extend molecular dynamics (MD) simulations of Li_xMn₂O₄ to nanosecond time scales, but these simulations did not provide information about the electronic structure. Here, we extend the use of neural networks to the prediction of atomic oxidation and spin states. The resulting high-dimensional neural network is able to predict the spins of the Mn ions with an error of only 0.03 ℏ. We find that the Mn e_g electrons are correctly conserved and that the number of Jahn-Teller distorted Mn^IIIO₆ octahedra is predicted precisely for different Li loadings. A charge ordering transition is observed between 280 K and 300 K, which matches resistivity measurements. Moreover, the activation energy of the electron hopping conduction above the phase transition is predicted to be 0.18 eV, deviating only 0.02 eV from experiment. This work demonstrates that machine learning is able to provide an accurate representation of both the geometric and the electronic structure dynamics of Li_xMn₂O₄ on time and length scales that are not accessible by ab initio MD.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.