Bridging the Homogeneous-Heterogeneous Divide: Modeling Spin for Reactivity in Single Atom Catalysis

Multistate Dynamics and Kinetics of CO2 Activation by Ta+ in the Gas Phase: Insights into Single-Atom Catalysis

The activation of carbon dioxide (CO2) by a transition-metal cation in the gas phase is a unique model system for understanding single-atom catalysis. The mechanism of such reactions is often attributed to a "two-state reactivity" model in which the high-energy barrier of a spin state correlating with ground-state reactants is avoided by intersystem crossing (ISC) to a different spin state with a lower barrier. However, such a "spin-forbidden" mechanism, along with the corresponding dynamics, has seldom been rigorously examined theoretically, due to the lack of global potential energy surfaces (PESs). In this work, we report full-dimensional PESs of the lowest-lying quintet, triplet, and singlet states of the TaCO2+ system, machine-learned from first-principles data. These PESs and the corresponding spin-orbit couplings enable us to provide an extensive theoretical characterization of the dynamics and kinetics of the reaction between the tantalum cation (Ta+) and CO2, which have recently been investigated experimentally at high collision energies using crossed beams and velocity map imaging, as well as at thermal energies using a selected-ion flow tube apparatus. The multistate quasi-classical trajectory simulations with surface hopping reproduce most of the measured product translational and angular distributions, shedding valuable light on the nonadiabatic reaction dynamics. The calculated rate coefficients from 200 to 600 K are also in good agreement with the latest experimental measurements. More importantly, these calculations revealed that the reaction is controlled by intersystem crossing, rather than potential barriers.

Enhanced interfacial water dissociation on a hydrated iron porphyrin single-atom catalyst in graphene

Single Atom Catalysis (SAC) is an expanding field of heterogeneous catalysis in which single metallic atoms embedded in different materials catalyze a chemical reaction, but these new catalytic materials still lack fundamental understanding when used in electrochemical environments. Recent characterizations of non-noble metals like Fe deposited on N-doped graphitic materials have evidenced two types of Fe-N4 fourfold coordination, either of pyridine type or of porphyrin type. Here, we study these defects embedded in a graphene sheet and immersed in an explicit aqueous medium at the quantum level. While the Fe-pyridine SAC model is clear cut and widely studied, it is not the case for the Fe-porphyrin SAC that remains ill-defined, because of the necessary embedding of odd-membered rings in graphene. We first propose an atomistic model for the Fe-porphyrin SAC. Using spin-polarized ab initio molecular dynamics, we show that both Fe SACs spontaneously adsorb two interfacial water molecules from the solvent on opposite sides. Interestingly, we unveil a different catalytic reactivity of the two hydrated SAC motives: while the Fe-porphyrin defect eventually dissociates an adsorbed water molecule under a moderate external electric field, the Fe-pyridine defect does not convey water dissociation.

A transferable recommender approach for selecting the best density functional approximations in chemical discovery

Approximate density functional theory has become indispensable owing to its balanced cost-accuracy trade-off, including in large-scale screening. To date, however, no density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from density functional theory. With electron density fitting and Δ-learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to the gold standard (but cost-prohibitive) coupled cluster theory in a system-specific manner. We demonstrate this recommender approach on the evaluation of vertical spin splitting energies of transition metal complexes. Our recommender predicts top-performing DFAs and yields excellent accuracy (about 2 kcal mol-1) for chemical discovery, outperforming both individual Δ-learning models and the best conventional single-functional approach from a set of 48 DFAs. By demonstrating transferability to diverse synthesized compounds, our recommender potentially addresses the accuracy versus scope dilemma broadly encountered in computational chemistry.

Ultrafast plasma method allows rapid immobilization of monatomic copper on carboxyl-deficient g-C3N4 for efficient photocatalytic hydrogen production

Transition-metal monometallic photocatalysts have received extensive attention owing to the maximization of atomic utilization efficiency. However, in previous related works, single-atom loading and stability are generally low due to limited anchor sites and mechanisms. Recently, adding transition-metal monatomic sites to defective carbon nitrides has a good prospect, but there is still lack of diversity in defect structures and preparation techniques. Here, a strategy for preparing defect-type carbon-nitride–coupled monatomic copper catalysts by an ultrafast plasma method is reported. In this method, oxalic acid and commercial copper salt are used as a carboxyl defect additive and a copper source, respectively. Carbon nitride samples containing carboxyl defects and monatomic copper can be processed within 10 min by one-step argon plasma treatment. Infrared spectroscopy and nuclear magnetic resonance prove the existence of carboxyl defects. Spherical aberration electron microscopy and synchrotron radiation analysis confirm the existence of monatomic copper. The proportion of monatomic copper is relatively high, and the purity is high and very uniform. The Cu PCN as-prepared shows not only high photo-Fenton pollutant degradation ability but also high photocatalytic hydrogen evolution ability under visible light. In the photocatalytic reaction, the reversible change of Cu⁺/Cu²⁺ greatly promotes the separation and transmission of photogenerated carriers and improves the utilization of photoelectrons. The photocatalytic hydrogen evolution rate of the optimized sample is 8.34 mmol g⁻¹·h⁻¹, which is 4.54 times that of the raw carbon nitride photocatalyst. The cyclic photo-Fenton experiment confirms the catalyst has excellent repeatability in a strong oxidation environment. The synergistic mechanism of the photocatalyst obtained by this plasma is the coordination of single-atom copper sites and carboxyl defect sites. The single copper atoms incorporated can act as an electron-rich active center, enhancing the h+ adsorption and reduction capacity of Cu PCN. At the same time, the carboxyl defect sites can form hydrogen bonds to stabilize the production of hydrogen atoms and subsequently convert them to hydrogen because of the unstable hydrogen bond structure. This plasma strategy is green, convenient, environment-friendly, and waste-free. More importantly, it has the potential for large-scale production, which brings a new way for the general preparation of high-quality monatomic catalysts.

Enabling High Loading in Single-Atom Catalysts on Bare Substrate with Chemical Scissors by Saturating the Anchoring Sites

Atomically dispersed metal catalysts often exhibit high catalytic performances, but the metal loading density must be kept low to avoid the formation of metal nanoparticles, making it difficult to improve the overall activity. Diverse strategies based on creating more anchoring sites (ASs) have been adopted to elevate the loading density. One problem of such traditional methods is that the single atoms always gather together before the saturation of all ASs. Here, a chemical scissors strategy is developed by selectively removing unwanted metallic materials after excessive loading. Different from traditional ways, the chemical scissors strategy places more emphasis on the accurate matching between the strength of etching agent and the bond energies of metal-metal/metal-substrate, thus enabling a higher loading up to 2.02 wt% even on bare substrate without any pre-treatment (the bare substrate without any pre-treatment generally only has a few ASs for single atom loading). It can be inferred that by combining with other traditional methods which can create more ASs, the loading could be further increased by saturating ASs. When used for CH₃ OH generation via photocatalytic CO₂ reduction, the as-made single-atom catalyst exhibits impressive catalytic activity of 597.8 ± 144.6 µmol h^-1 g^-1 and selectivity of 81.3 ± 3.8%.

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.

Density Functional Theory Study of the Oxygen Reduction Reaction Mechanism on Graphene Doped with Nitrogen and a Transition Metal

The active centers of carbon nonplatinum catalysts doped with cobalt, iron, nickel, and copper have been simulated by quantum-chemical density functional theory methods. The thermodynamics of the electrochemical oxygen reduction reaction (ORR) on model catalysts has been determined. It was found that among the studied catalysts, graphene doped with cobalt and iron showed the best properties. A two-state reactivity effect has been found on a cobalt-containing catalyst, and a more detailed reaction mechanism has been proposed, including the stages of charging by an extra electron and association with water. The proposed mechanism explains several effects that have arisen during the modeling in relation to the classical mechanism.

Toward Multicomponent Single-Atom Catalysis for Efficient Electrochemical Energy Conversion

Single-atom catalysts (SACs) have recently emerged as the ultimate solution for overcoming the limitations of traditional catalysts by bridging the gap between homogeneous and heterogeneous catalysts. Atomically dispersed identical active sites enable a maximal atom utilization efficiency, high activity, and selectivity toward the wide range of electrochemical reactions, superior structural robustness, and stability over nanoparticles due to strong atomic covalent bonding with supports. Mononuclear active sites of SACs can be further adjusted by engineering with multicomponent elements, such as introducing dual-metal active sites or additional neighbor atoms, and SACs can be regarded as multicomponent SACs if the surroundings of the active sites or the active sites themselves consist of multiple atomic elements. Multicomponent engineering offers an increased combinational diversity in SACs and unprecedented routes to exceed the theoretical catalytic performance limitations imposed by single-component scaling relationships for adsorption and transition state energies of reactions. The precisely designed structures of multicomponent SACs are expected to be responsible for the synergistic optimization of the overall electrocatalytic performance by beneficially modulating the electronic structure, the nature of orbital filling, the binding energy of reaction intermediates, the reaction pathways, and the local structural transformations. This Review demonstrates these synergistic effects of multicomponent SACs by highlighting representative breakthroughs on electrochemical conversion reactions, which might mitigate the global energy crisis of high dependency on fossil fuels. General synthesis methods and characterization techniques for SACs are also introduced. Then, the perspective on challenges and future directions in the research of SACs is briefly summarized. We believe that careful tailoring of multicomponent active sites is one of the most promising approaches to unleash the full potential of SACs and reach the superior catalytic activity, selectivity, and stability at the same time, which makes SACs promising candidates for electrocatalysts in various energy conversion reactions.

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.

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.

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.

Single-atom catalysis in advanced oxidation processes for environmental remediation

This review presents the recent advances in synthetic strategies, characterisation, and computations of carbon-based single-atom catalysts, as well as their innovative applications and mechanisms in advanced oxidation technologies.

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.

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.

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.