CatEmbed: A Machine-Learned Representation Obtained via Categorical Entity Embedding for Predicting Adsorption and Reaction Energies on Bimetallic Alloy Surfaces.

Machine-learning models for predicting adsorption energies on metallic surfaces often rely on basic elemental properties and electronic and geometric descriptors. Here, we apply categorical entity embedding, a featurization method inspired by natural language processing techniques, to predict adsorption energies on bimetallic alloy surfaces using categorical descriptors. Using this method, we develop a machine-learned representation from categorical descriptors (e.g., surface composition, adsorbate type, and site type) of the slab/adsorbate complex. By combining this representation with numerical features (e.g., slab metal stoichiometric ratios), we create the CatEmbed representation. Remarkably, decision tree models trained using CatEmbed, which includes no explicit geometric information, achieve a Mean Absolute Error (MAE) of 0.12 eV. Additionally, we extend this technique to predict reaction energies on bimetallic surfaces, creating the CatEmbed-React representation, which achieves an MAE of 0.08 eV. These findings highlight the effectiveness of categorical entity embedding for predicting adsorption and reaction energies on bimetallic alloy surfaces.

Contrasting Mechanisms of Aromatic and Aryl-Methyl Substituent Hydroxylation by the Rieske Monooxygenase Salicylate 5-Hydroxylase.

The hydroxylase component (S5HH) of salicylate-5-hydroxylase catalyzes C5 ring hydroxylation of salicylate but switches to methyl hydroxylation when a C5 methyl substituent is present. The use of 18O2 reveals that both aromatic and aryl-methyl hydroxylations result from monooxygenase chemistry. The functional unit of S5HH comprises a nonheme Fe(II) site located 12 Šacross a subunit boundary from a one-electron reduced Rieske-type iron-sulfur cluster. Past studies determined that substrates bind near the Fe(II), followed by O2 binding to the iron to initiate catalysis. Stopped-flow-single-turnover reactions (STOs) demonstrated that the Rieske cluster transfers an electron to the iron site during catalysis. It is shown here that fluorine ring substituents decrease the rate constant for Rieske electron transfer, implying a prior reaction of an Fe(III)-superoxo intermediate with a substrate. We propose that the iron becomes fully oxidized in the resulting Fe(III)-peroxo-substrate-radical intermediate, allowing Rieske electron transfer to occur. STO using 5-CD3-salicylate-d8 occurs with an inverse kinetic isotope effect (KIE). In contrast, STO of a 1:1 mixture of unlabeled and 5-CD3-salicylate-d8 yields a normal product isotope effect. It is proposed that aromatic and aryl-methyl hydroxylation reactions both begin with the Fe(III)-superoxo reaction with a ring carbon, yielding the inverse KIE due to sp2 → sp3 carbon hybridization. After Rieske electron transfer, the resulting Fe(III)-peroxo-salicylate intermediate can continue to aromatic hydroxylation, whereas the equivalent aryl-methyl intermediate formation must be reversible to allow the substrate exchange necessary to yield a normal product isotope effect. The resulting Fe(III)-(hydro)peroxo intermediate may be reactive or evolve through a high-valent iron intermediate to complete the aryl-methyl hydroxylation.

Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities.

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn-Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.

Hydrogen Evolving Activity of Dithiolene-Based Metal-Organic Frameworks with Mixed Cobalt and Iron Centers.

Electrocatalytic systems based on metal-organic frameworks (MOFs) have attracted great attention due to their potential application in commercially viable renewable energy-converting devices. We have recently shown that the cobalt 2,3,6,7,10,11-triphenylenehexathiolate (CoTHT) framework can catalyze the hydrogen evolution reaction (HER) in fully aqueous media with Tafel slopes as low as 71 mV/dec and near-unity Faradaic efficiency (FE). Taking advantage of the high synthetic tunability of MOFs, here, we synthesize a series of iron and mixed iron/cobalt THT-based MOFs. The incorporation of the iron and cobalt dithiolene moieties is verified by various spectroscopic techniques, and the integrity of the crystalline structure is maintained regardless of the stoichiometries of the two metals. The hydrogen evolving activity of the materials was explored in pH 1.3 aqueous electrolyte solutions. Unlike CoTHT, the FeTHT framework exhibits minimal activity due to a late catalytic onset [-0.440 V versus reversible hydrogen electrode (RHE)] and a large Tafel slope (210 mV/dec). The performance of the mixed-metal MOFs is adversely affected by the incorporation of Fe, where increasing Fe content results in MOFs with lower HER activity and diminished long-term stability and FE for H2 production. It is proposed that the FeTHT domains undergo alternative Faradaic processes under catalytic conditions, which alter its local structure and electrochemical behavior, eventually resulting in a material with diminished HER performance.

Magnetic ordering through itinerant ferromagnetism in a metal-organic framework.

Materials that combine magnetic order with other desirable physical attributes could find transformative applications in spintronics, quantum sensing, low-density magnets and gas separations. Among potential multifunctional magnetic materials, metal-organic frameworks, in particular, bear structures that offer intrinsic porosity, vast chemical and structural programmability, and the tunability of electronic properties. Nevertheless, magnetic order within metal-organic frameworks has generally been limited to low temperatures, owing largely to challenges in creating a strong magnetic exchange. Here we employ the phenomenon of itinerant ferromagnetism to realize magnetic ordering at TC = 225 K in a mixed-valence chromium(II/III) triazolate compound, which represents the highest ferromagnetic ordering temperature yet observed in a metal-organic framework. The itinerant ferromagnetism proceeds through a double-exchange mechanism, which results in a barrierless charge transport below the Curie temperature and a large negative magnetoresistance of 23% at 5 K. These observations suggest applications for double-exchange-based coordination solids in the emergent fields of magnetoelectrics and spintronics.

Improving and Understanding the Hydrogen Evolving Activity of a Cobalt Dithiolene Metal-Organic Framework.

Despite the promising previous reports on the development of electrocatalytic dithiolene-based metal-organic frameworks (MOFs) for the hydrogen evolution reaction (HER), these materials often display poor reproducibility of the HER performance because of their poor bulk properties upon integration with electrode materials. We demonstrate here an in-depth investigation of the electrocatalytic HER activity of a cobalt 2,3,6,7,10,11-triphenylenehexathiolate (CoTHT) MOF. To enhance the durability and charge transport properties of the constructed CoTHT/electrode architecture, CoTHT is deposited as an ink composite (1) composed of Nafion and carbon black. We leverage here the well-established use of catalyst inks in the literature to increase adhesion of the catalyst to the electrode surface and to improve the overall electrical conductivity of the integrated catalyst/electrode. The utilization of the composite 1 leads to a significant improvement in the overpotential (η) to reach a current density of 10 mA/cm2 (η = 143 mV) compared to prior reports, resulting in the most active MOF-based electrocatalyst for the HER that contains only earth-abundant elements. Extensive density functional theory (DFT) calculations were applied to understand the structure of CoTHT and the mechanistic pathways of the HER. The computational results suggest that an AB stacking geometry is energetically favorable, where one layer is slipped by 1.6 Šrelative to the neighboring one along the a and b vectors. Additionally, the DFT calculations indicate that the catalytic cycle likely involves a Volmer discharge step to generate a cobalt hydride, followed by a Heyrovsky step to form a cobalt-H2 intermediate, and finally the dissociation of H2.

Fundamental insight into electrochemical oxidation of methane towards methanol on transition metal oxides.

Electrochemical oxidation of CH4 is known to be inefficient in aqueous electrolytes. The lower activity of methane oxidation reaction (MOR) is primarily attributed to the dominant oxygen evolution reaction (OER) and the higher barrier for CH4 activation on transition metal oxides (TMOs). However, a satisfactory explanation for the origins of such lower activity of MOR on TMOs, along with the enabling strategies to partially oxidize CH4 to CH3OH, have not been developed yet. We report here the activation of CH4 is governed by a previously unrecognized consequence of electrostatic (or Madelung) potential of metal atom in TMOs. The measured binding energies of CH4 on 12 different TMOs scale linearly with the Madelung potentials of the metal in the TMOs. The MOR active TMOs are the ones with higher CH4 binding energy and lower Madelung potential. Out of 12 TMOs studied here, only TiO2, IrO2, PbO2, and PtO2 are active for MOR, where the stable active site is the O on top of the metal in TMOs. The reaction pathway for MOR proceeds primarily through *CH x intermediates at lower potentials and through *CH3OH intermediates at higher potentials. The key MOR intermediate *CH3OH is identified on TiO2 under operando conditions at higher potential using transient open-circuit potential measurement. To minimize the overoxidation of *CH3OH, a bimetallic Cu2O3 on TiO2 catalysts is developed, in which Cu reduces the barrier for the reaction of *CH3 and *OH and facilitates the desorption of *CH3OH. The highest faradaic efficiency of 6% is obtained using Cu-Ti bimetallic TMO.

Plasmon-Mediated Intramolecular Methyl Migration with Nanoscale Spatial Control.

Plasmonic materials interact strongly with light to focus and enhance electromagnetic radiation down to nanoscale volumes. Due to this localized confinement, materials that support localized surface plasmon resonances are capable of driving energetically unfavorable chemical reactions. In certain cases, the plasmonic nanostructures are able to preferentially catalyze the formation of specific photoproducts, which offers an opportunity for the development of solar-driven chemical synthesis. Here, using plasmonic environments, we report inducing an intramolecular methyl migration reaction, forming 4-methylpyridine from N-methylpyridinium. Using both experimental and computational methods, we were able to confirm the identity of the N-methylpyridinium by making spectral comparisons against possible photoproducts. This reaction involves breaking a C-N bond and forming a new C-C bond, highlighting the ability of plasmonic materials to drive complex and selective reactions. Additionally, we observe that the product yield depends strongly on optical illumination conditions. This is likely due to steric hindrance in specific regions on the nanostructured plasmonic substrate, providing an optical handle for driving plasmonic catalysis with spatial specificity. This work adds yet another class of reactions accessible by surface plasmon excitation to the ever-growing library of plasmon-mediated chemical reactions.

Cp2Ti(κ2-tBuNCNtBu): A Complex with an Unusual κ2 Coordination Mode of a Heterocumulene Featuring a Free Carbene.

Although there are myriad binding modes of heterocumulenes to metal centers, the monometallic κ2-ECE (E = O, S, NR) coordination mode has not been reported. Herein, the synthesis, isolation, and physical characterization of Cp2Ti(κ2-tBuNCNtBu) (3) (Cp = cyclopentadienyl, tBu = tert-butyl), a strained 4-membered metallacycle bearing a free carbene, is described. Computational (DFT, CASSCF, QT-AIM, ELF) and solid-state CP-MAS 13C NMR spectroscopic analysis indicate that 3 is best described as a free carbene with partial Ti-Cß bonding that results from Ti-N π-bonding mixing with N-C-N σ-bonding of the bent N-C-N framework. Reactivity studies of 3 corroborate its carbene-like nature: protonation with [LutH]I results in the formation of a Ti-formamidinate (4), while oxidation with S8 yields a Ti-thioureate (5). Additionally, a related bridged dititanamidocarbene, (Cp2Ti)2(µ-η1,η1-CyNCNCy) (10) (Cy = cyclohexyl) is reported. Taken together, this work suggests that the 2-electron reduction of heterocumulene moieties can allow access to unusual free carbene coordination geometries given the proper stabilizing coordination environment from the reducing transition metal fragment.

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems.

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal-ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal-organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. This work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

Mechanistic Studies of Bioorthogonal ATP Analogues for Assessment of Histidine Kinase Autophosphorylation.

Phosphorylation is an essential protein modification and is most commonly associated with hydroxyl-containing amino acids via an adenosine triphosphate (ATP) substrate. The last decades have brought greater appreciation to the roles that phosphorylation of myriad amino acids plays in biological signaling, metabolism, and gene transcription. Histidine phosphorylation occurs in both eukaryotes and prokaryotes but has been shown to dominate signaling networks in the latter due to its role in microbial two-component systems. Methods to investigate histidine phosphorylation have lagged behind those to study serine, threonine, and tyrosine modifications due to its inherent instability and the historical view that this protein modification was rare. An important strategy to overcome the reactivity of phosphohistidine is the development of substrate-based probes with altered chemical properties that improve modification longevity but that do not suffer from poor recognition or transfer by the protein. Here, we present combined experimental and computational studies to better understand the molecular requirements for efficient histidine phosphorylation by comparison of the native kinase substrate, ATP, and alkylated ATP derivatives. While recognition of the substrates by the histidine kinases is an important parameter for the formation of phosphohistidine derivatives, reaction sterics also affect the outcome. In addition, we found that stability of the resulting phosphohistidine moieties correlates with the stability of their hydrolysis products, specifically with their free energy in solution. Interestingly, alkylation dramatically affects the stability of the phosphohistidine derivatives at very acidic pH values. These results provide critical mechanistic insights into histidine phosphorylation and will facilitate the design of future probes to study enzymatic histidine phosphorylation.

Ti-catalyzed ring-opening oxidative amination of methylenecyclopropanes with diazenes.

The ring-opening oxidative amination of methylenecyclopropanes (MCPs) with diazenes catalyzed by py3TiCl2(NR) complexes is reported. This reaction selectively generates branched α-methylene imines as opposed to linear α,ß-unsaturated imines, which are difficult to access via other methods. Products can be isolated as the imine or hydrolyzed to the corresponding ketone in good yields. Mechanistic investigation via density functional theory suggests that the regioselectivity of these products results from a Curtin-Hammett kinetic scenario, where reversible ß-carbon elimination of a spirocyclic [2 + 2] azatitanacyclobutene intermediate is followed by selectivity-determining ß-hydrogen elimination of the resulting metallacycle. Further functionalizations of these branched α-methylene imine products are explored, demonstrating their utility as building blocks.

Iterative Supervised Principal Component Analysis Driven Ligand Design for Regioselective Ti-Catalyzed Pyrrole Synthesis.

The rational design of catalysts remains a challenging endeavor within the broader chemical community owing to the myriad variables that can affect key bond-forming events. Designing selective catalysts for any reaction requires an efficient strategy for discovering predictive structure-activity relationships. Herein, we describe the use of iterative supervised principal component analysis (ISPCA) in de novo catalyst design. The regioselective synthesis of 2,5-dimethyl-1,3,4-triphenyl-1H-pyrrole (C) via a Ti-catalyzed formal [2 + 2 +1] cycloaddition of phenylpropyne and azobenzene was targeted as a proof of principle. The initial reaction conditions led to an unselective mixture of all possible pyrrole regioisomers. ISPCA was conducted on a training set of catalysts, and their performance was regressed against the scores from the top three principal components. Component loadings from this PCA space and k-means clustering were used to inform the design of new test catalysts. The selectivity of a prospective test set was predicted in silico using the ISPCA model, and optimal candidates were synthesized and tested experimentally. This data-driven predictive-modeling workflow was iterated, and after only three generations the catalytic selectivity was improved from 0.5 (statistical mixture of products) to over 11 (>90% C) by incorporating 2,6-dimethyl-4-(pyrrolidin-1-yl)pyridine as a ligand. The origin of catalyst selectivity was probed by examining ISPCA variable loadings in combination with DFT modeling, revealing that ligand lability plays an important role in selectivity. A parallel catalyst search using multivariate linear regression (MLR), a popular approach in catalysis informatics, was also conducted in order to compare these strategies in a hypothetical catalyst scouting campaign. ISPCA appears to be more robust and predictive than MLR when sparse training sets are used that are representative of the data available during the early search for an optimal catalyst. The successful development of a highly selective catalyst without resorting to long, stochastic screening processes demonstrates the inherent power of ISPCA in de novo catalyst design and should motivate the general use of ISPCA in reaction development.

Absolutely Localized Projection-Based Embedding for Excited States.

We present a quantum embedding method that allows for calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge-transfer states and prevent overdelocalization of excited states. Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited-state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately and make computationally expensive WF methods applicable to systems beyond current computational limits.

The Stability of the Complex and the Basicity of the Anion Impact the Selectivity and Affinity of Tripodal Gadolinium Complexes for Anions.

The affinities and selectivities of lanthanide complexes with open coordination sites for anions vary considerably with the chelate. In order to determine the effect of the stability of a lanthanide complex on its affinity for anions, five different complexes featuring different bidentate chelating moieties were synthesized, and their affinity for anions in water at neutral pH were evaluated by longitudinal relaxometry measurements. The chelates comprise both oxygen and nitrogen donors including maltol, 1,2-hydroxypyridinone, hydroxamic acid, pyridin-2-ylmethanol, and carbamoylmethylphosphonate diester. They were chosen to span a range of basicities all the while maintaining a similar tripodal tris-bidentate architecture, thereby allowing for a direct study of the role of the coordinating motif on the supramolecular recognition of anions by the corresponding GdIII complex. Overall, for ligands containing the same number of protonation steps, and therefore the same charge at neutral pH, the lower the acidity of the chelate (higher ∑pKa's), the less stable the corresponding GdIII complex, and the higher its affinity for anions. Regardless of the number of protonation steps, the more stable GdIII complexes form ternary or quaternary assemblies with coordinating anions. In contrast, the same anions readily displace the chelate of the least stable complexes, resulting instead in the formation of GdIII·anion precipitates. Irrespective of the chelate, in the absence of steric hindrance at the open coordination site, the affinity of GdIII complexes for anions follows the order phosphate > arsenate > bicarbonate > fluoride. Hence, the selectivity and affinity of GdIII complexes of tripodal tris-bidentate chelates for anions is a function of the stability of the GdIII complex and the basicity of the anion.

Fully Quantum Embedding with Density Functional Theory for Full Configuration Interaction Quantum Monte Carlo.

We here develop a fully quantum embedded version of initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) and apply it to study an ionic bond (lithium hydride, LiH) and a covalent bond (hydrogen flouride, HF) physisorbed to a benzene molecule. The embedding is performed using a recently developed Huzinaga projection operator approach, which affords good synergy with i-FCIQMC by minimizing the number of orbitals in the calculation. When considering the dissociation energy of these bonds into closed-shell ionic fragments, we find that i-FCIQMC embedded in density functional theory (i-FCIQMC-in-DFT) delivers comparable accuracy with coupled cluster singles and doubles with perturbative triples embedded in density functional theory (CCSD(T)-in-DFT). In treating the bond dissociation energy curve of HF, i-FCIQMC-in-DFT has improved accuracy over CCSD(T)-in-DFT due to the presence of strong correlation. We discuss the implications of the new i-FCIQMC-in-DFT method as applied to bond breaking in catalysis.

Carbodiimide Synthesis via Ti-Catalyzed Nitrene Transfer from Diazenes to Isocyanides.

Simple Ti imido halide complexes such as [Br2Ti(N t Bu)py2]2 are competent catalysts for the synthesis of unsymmetrical carbodiimides via Ti-catalyzed nitrene transfer from diazenes or azides to isocyanides. Both alkyl and aryl isocyanides are compatible with the reaction conditions, although product inhibition with sterically unencumbered substrates sometimes limits the yield when diazenes are employed as the oxidant. The reaction mechanism has been investigated both experimentally and computationally, wherein a key feature is that the product release is triggered by electron transfer from an η 2-carbodiimide to a Ti-bound azobenzene. This ligand-to-ligand redox buffering obviates the need for high-energy formally TiII intermediates and provides further evidence that substrate and product "redox noninnocence" can promote unusual Ti redox catalytic transformations.

Mechanism of Ti-Catalyzed Oxidative Nitrene Transfer in [2 + 2 + 1] Pyrrole Synthesis from Alkynes and Azobenzene.

A combined computational and experimental study on the mechanism of Ti-catalyzed formal [2 + 2 + 1] pyrrole synthesis from alkynes and aryl diazenes is reported. This reaction proceeds through a formally TiII/TiIV redox catalytic cycle as determined by natural bond orbital (NBO) and intrinsic bond orbital (IBO) analysis. Kinetic analysis of the reaction of internal alkynes with azobenzene reveals a complex equilibrium involving Ti═NPh monomer/dimer equilibrium and Ti═NPh + alkyne [2 + 2] cycloaddition equilibrium along with azobenzene and pyridine inhibition equilibria prior to rate-determining second alkyne insertion. Computations support this kinetic analysis, provide insights into the structure of the active species in catalysis and the roles of solvent, and provide a new mechanism for regeneration of the Ti imido catalyst via disproportionation. Reductive elimination from a 6-membered azatitanacyclohexadiene species to generate pyrrole-bound TiII is surprisingly facile and occurs through a unique electrocyclic reductive elimination pathway similar to a Nazarov cyclization. The resulting TiII species are stabilized through backbonding into the π* of the pyrrole framework, although solvent effects also significantly stabilize free TiII species that are required for pyrrole loss and catalytic turnover. Further computational and kinetic analysis reveals that in complex reactions with unysmmetric alkynes the resulting pyrrole regioselectivity is driven primarily by steric effects for terminal alkynes and inductive effects for internal alkynes.

Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems.

We present a level shift projection operator-based embedding method for systems with periodic boundary conditions-where the "active" subsystem can be described using either density functional theory (DFT) or correlated wave function (WF) methods and the "environment" is described using DFT. Our method allows for k-point sampling, is shown to be exactly equal to the canonical DFT solution of the full system under the limit that we use the full system basis to describe each subsystem, and can treat the active subsystem either with periodic boundary conditions-in what we term "periodic-in-periodic" embedding-or as a molecular cluster-in "cluster-in-periodic" embedding. We explore each of these methods and show that cluster WF-in-periodic DFT embedding can accurately calculate the absorption energy of CO on to a Si(100)-2×1 surface.

Mechanistic insights into electrochemical reduction of CO2 over Ag using density functional theory and transport models.

Electrochemical reduction of CO2 using renewable sources of electrical energy holds promise for converting CO2 to fuels and chemicals. Since this process is complex and involves a large number of species and physical phenomena, a comprehensive understanding of the factors controlling product distribution is required. While the most plausible reaction pathway is usually identified from quantum-chemical calculation of the lowest free-energy pathway, this approach can be misleading when coverages of adsorbed species determined for alternative mechanism differ significantly, since elementary reaction rates depend on the product of the rate coefficient and the coverage of species involved in the reaction. Moreover, cathode polarization can influence the kinetics of CO2 reduction. Here, we present a multiscale framework for ab initio simulation of the electrochemical reduction of CO2 over an Ag(110) surface. A continuum model for species transport is combined with a microkinetic model for the cathode reaction dynamics. Free energies of activation for all elementary reactions are determined from density functional theory calculations. Using this approach, three alternative mechanisms for CO2 reduction were examined. The rate-limiting step in each mechanism is **COOH formation at higher negative potentials. However, only via the multiscale simulation was it possible to identify the mechanism that leads to a dependence of the rate of CO formation on the partial pressure of CO2 that is consistent with experiments. Simulations based on this mechanism also describe the dependence of the H2 and CO current densities on cathode voltage that are in strikingly good agreement with experimental observation.