Revisiting Competing Paths in Electrochemical CO2 Reduction on Copper via Embedded Correlated Wavefunction Theory

Unifying thermochemistry concepts in computational heterogeneous catalysis

Thermophysical properties of adsorbates and gas-phase species define the free energy landscape of heterogeneously catalyzed processes and are pivotal for an atomistic understanding of the catalyst performance. These thermophysical properties, such as the free energy or the enthalpy, are typically derived from density functional theory (DFT) calculations. Enthalpies are species-interdependent properties that are only meaningful when referenced to other species. The widespread use of DFT has led to a proliferation of new energetic data in the literature and databases. However, there is a lack of consistency in how DFT data is referenced and how the associated enthalpies or free energies are stored and reported, leading to challenges in reproducing or utilizing the results of prior work. Additionally, DFT suffers from exchange-correlation errors that often require corrections to align the data with other global thermochemical networks, which are not always clearly documented or explained. In this review, we introduce a set of consistent terminology and definitions, review existing approaches, and unify the techniques using the framework of linear algebra. This set of terminology and tools facilitates the correction and alignment of energies between different data formats and sources, promoting the sharing and reuse of ab initio data. Standardization of thermochemistry concepts in computational heterogeneous catalysis reduces computational cost and enhances fundamental understanding of catalytic processes, which will accelerate the computational design of optimally performing catalysts.

Graphene-based single-atom catalysts for electrochemical CO2 reduction: unraveling the roles of metals and dopants in tuning activity

Discovering electrocatalysts that can efficiently convert carbon dioxide (CO2) to valuable fuels and feedstocks using excess renewable electricity is an emergent carbon-neutral technology. A single metal atom embedded in doped graphene, i.e., single-atom catalyst (SAC), possesses high activity and selectivity for electrochemical CO2 reduction (CO2R) to CO, yet further reduction to hydrocarbons is challenging. Here, using density functional theory calculations, we investigate stability and reactivity of a broad SAC chemical space with various metal centers (3d transition metals) and dopants (2p dopants of B, N, O; 3p dopants of P, S) as electrocatalysts for CO2R to methane and methanol. We observe that the rigidities of these SACs depend on the type of dopants, with 3p-coordinating SACs exhibiting more severe out-of-plane distortion than 2p-coordinating SACs. Using CO adsorption energy as a descriptor for CO2R reactivity, we narrow down the candidates and identify seven SACs with near-optimal CO binding strength. We then elucidate full reaction mechanisms towards methane and methanol generation on these identified candidates and observe highly dopant-dependent activity and rate-limiting steps, divergent from conventional mechanistic understanding on metallic surfaces, calling into question whether previous design principles established on metals are directly transferrable to SACs. Consequently, we find that zinc embedded in boron-doped graphene (Zn-B-C) is a highly active catalyst for electrochemical CO2R to C1 hydrocarbons. Our work reveals the opportunities of tuning SAC reactivity via engineering dopants and metals and highlights the importance of re-elucidating CO2R reaction mechanisms on SACs towards unearthing new design principles for SAC chemistry.

Multiscale Modeling of CO2 Electrochemical Reduction on Copper Electrocatalysts: A Review of Advancements, Challenges, and Future Directions

Although CO2 contributes significantly to global warming, it also offers potential as a raw material for the production of hydrocarbons such as CH4, C2H4 and CH3OH. Electrochemical CO2 reduction reaction (eCO2RR) is an emerging technology that utilizes renewable energy to convert CO2 into valuable fuels, solving environmental and energy problems simultaneously. Insights gained at any individual scale can only provide a limited view of that specific scale. Multiscale modeling, which involves coupling atomistic-level insights (density functional theory, DFT) and (Molecular Dynamics, MD), with mesoscale (kinetic Monte Carlo, KMC, and microkinetics, MK) and macroscale (computational fluid dynamics, CFD) simulations, has received significant attention recently. While multiscale modeling of eCO2RR on electrocatalysts across all scales is limited due to its complexity, this review offers an overview of recent works on single scales and the coupling of two and three scales, such as "DFT+MD", "DFT+KMC", "DFT+MK", "KMC/MK+CFD" and "DFT+MK/KMC+CFD", focusing particularly on Cu-based electrocatalysts as copper is known to be an excellent electrocatalyst for eCO2RR. This sets it apart from other reviews that solely focus exclusively on a single scale or only on a combination of DFT and MK/KMC scales. Furthermore, this review offers a concise overview of machine learning (ML) applications for eCO2RR, an emerging approach that has not yet been reviewed. Finally, this review highlights the key challenges, research gaps and perspectives of multiscale modeling for eCO2RR.

Calculating Molecular Polarizabilities Using Exact Frozen Density Embedding with External Orthogonality

Frozen density embedding (FDE) with freeze-thaw cycles is a formally exact embedding scheme. In practice, this method is limited to systems with small density overlaps when approximate nonadditive kinetic energy functionals are used. It has been shown that the use of approximate nonadditive kinetic energy functionals can be avoided when external orthogonality (EO) is enforced, and FDE can then generate exact results even for strongly overlapping subsystems. In this work, we present an implementation of exact FDEc-EO (coupled FDE TDDFT with EO) for the calculation of polarizabilities in the Amsterdam density functional program package. EO is enforced using the level-shift projection operator method, which ensures that orbitals between fragments are orthogonal. For pure functionals, we show that only the symmetric EO contributions to the induced density matrix are needed. This leads to a simplified implementation for the calculation of polarizability that can exactly reproduce the supermolecular TDDFT results. We further discuss the limitation of exact FDEc-EO in interpreting subsystem polarizabilities due to the nonunique partitioning of the total density. We show that this limitation is due to the fact that subsystem polarizability partitioning is dependent on how the subsystems are initially polarized. As supermolecular virtual orbitals are exactly reproduced, this dependence is attributed to the description of the occupied orbitals. In contrast, for excitations of subsystems that are localized within one subsystem, we show that the excitation energies are stable with respect to the order of polarization. This observation shows that impacts from the nonunique nature of exact FDE on subsystem properties can be minimized by better fragmentation of the supermolecular systems if the property is localized. For global properties like polarizability, this is not the case, and nonuniqueness remains independent of the fragmentation used.

Benchmarking a Molecular Flake Model on the Road to Programmable Graphene-Based Single-Atom Catalysts

Single-atom catalysts (SACs) of embedding an active metal in nitrogen-doped graphene are emergent catalytic materials in various applications. The rational design of efficient SACs necessitates an electronic and mechanistic understanding of those materials with reliable quantum mechanical simulations. Conventional computational methods of modeling SACs involve using an infinite slab model with periodic boundary condition, limiting to the selection of generalized gradient approximations as the exchange correlation (XC) functional within density functional theory (DFT). However, these DFT approximations suffer from electron self-interaction error and delocalization error, leading to errors in predicted charge-transfer energetics. An alternative strategy is using a molecular flake model, which carved out the important catalytic center by cleaving C-C bonds and employing a hydrogen capping scheme to saturate the innocent dangling bonds at the molecular boundary. By doing so, we can afford more accurate hybrid XC functionals, or even high-level correlated wavefunction theory, to study those materials. In this work, we compared the structural, electronic, and catalytic properties of SACs simulated using molecular flake models and periodic slab models with first-row transition metals as the active sites. Molecular flake models successfully reproduced structural properties, including both global distortion and local metal-coordination environment, as well as electronic properties, including spin magnetic moments and metal partial charges, for all transition metals studied. In addition, we calculated CO binding strength as a descriptor for electrochemical CO2 reduction reactivity and noted qualitatively similar trends between two models. Using the computationally efficient molecular flake models, we investigated the effect of tuning Hartree-Fock exchange in a global hybrid functional on the CO binding strength and observed system-dependent sensitivities. Overall, our calculations provide valuable insights into the development of accurate and efficient computational tools to simulate SACs.

Advances in fundamentals and application of plasmon-assisted CO2 photoreduction

Artificial photosynthesis of hydrocarbons from carbon dioxide (CO2) has the potential to provide renewable fuels at the scale needed to meet global decarbonization targets. However, CO2 is a notoriously inert molecule and converting it to energy dense hydrocarbons is a complex, multistep process, which can proceed through several intermediates. Recently, the ability of plasmonic nanoparticles to steer the reaction down specific pathways and enhance both reaction rate and selectivity has garnered significant attention due to its potential for sustainable energy production and environmental mitigation. The plasmonic excitation of strong and confined optical near-fields, energetic hot carriers and localized heating can be harnessed to control or enhance chemical reaction pathways. However, despite many seminal contributions, the anticipated transformative impact of plasmonics in selective CO2 photocatalysis has yet to materialize in practical applications. This is due to the lack of a complete theoretical framework on the plasmonic action mechanisms, as well as the challenge of finding efficient materials with high scalability potential. In this review, we aim to provide a comprehensive and critical discussion on recent advancements in plasmon-enhanced CO2 photoreduction, highlighting emerging trends and challenges in this field. We delve into the fundamental principles of plasmonics, discussing the seminal works that led to ongoing debates on the reaction mechanism, and we introduce the most recent ab initio advances, which could help disentangle these effects. We then synthesize experimental advances and in situ measurements on plasmon CO2 photoreduction before concluding with our perspective and outlook on the field of plasmon-enhanced photocatalysis.

Single B-vacancy enriched α1-borophene sheet: an efficient metal-free electrocatalyst for CO2 reduction

By employing first principles calculations, we have studied the electronic structures of pristine (α1) and different defective (α1-t1, α1-t2) borophene sheets to understand the efficacy of such systems as metal-free electrocatalysts for the CO2 reduction reaction. Among the three studied systems, only α1-t1, the defective borophene sheet created by removal of a 5-coordinated boron atom, can chemisorb and activate a CO2 molecule for its subsequent reduction processes, leading to different C1 chemicals, followed by selective conversion into C2 products by multiple proton coupled electron transfer steps. The computed onset potentials for the C1 chemicals such as CH3OH and CH4 are low enough. On the other hand, in the case of the C2 reduction process, the C-C coupling barrier is only 0.80 eV in the solvent phase which produces CH3CHO and CH3CH2OH with very low onset potential values of -0.21 and -0.24 V, respectively, suppressing the competing hydrogen evolution reaction.

A comprehensive investigation of the plasmonic-photocatalytic properties of gold nanoparticles for CO2 conversion to chemicals

Understanding the interactions between plasmonic gold (Au) nanoparticles and the adsorbate is essential for photocatalytic and plasmonic applications. However, it is often challenging to identify a specific reaction mechanism in the ground state and to explore the optical properties in the excited states because of the complicated pathways of carriers. In this study, photocatalytic reduction of carbon dioxide (CO₂) to C1 products (for example, CO and CH₄) on the Au(111) nanoparticle (NP) surface was studied based on reaction pathway analysis, adsorbate reactivity, and its ability to stabilize or deactivate the surface. The calculated reaction Gibbs free energies and activation barriers revealed that the first step in CO reduction via a direct hydrogen transfer mechanism on Au(111) is the formation of formyl (*CHO) instead of hydroxymethylidyne (*COH). Furthermore, the size enhanced and symmetry sensitive optical responses of cuboctahedral Au(111) NPs on localized surface plasmon resonance (LSPR) were investigated by using time-dependent DFT (TDDFT) calculations. Although near field enhancement around cuboctahedral Au(111) NPs is only weakly dependent on the morphology of NPs, it was observed that corner sites stabilize *C-species to drive the CO₂ reduction to CO. The density of active surface states interacting with the adsorbate states near the Fermi level gradually decreases from the (111) on-top site toward the corner site of the Au(111) NP-CO system, which strongly affects the molecule's binding on catalytic sites and, in particular, electronic excitation. Finally, the spatial distribution of the charge oscillations was determined as a guide for the fabrication of Au NPs with an optimal LSPR response.

Accurate descriptions of molecule-surface interactions in electrocatalytic CO2 reduction on the copper surfaces

Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO₂ reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO₂ reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Electrochemical Hydrogenation of CO on Cu(100): Insights from Accurate Multiconfigurational Wavefunction Methods

Copper (Cu) remains the most efficacious electrocatalyst for electrochemical CO₂ reduction (CO₂R). Its activity and selectivity are highly facet-dependent. We recently examined the commonly proposed rate-limiting CO hydrogenation step on Cu(111) via embedded correlated wavefunction (ECW) theory and demonstrated that only this higher-level theory yields predictions consistent with potential-dependent experimental kinetics. Here, to understand the differing activities of Cu(111) and Cu(100) in catalyzing CO₂R, we explore CO hydrogenation on Cu(100) using ECW theory. We predict that the preferred pathway involves the reduction of adsorbed CO (*CO) to *COH via proton-coupled electron transfer (PCET) at working potentials, although *CHO also may form with a kinetically accessible but higher barrier. In contrast, our earlier work on Cu(111) concluded that *COH and *CHO formation via PCET are equally feasible. This work illustrates one possible origin of the facet dependence of CO₂R mechanisms and products on Cu electrodes and sheds light on how the selectivity of CO₂R electrocatalysts can be controlled by the surface morphology.

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C–C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C–C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH–CHO, *COH–*COH, and *OCH–*OCH. The most kinetically favorable path forms *COH–CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C–C coupling paths produce only *COH–*COH and *CO–*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C 2+ product formation via CO 2 RR electrocatalysts.

Flexible Cuprous Triazolate Frameworks as Highly Stable and Efficient Electrocatalysts for CO2 Reduction with Tunable C2 H4 /CH4 Selectivity

Cu-based metal-organic frameworks have attracted much attention for electrocatalytic CO₂ reduction, but they are generally instable and difficult to control the product selectivity. We report flexible Cu(I) triazolate frameworks as efficient, stable, and tunable electrocatalysts for CO₂ reduction to C₂ H₄ /CH₄ . By changing the size of ligand side groups, the C₂ H₄ /CH₄ selectivity ratio can be gradually tuned and inversed from 11.8 : 1 to 1 : 2.6, giving C₂ H₄ , CH₄ , and hydrocarbon selectivities up to 51 %, 56 %, and 77 %, respectively. After long-term electrocatalysis, they can retain the structures/morphologies without formation of Cu-based inorganic species. Computational simulations showed that the coordination geometry of Cu(I) changed from triangular to tetrahedral to bind the reaction intermediates, and two adjacent Cu(I) cooperated for C-C coupling to form C₂ H₄ . Importantly, the ligand side groups controlled the catalyst flexibility by the steric hindrance mechanism, and the C₂ H₄ pathway is more sensitive than the CH₄ one.

Metal-to-Ligand Charge-Transfer Spectrum of a Ru-Bipyridine-Sensitized TiO2 Cluster from Embedded Multiconfigurational Excited-State Theory

Understanding optical properties of the dye molecule in dye-sensitized solar cells (DSSCs) from first-principles quantum mechanics can contribute to improving the efficiency of such devices. While density functional theory (DFT) and time-dependent DFT have been pivotal in simulating optoelectronic properties of photoanodes used in DSSCs at the atomic scale, questions remain regarding DFT's adequacy and accuracy to furnish critical information needed to understand the various excited-state processes involved. Here, we simulate the absorption spectra of a dye-sensitized solar cell analogue, comprised of a Ru-bipyridine (Ru-bpy) dye molecule and a small TiO₂ cluster via DFT and via an accurate embedded correlated wavefunction (CW) theory. We generated CW spectra for the adsorbed Ru-bpy dye via a recently introduced capped density functional embedding theory or capped-DFET (to generate the embedding potential that accounts for the interaction of the molecule and the TiO₂ cluster). We then combined capped-DFET with the accurate but expensive multiconfigurational complete active space second-order perturbation theory (CASPT2)-embedded CASPT2. Because the CW theory is conducted on only a portion of the total system in the presence of an embedding potential that describes that portion's interaction with its environment, we efficiently obtain CW-quality predictions that reflect local properties of the entire system. Specifically, for example, with capped-DFET and embedded CW theory, we can simulate accurately a plethora of metal-to-ligand charge-transfer excited properties at a manageable computational cost. Here, we predict detailed electronic spectra within the visible region, featuring the lowest three singlet and triplet excited states, along with predictions of the singlets' lifetimes. We illustrated these results using a Jablonski diagram that show the relative energy position of the singlet and longer-lived triplet excited states and analyzed and proposed relaxation paths for the excited state corresponding to the most intense but short-lived absorption (interconversion, intersystem crossing, fluorescence, and phosphorescence) that may lead to longer-lived excited states necessary for efficient charge separation required to generate current in solar cells.

Revisiting Understanding of Electrochemical CO2 Reduction on Cu(111): Competing Proton-Coupled Electron Transfer Reaction Mechanisms Revealed by Embedded Correlated Wavefunction Theory

Copper (Cu) electrodes, as the most efficacious of CO₂ reduction reaction (CO₂RR) electrocatalysts, serve as prototypes for determining and validating reaction mechanisms associated with electrochemical CO₂ reduction to hydrocarbons. As in situ electrochemical mechanism determination by experiments is still out of reach, such mechanistic analysis typically is conducted using density functional theory (DFT). The semilocal exchange-correlation (XC) approximations most often used to model such catalysis unfortunately engender a basic error: predicting the wrong adsorption site for CO (a key CO₂RR intermediate) on the most ubiquitous facet of Cu, namely, Cu(111). This longstanding inconsistency casts lingering doubt on previous DFT predictions of the attendant CO₂RR kinetics. Here, we apply embedded correlated wavefunction (ECW) theory, which corrects XC functional error, to study the CO₂RR on Cu(111) via both surface hydride (*H) transfer and proton-coupled electron transfer (PCET). We predict that adsorbed CO (*CO) reduces almost equally to two intermediates, namely, hydroxymethylidyne (*COH) and formyl (*CHO) at -0.9 V vs the RHE. In contrast, semilocal DFT approximations predict a strong preference for *COH. With increasing applied potential, the dominance of *COH (formed via potential-independent surface *H transfer) diminishes, switching to the competitive formation of both *CHO and *COH (both formed via potential-dependent PCET). Our results also demonstrate the importance of including explicitly modeled solvent molecules in predicting electron-transfer barriers and reveal the pitfalls of overreliance on simple surface *H transfer models of reduction reactions.

Density functional theory based embedding approaches for transition-metal complexes

Transition metal species are commonly discussed by considering the metal atom embedded in a ligand environment. This apparently makes them interesting targets for modern embedding strategies based on Kohn-Sham density functional theory (DFT), which aim at modelling accurate predictions for large systems by combining different quantum chemical methods. In this perspective, we will focus on subsystem density functional theory and projection-based embedding. We review the developments in the field for transition metal species, demonstrate benefits, drawbacks and analyse error sources of the different strategies using the example of chromium hexacarbonyle, before giving a perspective where the field is currently heading.