Theoretical Investigation of the Adsorbate and Potential-Induced Stability of Cu Facets During Electrochemical CO2 and CO Reduction

The activity and product selectivity of electrocatalysts for reactions like the carbon dioxide reduction reaction (CO2RR) are intimately dependent on the catalyst's structure and composition. While engineering catalytic surfaces can improve performance, discovering the key sets of rational design principles remains challenging due to limitations in modeling catalyst stability under operating conditions. Herein, we perform first-principles density functional calculations adopting implicit solvation methods with potential control to study the influence of adsorbates and applied potential on the stability of different facets of model Cu electrocatalysts. Using coverage dependencies extracted from microkinetic models, we describe an approach for calculating potential and adsorbate-dependent contributions to surface energies under reaction conditions, where Wulff constructions are used to understand the morphological evolution of Cu electrocatalysts under CO2RR conditions. We identify that CO*, a key reaction intermediate, exhibits higher kinetically and thermodynamically accessible coverages on (100) relative to (111) facets, which can translate into an increased relative stabilization of the (100) facet during CO2RR. Our results support the known tendency for increased (111) faceting of Cu nanoparticles under more reducing conditions and that the relative increase in (100) faceting observed under CO2RR conditions is likely attributed to differences in CO* coverage between these facets.

Importance of Site Diversity and Connectivity in Electrochemical CO Reduction on Cu

Electrochemical CO2 reduction on Cu is a promising approach to produce value-added chemicals using renewable feedstocks, yet various Cu preparations have led to differences in activity and selectivity toward single and multicarbon products. Here, we find, surprisingly, that the effective catalytic activity toward ethylene improves when there is a larger fraction of less active sites acting as reservoirs of *CO on the surface of Cu nanoparticle electrocatalysts. In an adaptation of chemical transient kinetics to electrocatalysis, we measure the dynamic response of a gas diffusion electrode (GDE) cell when the feed gas is abruptly switched between Ar (inert) and CO. When switching from Ar to CO, CO reduction (COR) begins promptly, but when switching from CO to Ar, COR can be maintained for several seconds (delay time) despite the absence of the CO reactant in the gas phase. A three-site microkinetic model captures the observed dynamic behavior and shows that Cu catalysts exhibiting delay times have a less active *CO reservoir that exhibits fast diffusion to active sites. The observed delay times and the estimated *CO reservoir sizes are affected by catalyst preparation, applied potential, and microenvironment (electrolyte cation identity, electrolyte pH, and CO partial pressure). Notably, we estimate that the *CO reservoir surface coverage can be as high as 88 ± 7% on oxide-derived Cu (OD-Cu) at high overpotentials (-1.52 V vs SHE) and this increases in reservoir coverage coincide with increased turnover frequencies to ethylene. We also estimate that *CO can travel substantial distances (up to 10s of nm) prior to desorption or reaction. It appears that active C-C coupling sites by themselves do not control selectivity to C2+ products in electrochemical COR; the supply of CO to those sites is also a crucial factor. More generally, the overall activity of Cu electrocatalysts cannot be approximated from linear combinations of individual site activities. Future designs must consider the diversity of the catalyst network and account for intersite transportation pathways.

Dangling Bonds as Possible Contributors to Charge Noise in Silicon and Silicon-Germanium Quantum Dot Qubits

Spin qubits based on Si and Si1-xGex quantum dot architectures exhibit among the best coherence times of competing quantum computing technologies, yet they still suffer from charge noise that limit their qubit gate fidelities. Identifying the origins of these charge fluctuations is therefore a critical step toward improving Si quantum-dot-based qubits. Here, we use hybrid functional calculations to investigate possible atomistic sources of charge noise, focusing on charge trapping at Si and Ge dangling bonds (DBs). We evaluate the role of global and local environment in the defect levels associated with DBs in Si, Ge, and Si1-xGex alloys, and consider their trapping and excitation energies within the framework of configuration coordinate diagrams. We additionally consider the influence of strain and oxidation in charge-trapping energetics by analyzing Si and GeSi DBs in SiO2 and strained Si layers in typical Si1-xGex quantum dot heterostructures. Our results identify that Ge dangling bonds are more problematic charge-trapping centers both in typical Si1-xGex alloys and associated oxidation layers, and they may be exacerbated by compositional inhomogeneities. These results suggest the importance of alloy homogeneity and possible passivation schemes for DBs in Si-based quantum dot qubits and are of general relevance to mitigating possible trap levels in other Si, Ge, and Si1-xGex-based metal-oxide-semiconductor stacks and related devices.

Tackling Disorder in γ-Ga2 O3

Ga₂ O₃ and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga₂ O₃ offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. γ-Ga₂ O₃ presents a particular challenge across synthesis, characterization, and theory due to its inherent disorder and resulting complex structure-electronic-structure relationship. Here, density functional theory is used in combination with a machine-learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the γ-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of γ-Ga₂ O₃ . The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by photoluminescence excitation spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step toward exploring how their electronic structure can be understood in terms of local coordination and overall structure.

Crystallographic Effects of GaN Nanostructures in Photoelectrochemical Reaction

Tuning the surface structure of the photoelectrode provides one of the most effective ways to address the critical challenges in artificial photosynthesis, such as efficiency, stability, and product selectivity, for which gallium nitride (GaN) nanowires have shown great promise. In the GaN wurtzite crystal structure, polar, semipolar, and nonpolar planes coexist and exhibit very different structural, electronic, and chemical properties. Here, through a comprehensive study of the photoelectrochemical performance of GaN photocathodes in the form of films and nanowires with controlled surface polarities we show that significant photoelectrochemical activity can be observed when the nonpolar surfaces are exposed in the electrolyte, whereas little or no activity is measured from the GaN polar c-plane surfaces. The atomic origin of this fundamental difference is further revealed through density functional theory calculations. This study provides guideline on crystal facet engineering of metal-nitride photo(electro)catalysts for a broad range of artificial photosynthesis chemical reactions.

Persistent Room-Temperature Photodarkening in Cu-Doped β-Ga_{2}O_{3}

β-Ga_{2}O_{3} is an ultrawide band gap semiconductor with emerging applications in power electronics. The introduction of acceptor dopants yields semi-insulating substrates necessary for thin-film devices. In the present work, exposure of Cu-doped β-Ga_{2}O_{3} to UV light >4  eV is shown to cause large, persistent photo-induced darkening at room temperature. Electron paramagnetic resonance spectroscopy indicates that light exposure converts Cu^{2+} to Cu^{3+}, a rare oxidation state that is responsible for the optical absorption. The photodarkening is accompanied by the appearance of O─H vibrational modes in the infrared spectrum. Hybrid function calculations show that Cu acceptors can favorably complex with hydrogen donors incorporated as interstitial (H_{i}) or substitutional (H_{O}) defects. When Cu_{Ga}-H_{O} complexes absorb light, hydrogen is released, contributing to the observed Cu^{3+} species and O─H modes.

Paradigms of frustration in superionic solid electrolytes

Superionic solid electrolytes have widespread use in energy devices, but the fundamental motivations for fast ion conduction are often elusive. In this Perspective, we draw upon atomistic simulations of a wide range of superionic conductors to illustrate some ways frustration can lower diffusion cation barriers in solids. Based on our studies of halides, oxides, sulfides and hydroborates and a survey of published reports, we classify three types of frustration that create competition between different local atomic preferences, thereby flattening the diffusive energy landscape. These include chemical frustration, which derives from competing factors in the anion-cation interaction; structural frustration, which arises from lattice arrangements that induce site distortion or prevent cation ordering; and dynamical frustration, which is associated with temporary fluctuations in the energy landscape due to anion reorientation or cation reconfiguration. For each class of frustration, we provide detailed simulation analyses of various materials to show how ion mobility is facilitated, resulting in stabilizing factors that are both entropic and enthalpic in origin. We propose the use of these categories as a general construct for classifying frustration in superionic conductors and discuss implications for future development of suitable descriptors and improvement strategies. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Paradigms of frustration in superionic solid electrolytes

Superionic solid electrolytes have widespread use in energy devices, but the fundamental motivations for fast ion conduction are often elusive. In this Perspective, we draw upon atomistic simulations of a wide range of superionic conductors to illustrate some ways frustration can lower diffusion cation barriers in solids. Based on our studies of halides, oxides, sulfides and hydroborates and a survey of published reports, we classify three types of frustration that create competition between different local atomic preferences, thereby flattening the diffusive energy landscape. These include chemical frustration, which derives from competing factors in the anion-cation interaction; structural frustration, which arises from lattice arrangements that induce site distortion or prevent cation ordering; and dynamical frustration, which is associated with temporary fluctuations in the energy landscape due to anion reorientation or cation reconfiguration. For each class of frustration, we provide detailed simulation analyses of various materials to show how ion mobility is facilitated, resulting in stabilizing factors that are both entropic and enthalpic in origin. We propose the use of these categories as a general construct for classifying frustration in superionic conductors and discuss implications for future development of suitable descriptors and improvement strategies. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Evaluating the stability and activity of dilute Cu-based alloys for electrochemical CO2 reduction

Cu-based catalysts currently offer the most promising route to actively and selectively produce value-added chemicals via electrochemical reduction of CO₂ (eCO₂R); yet further improvements are required for their wide-scale deployment in carbon mitigation efforts. Here, we systematically investigate a family of dilute Cu-based alloys to explore their viability as active and selective catalysts for eCO₂R through a combined theoretical-experimental approach. Using a quantum-classical modeling approach that accounts for dynamic solvation effects, we assess the stability and activity of model single-atom catalysts under eCO₂R conditions. Our calculations identify that the presence of eCO₂R intermediates, such as CO*, H*, and OH*, may dynamically influence the local catalyst surface composition. Additionally, we identify through binding energy descriptors of the CO*, CHO*, and OCCO* dimer intermediates that certain elements, such as group 13 elements (B, Al, and Ga), enhance the selectivity of C₂₊ species relative to pure Cu by facilitating CO dimerization. The theoretical work is corroborated by preliminary testing of eCO₂R activity and selectivity of candidate dilute Cu-based alloy catalyst films prepared by electron beam evaporation in a zero-gap gas diffusion electrode-based reactor. Of all studied alloys, dilute CuAl was found to be the most active and selective toward C₂₊ products like ethylene, consistent with the theoretical predictions. We attribute the improved performance of dilute CuAl alloys to more favorable dimerization reaction energetics of bound CO species relative to that on pure Cu. In a broader context, the results presented here demonstrate the power of our simulation framework in terms of rational catalyst design.

Chemical Modifications of Ag Catalyst Surfaces with Imidazolium Ionomers Modulate H2 Evolution Rates during Electrochemical CO2 Reduction

Bridging polymer design with catalyst surface science is a promising direction for tuning and optimizing electrochemical reactors that could impact long-term goals in energy and sustainability. Particularly, the interaction between inorganic catalyst surfaces and organic-based ionomers provides an avenue to both steer reaction selectivity and promote activity. Here, we studied the role of imidazolium-based ionomers for electrocatalytic CO₂ reduction to CO (CO₂R) on Ag surfaces and found that they produce no effect on CO₂R activity yet strongly promote the competing hydrogen evolution reaction (HER). By examining the dependence of HER and CO₂R rates on concentrations of CO₂ and HCO₃^-, we developed a kinetic model that attributes HER promotion to intrinsic promotion of HCO₃^- reduction by imidazolium ionomers. We also show that varying the ionomer structure by changing substituents on the imidazolium ring modulates the HER promotion. This ionomer-structure dependence was analyzed via Taft steric parameters and density functional theory calculations, which suggest that steric bulk from functionalities on the imidazolium ring reduces access of the ionomer to both HCO₃^- and the Ag surface, thus limiting the promotional effect. Our results help develop design rules for ionomer-catalyst interactions in CO₂R and motivate further work into precisely uncovering the interplay between primary and secondary coordination in determining electrocatalytic behavior.

Development of a Multiphase Beryllium Equation of State and Physics-based Variations

We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.

Indium Gallium Oxide Alloys: Electronic Structure, Optical Gap, Surface Space Charge, and Chemical Trends within Common-Cation Semiconductors

The electronic and optical properties of (In_xGa_1-x)₂O₃ alloys are highly tunable, giving rise to a myriad of applications including transparent conductors, transparent electronics, and solar-blind ultraviolet photodetectors. Here, we investigate these properties for a high quality pulsed laser deposited film which possesses a lateral cation composition gradient (0.01 ≤ x ≤ 0.82) and three crystallographic phases (monoclinic, hexagonal, and bixbyite). The optical gaps over this composition range are determined, and only a weak optical gap bowing is found (b = 0.36 eV). The valence band edge evolution along with the change in the fundamental band gap over the composition gradient enables the surface space-charge properties to be probed. This is an important property when considering metal contact formation and heterojunctions for devices. A transition from surface electron accumulation to depletion occurs at x ∼ 0.35 as the film goes from the bixbyite In₂O₃ phase to the monoclinic β-Ga₂O₃ phase. The electronic structure of the different phases is investigated by using density functional theory calculations and compared to the valence band X-ray photoemission spectra. Finally, the properties of these alloys, such as the n-type dopability of In₂O₃ and use of Ga₂O₃ as a solar-blind UV detector, are understood with respect to other common-cation compound semiconductors in terms of simple chemical trends of the band edge positions and the hydrostatic volume deformation potential.

Toward Engineering of Solution Microenvironments for the CO2 Reduction Reaction: Unraveling pH and Voltage Effects from a Combined Density-Functional-Continuum Theory

Engineering the electrolyte microenvironment represents an attractive route to tuning the selectivity of electrocatalytic reactions beyond catalyst composition and morphology. However, harnessing the full potential of this approach requires understanding the interplay between voltage, electrolyte composition, and adsorbate binding within the electrical double layer, which is absent from the usual theoretical approaches. In this work, we apply a recently developed density functional theory (DFT)-continuum approach based on the effective screening medium method and reference interaction site model (ESM-RISM) to explore electrolyte effects with an enhanced description of the electrochemical interface. Applying this method to the binding of CO adsorbates in potassium-containing electrolytes on copper, a problem of direct relevance to CO₂ electroreduction to value-added products, we show that the interdependence of voltage and pH leads to an unexpected change in adsorption site preference on Cu(001) terraces. Our findings highlight the often-overlooked importance of the electrical double-layer structure for predicting catalyst operation.

Descriptor-Based Approach for the Prediction of Cation Vacancy Formation Energies and Transition Levels

Point defects largely determine the observed optical and electrical properties of a given material, yet the characterization and identification of defects has remained a slow and tedious process, both experimentally and theoretically. We demonstrate a computationally-cheap model that can reliably predict the formation energies of cation vacancies as well as the location of their electronic states in a large set of II-VI and III-V materials using only parameters obtained from the bulk primitive unit cell (2-4 atoms). We apply our model to ordered alloys within the CdZnSeTe, CdZnS, and ZnMgO systems and predict the positions of cation vacancy charge-state transition levels with a mean absolute error of < 0.2 eV compared to the explicitly calculated values, showing useful accuracy without the need for the expensive and large-scale calculations typically required. This suggests the properties of other point defects may also be predicted with useful accuracy from only bulk-derived properties.

Stability of Cd1-xZnxOyS1-y Quaternary Alloys Assessed with First-Principles Calculations

One route to decreasing the absorption in CdS buffer layers in Cu(In,Ga)Se₂ and Cu₂ZnSn(S,Se)₄ thin-film photovoltaics is by alloying. Here we use first-principles calculations based on hybrid functionals to assess the energetics and stability of quaternary Cd, Zn, O, and S (Cd_1-xZn_xO_yS_1-y) alloys within a regular solution model. Our results identify that full miscibility of most Cd_1-xZn_xO_yS_1-y compositions and even binaries like Zn(O,S) is outside typical photovoltaic processing conditions. The results suggest that the tendency for phase separation of the oxysulfides may drive the nucleation of other phases such as sulfates that have been increasingly observed in oxygenated CdS and ZnS.

Mechanistic insights into nitrogen fixation by nitrogenase enzymes

Biological nitrogen fixation by nitrogenase enzymes is a process that activates dinitrogen (N2) one of the most inert molecules in nature, within the confines of a living organism and at ambient conditions. Despite decades of study, there are still no complete explanations as to how this is possible. Here we describe a model of N2 reduction using the Mo-containing nitrogenase (FeMoco) that can explain the reactivity of the active site via a series of electrochemical steps that reversibly unseal a highly reactive Fe edge site. Our model can explain the 8 proton-electron transfers involved in biological ammonia synthesis within the kinetic scheme of Lowe and Thorneley, the obligatory formation of one H2 per N2 reduced, and the behavior of known inhibitors.

Understanding Trends in the Electrocatalytic Activity of Metals and Enzymes for CO2 Reduction to CO

We develop a model based on density functional theory calculations to describe trends in catalytic activity for CO2 electroreduction to CO in terms of the adsorption energy of the reaction intermediates, CO and COOH. The model is applied to metal surfaces as well as the active site in the CODH enzymes and shows that the strong scaling between adsorbed CO and adsorbed COOH on metal surfaces is responsible for the persistent overpotential. The active site of the CODH enzyme is not subject to these scaling relations and optimizes the relative binding energies of these adsorbates, allowing for an essentially reversible process with a low overpotential.

Hydrogenated cation vacancies in semiconducting oxides

Using first-principles calculations we have studied the electronic and structural properties of cation vacancies and their complexes with hydrogen impurities in SnO(2), In(2)O(3) and β-Ga(2)O(3). We find that cation vacancies have high formation energies in SnO(2) and In(2)O(3) even in the most favorable conditions. Their formation energies are significantly lower in β-Ga(2)O(3). Cation vacancies, which are compensating acceptors, strongly interact with H impurities resulting in complexes with low formation energies and large binding energies, stable up to temperatures over 730 °C. Our results indicate that hydrogen has beneficial effects on the conductivity of transparent conducting oxides: it increases the carrier concentration by acting as a donor in the form of isolated interstitials, and by passivating compensating acceptors such as cation vacancies; in addition, it potentially enhances carrier mobility by reducing the charge of negatively charged scattering centers. We have also computed vibrational frequencies associated with the isolated and complexed hydrogen, to aid in the microscopic identification of centers observed by vibrational spectroscopy.

Quantum computing with defects

Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV(-1)) center stands out for its robustness--its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV(-1) center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors.