Canonical Density Functional Theory Research Articles

Revisiting Factors Controlling the Electrochemical CO2 Reduction to CO and HCOOH on Transition Metals with Grand Canonical Density Functional Theory Calculations

Revisiting Factors Controlling the Electrochemical CO₂ Reduction to CO and HCOOH on Transition Metals with Grand Canonical Density Functional Theory Calculations

Mapping the Binary Covalent Alloy Space to Pursue Superior Nitrogen Reduction Reaction Catalysts

AbstractThe electrochemical nitrogen reduction reaction (NRR) has the potential to decarbonize industrial ammonia production. However, NRR has poor activity and selectivity versus the competing hydrogen evolution reaction for catalysts that adhere to scaling relations. Overcoming the limitations imposed by scaling relations requires more complex catalyst materials, however, evaluating materials beyond simple metal systems is a large combinatorial problem that requires an improved understanding of the electrocatalyst surface to rationally guide the discovery of superior catalysts. The study uses grand canonical density functional theory to uncover NRR trends on a large and disparate set of binary covalent alloys (BCA) with variable compositions and active‐site geometries. The studied BCAs generally follow scaling relations, albeit with larger variance and several systems that significantly break scaling. BCAs with early‐ to mid‐transition metals tend to lie near the volcano peak and activate the N2 triple bond via a side‐on binding configuration. Trends in the BCA space cannot be readily predicted using simple electronic descriptors, which is ascribed to the large geometric variability of the BCA surfaces. It is anticipated that these findings will provide a foundation for the rational design of superior NRR electrocatalysts with increasing material complexity.

Activating Nitrogen for Electrochemical Ammonia Synthesis via an Electrified Transition-Metal Dichalcogenide Catalyst.

The complex interplay between local chemistry, the solvent microenvironment, and electrified interfaces frequently present in electrocatalytic reactions has motivated the development of quantum chemical methods that can accurately model these effects. Here, we predict the thermodynamics of the nitrogen reduction reaction (NRR) at sulfur vacancies in 1T'-phase MoS2 and highlight how the realistic treatment of potential within grand canonical density functional theory (GC-DFT) seamlessly captures the multiple competing effects of applied potential on a catalyst interface interacting with solvated molecules. In the canonical approach, the computational hydrogen electrode is widely used and predicts that adsorbed N2 structure properties are potential-independent. In contrast, GC-DFT calculations show that reductive potentials activate N2 toward electroreduction by controlling its back-bonding strength and lengthening the N-N triple bond while decreasing its bond order. Similar trends are observed for another classic back-bonding ligand in CO, suggesting that this mechanism may be broadly relevant to other electrochemistries involving back-bonded adsorbates. Furthermore, reductive potentials are required to make the subsequent N2 hydrogenation steps favorable but simultaneously destabilizes the N2 adsorbed structure resulting in a trade-off between the favorability of N2 adsorption and the subsequent reaction steps. We show that GC-DFT facilitates modeling all these phenomena and that together they can have important implications in predicting electrocatalyst selectivity for the NRR and potentially other reactions.

Continuous constant potential model for describing the potential-dependent energetics of CO2RR on single atom catalysts.

In this work, we have proposed a Continuous Constant Potential Model (CCPM) based on grand canonical density functional theory for describing the electrocatalytic thermodynamics on single atom electrocatalysts dispersed on graphene support. The linearly potential-dependent capacitance is introduced to account for the net charge variation of the electrode surface and to evaluate the free energetics. We have chosen the CO2 electro-reduction reaction on single-copper atom catalysts, dispersed by nitrogen-doped graphene [CuNX@Gra (X = 2, 4)], as an example to show how our model can predict the potential-dependent free energetics. We have demonstrated that the net charges of both catalyst models are quadratically correlated with the applied potentials and, thus, the quantum capacitance is linearly dependent on the applied potentials, which allows us to continuously quantify the potential effect on the free energetics during the carbon dioxide reduction reaction instead of confining it to a specific potential. On the CuN4@Gra model, it is suggested that CO2 adsorption, coupled with an electron transfer, is a potential determining step that is energetically unfavorable even under high overpotentials. Interestingly, the hydrogen adsorption on CuN4@Gra is extremely easy to occur at both the Cu and N sites, which probably results in the reconstruction of the CuN4@Gra catalyst, as reported by many experimental observations. On CuN2@Gra, the CO2RR is found to exhibit a higher activity at the adjacent C site, and the potential determining step is shifted to the *CO formation step at a wide potential range. In general, CCPM provides a simple method for studying the free energetics for the electrocatalytic reactions under constant potential.

Strain enhances the activity of molecular electrocatalysts via carbon nanotube supports

Support-induced strain engineering is useful for modulating the properties of two-dimensional materials. However, controlling strain of planar molecules is technically challenging due to their sub-2 nm lateral size. Additionally, the effect of strain on molecular properties remains poorly understood. Here we show that carbon nanotubes (CNTs) are ideal substrates for inducing optimum properties through molecular curvature. In a tandem-flow electrolyser with monodispersed cobalt phthalocyanine (CoPc) on single-walled CNTs (CoPc/SWCNTs) for CO2 reduction, we achieve a methanol partial current density of >90 mA cm−2 with >60% selectivity, surpassing wide multiwalled CNTs at 16.6%. We report vibronic and X-ray spectroscopies to unravel the distinct local geometries and electronic structures induced by the strong molecule–support interactions. Grand canonical density functional theory confirms that curved CoPc/SWCNTs improve *CO binding to enable subsequent reduction, whereas wide multiwalled CNTs favour CO desorption. Our results show the important role of SWCNTs beyond catalyst dispersion and electron conduction.

Adsorption Site Screening on a PGM-Free Electrocatalyst: Insights from Grand Canonical Density Functional Theory

Adsorption Site Screening on a PGM-Free Electrocatalyst: Insights from Grand Canonical Density Functional Theory

Grand canonical DFT based constant charge method for electrochemical deuterium/hydrogen evolution reaction micro-kinetics on Pt (1 1 1)

Applied external potential is considered to have significant impact on the reaction mechanisms and kinetic behaviors for electrochemical reactions. The electrochemical isotope deuterium/hydrogen (D/H) evolution shows significant different kinetic behavior under applied potential conditions, but the intrinsic mechanisms from the electrochemical isotope effect remains unclear. In this work, the grand canonical density functional theory (GC-DFT) based constant charge method was used to systematically investigate the electrochemical D/H evolution reactions (DER/HER) on the Pt (111) surface. By using this method, the linear and quadratic relationship between charge distribution (q), electronic energy (Eelect) and applied potential (U) were observed respectively, which are resulted from solving of linear Poisson-Boltzmann equation and Kohn-Sham-Mermin equations in combination of solvent modification. Equilibrium Pourbaix diagrams of D/H adsorbing on Pt (111) surface was subsequently investigated to revealed the electrode structure in real reaction condition, with θD/H coverages on the cathode surface calculated to be 0.0 monolayer (ML) and 1/6 ML for alkaline and acidic solvent at −1.23 V to 0.0 V vs. SHE. Mechanistic studies of HER/DER on the Pt (111) surface revealed that Volmer-Tafel reaction pathway is more favorable than the Volmer-Heyrovsky pathway. Analysis of the applied potential effect on the reaction energy barriers show that the acidic Volmer step is very sensitive toward the applied potential condition, with the structure of transition state likely to shift. Comparisons of the calculated current–potential polarization curves between HER and DER revealed that in the acidic condition, the calculated current density of HER is close to DER, revealing that the H*/D* migration and coupling on the electrode is comparable to each other when the solution is saturated with H3O+/D3O+. In the alkaline reaction condition, discrepancies of j value between DER and HER becomes slightly larger, revealing that jointly control effect from Volmer and Tafel step was enhanced. This work provides the new insight for investigating the microkinetic properties of electrochemical isotope reaction.

Potential–dependent Ru (0 0 0 1) surface oxidative corrosion and OER performance by grand canonical method

Applied external potential and the exposed solvent condition have significant impact on the surface state of electrodes in electrochemical reactions. In this work, the grand canonical density functional theory (DFT) calculations were performed to systematically investigate the surface state and oxygen evolution reaction (OER) performances of the Ru (0001) surface. Equilibrium Pourbaix diagrams demonstrated the oxidation state of either O* or OH*. Even in the negative polarized potential of USHE < 0.0 V, the Ru (0001) surface exhibited the surface state of 1/9 ML O* preoccupying instead of the clean surface. Mechanistic studies of OER on the clean Ru (0001) surface and Ru (0001)O* (1/9 ML) surface revealed that in acidic OER process on clean Ru (0001) surface, the oxygen coupling mechanism is more favorable than the nucleophilic attack mechanism involving OOH* intermediate formation.

Solvation–Reduction Coupling in Ca2+ Electroactivity in Glyme‐Based Electrolytes: A First Principles Study

AbstractThe electrochemical activity of solvated Ca2+ in glyme‐based electrolytes is investigated using grand canonical density functional theory approach and Fukui functions. The obtained results reveal that the length of glyme molecules has little effect on the reduction potentials, but has significant impacts on the effective electron transfer process. In short chain glymes, the transferred electron is located on a Ca2+ center and the organic part of the solvation sphere, leading to a direct Ca2+ reduction and a partial degradation of the glyme molecules. As the glyme's length increases, the reduction process turns into the formation of solvated electrons rather than Ca2+ reduction, unless a partial desolvation occurs. Consequently, an effective Ca2+ reduction in long chain glyme‐based electrolytes is controlled by a (partial) desolvation of the solvation sphere. These results can be used as guiding information to design new electrolytes having the Ca2+ reduction potential in an accessible voltage range together with an effective Ca2+ reduction process. The methodology developed in this study can be universally applied to investigate the thermodynamic and kinetic properties of other battery systems using metal anodes, which might lead to a paradigm shift in the design of prospective electrolytes for future battery technologies.

Approximating constant potential DFT with canonical DFT and electrostatic corrections.

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO2 adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT.

Restructuring and Activation of Cu(111) under Electrocatalytic Reduction Conditions.

The dynamic restructuring of Cu surfaces in electroreduction conditions is of fundamental interest in electrocatalysis. We decode the structural dynamics of a Cu(111) electrode under reduction conditions by joint first-principles calculations and operando electrochemical scanning tunneling microscopy (ECSTM) experiments. Combining global optimization and grand canonical density functional theory, we unravel the potential- and pH-dependent restructuring of Cu(111) in acidic electrolyte. At reductive potential, Cu(111) is covered by a high density of H atoms and, below a threshold potential, Cu adatoms are formed on the surface in a (4×4) superstructure, a restructuring unfavorable in vacuum. The strong H adsorption is the driving force for the restructuring, itself induced by the electrode potential. On the restructured surface, barriers for hydrogen evolution reaction steps are low. Restructuring in electroreduction conditions creates highly active Cu adatom sites not present on Cu(111).

Restructuring and Activation of Cu(111) under Electrocatalytic Reduction Conditions

AbstractThe dynamic restructuring of Cu surfaces in electroreduction conditions is of fundamental interest in electrocatalysis. We decode the structural dynamics of a Cu(111) electrode under reduction conditions by joint first‐principles calculations and operando electrochemical scanning tunneling microscopy (ECSTM) experiments. Combining global optimization and grand canonical density functional theory, we unravel the potential‐ and pH‐dependent restructuring of Cu(111) in acidic electrolyte. At reductive potential, Cu(111) is covered by a high density of H atoms and, below a threshold potential, Cu adatoms are formed on the surface in a (4×4) superstructure, a restructuring unfavorable in vacuum. The strong H adsorption is the driving force for the restructuring, itself induced by the electrode potential. On the restructured surface, barriers for hydrogen evolution reaction steps are low. Restructuring in electroreduction conditions creates highly active Cu adatom sites not present on Cu(111).

Insight into alkali cation effect on CO2 electroreduction catalyzed by monodispersed Cu-N-C under applied potential

Atomically dispersed copper and nitrogen-doped carbon (Cu-N-C) materials are promising electrodriven CO2 reduction (CO2RR) catalysts. A comprehensive mechanistic understanding of Cu-N-C towards systematic improvement, however, is hampered by the complexity of electrode-electrolyte interface around Cu. Here, we adopted an electric double layer model to investigate the impact of alkali metal cations on the two-electron CO2RR catalyzed by Cu-N4-C under applied potential. The grand canonical density functional theory calculations show that, at U=−1.2 V vs. SHE, hydrated Na+ ions near the surface facilitate formation of bent CO2− bonding with Cu; with an increasingly negative potential, the electrosorption of CO2 (Cu+CO2+e−→Cu-CO2−) instead of the formation of COOH becomes the presumable rate determining step for Na+-aided CO formation. Further, a possible Cu(I) may be vital for the adsorption of anionic COOH. Our study demonstrates the crucial role of alkali metal ion in the early stage of CO2RR on Cu-N4-C and the importance of explicit consideration of the applied potential in simulation for a better understanding of the reaction mechanism.

Axial Coordination Effect on the Oxygen Reduction Reaction of FeN4 Electrocatalysts Based on Grand Canonical Density Functional Theory

The Fe–N–C materials are promising noble-free alternatives to Pt-based oxygen reduction reaction (ORR) electrocatalysts. Identifying the actual active structure of FeN4-based moieties is helpful for the regulation and design of high-performance electrocatalysts. However, the current theoretical researches were mostly based on the charge-neutral model (CNM), which cannot accurately describe the electrochemical interface. Herein, we employed the constant potential based grand canonical density functional theory (GC-DFT) computations to study the ORR mechanism of axially decorated FeN4 electrocatalysts. We studied around ten types of axial ligands, and the constant potential energetics and microkinetic modeling demonstrated that the Fe center can exhibit excellent activity for boosting the four-electron ORR via covalently linked −NH2 ligand. The lowering of the antibonding dz2–pz orbital is responsible for weakening the adsorption of oxygen in FeN4–Ls to promote ORR activity, and the −NH2 decoration led to the lowest antibonding orbital energy. In particular, the adsorption free energy (ΔG*O2) and O–O bond length (LO–O) of the adsorbed O2 reactant can be used as the effective energetic and geometric descriptors to describe the ORR activity of FeN4–Ls electrocatalysts. Our results not only elucidate the axial coordination effect on the ORR performance of FeN4 SACs but also demonstrate the importance of electrode potential in computational electrochemistry.

Potential dependence of OER/EOP performance on heteroatom-doped carbon materials by grand canonical density functional theory.

Revealing the effect of external applied potential on the reaction mechanism and product selectivity is of great significance in electrochemical studies. In this work, the grand canonical density functional theory method was applied to simulate the explicit electrocatalytic process of oxygen evolution reaction and electrochemical ozone production due to the O3 product sensitivity toward the applied potential. Over the Pt/Pd single atom embedded on B/N co-doped graphene (Pt/Pd-BNC) surface, crossover points of O2/O3 selectivity inversion were predicted to be 1.33 and 0.89V vs standard hydrogen electrode, which were also consistent with the previous experimental results. An in-depth analysis of the energetic terms in the reaction free energies also found the considerable impact of the applied potential on the Helmholtz free energy term, with optimal potential predicted for the key elementary steps, and linear correlations between electrode potential (U) and reaction free energy were found for each elementary step. This study offers extensive knowledge on the potential effect on the O2/O3 selective formation on two-dimensional anode surfaces and provides new insights for investigating the reactivity/selectivity on electrode surfaces in real reaction conditions.

Effect of applied potential on metal surfaces: Surface energy, Wulff shape and charge distribution

We use grand canonical density functional theory to predict the surface energies, Wulff shapes, charge distributions and catalytically active sites of different metal surfaces under electrochemical conditions. We propose a method for computing surface energies from grand canonical density functional theory (GC-DFT) calculations of periodic slab models and use it to compute the surface energies of the facets of Pt, Cu, and Ag crystals to predict their Wulff shapes under electrochemical conditions. GC-DFT predicts that, for the pure metals studied, solvation only slightly affects the Wulff shape while applied potentials considerably affect the surface energies and corresponding Wulff shapes. We used Bader charge analysis of GC-DFT computed electron densities to investigate the effect of applied potential on the distribution of electron density over the atoms of the surfaces of Pt, Cu, Ag, and the 75–25 Ag-Pt and Au-Ni alloys. This analysis shows that, under an applied potential, the electron density is unevenly distributed over the surface atoms and that the charges of atoms more exposed to solvent are more sensitive to bias. Our results show that the most sensitive atom to bias can be used to identify the most favorable adsorption site and thus, the active sites of electrochemical reactions, which is computationally less demanding than calculating the adsorption energies on all possible adsorption sites.

Hydrogen-Induced Restructuring of a Cu(100) Electrode in Electroreduction Conditions

The rearrangement of Cu surfaces under electrochemical conditions is known to play a key role in the surface activation for major electrocatalytic reactions. Despite the extensive experimental insights into such rearrangements, from surface-sensitive spectroscopy and microscopy, the spatial and temporal resolution of these methods is insufficient to provide an atomistic picture of the electrochemical interface. Theoretical characterization has also been challenged by the diversity of restructuring configurations, surface stoichiometry, adsorbate configurations, and the effect of the electrode potential. Here, atomistic insight into the restructuring of the electrochemical interface is gained from first principles. Cu(100) restructuring under varying applied potentials and adsorbate coverages is studied by grand canonical density functional theory and global optimization techniques, as well as ab initio molecular dynamics and mechanistic calculations. We show that electroreduction conditions cause the formation of a shifted-row reconstruction on Cu(100), induced by hydrogen adsorption. The reconstruction is initiated at 1/6 ML H coverage, when the Cu-H bonding sufficiently weakens the Cu-Cu bonds between the top- and sublayer, and further stabilized at 1/3 ML when H adsorbates fill all the created 3-fold hollow sites. The simulated scanning tunneling microscopy (STM) images of the calculated reconstructed interfaces agree with experimental in situ STM. However, compared to the thermodynamic prediction, the onsets of reconstruction events in the experiment occur at more negative applied voltages. This is attributed to kinetic effects in restructuring, which we describe via different statistical models, to produce the potential- and pH-dependent surface stability diagram. This manuscript provides rich atomistic insight into surface restructuring in electroreduction conditions, which is required for the understanding and design of Cu-based materials for electrocatalytic processes. It also offers the methodology to study the problem of in situ electrode reconstruction.

Perspectives on the Competition between the Electrochemical Water and N2 Oxidation on a TiO2(110) Electrode.

The electrochemical nitrogen oxidation reaction (NOR) has recently drawn attention due to promising experimental and theoretical results. It provides an alternative, environmentally friendly route to directly synthesize nitrate from N2(g). There is to date a limited number of investigations focused on the electrochemical NOR. Herein, we present a detailed computational study on the kinetics of both the NOR and the competing oxygen evolution reaction (OER) on the TiO2(110) electrode under ambient conditions. The use of grand canonical density functional theory in combination with the linearized Poisson-Boltzmann equation allows a continuous tuning of the explicitly applied electrical potential. We find that the OER may either promote or suppress the NOR on TiO2(110) depending on reaction conditions. The detailed atomistic insights provided on the mechanisms of these competing processes make possible further developments toward a direct electrochemical NOR process.

Mechanistic Insight into the Photo-Oxidation of Perfluorocarboxylic Acid over Boron Nitride.

Hexagonal boron nitride (hBN) can photocatalytically oxidize and degrade perfluorocarboxylic acids (PFCA), a common member of the per/polyfluoroalkyl substance (PFAS) family of water contaminants. However, the reaction mechanism governing PFCA activation on hBN is not yet understood. Here, we apply electronic grand canonical density functional theory (GC-DFT) to assess the thermodynamic and kinetic favorability of PFCA photo-oxidative activation on hBN: CnF2n+1COO- + h+ → CnF2n+1· + CO2. The oxidation of all PFCA chains is exothermic under illumination with a moderate barrier. However, the longer-chain PFCAs are degraded more effectively because they adsorb on the surface more strongly as a result of increased van der Waals interactions with the hBN surface. The ability of hBN to act as a photocatalyst is unexpected because of its wide band gap. Therefore, we apply both theoretical and experimental analyses to examine possible defects on hBN that could account for its activity. We find that a nitrogen-boron substitutional defect (NB), which generates a mid-gap state, can enhance UVC (ultraviolet C) absorption and PFCA oxidation. This work provides insight into the PFCA oxidation mechanism and reveals engineering strategies to design better photocatalysts for PFCA degradation.

Experimental and Theoretical Comparison of Potential-dependent Methylation on Chemically Exfoliated WS2 and MoS2.

Reductant-activated functionalization is shown to enhance the methylation of chemically exfoliated MoS2 (ceMoS2) and ceWS2 by introducing excess negative charge to facilitate a nucleophilic attack reaction. Relative to methylation in the absence of a reductant, the reaction produces a twofold increase in coverage of ceWS2, from 25 to 52% coverage per WS2. However, at every potential, the methyl coverage on ceWS2 was ∼20% lower than that on ceMoS2. We applied grand canonical density functional theory to show that at constant potential, more negative charge is present on 1T'-MoS2 than on 1T'-WS2, making methylation both thermodynamically and kinetically more favorable for 1T'-MoS2 than 1T'-WS2. This effect was moderated when the reactions were compared at constant charge, emphasizing the importance of comparing the reactivity of materials at nominally identical electrode potentials.