Grand Canonical Density Functional Theory Research Articles

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.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces.

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS2. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS2: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

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.

Potential and support-dependent hydrogen evolution reaction activation energies on sulfur vacancies of MoS2 from GC-DFT

We present a detailed mechanistic study of HER at the sulfur vacancy VS of 2H–MoS2. We evaluate the Volmer, Tafel, and Heyrovsky transition states for the different possible reaction steps, determining the activation energy as a function of the electrochemical potential via grand-canonical density functional theory. The results show that the Volmer and Heyrovsky steps depend on the electrochemical potential and the activation energies decrease for more negative potentials, while this is not the case for the Tafel step, for which the activation energy is constant. From the activation energies at −0.2 V vs SHE, it can be concluded that during HER on VS a first hydrogen atom is adsorbed as a spectator via a Volmer step. Then, the catalytic cycle consists of a Volmer and a Heyrovsky step, with the latter being rate determining. In addition, we investigate for the first time the effect of a conductive support on the HER activity of these sulfur vacancies. Our results show that copper, gold and graphite supports have little effects on the activation energies of all steps. Hence, we conclude that cheap, acid-stable, high-surface area carbon supports are well suited for MoS2-based HER catalysts.

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.

How to dope the basal plane of 2H-MoS2 to boost the hydrogen evolution reaction?

Molybdenum disulfide (MoS2) is considered one of the most likely materials that could be turned into low-cost hydrogen evolution reaction (HER) catalysts to replace noble metals in acidic solutions. However, several challenges prevent MoS2 from being truly applicable, including limited number of active sites (typically only the edges are active) and poor conductivity. In this work, we perform an extensive density functional theory (DFT) screening of substitutional doping as a possibility to activate the otherwise inert basal surface. We assess 17 Earth abundant elements for molybdenum doping and 5 elements for sulfur substitution. Systematically determining the preference of the metallic dopants to be located on the edges rather than in the basal plane, we reveal that most dopants are much more likely to be incorporated at the edges, suggesting that advanced synthesis methods are required to obtain basal-plane doped catalysts. The latter may, however, feature many more active sites per MoS2 formula unit, motivating our study on the properties of such substitutionally doped surfaces. For the first time for such a screening study, we explore not only the formation of H*, but also of OH* and H2O* to explore the reactivity of the solvent. Two additional phenomena that could hinder the hydrogen production at these sites are investigated, namely H2S release and the (local) segregation/dispersion tendency of the dopants in the basal surface. Moreover, to assess the electrocatalytic activity, we take the electrochemical potential explicitly into account via grand canonical DFT. Compared with pristine MoS2 nanosheets, our results show that most doping elements significantly enhanced the electrocatalytic activity. Considering all assessed factors, we identify the most promising systems: Dimers of Ti, Zr and Hf and the substitution of S by P are predicted to lead to stable active sites on the basal plane with overpotentials of about 0.2 V.

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.

Unraveling the electrocatalytic reduction mechanism of enols on copper in aqueous media

Deoxygenation of aldehydes and their tautomers to alkenes and alkanes has implications in refining biomass-derived fuels for use as transportation fuel. Electrochemical deoxygenation in ambient, aqueous solution is also a potential green synthesis strategy for terminal olefins. In this manuscript, direct electrochemical conversion of vinyl alcohol and acetaldehyde on polycrystalline Cu to ethanol, ethylene and ethane; and propenol and propionaldehyde to propanol, propene and propane is reported. Sensitive detection was achieved using a rotating disk electrode coupled with gas chromatography-mass spectrometry. In-situ attenuated total reflection surface-enhanced infrared absorption spectroscopy, and in-situ Raman spectroscopy confirmed the adsorption of the vinyl alcohol. Calculations using canonical and grand-canonical density functional theory and experimental findings suggest that the rate-determining step for ethylene and ethane formation is an electron transfer step to the adsorbed vinyl alcohol. Finally, we extend our conclusions to the enol reaction from higher-order soluble aldehyde and ketone. The products observed from the reduction reaction also sheds insights into plausible reaction pathways of CO2 to C2 and C3 products.

Electrochemical CO2 Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory

Electrochemical CO₂ Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory

How the Bioinspired Fe2Mo6S8 Chevrel Breaks Electrocatalytic Nitrogen Reduction Scaling Relations.

The nitrogen reduction reaction (NRR) is a renewable alternative to the energy- and CO2-intensive Haber-Bosch NH3 synthesis process but is severely limited by the low activity and selectivity of studied electrocatalysts. The Chevrel phase Fe2Mo6S8 has a surface Fe-S-Mo coordination environment that mimics the nitrogenase FeMo-cofactor and was recently shown to provide state-of-the-art activity and selectivity for NRR. Here, we elucidate the previously unknown NRR mechanism on Fe2Mo6S8 via grand-canonical density functional theory (GC-DFT) that realistically models solvated and biased surfaces. Fe sites of Fe2Mo6S8 selectively stabilize the key *NNH intermediate via a narrow band of free-atom-like surface d-states that selectively hybridize with p-states of *NNH, which results in Fe sites breaking NRR scaling relationships. These sharp d-states arise from an Fe-S bond dissociation during N2 adsorption that mimics the mechanism of the nitrogenase FeMo-cofactor. Furthermore, we developed a new GC-DFT-based approach for calculating transition states as a function of bias (GC-NEB) and applied it to produce a microkinetic model for NRR at Fe2Mo6S8 that predicts high activity and selectivity, in close agreement with experiments. Our results suggest new design principles that may identify effective NRR electrocatalysts that minimize the barriers for *N2 protonation and *NH3 desorption and that may be broadly applied to the rational discovery of stable, multinary electrocatalysts for other reactions where narrow bands of surface d-states can be tuned to selectively stabilize key reaction intermediates and guide selectivity toward a target product. Furthermore, our results highlight the importance of using GC-DFT and GC-NEB to accurately model electrocatalytic reactions.

(Digital Presentation) Understanding Kinetics of Metal Dissolution from Integrated Multiscale Simulations and Experiments

Understanding dissolution kinetics is essential for predicting and mitigating materials corrosion; however, many mechanistic details still remain enigmatic. Examples include the evolution of solvation properties of ions and nature of electron transfer during dissolution. In this work, we integrate high-fidelity first-principles calculations based on grand-canonical density functional theory (DFT) and mesoscale simulations to predict dissolution kinetics of aluminum metal in acidic conditions. First, we show that the inclusion of an explicit solvation shell is crucial for accurately predicting the redox potential of metal dissolution. Second, we show that metal dissolution is governed by two kinetically limited processes, which are associated with the metal-metal bond breaking and ion diffusion within the electric double layer. Interestingly, it is found that kinetics and thermodynamics of these processes can be described with a simple model functionally based on Marcus theory, and their relative importance can be switched, depending on the applied potentials. Third, we show how dissolution kinetics derived from DFT is integrated with mesoscale simulations to elucidate the role of microstructure on the global metal dissolution. Comparison with experimental measurements will also be discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and was supported with Laboratory Directed Research and Development funding under Project 20-SI-004.

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.