Grand Canonical Density Functional Theory Research Articles

Overlooked Role of Electrostatic Interactions in HER Kinetics on MXenes: Beyond the Conventional Descriptor ΔG ∼ 0 to Identify the Real Active Site.

Understanding the atomic-level mechanism of the hydrogen evolution reaction (HER) on MXene materials is crucial for developing affordable HER catalysts, while their complex surface terminations present a substantial challenge. Herein, employing constant-potential grand canonical density functional theory calculations, we elucidate the reaction kinetics of the HER on MXenes with various surface terminations by taking experimentally reported Mo2C as a prototype. We observe a contradictory scenario on Mo2C MXene when using conventional thermodynamic descriptor ΔGH* (hydrogen binding energy). Both competing surface phases that emerge close to the equilibrium potential meet the ΔGH* ∼ 0 criterion, while they exhibit distinctly different reaction kinetics. Contrary to previous studies that identified surface *O species as active sites, our research reveals that these *O sites are kinetically inert for producing H2 but are easily reduced to H2O. Consequently, the surface Mo atoms, exposed from the rapid reduction of the surface *O species, serve as the actual active sites catalyzing the HER via the Volmer-Heyrovsky mechanism, as confirmed by experimental studies. Our findings highlight the overlooked role of electrostatic repulsion in HER kinetics, a factor not captured by thermodynamic descriptor ΔGH*. This work provides new insights into the HER mechanism and emphasizes the importance of kinetic investigations for a comprehensive understanding of the HER.

Adsorption grand potential of OH on metal oxide surfaces.

Describing chemical processes at solid-liquid interfaces as a function of a fixed electron chemical potential presents a challenge for electronic structure calculations and is essential for understanding electrochemical phenomena. Grand Canonical Density Functional Theory (GCDFT) allows treating solid-liquid interfaces in such a way that studying the influence of a fixed electron potential arises naturally. In this work, GCDFT is used to compute the adsorption grand potential (AGP), a key parameter for understanding and predicting the behavior of adsorbates on surfaces. We focused on the adsorption of an OH molecule on three metallic surfaces commonly used in electrochemical processes, such as the oxygen evolution reaction (OER). Our study aims to offer insights into how AGP can be used to compare adsorption strengths under different fixed electron chemical potentials, which is crucial for designing efficient electrode materials. By determining the average number of electrons self-consistently under varying chemical potentials, we showed how one can distinguish between electron acquisition and depletion during the adsorption process, offering a deeper understanding of the adsorbate-surface interactions. The approach used in this work employs the Kohn-Sham-Mermin formulation of the Grand Canonical Density Functional Theory. The computations were performed using the periodic open-source density functional theory software, JDFTx, with the Garrity-Bennett-Rabe-Vanderbilt library of ultrasoft pseudopotentials. Calculations were made using truncated Coulomb potentials and the auxiliary Hamiltonian method with the PBE exchange-correlation functional, along with DFT-D2 long-range dispersion corrections. The implicit solvation model CANDLE was used to describe the electrolyte with a 1M concentration.

Potential-dependent kinetics of oxygen chemisorption as the crucial step of oxygen reduction reaction: GCDFT study

Nitrogen-doped carbon materials (NCMs) are widely regarded as promising alternatives to expensive platinum-based electrocatalysts for the oxygen reduction reaction (ORR). While NCMs exhibit considerable electrochemical activity in alkaline media, their performance in acidic environments remains a significant challenge. However, acidic conditions are commercially desirable for ORR’s catalysis in proton-exchange membrane fuel cells (PEMFCs). The dramatic pH dependence of NCM effectiveness has sparked ongoing debate, with several factors under consideration, including surface protonation, variations in hydrogen binding energy, differences in proton donors, and interface structure. In this work, we present a grand canonical density functional theory (GCDFT) study of the chemisorption step on pristine and nitrogen-doped graphene. Through nudged elastic band (NEB) calculations at various electrode potentials, we propose a potential-dependent (and thus pH-dependent) mechanism of oxygen chemisorption at graphitic nitrogen (Ngr) defects, offering new insights into the pH dependency of the onset potential in NCM catalysts.

Revisiting the role of foreign atoms in [formula omitted] reduction on CuSn single-atom surface alloys

The electrochemical CO2 reduction is a promising process for capturing the emitted carbon dioxide by converting CO2 into value-added chemicals. Although copper-based catalysts have a unique ability to produce multi-carbon products, they suffer from poor selectivity. Copper-based alloys and, in particular, single atom alloys, hold promise for fine-tuning the selectivity of CO2 reduction reaction. In this study, we applied the grand canonical density functional theory in combination with the implicit solvent to model CO2 electroreduction with the formation of CO and HCOO− on copper and highly diluted copper-tin alloys. We demonstrate that the insertion of a substitutional Sn atom introduces a destabilization effect for all intermediates and completely disrupts the adsorption positions of the CO, H, and H/CO2 co-adsorption. However, the influence of Sn on intermediate adsorption energies is primarily localized in its immediate vicinity. We demonstrate that sparsely distributed single Sn atoms do not account for the experimentally observed significant reduction in formate and hydrogen generation across the entire Sn-substituted Cu surface. This discrepancy underscores the need to reevaluate the proposed surface structure and the nature of the active sites on CuSn single-atom surface alloys.

Theoretical investigation of graphdiyne-supported single-cluster catalysts for electroreduction of nitric oxide

The electrochemical NO reduction reaction (NORR) to NH3 offers an efficient, environmentally friendly strategy for NO removal and NH3 production, but developing effective catalysts to facilitate the conversion of NO into NH3 remains a challenge. Single-cluster catalysts (SCCs) with multi-metallic sites show promise due to the synergistic interactions among the active atoms. Herein, utilizing density functional theory (DFT) and grand-canonical DFT (GC-DFT), we systematically investigated the potential of late transition metal (TM = Fe, Co, Ni, Cu, Ru, Rh, Pd, Pt) clusters on graphdiyne (TMx/GDY, x = 1–5) for NORR. Ni3/GDY, Pd3/GDY, and Pt3/GDY emerged as the most promising candidates, demonstrating stability, excellent NORR activity, and HER suppression. Their outstanding performance is attributed to the moderate adsorption of NO, with the dxz/dyz orbitals playing a key role in NO activation. GC-DFT results highlight nonlinear variation of intermediate grand free energies with the applied potential. Detailed electronic property analyses were conducted to reveal the charge effects induced by the applied chemical potential. This study provides valuable insights into SCC-catalyzed NO reduction and highlights the significance of potential effects in theoretical simulations of electrochemical systems.

Dynamic Adaptation of Active Site Driven by Dual-side Adsorption in Single-Atomic Catalysts During CO2 Electroreduction.

Single-atom iron embedded in N-doped carbon (Fe-N-C) is among the most representative single-atomic catalysts (SACs) for electrochemical CO2 reduction reaction (CO2RR). Despite the simplicity of the active site, the CO2-to-CO mechanism on Fe-N-C remains controversial. Firstly, there is a long debate regarding the rate-determining step (RDS) of the reactions. Secondly, recent computational and experimental studies are puzzled by the fact that the CO-poisoned Fe centers still remain highly active at high potentials. Thirdly, there are ongoing challenges in elucidating the high selectivity of hydrogen evolution reaction (HER) over CO2RR at high potentials. In this work, we introduce a novel CO2RR mechanism on Fe-N-C, which was inspired by the dynamic of active sites in biological systems. By employing grand-canonical density functional theory and kinetic Monte-Carlo, we found that the RDS is not fixed but changes with the applied potential. We demonstrated that our proposed dual-side mechanisms could clarify the reason behind the high catalytic activity of CO-poisoned metal centers, as well as the high selectivity of HER over CO2RR at high potential. This study provides a fundamental explanation for long-standing puzzles of an important catalyst and calls for the importance of considering the dynamic of active sites in reaction mechanisms.

Modelling the activity trend of the hydrogen oxidation reaction under constant potential conditions.

A microkinetic model is constructed for the electrocatalytic alkaline hydrogen oxidation reaction based on grand canonical density functional theory calculations and linear relationships with the adsorption energies of hydrogen and hydroxide as descriptors. Using this model, the activity trend suitable for efficient catalyst screening has been identified.

Origin of copper dissolution under electrocatalytic reduction conditions involving amines.

Cu dissolution has been identified as the dominant process that causes cathode degradation and losses even under cathodic conditions involving methylamine. Despite extensive experimental research, our fundamental and theoretical understanding of the atomic-scale mechanism for Cu dissolution under electrochemical conditions, eventually coupled with surface restructuring processes, is limited. Here, driven by the observation that the working Cu electrode is corroded using mixtures of acetone and methylamine even under reductive potential conditions (-0.75 V vs. RHE), we employed Grand Canonical density functional theory to understand this dynamic process under potential from a microscopic perspective. We show that amine ligands in solution directly chemisorb on the electrode, coordinate with the metal center, and drive the rearrangement of the copper surface by extracting Cu as adatoms in low coordination positions, where other amine ligands can coordinate and stabilize a surface copper-ligand complex, finally forming a detached Cu-amine cationic complex in solution, even under negative potential conditions. Calculations predict that dissolution would occur for a potential of -1.1 V vs. RHE or above. Our work provides a fundamental understanding of Cu dissolution facilitated by surface restructuring in amine solutions under electroreduction conditions, which is required for the rational design of durable Cu-based cathodes for electrochemical amination or other amine involving reduction processes.

Influence of Simple Salts on Solvent Reduction Stability at Mg‐Alloy Anodes Interface: A Potential‐Dependent DFT Study

AbstractThe significance of incorporating anion species into electrolyte solvation structures, particularly with doubly charged Mg2 + ions, is investigated using the grand canonical density functional theory (GC‐DFT) approach. In an extension of previously established methodology, the work explores the thermodynamic stability in acetonitrile (AN) at the interface with Mg3Bi2 and Mg2Sn. Two different anions, TFSI− and , are strategically incorporated based on energy comparisons. Despite the known chemical compatibility of alloy anodes with the electrolyte solution, the research reveals a novel form of solvent degradation, which is also reported in the case of pure Mg anode with conventional electrolytes. Notably, the AN molecule adjacent to anion species exhibits reduced susceptibility to reduction (−0.8 – −0.4 V vs Mg2 +/Mg) in the lower potential range in comparison with the solvation structure of full dissociation. Charge density difference and density of states analyses detail solvent molecules becoming electrophilic, with the LUMO overlapping with the Fermi level at lower potentials when the electrostatic interaction with anion species are considered. Experimental studies using nuclear magnetic resonance (NMR) spectroscopy and linear sweep voltammetry (LSV) validate the theoretical results, providing a comprehensive understanding. This methodology, augmenting prior approaches, provides valuable guidance for electrolyte composition based on predominant solvation structures in multivalent solutions.

(Invited) Activating Nitrogen for Electrochemical Ammonia Synthesis: Modeling the Effects of Electrified Interfaces on π-Backbonding Molecules

Electrocatalysts are expected to play a pivotal role in shaping our future sustainable energy landscape by enabling storage of renewable energy and its conversion into globally important chemicals. Computational simulations yield mechanistic insights that have supported catalyst discovery and optimization. However, the complexity of electrocatalyst interfaces has necessitated the development of quantum chemical methods that can accurately model these effects at reasonable computational cost.In this work, we employ grand canonical density functional theory (GC-DFT) to capture the nuanced effects of applied potential on a solvated catalyst interface, specifically focusing on the nitrogen reduction reaction (NRR) at sulfur vacancies in 1T'-phase MoS2. In the canonical method, the widely used the computational hydrogen electrode (CHE) predicts that adsorbed N2 structure properties are potential independent. In contrast, GC-DFT calculations reveal that reductive potentials activate N2 towards electroreduction by modulating backbonding strength, lengthening the N–N triple bond, and reducing its bond order. Similar trends are identified for CO, a classic backbonding ligand, suggesting broader relevance of this mechanism to diverse electrochemistries involving backbonded adsorbates. Furthermore, reductive potentials are required to make the subsequent N2 hydrogenation steps favorable, but concurrently destabilize both N2 and hydrogen adsorption.Our findings demonstrate that GC-DFT facilitates the comprehensive modeling of these phenomena, underscoring their collective implications in predicting electrocatalyst selectivity for the nitrogen reduction reaction and potentially other reactions. This research contributes valuable insights into the design and optimization of electrocatalysts for sustainable energy conversion. Figure 1

Destabilization of Oxygen Reduction Reaction Intermediates on a PGM-Free Electrocatalyst By Axial Spectator Ligands

Platinum-group free Fe-N-C catalysts have been shown to be a promising class of electrocatalysts for the oxygen reduction reaction (ORR) in acidic media. However, typical synthesis methods can result in a variety of FeN4 sites embedded in graphene, including bulk-hosted and edge-hosted FeN4. The planar structure of the FeN4 active site allows two additional ligands to adsorb to Fe on either side of the graphene, which can be present from ORR reaction intermediates and other solution phase species. Here, we studied the impact of axially adsorbed ligands on bulk-hosted and edge-hosted FeN4 sites by screening over all pairs of H, O, OH, OOH, O2, H2O, NO, SO4, HSO4, and ClO4 axial ligands using solvated grand canonical density functional theory (GCDFT) to self-consistently account for applied potential. The first axial Fe adsorbate can strongly influence the binding of a second axial adsorbate and increase its adsorption energy by up to 2 eV, with more destabilization occurring for a more positive applied potential and the O* ORR intermediate being affected most. However, GCDFT calculations on these same sites without axial spectator ligands show that O* and OH* are both thermodynamically persistent, suggesting that axial spectator ligands might play a role in explaining this catalyst’s high experimental activity. Additionally, we show how the combined effects of potential, nature of the FeN4 site, and axial ligand impact O2 adsorption favorability and availability of sites in the presence of competing molecules. This work highlights the need for the continued development of advanced electrocatalyst models that account for a wide range of active site structures to facilitate comparison with experiment.

Cu Based Dilute Alloys for Tuning the C2+ Selectivity of Electrochemical CO2 Reduction.

Electrochemical CO2 reduction is a promising technology for replacing fossil fuel feedstocks in the chemical industry but further improvements in catalyst selectivity need to be made. So far, only copper-based catalysts have shown efficient conversion of CO2 into the desired multi-carbon (C2+) products. This work explores Cu-based dilute alloys to systematically tune the energy landscape of CO2 electrolysis toward C2+ products. Selection of the dilute alloy components is guided by grand canonical density functional theory simulations using the calculated binding energies of the reaction intermediates CO*, CHO*, and OCCO* dimer as descriptors for the selectivity toward C2+ products. A physical vapor deposition catalyst testing platform is employed to isolate the effect of alloy composition on the C2+/C1 product branching ratio without interference from catalyst morphology or catalyst integration. Six dilute alloy catalysts are prepared and tested with respect to their C2+/C1 product ratio using different electrolyzer environments including selected tests in a 100-cm2 electrolyzer. Consistent with theory, CuAl, CuB, CuGa and especially CuSc show increased selectivity toward C2+ products by making CO dimerization energetically more favorable on the dominant Cu facets, demonstrating the power of using the dilute alloy approach to tune the selectivity of CO2 electrolysis.

Theoretical Investigation of the Potential-Dependent CO Adsorption on Copper Electrodes.

Despite the importance of CO adsorption in many electrocatalytic reaction mechanisms, there has been little investigation of the dependence of the free energy of CO adsorption on the applied potential. Herein, we report on the potential-dependent adsorption of CO on Cu electrodes using a grand-canonical density functional theory approach. We demonstrate that, within the working potential range of electrocatalytic CO2 reduction on Cu(111) and Cu(100), the CO adsorption strength can change by over 0.1 eV. Our analyses explain the potential dependence through an interfacial capacitance loss upon CO adsorption as well as orbital relaxation induced by the electrode potential. Via sensitivity analysis with respect to two electrolyte model parameters (solvent dielectric constant and Debye screening length), we find that the surface excess charge density is a useful descriptor of the CO adsorption free energy.

Insights into Electrochemical CO2 Reduction on Metallic and Oxidized Tin Using Grand-Canonical DFT and In Situ ATR-SEIRA Spectroscopy.

Electrochemical CO2 reduction (CO2R) to formate is an attractive carbon emissions mitigation strategy due to the existing market and attractive price for formic acid. Tin is an effective electrocatalyst for CO2R to formate, but the underlying reaction mechanism and whether the active phase of tin is metallic or oxidized during reduction is openly debated. In this report, we used grand-canonical density functional theory and attenuated total reflection surface-enhanced infrared absorption spectroscopy to identify differences in the vibrational signatures of surface species during CO2R on fully metallic and oxidized tin surfaces. Our results show that CO2R is feasible on both metallic and oxidized tin. We propose that the key difference between each surface termination is that CO2R catalyzed by metallic tin surfaces is limited by the electrochemical activation of CO2, whereas CO2R catalyzed by oxidized tin surfaces is limited by the slow reductive desorption of formate. While the exact degree of oxidation of tin surfaces during CO2R is unlikely to be either fully metallic or fully oxidized, this study highlights the limiting behavior of these two surfaces and lays out the key features of each that our results predict will promote rapid CO2R catalysis. Additionally, we highlight the power of integrating high-fidelity quantum mechanical modeling and spectroscopic measurements to elucidate intricate electrocatalytic reaction pathways.

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

Potential-dependent insights into the origin of high ammonia yield rate on copper surface via nitrate reduction: A computational and experimental study

Focusing on revealing the origin of high ammonia yield rate on Cu via nitrate reduction (NO3RR), we herein applied constant potential method via grand-canonical density functional theory (GC-DFT) with implicit continuum solvation model to predict the reaction energetics of NO3RR on pure copper surface in alkaline media. The potential-dependent mechanism on the most prevailing Cu (111) and the minor (100) and (110) facets were established, in consideration of NO2−, NO, NH3, NH2OH, N2, and N2O as the main products. The computational results show that the major Cu (111) is the ideal surface to produce ammonia with the highest onset potential at 0.06 V (until −0.37 V) and the highest optimal potential at −0.31 V for ammonia production without kinetic obstacles in activation energies at critical steps. For other minor facets, the secondary Cu (100) shows activity to ammonia from −0.03 to −0.54 V with the ideal potential at −0.50 V, which requires larger overpotential to overcome kinetic activation energy barriers. The least Cu (110) possesses the longest potential range for ammonia yield from −0.27 to −1.12 V due to the higher adsorption coverage of nitrate, but also with higher tendency to generate di-nitrogen species. Experimental evaluations on commercial Cu/C electrocatalyst validated the accuracy of our proposed mechanism. The most influential (111) surface with highest percentage in electrocatalyst determined the trend of ammonia production. In specific, the onset potential of ammonia production at 0.1 V and emergence of yield rate peak at −0.3 V in experiments precisely located in the predicted potentials on Cu (111). Four critical factors for the high ammonia yield and selectivity on Cu surface via NO3RR are summarized, including high NO3RR activity towards ammonia on the dominant Cu (111) facet, more possibilities to produce ammonia along different pathways on each facet, excellent ability for HER inhibition and suitable surface size to suppress di-nitrogen species formation at high nitrate coverage. Overall, our work provides comprehensive potential-dependent insights into the reaction details of NO3RR to ammonia, which can serve as references for the future development of NO3RR electrocatalysts, achieving higher activity and selectivity by maximizing these characteristics of copper-based materials.

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.

Novel metal-free holey BC4N nanostructure for enhanced photoelectrocatalytic nitrogen reduction: insight from grand-canonical density functional theory

Novel metal-free holey BC4N nanostructure for enhanced photoelectrocatalytic nitrogen reduction: insight from grand-canonical density functional theory

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.