Descriptor-Based Insights into Hydrazine Selectivity in Electrochemical Ammonia Oxidation on Single-Atom Centers of MXenes

Abstract

Selective electrochemical synthesis of hydrazine (N₂H₄) from ammonia oxidation offers a promising route toward value-added nitrogen chemicals but remains challenging due to competing oxidation pathways. Here, density functional theory calculations are employed to investigate hydrazine formation at electrochemically formed single-atom centers on 14 carbide- and nitride-based MXenes (MXene-SACs). Hydrazine selectivity is assessed using three descriptors, namely the thermodynamic free-energy span G _max(U), the kinetic descriptor G ^‡(U) associated with the N–N coupling activation barrier, and the hydrazine desorption energy (ΔG _des) governing product release from the catalytic surface. Evaluation of G _max(U) identifies Nb₂C-, V₂C-, Cr₂C-, and V₂N-SAC motifs as promising materials for efficient hydrazine formation. However, transition state calculations for N–N coupling barriers modify the thermodynamic activity trends, as reflected by G ^‡(U), and indicate that selectivity remains generally biased toward N₂ formation. A combined descriptor assessment shows that carbide-based MXene-SAC motifs, particularly V₂C and Cr₂C, remain the most promising hydrazine-competitive candidates due to their balanced intermediate stabilization and favorable desorption energetics, while V₂N-SAC lies closest to the ideal hydrazine-selective regime in descriptor space. Overall, the descriptor-guided screening strategy provides a transferable basis for analyzing catalyst selectivity toward hydrazine formation in ammonia electro-oxidation and related catalytic systems.

1. Introduction

Electrochemical ammonia oxidation reaction (AOR) has attracted increasing attention as an anodic reaction capable of replacing the energy-intensive oxygen evolution reaction (OER) while simultaneously producing value-added nitrogen-containing chemicals. − In coupled electrolysis systems, replacing OER with AOR can significantly lower the anodic energy requirement and thereby facilitate energy-efficient hydrogen production at the cathode. Depending on catalyst composition and reaction conditions, AOR can yield a variety of products including dinitrogen (N₂), nitrite (NO₂ ^–), nitrate (NO₃ ^–), or partially oxidized nitrogen species such as hydrazine (N₂H₄). ,, Among these, N₂H₄ is particularly attractive owing to its high energy density and wide range of applications in chemical synthesis, pharmaceuticals, polymer manufacturing, and aerospace propulsion. , Hydrazine is also an important fuel in direct hydrazine fuel cells and has therefore attracted interest as a potential energy carrier.

Conventional industrial hydrazine production routes, such as the Raschig and peroxide processes, − rely on strong oxidants and generate substantial waste streams. These limitations motivate the development of cleaner and more sustainable electrochemical synthesis strategies. In the context of AOR, the partial oxidation of ammonia to hydrazine can be written as

$$2{\mathrm{N}\mathrm{H}}_3\to {\mathrm{N}}_2{\mathrm{H}}_4+{2\mathrm{H}}^{+}+{2\mathrm{e}}^{-}(E^{°}=1.00\mathrm{v}\mathrm{s}\mathrm{R}\mathrm{H}\mathrm{E}/\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{e})$$ 1

Despite its attractive applications, achieving selective electrochemical synthesis of hydrazine remains challenging. , Under electrochemical conditions, ammonia oxidation proceeds through a complex network of coupled proton–electron transfer steps and competing surface reactions. Progressive dehydrogenation frequently drives the reaction toward N₂ formation under moderate anodic conditions unless partially hydrogenated intermediates can be stabilized and released before further transformation occurs. Previous theoretical studies on transition-metal surfaces have further demonstrated that sequential NH _x → N dehydrogenation pathways can compete kinetically with N–N coupling processes during ammonia oxidation. ,

At the mechanistic level, product selectivity during ammonia oxidation is governed by nitrogen–nitrogen bond formation involving adsorbed *NH _x intermediates along competing reaction pathways. , Coupling between partially hydrogenated species can lead to hydrazine formation, whereas deeper dehydrogenation (adsorbed *NH and *N) before coupling favors dinitrogen formation. Consequently, achieving hydrazine selectivity requires a delicate balance between stabilization of partially hydrogenated intermediates, accessibility of the N–N coupling transition state, and the ability of the catalyst surface to release hydrazine before further oxidation occurs.

Previous studies have demonstrated hydrazine formation in well-defined molecular catalytic systems, particularly in ruthenium-based complexes where controlled coordination environments facilitate N–N bond formation. − More recently, a polymer-supported ruthenium catalyst has been reported as a heterogeneous system capable of promoting direct electrochemical oxidation of ammonia to hydrazine, although N₂ remained the dominant product. These findings indicate that, although selective hydrazine formation can be achieved to some extent in molecular ruthenium systems, a broadly effective catalyst capable of steering ammonia electro-oxidation toward hydrazine has not yet been established.

In this regard, heterogeneous catalysts can offer several practical advantages, including structural robustness, tunable adsorption energetics, and direct integration with conductive electrodes, which may enable improved control over surface–adsorbate interactions and reaction selectivity. ,, Noble-metal catalysts, particularly Pt- and Ir-based materials and their alloys, have been extensively investigated for electrochemical ammonia oxidation owing to their high intrinsic activity. However, these systems predominantly promote full oxidation toward dinitrogen rather than selective hydrazine formation. − The high cost of noble metals and the limited control over product selectivity motivate the exploration of alternative catalyst platforms based on earth-abundant elements. Two-dimensional transition-metal carbides and nitrides, known as MXenes, have recently emerged as promising electrocatalyst supports because of their metallic conductivity, tunable surface chemistry, and high density of accessible active sites. Since their discovery through selective etching of MAX phases, MXenes have been widely explored for electrochemical reactions such as hydrogen evolution, − carbon dioxide reduction − and nitrogen reduction. − These studies highlight the ability of MXene surfaces to stabilize reactive intermediates at electrified interfaces and motivates their investigation for AOR.

While early theoretical studies often treated pristine MXene basal planes as the catalytic surface, more recent investigations have shown that MXenes can undergo water-mediated surface reconstruction under anodic polarization. , Depending on the applied electrode potential and electrolyte environment, this process can expose out-of-plane transition-metal atoms coordinated by oxygen species, creating single-atom-like active centers (SAC sites) directly on the MXene surface (Figure ). Under anodic conditions relevant to AOR, these electrochemically generated MXene-SAC motifs do not undergo degradation and thus provide catalytically active sites for energy conversion. , In recent years, the MXene-SAC (M_SAC–*O) motif has been investigated for several electrochemical reactions, including oxygen and chlorine evolution, , hydrazine oxidation, and nitrogen reduction, demonstrating its versatility for both anodic reactions and reduction processes through pulsing the electrochemical potential.

1.

Schematic representation of the MXene-SAC motif (M_SAC–*O), featuring a spectator *O adsorbed on the out-of-plane metal center formed during anodic polarization.

Recently, we investigated electrochemical ammonia oxidation toward dinitrogen formation across a homologous series of MXene-SAC motifs using a dual-descriptor approach that combines the potential-dependent thermodynamic free-energy span modelG _max(U)with the kinetic descriptor G ^‡(U). By accounting for both intermediate energetics and N–N coupling barriers, this framework enabled a systematic evaluation of electrocatalytic activity across different metals of MXene-SAC and provided insight into trends governing the formation of N₂. These findings motivate extending the descriptor framework toward analyzing the selectivity competition between N₂ and N₂H₄, as it remains unclear whether catalyst motifs identified as active for N₂ evolution can also favor selective hydrazine production.

The present study investigates hydrazine formation during electrochemical AOR on the same homologous series of electrochemically formed MXene-SAC motifs previously examined for N₂ formation (M₂X-SAC, where M = Ti, Hf, V, Nb, Ta, Cr, Mo, or W and X = C or N; Figure ). Density functional theory calculations are employed to evaluate three descriptors governing hydrazine selectivity, namely G _max(U), G ^‡(U), and the hydrazine desorption energy (ΔG _des). This extends the previously established dual-descriptor activity framework toward a selectivity analysis that incorporates hydrazine desorption when product release becomes decisive, thereby revealing energetic factors governing the competition between N₂ and N₂H₄ formation.

2. Computational Methods

To unravel the mechanistic pathways governing partial ammonia oxidation and to quantify the thermodynamic and kinetic factors controlling hydrazine formation on MXene-SACs, periodic density functional theory (DFT) calculations were carried out using the Vienna Ab initio Simulation Package (VASP 6.4.1). − All structures, including catalyst models, adsorbed intermediates, and transition states, were fully optimized using the same computational setup and parameters as in our previous MXene-SAC study to ensure direct comparability. No fixed adsorption geometries were imposed across different MXene compositions, thereby allowing each MXene-SAC system to relax to its energetically preferred adsorption configuration.

Exchange–correlation effects were described within the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional, together with Grimme’s D3 dispersion correction. Solvation effects were included using the VASPsol , implicit solvation model, assuming an aqueous medium (ε = 78.4) with an electrolyte concentration of 1 (M), corresponding to a Debye screening length of 3.0 Å. Core–valence interactions were treated using the projector augmented wave (PAW) method with a plane-wave cutoff of 440 eV. Spin–orbit coupling (SOC) effects were not considered, as they are expected to have only a minor influence on adsorption and reaction energetics and are unlikely to alter overall catalytic trends. Spin polarization was likewise omitted because its inclusion changes reaction free energies by less than 0.02 eV while significantly increasing computational cost. , While the absolute energetics may exhibit some sensitivity to the chosen electrochemical solvation parameters, the comparative descriptor trends discussed here are expected to remain robust within the consistently applied computational framework.

Periodic (3 × 3) MXene supercells were used to construct the catalyst models. Structural relaxations were performed with a Γ-centered 5 × 5 × 1 Monkhorst–Pack k-point mesh and a vacuum spacing of at least 20 Å along the surface-normal direction to prevent interactions between periodic images. Geometry optimizations were considered converged when the electronic energy change was below 10^–6 eV and the residual atomic forces were smaller than 0.01 eV Å^–1.

Vibrational frequency analyses were carried out within the harmonic approximation to obtain zero-point energy and entropic contributions of adsorbed intermediates. Gibbs free energies (G) were evaluated at 298.15 K according to

$$G=E_{\mathrm{D}\mathrm{F}\mathrm{T}}+E_{\mathrm{Z}\mathrm{P}\mathrm{E}}+{\int }_0^T{C_{\mathrm{v}}}_{\mathrm{v}\mathrm{i}\mathrm{b}}\mathrm{d}\mathrm{T}-{\mathrm{T}\mathrm{S}}_{\mathrm{v}\mathrm{i}\mathrm{b}}$$ 2

where E _DFT denotes the electronic energy obtained from DFT calculations, E _ZPE represents the zero-point energy correction, ∫₀ ^T C _v vib dT represents the vibrational heat capacity at constant volume and S _vib is the vibrational entropy. The full mathematical formalism used to evaluate these thermodynamic contributions can be found in our previous study. To reduce systematic errors associated with GGA-level calculations, established corrections were applied to reference gas-phase molecules, including NH₃, H₂, N₂, and N₂H₄.

Electrochemical reaction energetics were described using the computational hydrogen electrode (CHE) approach, in which the free energy of a proton–electron pair is referenced to one-half of the energy of molecular hydrogen at standard conditions (T = 298.15 K and p_H2 = 1 atm).

$${\mathrm{H}}_{(\mathrm{a}\mathrm{q})}^{+}+{\mathbb{e}}^{-}\rightleftharpoons {\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\mathrm{H}}_{2(\mathrm{g})}$$ 3

free-energy changes calculated at U = 0 V vs RHE were converted to potential-dependent values according to

$$\mathrm{\Delta }G(U)=\mathrm{\Delta }G(0)-neU$$ 4

where n represents the number of transferred electrons and U denotes the applied electrode potential on the RHE scale. In contrast, nonelectrochemical steps, such as adsorption, desorption, and N₂H₄ release steps without explicit charge transfer, were treated as potential-independent within the present formalism.

Experimentally, ammonia oxidation is commonly investigated under alkaline conditions. , In the present theoretical analysis, however, no explicit electrolyte pH is imposed. Instead, the energetics are evaluated within the CHE formalism referenced to the reversible hydrogen electrode (RHE). Under this framework, proton–electron transfer (PCET) energetics become formally independent of pH because the proton chemical potential is implicitly incorporated into the electrode reference scale. Nevertheless, pH may still influence catalyst behavior through changes in surface protonation equilibria, solvation structure, and interfacial effects not explicitly considered in the present treatment.

Electrocatalytic kinetics depend on the applied electrode potential and interfacial charge redistribution, which can be described more rigorously within grand-canonical electronic-structure frameworks that enable the evaluation of potential-dependent activation barriers. However, the determination of such barriers for complex heterogeneous reaction networks remains computationally demanding. Consequently, constant-charge approaches continue to provide a practical and widely adopted strategy for analyzing mechanistic trends and catalytic activity relationships in heterogeneous electrocatalysis.

The determination of activation barriers is essential for evaluating catalytic performance in electrocatalytic systems, as relatively small differences in transition-state energetics can lead to pronounced variations in intrinsic activity trends and product selectivity across catalyst materials. , Accordingly, transition states associated with N–N bond formation during hydrazine formation were located using the same protocol as in our previous study. This involves initial pathway identification via the nudged elastic band (NEB) method followed by refinement with the dimer method using a force criterion of less than 0.03 eV Å^–1. , The resulting saddle points were confirmed by the presence of a single imaginary frequency corresponding to the expected reaction coordinate.

3. Results and Discussion

3.1. Reaction Network and Descriptors

The MXene-SAC motifs considered in this study are formed during water-mediated surface reconstruction under anodic polarization, in which a spectator *O adsorbate remains coordinated to the out-of-plane metal atom and is denoted as M_SAC–*O (Figure ). Under oxidizing conditions relevant to ammonia oxidation, anodic polarization generally favors deprotonated oxygen-coordinated active states, which therefore serve as representative active-state structures for the comparative descriptor analysis performed in this work. In all reaction pathways considered here, the NH _x intermediates adsorb at the exposed out-of-plane metal center of the reconstructed M_SAC–*O motif, whereas the coordinated spectator oxygen species remains bound to the metal center throughout the catalytic cycle. The mechanistic landscape governing hydrazine formation from ammonia oxidation is illustrated in Figure . The pathway can be viewed from three complementary energetic perspectives. From a purely electrochemical standpoint, the first proton–electron transfer (PCET) step converts NH₃ into surface-bound *NH₂, which is followed by a second PCET event that results into product formation. In a first approximation, the feasibility of hydrazine formation is governed by the thermodynamics of these hydrogen-removal steps. A second perspective arises when the chemical N–N coupling between two adjacent *NH₂ species is considered, introducing a transition state and a corresponding kinetic barrier that cannot be captured by intermediate energetics alone. Importantly, hydrazine selectivity further requires that the coupled *NH₂–NH₂ intermediate desorbs as N₂H₄ to avoid further dehydrogenation toward N₂. Thus, hydrazine formation is ultimately controlled by the interplay of electrochemical PCET steps, chemical bond formation, and product release.

2.

Reaction pathways of ammonia oxidation (AOR) to N₂H₄: electrochemical proton–electron transfer steps generate *NH₂ intermediates, followed by chemical N–N coupling via a transition state leading to hydrazine formation, and desorption of *N₂H₄ regenerates the active catalytic site.

To evaluate the different contributions to hydrazine formation under applied potential conditions, we analyze the free-energy landscape shown in Figure using a descriptor-based framework. The thermodynamic feasibility of the hydrazine pathway is first quantified through the free-energy span descriptor G _max(U), defined as the largest free-energy increase along the forward reaction pathway between sequentially connected reaction intermediates at a given applied electrode potential. Incorporating the N–N coupling transition state into the evaluation of a free-energy span yields the kinetic descriptor G ^‡(U), defined as the free-energy difference between the most stable intermediate and the highest free-energy transition state. We refer to our previous work, where it was demonstrated that under the potential conditions of AOR, the barrier associated with N–N bond formation governs the transition state with highest free energy along the reaction coordinate. The desorption free energy of N₂H₄ (ΔG _des) is evaluated separately to determine whether the coupled intermediate can be released before further oxidation occurs. Together, G _max(U), G ^‡(U), and ΔG _des provide a multidimensional framework for assessing hydrazine-selective AOR across the MXene-SAC series. Descriptor-based multiparameter screening approaches have been shown to provide valuable insight into catalytic trends and optimal binding regimes in complex reaction networks.

3.

Schematic free-energy diagram illustrating the definition of the thermodynamic free-energy span (G _max), the kinetic span (G ^‡), and the desorption free energy (ΔG _des) for hydrazine formation during ammonia oxidation.

3.2. Thermodynamic Analysis

Following the descriptor framework introduced above, we first examine hydrazine formation from a thermodynamic perspective by considering the electrochemical proton–electron transfer (PCET) steps that generate the key *NH₂ intermediate (Figure ). Within this framework, ammonia first interacts with the active M_SAC–*O site and undergoes a proton–electron transfer to form the surface-bound *NH₂ species. A second electrochemical transformation then converts this intermediate into hydrazine while regenerating the active catalytic site. These elementary steps can be written as

$$\begin{array}{lrr}{\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}+{\mathrm{N}\mathrm{H}}_3\to {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}& & \\ -{}^{*}\mathrm{N}\mathrm{H}_2+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}& \mathrm{\Delta }{G}_1& (5)\\ {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-{}^{*}\mathrm{N}\mathrm{H}_2+{\mathrm{N}\mathrm{H}}_3\to & & \\ {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}+{\mathrm{N}}_2{\mathrm{H}}_4+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}& \mathrm{\Delta }{G}_2& (6)\end{array}$$

The corresponding free-energy landscapes for the investigated MXene-SACs are summarized in Figure at U = 1.20 V vs RHE. This potential was chosen because it corresponds to an overpotential of 200 mV relative to the equilibrium potential for partial ammonia oxidation to hydrazine (E° = 1.00 vs RHE), thereby providing a meaningful basis for comparing catalyst energetics under anodic operating conditions. The underlying step energetics at U = 0 V vs RHE are compiled in Table S1 in Section S1 of the Supporting Information.

4.

Gibbs free-energy diagrams (ΔG, eV) for electrochemical ammonia oxidation reaction (AOR) to hydrazine formation at U = 1.20 V vs RHE on MXene-supported single-atom catalysts. (a) Carbide-based M₂C-SAC motifs and (b) nitride-based M₂N-SAC motifs.

Inspection of the free-energy diagrams shown in Figure reveals systematic differences between carbide- and nitride-based MXene-SAC motifs. For the nitride series, all investigated materials exhibit ΔG ₁ < 0 at U = 1.20 V vs RHE, indicating that ammonia adsorption and activation to form the *NH₂ intermediate are thermodynamically favorable under anodic conditions. A similar trend is observed for most carbide-based catalysts, for which the first PCET step also becomes exergonic under anodic potentials. Only Ti₂C-SAC, V₂C-SAC, and Cr₂C-SAC retain slightly positive free-energy values of approximately 0.08, 0.14, and 0.03 eV, respectively, for *NH₂ formation, indicating that ammonia activation on these surfaces remains only weakly endergonic.

In contrast, the thermodynamics of the second PCET step (ΔG ₂) shows a stronger dependence on catalyst composition and adsorption strength. MXene-SAC motifs that bind the *NH₂ intermediate weakly or moderate strongly, ΔG ₂ (Table S1 in Section S1 of the Supporting Information) is either exergonic or thermoneutral under anodic bias, resulting in a nearly thermoneutral reaction landscapes for hydrazine formation. However, for more strongly binding systems such as Mo₂N-SAC, W₂C-SAC, and W₂N-SAC, the formation and release of hydrazine become thermodynamically demanding, leading to substantially larger ΔG ₂ values. This trend reflects the excessive stabilization of surface-bound intermediates on these materials, which increases the energetic penalty associated with the later electrochemical transformation.

To obtain a more systematic picture of these thermodynamic trends across the entire catalyst series, we evaluate the free-energy span descriptor G _max(U = 1.20 V) introduced in Section . The resulting activity trends are summarized in Figure . Several catalysts, including Nb₂C-SAC, Hf₂N-SAC, Cr₂C-SAC, Ti₂C-SAC, V₂N-SAC and V₂C-SAC, exhibit small G _max(U = 1.20 V) values in the range of 0–0.14 eV, indicating nearly thermoneutral reaction landscapes in which no individual intermediate step introduces a pronounced thermodynamic constraint. In contrast, catalysts such as Mo₂C-SAC, Hf₂C-SAC and Ta₂C-SAC show G _max(U = 1.20 V) spans between 0.30 and 0.60 eV. Finally, W₂C-SAC, Mo₂N-SAC and W₂N-SAC display larger spans of 1.45, 1.06, and 1.82 eV, respectively. These larger spans are consistent with the stabilization patterns observed in the free-energy diagrams and suggest that efficient hydrazine formation on these surfaces may require higher applied electrode potentials.

5.

Activity trends for the ammonia oxidation reaction (AOR) to N₂H₄ across the 14 MXene-SAC motifs at U = 1.20 V vs RHE, evaluated based on the G _max(U) descriptor.

Overall, the thermodynamic descriptor analysis identifies several MXene-SAC motifs, particularly Nb₂C-SAC and Hf₂N-SAC, followed by Cr₂C-SAC, Ti₂C-SAC, V₂N-SAC, and V₂C-SAC, as promising candidates from an intermediate-stability standpoint. These catalysts exhibit relatively small G _max(U = 1.20 V) values, indicating that the electrochemical steps required to access the hydrazine-forming configuration proceed without large thermodynamic penalties. However, thermodynamic feasibility alone does not ensure catalytic activity because hydrazine formation ultimately involves a N–N coupling step, which typically has a non-negligible activation barrier. Therefore, to obtain a more complete understanding of catalytic performance, the kinetic accessibility of the hydrazine pathway is examined in the following section.

3.3. Kinetic Analysis

To evaluate the kinetic feasibility of hydrazine formation on MXene-SAC motifs, we determine the kinetic descriptor G ^‡(U = 1.20 V) by analyzing the elementary reaction sequence associated with the activation barrier for N–N bond formation and the subsequent production of N₂H₄ on the active catalytic site. In this pathway, successive proton–electron transfer steps generate two adjacent *NH₂ species on the M_SAC–*O surface, thereby forming the precursor configuration required for hydrazine release. The corresponding elementary steps can be written as

$$\begin{array}{lrr}{\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}+{\mathrm{N}\mathrm{H}}_3\to {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}& & \\ -{}^{*}\mathrm{N}\mathrm{H}_2+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}& \mathrm{\Delta }{G}_1& (7)\\ {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-{}^{*}\mathrm{N}\mathrm{H}_2+{\mathrm{N}\mathrm{H}}_3\to {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}& & \\ -{}^{*}\mathrm{O}-({}^{*}\mathrm{N}\mathrm{H}_2)({}^{*}\mathrm{N}\mathrm{H}_2)+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}& \mathrm{\Delta }{G}_3& (8)\\ {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-({}^{*}\mathrm{N}\mathrm{H}_2)({}^{*}\mathrm{N}\mathrm{H}_2)\to & & \\ {[{\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-{}^{*}\mathrm{N}\mathrm{H}_2···{}^{*}\mathrm{N}\mathrm{H}_2]}^{‡}& \mathrm{\Delta }{G}_1^{‡}& (9)\\ {[{\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-{}^{*}\mathrm{N}\mathrm{H}_2···{}^{*}\mathrm{N}\mathrm{H}_2]}^{‡}\to {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}& & \\ -{}^{*}\mathrm{O}+{\mathrm{N}}_2{\mathrm{H}}_4& \mathrm{\Delta }{G}_4& (10)\end{array}$$

The associated kinetic profiles at U = 1.20 V vs RHE are shown in Figure , while Table S2 (Section S2 of the Supporting Information) summarizes the underlying step energetics and coupling barriers (ΔG ^‡ ₁) at U = 0 V vs RHE. Here, ΔG ^‡ ₁ refers to the free-energy change associated with the transition state linked to the respective RI, i.e., (*NH₂)­(*NH₂) → [*NH₂···*NH2]^‡, which is pictorially illustrated in Figure S1 of the Supporting Information.

6.

Gibbs free-energy diagrams (ΔG, eV) for electrochemical ammonia oxidation reaction (AOR) to hydrazine formation at U = 1.20 V vs RHE on MXene-supported single-atom catalysts. (a) Carbide-based M₂C-SAC motifs and (b) nitride-based M₂N-SAC motifs.

Table S2 shows that the activation barriers for N–N bond formation span a broad range of 0.30–2.70 eV, depending on the chemical nature of the metal and the carbide or nitride in the MXene lattice. Importantly, these barriers do not directly follow the trends of the thermodynamic analysis of the PCET steps in Section . Within the carbide series, V₂C-SAC exhibits one of the lowest coupling barriers (ΔG ^‡ ₁ = 1.03 eV), followed closely by Cr₂C-SAC (1.13 eV) and Ti₂C-SAC (1.37 eV), indicating relatively accessible N–N bond formation on these surfaces. In contrast, Hf₂C-SAC (ΔG ^‡ ₁ = 1.87 eV) displays a higher barrier, whereas W₂C-SAC (2.20 eV) shows the largest barrier within the carbide set.

A comparable spread is observed for the nitride series. Ta₂N-SAC exhibits the lowest local coupling barrier in the series, with ΔG ^‡ ₁ = 0.30 eV, indicating that N–N bond formation itself is highly accessible on this surface. V₂N-SAC and Nb₂N-SAC also show relatively low barriers of 1.12 and 1.19 eV, respectively, while Hf₂N-SAC exhibits a somewhat higher value of 1.58 eV. In contrast, Mo₂N-SAC and W₂N-SAC display much larger barriers of 2.03 and 2.69 eV, indicating that N–N coupling becomes kinetically difficult on these strongly binding systems. A similar decoupling between thermodynamic intermediate stabilization and kinetic accessibility was previously identified for ammonia oxidation leading to N₂ formation, indicating that transition-state energetics represent a general controlling factor in MXene-SAC based AOR catalysis.

To translate these transition-state energetics into a catalyst-comparable kinetic measure, we evaluate the descriptor G ^‡(U) at U = 1.20 V vs RHE, shown in Figure . Incorporating the coupling barrier modifies the activity ranking of the SAC-type catalysts relative to the thermodynamic descriptor G _max(U): while Ta₂N-SAC, V₂C-SAC, Cr₂C-SAC, Ti₂C-SAC, Nb₂C-SAC, and V₂N-SAC are favorable based on the G ^‡(U) analysis, W₂C-SAC, Mo₂N-SAC, and W₂N-SAC fall into a less favorable kinetic regime. Notably, the evaluation of the coupling barrier (ΔG ^‡ ₁) alone is not sufficient: although ΔG ^‡ ₁ identifies the ease of the bond-forming step, the kinetic descriptor G ^‡(U) captures both thermodynamic and kinetic restraints through the free-energy span model under operating conditions. Overall, these kinetic trends suggest that MXene-SAC motifs exhibiting weak to moderate stabilization of the precoupling M_SAC–*O–(*NH₂)­(*NH₂) intermediate provide more favorable conditions for N–N coupling, whereas strongly binding motifs remain kinetically limited by substantial activation penalties.

7.

Activity trends for the ammonia oxidation reaction (AOR) to N₂H₄ across the 14 MXene-SAC motifs at U = 1.20 V vs RHE, evaluated based on the descriptor G ^‡(U).

3.4. Desorption & Selectivity

After establishing the thermodynamic and kinetic requirements for hydrazine formation, it is essential to assess whether the generated N₂H₄ molecule can be effectively released from the catalyst surface. Even when both intermediate stabilization and transition state accessibility are favorable, excessively strong adsorption of hydrazine may inhibit catalytic turnover by promoting surface trapping or subsequent deep oxidation pathways to N₂. Therefore, we finally examine the desorption energetics of N₂H₄ from the active M_SAC–*O motif in order to evaluate the overall feasibility of hydrazine production on MXene-SAC systems. In this context, the N₂H₄ desorption free energy is treated separately from the G _max(U) analysis because product release represents a distinct physicochemical process from the surface reaction energetics governing NH _x transformation and N–N coupling. This separation enables discrimination between catalysts that favor hydrazine formation thermodynamically and those that additionally permit efficient product release and catalytic turnover.

To assess the feasibility of product release, we consider the desorption step of hydrazine from the surface-coupled intermediate, which can be expressed as

$$\begin{array}{lrr}{\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}-{}^{*}\mathrm{N}\mathrm{H}_2-{}^{*}\mathrm{N}\mathrm{H}_2\to & & \\ {\mathrm{M}}_{\mathrm{S}\mathrm{A}\mathrm{C}}-{}^{*}\mathrm{O}+{\mathrm{N}}_2{\mathrm{H}}_4& \mathrm{\Delta }{G}_{\mathrm{d}\mathrm{e}\mathrm{s}}& (11)\end{array}$$

The calculated hydrazine desorption free energies for the MXene-SAC series are compiled in Table S3 (Section S4 of the Supporting Information), revealing substantial variation across the homologous series of materials. In general, carbide-based systems exhibit more favorable hydrazine release characteristics. For example, Ti₂C-SAC shows strongly exergonic desorption (ΔG _des = −0.83 eV), while V₂C-SAC and Cr₂C-SAC also display negative values of −0.54 and −0.21 eV, respectively. These values indicate that the *NH₂–*NH₂ adsorbate can readily leave the surface. In contrast, several nitride-based catalysts exhibit positive desorption energies, suggesting stronger binding of the *NH₂–*NH₂ intermediate. For example, Mo₂N-SAC and W₂N-SAC show ΔG _des values of 1.40 and 1.81 eV, respectively, implying that hydrazine release is thermodynamically unfavorable on these surfaces. We note that N₂H₄ desorption is not assumed to be universally more favorable than continued electrochemical dehydrogenation. Rather, ΔG _des is evaluated as a separate descriptor because product release competes with further surface oxidation of the coupled intermediate toward N₂. Accordingly, strongly positive ΔG _des values indicate that stabilization and surface retention of the coupled intermediate may promote continued dehydrogenation rather than selective hydrazine release.

To understand how the desorption energetics interact with the thermodynamic and kinetic descriptors discussed earlier, these results are evaluated within a combined descriptor framework summarized in Table . Both the thermodynamic free-energy spans governing hydrazine and N₂ formation, together with the corresponding N–N coupling barriers, are considered at an applied potential of U = 1.20 V vs RHE in order to ensure a consistent comparison under identical electrochemical driving conditions. Selectivity toward hydrazine relative to the competing N₂ forming pathway is therefore assessed by comparing the energetic spans and transition state barriers of the two reaction channels. Accordingly, the thermodynamic selectivity descriptor

$$\mathrm{\Delta }{G}_{\max }=G_{\max }({\mathrm{N}}_2{\mathrm{H}}_4)-G_{\max }({\mathrm{N}}_2)$$ 12

1. G _max, G ^‡ _selectivity, and Desorption Geoverning Hydrazine Formation during Ammonia Oxidation on 14 MXene-SAC motifs at U = 1.20 V vs RHE.

MXene-SAC	G max(N2)	G max(N2H4)	ΔG max	G ‡(N2)	G ‡(N2H4)	ΔG ‡ selectivity	ΔG des (N2H4)
Ti2C	0.63	0.08	–0.55	0.86	1.37	0.51	–0.83
Hf2C	0.30	0.36	0.06	0.76	1.87	1.11	–0.16
V2C	0.55	0.14	–0.41	1.06	1.52	0.46	–0.54
Nb2C	0.16	0.00	–0.16	0.67	1.43	0.76	0.20
Ta2C	0.40	0.58	0.18	0.55	1.60	1.05	0.79
Cr2C	0.13	0.03	–0.10	0.61	1.17	0.56	–0.21
Mo2C	0.0	0.31	0.31	1.05	1.44	0.39	0.48
W2C	0.15	1.45	1.30	1.06	3.19	2.13	1.85
Hf2N	0.50	0.00	–0.50	0.50	1.58	1.08	0.20
V2N	0.08	0.10	0.02	0.86	1.12	0.26	0.29
Nb2N	0.00	0.22	0.22	0.77	1.19	0.42	0.82
Ta2N	0.45	0.79	0.34	0.55	0.79	0.24	1.28
Mo2N	0.00	1.06	1.06	1.01	2.38	1.37	1.40
W2N	0.21	1.82	1.61	0.96	3.69	2.73	1.81

and the kinetic selectivity descriptor

$$\mathrm{\Delta }{G}_{\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}}^{‡}=G^{‡}({\mathrm{N}}_2{\mathrm{H}}_4)-G^{‡}({\mathrm{N}}_2)$$ 13

are used to quantify pathway competition. Here, the energetic parameters associated with hydrazine formation are obtained in the present work, whereas the corresponding thermodynamic free-energy spans and transition state barriers for the N₂ forming pathway are adopted from our previous investigation of ammonia oxidation on analogous MXene-SAC motifs. For clarity, the preferred N–N coupling pathways and the corresponding activation barriers associated with N₂ formation on the investigated MXene-SAC systems are summarized in Table S4 (Section S5 of the Supporting Information). Within this definition, negative values of ΔG _max indicate thermodynamic preference for hydrazine formation, whereas positive values imply that ammonia oxidation toward N₂ is thermodynamically favorable. Likewise, negative values of ΔG ^‡ _selectivity would correspond to kinetic preference for hydrazine formation relative to the competing N₂ pathway, while positive values indicate that N₂ evolution is kinetically favored. As summarized in Table , several MXene-SAC motifs exhibit negative ΔG _max values (Table ), including Ti₂C (−0.55 eV), V₂C (−0.41 eV), Cr₂C (−0.10 eV), and Nb₂C (−0.16 eV), demonstrating that hydrazine formation can become thermodynamically competitive under the applied electrochemical conditions. In contrast, ΔG ^‡ _selectivity remains positive for all investigated systems, indicating that the N₂ forming pathway retains a lower kinetic barrier even when hydrazine formation is thermodynamically accessible.

To obtain a more comprehensive interpretation of the catalytic behavior summarized in Table , we plot the thermodynamic activity descriptor G _max(N₂H₄) against the kinetic selectivity descriptor ΔG ^‡ _selectivity, as shown in Figure . The resulting map can be conveniently interpreted by introducing two reference boundaries that reflect the thermodynamic competitiveness and kinetic preference of hydrazine formation. A vertical separation at G _max(N₂H₄) = 0.50 eV separates systems for which hydrazine formation can be considered thermodynamically competitive from those associated with larger energetic spans. In addition, a horizontal division at ΔG ^‡ _selectivity = 0 eV differentiates between regimes where hydrazine formation would be kinetically favored and those where N₂ evolution remains preferred. The intersection of these two criteria gives rise to four distinct regions in the descriptor space, which provide a convenient framework for analyzing catalytic trends. In addition to the thermodynamic and kinetic descriptors discussed above, hydrazine release characteristics must also be considered when evaluating overall catalytic selectivity. In this context, the approximate 0.5 eV reference value associated with N₂H₄ desorption should be regarded as a qualitative screening guideline rather than a strict mechanistic threshold. Within the present descriptor framework, comparatively small desorption free energies indicate accessible hydrazine release, whereas substantially larger positive values suggest stronger surface retention and a higher likelihood of continued oxidation toward N₂.

8.

Descriptor-based classification map for hydrazine formation during electrochemical ammonia oxidation on MXene-SAC motifs at U = 1.20 V vs RHE.

Region I, located in the lower-left quadrant, corresponds to catalysts that combine thermodynamic competitiveness with kinetic selectivity toward hydrazine formation. However, no MXene-SAC motif is found in this ideal domain. Region II, situated in the upper-left quadrant, comprises systems that satisfy the thermodynamic competitiveness criterion but remain kinetically biased toward N₂ evolution. Several carbide-based MXene-SAC motifs, including Ti₂C-, V₂C-, Cr₂C-, and Nb₂C-SAC, populate this region, indicating that hydrazine formation is energetically accessible yet not intrinsically preferred. Notably, the nitride system V₂N is positioned closest to the boundary of Region I, reflecting its comparatively small thermodynamic span and relatively low kinetic selectivity penalty among the investigated catalysts.

Region III, located in the upper-right quadrant, contains catalysts that are both thermodynamically noncompetitive and kinetically disfavored for hydrazine formation. Strongly binding systems such as Mo₂N-, W₂N-, and W₂C-SAC fall predominantly into this regime, where large thermodynamic free-energy spans, elevated N–N coupling barriers, and hindered hydrazine desorption collectively limit catalytic performance. Finally, Region IV, positioned in the lower-right quadrant, would correspond to kinetically hydrazine-selective yet thermodynamically noncompetitive catalysts. However, no MXene-SAC motif is identified in this region within the present catalyst set.

In summary, the combined descriptor framework reveals that achieving hydrazine selectivity requires a delicate balance between moderate intermediate stabilization, reduced N–N coupling barriers, and sufficiently weak product binding. Although some carbide-based MXene-SAC systems exhibit hydrazine-competitive thermodynamic characteristics, as observed for systems such as V₂C- and Cr₂C-SAC, the nitride system V₂N-SAC lies closest to the ideal selectivity regime in descriptor space. Nevertheless, none of the investigated catalysts simultaneously fulfils all energetic requirements necessary for hydrazine selective operation.

3.5. Design Principles for Hydrazine Selective Catalysis

The descriptor landscape shown in Figure indicates that, although several MXene-SAC motifs approach hydrazine-competitive behavior, the ideal selectivity region characterized by ΔG ^‡ _selectivity < 0 has not yet been reached. Advancing catalyst performance toward this regime requires lowering the energetic span for hydrazine formation while simultaneously increasing the energetic demand for the competing N₂ pathway.

From a mechanistic perspective, this balance may be achieved by tuning the interaction between the active site and nitrogen-containing intermediates. In particular, selective destabilization of deeply dehydrogenated species such as *NH and *N could suppress complete oxidation sequences while maintaining favorable energetics for partially hydrogenated configurations involved in N–N coupling toward hydrazine. Such effects may be realized through variation of MXene composition, surface termination, or the coordination environment of the single-atom center.

Additional control may arise from structural and operational factors. Strain can influence adsorption strengths and transition-state energetics, whereas dynamic electrochemical operation, for example pulsed-potential protocols, may transiently weaken strongly adsorbed intermediates and alter the competition between hydrazine formation and further dehydrogenation. In this view, hydrazine selectivity could potentially emerge from balancing intermediate stabilization, accessible N–N bond formation, and favorable product release along the reaction pathway through strain engineering or pulsing the electrochemical potential.

Overall, the combined descriptor framework established in this study provides a general strategy for analyzing selectivity in multistep electrochemical reactions. Although demonstrated here for MXene-SAC catalysts in ammonia oxidation, this approach can be extended to other catalyst systems and nitrogen-conversion processes governed by coupled thermodynamic and kinetic constraints.

4. Conclusions

In this work, hydrazine formation during electrochemical ammonia oxidation was systematically investigated on a series of MXene-SAC catalysts using density functional theory calculations. By combining thermodynamic analysis, transition-state calculations for N–N bond formation, and evaluation of product desorption energetics, we examined the key factors that govern partial ammonia oxidation toward hydrazine formation. The thermodynamic free-energy profiles reveal that several carbide and nitride MXene-SAC systems are capable of stabilizing surface-bound *NH₂ intermediates required for hydrazine formation. In particular, catalysts such as Nb₂C-SAC, V₂C-SAC, Cr₂C-SAC, Ti₂C-SAC, and V₂N-SAC exhibit small free-energy spans together with favorable desorption energetics, indicating that hydrazine formation appears thermodynamically feasible when evaluated solely from a thermodynamic standpoint.

When kinetic effects are incorporated through explicit N–N coupling transition-state calculations, the catalytic trends change significantly. The descriptor G ^‡(U) shows that hydrazine formation is largely limited by the accessibility of the N–N bond-forming step rather than by the thermodynamic stability of intermediates. Strongly binding systems, such as Mo₂N-SAC and W₂N-SAC, overstabilize surface-bound *NH _x intermediates, especially *NH₂, and consequently also the precoupling M_SAC–*O–(*NH₂)­(*NH₂) configuration, leading to large energetic requirements for N–N couping. This behavior highlights an important limitation of purely thermodynamic descriptors when reactions are governed by bond-formation kinetics. A combined assessment indicates that carbide-based motifs, especially V₂C-SAC and Cr₂C-SAC, remain the most hydrazine-competitive candidates within the series, whereas V₂N-SAC is positioned closest to the ideal hydrazine-selective regime in descriptor space despite an overall selectivity still favoring N₂ formation.

Beyond intermediate formation and transition-state accessibility, hydrazine selectivity also depends critically on product desorption. Catalysts that bind hydrazine too strongly tend to retain the coupled intermediate on the surface, which can promote continued dehydrogenation toward N₂ rather than releasing N₂H₄.

The mechanistic insights resolved in this work highlight the need for a combined descriptor-based perspective when evaluating partial ammonia oxidation pathways. Integrating the descriptors G _max(U), G ^‡(U), and ΔG _des into a unified framework provides the basis for analyzing partial ammonia oxidation and clarifies why catalysts that are effective for ammonia oxidation to N₂ do not necessarily promote hydrazine formation. Overall, the generality of this combined descriptor approach suggests that its applicability extends beyond the homologous MXene-SAC series examined here and beyond the specific selectivity problem addressed in this study, thereby offering wider implications for catalyst screening in complex multistep electrochemical reaction networks.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.6c00051.

• Thermodynamic reaction energetics of hydrazine formation on MXene-SACs; thermodynamic–kinetic reaction energetics; definition of the descriptor ΔG ^‡ ₁; hydrazine desorption energies (PDF)

The authors declare no competing financial interest.