Atomic-Scale Insights into CO₂ and H₂O Co-Adsorption on Sr₂Fe_1.5Mo_0.5O₆ Surfaces: Role of Electronic Structure and Dual-Site Interactions

Abstract

Co-electrolysis of CO₂ and H₂O offers a promising route for efficient and controllable syngas production from greenhouse gases and water. However, the atomic-scale reaction mechanism remains elusive, especially on complex oxide surfaces. In this study, we employ density functional theory (DFT) to investigate the adsorption and activation of CO₂ and H₂O on the FeMoO-terminated (001) surface of Sr₂Fe_1.5Mo_0.5O₆ (SFM), a double perovskite of growing interest for solid oxide electrolysis. Our results show that CO₂ strongly interacts with surface lattice oxygen, adopting a bent configuration with substantial charge transfer. In contrast, H₂O binds more weakly at Mo sites through predominantly electrostatic interactions. Co-adsorption analyses reveal a bidirectional interplay: pre-adsorbed H₂O enhances CO₂ binding by altering its adsorption geometry, whereas pre-adsorbed CO₂ weakens H₂O adsorption due to competitive site occupation. This balance suggests that moderate co-adsorption may facilitate proton–electron coupling, while excessive coverage of either species suppresses activation of the other. Bader charge analysis, charge density differences, and projected density of states highlight the key role of Fe/Mo–O hybridized states near the Fermi level in mediating surface reactivity. These results, obtained for a perfect defect-free surface, provide a theoretical benchmark for disentangling intrinsic molecule–surface and molecule–molecule interactions, and offer guidance for designing high-performance perovskite electrocatalysts for CO₂ + H₂O co-electrolysis.

1. Introduction

The electrochemical co-reduction of CO₂ and H₂O in solid oxide electrolysis cells (SOECs) represents a promising strategy for sustainable syngas (CO + H₂) production, bridging the gap between renewable energy sources and synthetic fuels. Compared to conventional water electrolysis, the co-electrolysis approach offers enhanced carbon utilization, direct coupling to carbon capture, and greater thermodynamic efficiency at high operating temperatures, typically in the range of 700–900 °C [1,2,3]. These conditions not only reduce the kinetic barriers for gas activation but also allow reversible operation in solid oxide fuel cell (SOFC) and SOEC modes, providing system-level flexibility [4]. Moreover, syngas generated via co-electrolysis can be further processed through Fischer–Tropsch synthesis or methanol production, forming the basis for renewable liquid fuels and value-added chemicals [5,6,7,8]. In this process, the initial adsorption and activation of H₂O and CO₂ on the cathode surface govern the rates of the electrochemical reactions, so understanding these surface steps is critical for improving overall performance.

Traditionally, Ni-based electrodes have been the dominant choice in SOECs due to their high electronic conductivity and catalytic activity. However, Ni catalysts suffer from several issues including carbon deposition (coking), sulfur poisoning, and mechanical instability under redox cycling [9,10]. These limitations have motivated the exploration of alternative oxide-based electrodes, especially mixed ionic-electronic conductors (MIECs) with perovskite or double-perovskite structures [11]. In this context, the double perovskite Sr₂Fe_1.5Mo_0.5O₆ (SFM) has emerged as a particularly promising candidate. SFM exhibits favorable redox stability, high electrical conductivity, and fast oxygen-ion transport under reducing conditions, making it well-suited for the harsh environment of SOEC cathodes [12,13,14]. The synergistic interaction between Fe and Mo cations in the B-site lattice of SFM promotes oxygen vacancy formation and electron delocalization, which can enhance surface reactivity toward gas-phase molecules such as CO₂ and H₂O [15]. Furthermore, the Fe-centered electronic states provide redox-active sites, while the structural flexibility of the perovskite lattice enables compositional tuning through A-site or B-site doping to optimize adsorption and catalytic behavior [16].

Despite these advantages, the fundamental surface mechanisms by which CO₂ and H₂O adsorb and interact on SFM remain insufficiently understood. Experimental studies have provided indirect evidence of gas conversion performance and long-term stability, yet lack the atomic-scale resolution needed to unravel the initial activation steps. Here, we emphasize that our DFT calculations are performed on a defect-free, idealized SFM surface, which serves as a theoretical benchmark to systematically explore adsorption energetics and electronic interactions [17,18,19,20,21]. While real materials may contain vacancies or mixed-valence cations, the perfect-surface model provides a clear reference point for understanding fundamental molecule–surface interactions. Previous First-principles density functional theory (DFT) studies have shown that oxygen vacancies can strongly modify adsorption energetics and surface redox chemistry [22,23]. Therefore, our defect-free surface results should be viewed as a theoretical benchmark, with future work extending to defective surfaces to bridge with realistic SOEC conditions. Within this framework, a key open question is how the simultaneous presence of CO₂ and H₂O influences charge redistribution, adsorption energetics, and electronic structure on SFM surfaces. DFT simulations offer a powerful tool to fill this gap by quantifying adsorption energies, surface charge transfer, and electronic reorganization in a controlled and systematic manner [24,25,26,27].

In this study, we focus on the FeMoO-terminated (001) surface of Sr₂Fe_1.5Mo_0.5O₆ to explore the detailed adsorption configurations of CO₂ and H₂O, both individually and in co-adsorption states. We employ spin-polarized DFT calculations with Hubbard U corrections to account for the strong correlation effects of the transition metal d-orbitals, ensuring reliable treatment of the surface electronic structure. By computing adsorption energies, differential charge densities, Bader charges, and partial density of states (PDOS), we elucidate how the interplay between adsorbates and surface cations modulates the local chemical environment. Our results reveal competitive and cooperative interactions between CO₂ and H₂O during co-adsorption, providing insight into the initial stages of CO and H₂ evolution. This study contributes to a molecular-level understanding of syngas generation on SFM and provides a theoretical foundation for future design of high-performance perovskite-based cathodes for CO₂ + H₂O co-electrolysis.

2. Results and Discussion

In this study, we constructed and optimized the geometry of the Sr₂Fe_1.5Mo_0.5O₆ (SFM) perovskite structure, as shown in Figure 1. In the optimized unit cell, Fe atoms are represented in brown, Mo in purple, O in red, and Sr in green. The calculated bond lengths of Fe-O and Mo-O in pristine SFM are 1.99 Å and 1.91 Å, respectively. A comparison of the lattice constants obtained in this work with those reported in the previous literature is provided in

Table 1. Comparison of lattice parameters for Sr₂Fe_1.5Mo_0.5O₆ and related perovskite materials.

Compound	Lattice Parameters (Å)	Method	Space Group	Reference
Sr2Fe1.5Mo0.5O6	a = 5.542 Å, c = 7.940 Å	GGA + U	I4/mmm	This work
Sr2Fe1.5Mo0.5O6−δ	a ≈ 5.543 Å, c = 7.847 Å	sol–gel synthesis	I4/mmm	[28]
Sr2Fe0.5Mo0.5O6	a = 5.555 Å, c = 7.878 Å	In situ powder neutron diffraction	I4/mmm	[29]
Sr2−xCaxFe1.5Mo0.5O6−δ	a = 5.55 Å, c = 7.90 Å	XRD (wet H2)	I4/mmm	[30]

. The optimized parameters, with a = 5.542 Å and c = 7.940 Å, are in excellent agreement with literature values, confirming the reliability of our computational model for subsequent investigations.

Based on the optimized bulk structure, a 2 × 3 × 1 supercell was constructed, followed by cleaving along the (001) plane to model the surface. The surface slab contains 120 atoms and includes a 15 Å vacuum layer to simulate the molecular adsorption environment. The bottom two atomic layers were fixed to mimic the bulk environment, while the top two layers were fully relaxed. Structural relaxation revealed moderate adjustments in the Fe-O and Mo-O bond lengths at the surface. Figure 2 illustrates the atomic layer stacking along the (001) orientation of the optimized surface. The (001) direction of the SFM crystal contains alternating SrO, FeO₂, and FeMoO layers (Figure S1). Among these, the difference in oxidation states between Fe and Mo (Fe³⁺/Fe²⁺ vs. Mo⁶⁺/Mo⁵⁺) can promote the formation of oxygen vacancies and enhance the activity of lattice oxygen, thereby improving surface stability [31]. To clearly justify our surface selection, we note that our stoichiometric surface-energy calculations show FeMoO- and FeO₂-terminated (001) surfaces are nearly degenerate in stability, with γ_FeMoO = 0.09172 eV Å⁻² and γ_FeO2 = 0.09171 eV Å⁻² (differing only in the fifth decimal place and thus within the accuracy of our DFT + U approach). However, the FeMoO termination is particularly advantageous because it simultaneously exposes both Fe and Mo cations, providing dual redox-active sites directly relevant to CO₂/H₂O adsorption and activation. By contrast, the SrO termination is significantly less stable (γ ≈ 0.146 eV Å⁻²). Previous DFT + U thermodynamic analysis also indicates that Mo-containing (plane-Mo) terminations can be competitive in stability, whereas FeO₂ termination is favored only under strongly oxidizing conditions [32]. Considering both comparable energetic stability under stoichiometric conditions and the direct availability of Fe and Mo active sites, the FeMoO surface was selected as the preferred cleavage plane for subsequent adsorption and activation studies.

We investigated both single and co-adsorption of CO₂ and H₂O molecules on the FeMoO-terminated surface. The configurations of CO₂ adsorption are shown in Figure S2. CO₂ molecules were initially placed with their molecular axis either perpendicular or parallel to the surface over Fe, Mo, and O surface sites. Configurations (a,b) correspond to adsorption on Fe sites with the molecular axis perpendicular (a) or parallel (b) to the surface, (c,d) to adsorption on Mo sites with similar perpendicular (c) and parallel (d) orientations, and adsorption on O sites was considered by allowing the carbon atom to interact directly with surface oxygen atoms. Upon optimization (Figure 3), CO₂ adsorbed on metal sites tended to reorient to perpendicular configurations, whereas adsorption over O sites led to full activation of the CO₂ molecule. Adsorption energies, bond lengths, and bond angles for each configuration are summarized in

Table 2. The adsorption energy, bond length, bond angle and distance from the surface of the CO₂ adsorption configuration of SFM (d (Å)).

Adsorption Configuration	Fe-1	Fe-2	Mo-1	Mo-2	O
Eads (eV)	−1.853	−1.756	0.959 (unstable)	−1.727	−2.047
bond length (Å)	1.173	1.178	1.174	1.179	1.256
bond angle (°)	179.781	178.822	179.259	178.567	128.053
d (Å)	2.460	2.679	2.545	2.741	1.343

. In the table, “-1” denotes perpendicular adsorption (molecular axis roughly perpendicular to the surface), “-2” denotes parallel adsorption (molecular axis roughly parallel to the surface), and the preceding letter indicates the adsorption site. It should be noted that because the surface slab is periodic in the lateral directions, all top-layer Fe, Mo, and O atoms are crystallographically equivalent; therefore, sampling one representative Fe, Mo, and O site exhausts all non-equivalent adsorption centers on this surface.

While our comprehensive screening identified initial adsorption configurations across all geometrically plausible sites, thermodynamic analysis revealed fundamental limitations. For instance, CO₂ adsorption on the Mo-1 site yielded a positive adsorption energy (E_ads = +0.959 eV), which indicates that this configuration is thermodynamically unstable and would spontaneously desorb. Such unstable cases are therefore excluded from further consideration as viable intermediates. In stark contrast, among the thermodynamically stable configurations, CO₂ adsorption at the O site exhibited exceptionally strong interaction, with E_ads = −2.047 eV. This pronounced binding was accompanied by significant molecular distortion, including contraction of the C=O bond and alteration of the O-C-O bond angle, indicative of profound electronic interaction with the surface. The short adsorption distance and substantial electron transfer observed in the O-2 configuration further suggest enhanced CO₂ activation, likely mediated through covalent character or significant polarization effects.

To further explore the electronic behavior of CO₂ adsorption, we computed the charge density difference and Bader charges for the most favorable configurations: Fe-1, Mo-2, and O-2. The charge density difference plots are shown in Figure 4. Yellow regions indicate electron accumulation, while blue regions indicate depletion. An isosurface value of 0.002 e/ų was used. Minor electron transfer was observed between CO₂ and the Fe or Mo atoms at the respective adsorption sites, supporting the presence of moderate chemical interaction. In contrast, the O-2 configuration displayed significant charge redistribution between the CO₂ molecule and surface oxygen atoms, indicating a stronger interaction possibly involving covalent character.

Quantitative analysis using Bader charge (

Table 3. Bader charge.

Adsorption Configuration	Average Bader Net Atomic Charge (e)
	Sr	Fe	Mo	O-Slab	C	O-CO2
Fe-1	1.576	1.702	2.644	−1.171	1.530	−0.769
Mo-2	1.574	1.692	2.367	−1.145	1.860	−0.942
O site	1.640	1.604	3.095	−1.199	0.608	−0.571

and Figure S3) further confirms this behavior. Since the calculated actual number of charges has no absolute physical meaning, the charge state of each atom is determined by comparing its calculated charge with the corresponding valence charge, and the average Bader net atomic charge is obtained by averaging the charge transfer of all atoms of the same type. In this convention, a negative charge indicates that the atom has gained electrons, while a positive charge indicates electron loss relative to the isolated atom. The average net Bader charge on O atoms in the CO₂ molecule for the O-2 configuration is −1.199 e, the most negative among all configurations, indicating substantial electron gain. This trend is consistent with the adsorption energy and charge density difference results.

To further clarify the surface redox behavior, we calculated the net charge transfer to the entire adsorbate molecule by summing the Bader charges of all its constituent atoms and comparing them with the isolated molecule. For O-site CO₂ adsorption, the molecule gains a total of 0.53 e, with the C atom (+0.608 e) and the two O atoms bound to Mo (−0.629 e) and Fe (−0.513 e) serving as the main electron-accepting sites (Figure S3a). The adjacent Fe (1.653 e) and Mo (3.114 e) centers exhibit decreased electron density compared to the pristine surface, consistent with partial oxidation of these cations during CO₂ activation.

Through the adsorption of a single CO₂ molecule, it was found that CO₂ preferentially adsorbs on the SFM surface with the carbon atom binding to surface oxygen sites. Fe and Mo atoms dynamically activate two adjacent oxygen atoms, which helps to partially weaken the strong C=O double bonds. This bond weakening facilitates subsequent surface reactions.

Similarly, the adsorption behavior of a single H₂O molecule on the SFM surface was investigated, as shown in Figure S4. Panels (a,b) illustrate adsorption configurations at the Fe site with the molecular plane either roughly parallel to the surface or with one O–H bond pointing toward the surface, while panels (c,d) show the corresponding configurations at the Mo site. For adsorption at the O site, only interactions between hydrogen atoms and surface oxygen atoms were considered. The optimized structures (Figure 5) reveal that H₂O molecules at metal sites tend to adopt configurations with the molecular plane parallel to the surface, which contrasts with the perpendicular adsorption observed for CO₂. In the case of initial adsorption at the oxygen site, H₂O molecules eventually migrate toward adjacent metal atoms and stabilize there. This suggests that H₂O prefers to interact with metal sites on the surface, where hydrogen atoms oriented toward the surface are more likely to form stable hydrogen bonds with surface oxygen atoms.

Table 4. The adsorption energy, bond length, bond angle, and distance from the surface of the SFM adsorption H₂O configuration (d (Å)).

Adsorption Configuration	Fe-1	Fe-2	Mo-1	Mo-2	O
Eads (eV)	1.396	−0.816	−0.900	0.066	−0.211
bond length (Å)	0.987	0.984	0.976	0.977	0.978
bond angle (°)	104.425	103.107	105.622	105.776	105.334
d (Å)	1.970	1.985	2.344	2.347	2.345

summarizes the adsorption energy, bond lengths, bond angles, and surface distances of H₂O molecules at different adsorption sites. Since H₂O molecules tend to interact with nearby metal atoms regardless of the initial placement configuration, the bond lengths, bond angles, and surface distances across different configurations do not vary significantly. Notably, the Mo-1 site exhibits the highest adsorption energy, reaching −0.900 eV. These results indicate that H₂O adsorption can adopt multiple local configurations—ranging from chemisorption to physisorption—depending on whether the hydrogen atoms form hydrogen bonds with surface oxygen atoms, or even desorb under certain conditions.

To further investigate the electronic behavior of H₂O adsorption, charge density difference and Bader charge analyses were performed. Given the unique adsorption characteristics of H₂O, we focused on comparing the two most stable adsorption configurations at metal sites—Fe-2 and Mo-1. The isosurface value for the charge difference plots in Figure 6 was set to 0.002. It is evident from Figure 6 that there is significant charge accumulation between the surface metal atoms and the oxygen atom in the H₂O molecule, which is likely a key factor contributing to stable adsorption on the SFM surface. The Bader charge analysis in

Table 5. Bader charge.

Adsorption Configuration	Average Bader Net Atomic Charge (e)
	Sr	Fe	Mo	O-Slab	H	O-H2O
Fe-1	1.637	1.619	3.082	−1.205	−0.425	0.652
Mo-2	1.637	1.615	3.083	−1.205	−0.378	0.641

shows minimal differences in charge transfer at the metal sites between the two configurations, with only slight variations observed in the electron gain of the hydrogen atoms. Combined with the similar adsorption energies in both cases, these results indicate that H₂O molecules can stably adsorb with their molecular plane roughly parallel to the surface at both Fe and Mo sites on the SFM surface.

To quantify the electron redistribution, the net charge transfer to the entire H₂O molecule was evaluated (Figure S3b). For adsorption on a Mo site, the molecule undergoes a net electron loss of 0.11 e (O: +0.641 e; H: −0.400 e, −0.355 e), while the coordinated Mo atom becomes slightly oxidized (3.141 e), indicating electron donation from water to the surface.

Building on the results of individual CO₂ and H₂O adsorption, we investigated the co-adsorption behavior of CO₂ and H₂O on the SFM surface. Among several possible co-adsorption geometries, the configuration shown in Figure 7—H₂O adsorbed on the Mo site with CO₂ nearby—was found to be the most stable. As shown in Figure 7, the H₂O molecule remains adsorbed with its molecular plane roughly parallel to the Mo site, consistent with the single adsorption results. However, the CO₂ molecule, influenced by the presence of H₂O at the interface, adopts a configuration with its molecular axis roughly parallel to the surface. The corresponding charge density difference map in Figure 7b reveals that CO₂ adsorption significantly alters the surface electronic structure by inducing pronounced charge redistribution at metal sites, thereby affecting the overall co-adsorption process.

Furthermore, we calculated the co-adsorption energy and differential adsorption energies to evaluate the interaction between CO₂ and H₂O. As shown in Figure 8, the co-adsorption energy is −1.378 eV, indicating that the simultaneous adsorption of CO₂ and H₂O on the surface is energetically favorable, although the stabilization is less pronounced compared to single-molecule adsorption. Additionally, the charge density difference map (Figure 7) reveals substantial electron redistribution between the adsorbates, confirming the presence of intermolecular interactions. The differential adsorption energy analysis shows that when CO₂ adsorbs first, the subsequent H₂O adsorption is unfavorable, with a differential adsorption energy of +0.670 eV, indicating that pre-adsorbed CO₂ can hinder H₂O binding at the same site. In contrast, when H₂O is adsorbed first, the subsequent CO₂ adsorption remains favorable, with a differential adsorption energy of −0.477 eV. These results suggest that, during surface co-electrolysis processes on SFM, initial H₂O adsorption does not prevent CO₂ from binding, whereas pre-adsorbed CO₂ may block H₂O adsorption sites, potentially affecting subsequent surface reactions involving water.

To identify the electronic states responsible for CO₂ and H₂O adsorption, we analyzed the projected density of states (PDOS) for surface Fe-3d, Mo-3d, O-2p, as well as molecular C-2p, C-1s, and H-1s states (Figure 9 and Figures S5–S7). For CO₂ adsorbed at a surface O site, the C-2p states show modest overlap with surface O-2p states in the −8 to −6 eV range, with the peak near −7 eV also intersecting weakly with Fe-3d and Mo-3d states. This indicates σ-bond formation and partial π* back-donation from surface O to the CO₂ antibonding orbitals, consistent with moderate electron transfer to CO₂, as reflected in the differential charge analysis [33]. In the 4–5 eV region, C-2p again overlaps with O-2p, Fe-3d, and Mo-3d, with spin-down Fe-3d exhibiting slightly higher intensity, highlighting the role of Fe d-orbitals in mediating surface reactivity and stabilizing the activated CO₂ [34].

For H₂O adsorption at a Mo site, H-1s states overlap with O-2p states near −10 eV, confirming O–H bond formation. Fe-3d states near the Fermi level show similar features to CO₂ adsorption, while Mo-3d contributions are slightly diminished, indicating that Fe is more responsive to adsorbate interaction than Mo [35].

In the co-adsorption configuration, C-2p states around 3 eV overlap with Fe-3d, Mo-3d, and O-2p states. Spin-up C-2p shows the largest intensity, followed by O-2p and Mo-3d, whereas spin-down Fe-3d dominates relative to other orbitals, reflecting competition for Fe-centered states. These observations, together with differential charge, suggest that CO₂ and H₂O interact synergistically via surface O atoms, with Fe-3d orbitals being highly sensitive to adsorption environment and mediating electron redistribution, while Mo-3d states serve a stabilizing role [36].

In addition, bader analysis (Figure S3c and Table S1) shows ΔQ(CO₂) ≈ −0.001 e (C: +1.607 e; O: −0.774 e, −0.834 e), indicating no appreciable net charge transfer to CO₂ but pronounced intramolecular polarization (electron accumulation on O and depletion on C). Water gains a small amount of charge, ΔQ(H₂O) = −0.047 e (H: +0.303 e, +0.382 e; O: −0.732 e). The adjacent cations become more reduced relative to the single-adsorption cases, with Fe = 1.567 e and Mo = 2.325 e, consistent with enhanced Fe/Mo–O covalency rather than large net electron flow to the adsorbates.

The sign reversal of the Bader charge on the water O atom from +0.641 e (single adsorption on Mo) to −0.732 e (co-adsorption) can be rationalized by a change in adsorption geometry, electronic coupling mode, and local electrostatic environment. In the single-adsorption case, H₂O primarily binds via σ-donation from the O lone pair into Mo-3d states, which depletes electron density on O (positive Bader charge) and renders the H atoms slightly electron-rich. In the co-adsorbed configuration, the strongly polarized CO₂ (electron-rich O, electron-deficient C) and the resulting H···O(CO₂) hydrogen bonds reorient H₂O and increase the degree of metal–oxygen covalency. Consistently, the two H atoms become more positive (H: +0.303/+0.382 e) while the O atom accumulates electron density (O: −0.732 e). This is in line with the PDOS, which exhibits a modest increase in Mo-3d intensity near E_F in the co-adsorption state, suggestive of strengthened d–p hybridization between Mo-3d and O-2p orbitals.

The sign reversal of the Bader charge on the water O atom from +0.641 e (single adsorption on Mo) to −0.732 e (co-adsorption) can be rationalized by a change in adsorption geometry, electronic coupling mode, and local electrostatic environment. In the single-adsorption case, H₂O primarily binds via σ-donation from the O lone pair into Mo-3d states, which depletes electron density on O (positive Bader charge) and renders the H atoms slightly electron-rich. In the co-adsorbed configuration, the strongly polarized CO₂ (electron-rich O, electron-deficient C) and the resulting H···O(CO₂) hydrogen bonds reorient H₂O and increase the degree of metal–oxygen covalency. Consistently, the two H atoms become more positive (H: +0.303/+0.382 e) while the O atom accumulates electron density (O: −0.732 e). This is in line with the PDOS, which exhibits a modest increase in Mo-3d intensity near E_f in the co-adsorption state, suggestive of strengthened d–p hybridization between Mo-3d and O-2p orbitals.

Taken together with the PDOS results, these findings indicate that co-adsorption primarily polarizes CO₂ and H₂O and strengthens metal–oxygen bonding, which could lower the barriers for subsequent proton–electron-coupled steps, even in the absence of significant net charge transfer to CO₂. These electronic features have direct implications for electrochemical co-electrolysis mechanisms. For CO₂, electron accumulation on the O atoms and depletion at the C center indicate weakening of the C–O bonds, which is typically associated with the CO pathway. At the same time, polarization of the C atom suggests that proton attack could also stabilize a formate (HCOO⁻) intermediate, consistent with competing reduction routes reported in experiments. For H₂O, the hybridization between H-1s and O-2p orbitals and the observed charge accumulation around the O atom point to facilitated O–H bond cleavage, a critical step for providing protons and hydroxyl species during co-electrolysis. Together, these trends suggest that the Fe/Mo–O electronic states not only stabilize adsorption but also mediate the initial bond-breaking steps required for syngas evolution. Importantly, these microscopic insights align with experimental SOEC studies, which report that SFM-based cathodes exhibit relatively low polarization resistance and moderate activation energies [37,38]. Such macroscopic performance indicators are consistent with our finding that Fe/Mo–O hybridized states enhance the ease of CO₂ activation and H₂O dissociation. While our DFT calculations do not directly predict electrochemical resistances, the identified electronic interactions provide a mechanistic rationale for the favorable kinetics observed experimentally, highlighting the connection between atomic-scale electronic structure and operando catalytic behavior.

It should be emphasized, however, that the present study was performed on a defect-free SFM surface. In real SOEC environments, oxygen vacancies are prevalent and have been shown to significantly influence adsorption energetics and redox chemistry [23]. Therefore, the present results should be regarded as a theoretical benchmark, with future work extending to defective surfaces to better capture realistic catalytic conditions. Beyond the static adsorption configurations considered here, the interplay between CO₂ and H₂O is expected to be strongly dependent on surface coverage and operating environment. At moderate coverage, pre-adsorbed H₂O can stabilize CO₂ via hydrogen bonding and enhanced Fe/Mo–O covalency, leading to a synergistic effect that may lower activation barriers for proton–electron transfer. In contrast, excessive CO₂ coverage may inhibit H₂O adsorption by occupying adjacent oxygen sites, thereby reducing the availability of surface protons and suppressing co-electrolysis activity. Under operando conditions, elevated temperatures (700–900 °C) are likely to shift adsorption–desorption equilibria toward dynamic exchange, while applied cathodic bias can enhance charge transfer to CO₂, favoring its reduction pathway. These considerations suggest that the balance between synergy and inhibition is not fixed but instead depends sensitively on both surface coverage and reaction environment, providing guidance for interpreting experimental trends and designing more robust SOEC cathodes.

3. Computational Approach

All calculations were performed within the framework of density functional theory (DFT) using the projector-augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP 5.4.4) [39]. The exchange-correlation effects were described using the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) [40]. A plane-wave energy cutoff of 520 eV was employed. Brillouin zone sampling was carried out using the Monkhorst-Pack scheme, with a k-point grid of 2 × 2 × 1 for surface calculations and 4 × 4 × 3 for bulk calculations, ensuring adequate convergence. The electronic self-consistent field (SCF) convergence criterion was set to 10⁻⁶ eV. Structural optimizations were performed until the residual forces on all atoms were reduced to below 0.05 eV/Å. A vacuum layer of 15 Å was applied along the surface normal to eliminate spurious interactions between periodic images. To account for long-range dispersion interactions, the Grimme DFT-D2 method [41] was employed in all calculations. Since GGA-based DFT tends to underestimate band gaps due to self-interaction errors, on-site Coulomb interactions were incorporated using the Hubbard U approach. Specifically, U values of 4.0 eV and 3.3 eV were applied to the Fe 3d and Mo 3d orbitals, respectively. These values are widely used in previous studies and related Fe/Mo-based perovskites, and have been shown to reproduce structural, electronic, and catalytic properties with good accuracy [42,43,44]. Additionally, spin polarization was considered in all calculations.

In terms of adsorption energy, the formula is as follows:

$$E_{\mathit{ads}} ={ E}_{\mathit{gas} + \mathit{surface}} -{ E}_{\mathit{gas}} -{ E}_{\mathit{surface}}$$

(1)

where $E_{\mathit{gas} + \mathit{surface}}$ and $E_{\mathit{gas}}$ are the calculated energies of the model after adsorption of the gas on the surface and the free gas molecule, respectively. $E_{\mathit{surface}}$ is the total energy of the relaxed clean surface.

The differential adsorption energy was calculated to assess the effect of pre-adsorbed molecule 1 on the adsorption of molecule 2:

$$E_{\mathit{ads},mol2/mol1} = E_{\mathit{surface} + mol1 + mol2} -{ E}_{\mathit{surface} + mol1} -{ E}_{mol2}$$

(2)

A decrease in the adsorption energy compared to the isolated adsorption case suggests that molecule 1 promotes the adsorption of molecule 2, likely through induced dipole interactions or charge transfer. Conversely, a reduced adsorption affinity may indicate a competitive adsorption mechanism, where molecule 1 modifies the local electronic structure of the surface, making it less favorable for molecule 2 adsorption.

The formula for calculating co-adsorption energy is as follows:

$$E_{co\text{-}ads} ={ E}_{\mathit{surface} + mol1 + mol2} -{ E}_{\mathit{surface}} - E_{mol1} - E_{mol2}$$

(3)

Charge Density Difference refers to the change in the density of electrons in a certain state (e.g., molecule formation, adsorption process) relative to the initial state (e.g., isolated atoms). The formula is usually expressed as:

$$∆\rho ={ \rho }_{\mathit{Total}} - {({\rho }_{\mathit{surface}} + \rho }_{\mathit{mol}})$$

(4)

where ${\rho }_{\mathit{Total}}$ is the electron density of the combined adsorbate-surface system, ${\rho }_{\mathit{surface}}$ and ${\rho }_{\mathit{mol}}$ are the electron densities of the isolated surface and molecule, respectively. Both isolated densities are computed with the atomic positions fixed to those in the combined system to accurately capture charge rearrangement due to adsorption.

For symmetric slabs the surface free energy γ was evaluated as:

$$\gamma = {\displaystyle \frac{E_{\mathit{slab} } -{ N}_{\mathit{fu}}{E}_{\mathit{bulk}} - ∆N_O{\mu }_O}{2A}}$$

(5)

where $E_{\mathit{slab}}$ is the total energy of the slab, $E_{\mathit{bulk}}$ is the energy per bulk formula unit, $N_{\mathit{fu}}$ is the number of formula units in the slab, $∆N_O$ is the oxygen excess/deficit relative to bulk stoichiometry, and A is the surface area of one side. For our slab constructions $∆N_O$ = 0 (each slab contains 72 O atoms while the bulk formula unit contains 12 O atoms, hence $N_{\mathit{fu}}$ = 6), so $∆N_O$= 0 and $\gamma$ reduces to ($E_{\mathit{slab}} -{ N}_{\mathit{fu}}{E}_{\mathit{bulk}}$)/(2A). Using $E_{\mathit{bulk}}$= −138.572 eV and A = 184.265 Ų.

To quantitatively assign the redistributed charge to individual atoms, we employed Bader charge population analysis, which partitions the electron density using real-space zero-flux surfaces in ∇ρ. Such a topology-based scheme is particularly suitable for plane-wave DFT calculations, as it avoids the basis-set dependence inherent in Mulliken- or Löwdin-type population analyses that are commonly used in localized (Gaussian) basis sets. All Bader charge values reported in this work are expressed in units of the elementary charge |e|.

4. Conclusions

In summary, we conducted a comprehensive DFT investigation on the adsorption behavior of CO₂ and H₂O molecules on the FeMoO-terminated (001) surface of Sr₂FeMoO₆ (SFM) perovskite. The results show that CO₂ strongly interacts with surface oxygen sites with a binding energy of −2.047 eV, leading to notable molecular activation and substantial charge transfer, while H₂O displays weaker adsorption (−0.900 eV) and preferentially binds to Mo sites. Charge density difference and Bader charge analyses confirm the distinct electronic responses of the surface upon adsorption, revealing covalent bonding features in CO₂ adsorption and more electrostatic characteristics in H₂O interaction. Co-adsorption studies indicate that the presence of H₂O modifies the adsorption geometry of CO₂ and enhances the co-adsorption energy of CO₂ and H₂O on the surface, suggesting a synergistic effect that may facilitate surface proton–electron coupling processes. However, pre-adsorbed CO₂ weakens the adsorption of H₂O, and due to competitive site occupation, excessive CO₂ coverage could inhibit the activation of H₂O. Density of states analysis suggests that the Fe/Mo–O hybridized states near the Fermi level play a crucial role in mediating surface reactivity. It should be noted that all results were obtained on a perfect, defect-free SFM surface, which, while idealized compared to real materials containing vacancies or mixed-valence cations, serves as a theoretical benchmark for understanding fundamental molecule–surface and molecule–molecule interactions. Overall, these findings contribute to a molecular-level understanding of the surface interaction mechanisms of perovskite materials under conditions relevant to CO₂ + H₂O co-electrolysis and offer theoretical guidance for the rational design of high-performance double perovskite electrocatalysts.