Insights into Pd-Nb@In₂Se₃ Electrocatalyst for High-Performance and Selective CO₂ Reduction Reaction from DFT

Abstract

The electrochemical CO₂ reduction reaction (eCO₂RR), driven by renewable energy, represents a promising strategy for mitigating atmospheric CO₂ levels while generating valuable fuels and chemicals. Its practical implementation hinges on the development of highly efficient electrocatalysts. In this study, a novel dual-metal atomic catalyst (DAC), composed of niobium and palladium single atoms anchored on a ferroelectric α-In₂Se₃ monolayer (Nb-Pd@In₂Se₃), is proposed based on density functional theory (DFT) calculations. The investigation encompassed analyses of structural and electronic characteristics, CO₂ adsorption configurations, transition-state energetics, and Gibbs free energy changes during the eCO₂RR process, elucidating a synergistic catalytic mechanism. The Nb-Pd@In₂Se₃ DAC system demonstrates enhanced CO₂ activation compared to single-atom counterparts, which is attributed to the complementary roles of Nb and Pd sites. Specifically, Nb atoms primarily drive carbon reduction, while neighboring Pd atoms facilitate oxygen species removal through proton-coupled electron transfer. This dual-site interaction lowers the overall reaction barrier, promoting efficient CO₂ conversion. Notably, the polarization switching of the In₂Se₃ substrate dynamically modulates energy barriers and reaction pathways, thereby influencing product selectivity. Our work provides theoretical guidance for designing ferroelectric-supported DACs for the eCO₂RR.

1. Introduction

Carbon dioxide (CO₂), a principal climate-altering gas, drives critical environmental challenges including rising global temperatures, climatic instability, ocean acidification, and ecological carbon cycle disturbances [1,2]. Urgent action is required to achieve net-zero anthropogenic carbon dioxide equivalent emissions by 2050, as mandated by the Intergovernmental Panel on Climate Change (IPCC) to cap global temperature increases at 1.5 °C above preindustrial baselines [3]. This imperative is becoming increasingly critical given the persistent reliance on emission-generating technologies and escalating global energy demands. Addressing the dual challenge of atmospheric CO₂ mitigation and sustainable utilization has emerged as a pivotal research frontier [4,5,6,7]. Carbon management encompasses three interconnected approaches to mitigating anthropogenic CO₂ emissions. First, energy generation processes are being optimized through advanced combustion technologies, such as oxy-fuel combustion with pure oxygen injection and homogeneous charge compression ignition (HCCI) engines using biofuel blends [8,9]. Second, modern carbon capture technologies are advancing beyond conventional geological storage in saline aquifers or depleted oil fields by transforming captured CO₂ into value-added products like construction aggregates, agricultural bio-fertilizers, and energy-efficient syngas, leveraging advanced separation processes such as pressure swing adsorption (PSA) and membrane systems [10,11]. Third, the chemical conversion pathways, particularly electrocatalytic CO₂ reduction reaction (eCO₂RR), utilize multi-electron transfer processes (2e⁻ to 12e⁻) with tailored catalysts (e.g., Cu for hydrocarbons, Ag/Zn for CO) to produce value-added fuels and chemicals like CO, formate, methane, ethylene, and ethanol, while enabling renewable energy integration and high-pressure reactor designs for industrial scalability [12,13].

Among the above approaches, the eCO₂RR stands out for its dual capacity to mitigate emissions and generate valuable chemical feedstocks [14,15,16]. And this technology has four key advantages. First, the eCO₂RR leverages renewable electricity from solar, wind, or tidal energy to convert CO₂ into chemicals, enabling carbon-neutral cycles while reducing reliance on fossil fuels [17]. Second, the process generates high-value chemicals like ethylene (feedstock for plastics) [18], methane (fuel) [19], and formate (industrial reagent) [20], directly replacing fossil-derived equivalents in existing supply chains. Third, unlike thermocatalytic methods requiring high temperatures/pressures, the eCO₂RR operates efficiently at room temperature and atmospheric pressure, reducing energy demands and infrastructure complexity. Forth, modular flow cell designs and membrane electrode assemblies (MEAs) allow scalable deployment for industrial adoption [21].

The eCO₂RR process involves intricate multi-stage reaction sequences: (1) CO₂ adsorption at electrode interfaces; (2) proton=coupled electron transfer (PCET) steps, which forms C–H bonds with broken C=O bonds; and (3) detachment of synthesized compounds from active sites through desorption mechanisms and their subsequent transport into the bulk reaction medium via dissolution–diffusion pathways [22]. This sequential process becomes particularly consequential in water-containing systems where the parasitic hydrogen evolution reaction (HER) actively competes with the CO₂RR for catalytic resources and electron transfer, fundamentally altering the thermodynamic landscape and resulting in suboptimal product distributions [23].

In the process of reducing CO₂ with metal electrodes, there are many challenges, including the impact of the poor stability of the electrodes. Many metal electrodes, such as palladium (Pd), indium (In), and tin (Sn), have stability issues when reducing CO₂. Take Pd as an example; CO has strong adsorption energy on its surface, which causes the electrode to be easily poisoned and deactivated, greatly shortening its service life [24]. Although In and Sn electrodes can achieve the reduction of CO₂, they often require a higher voltage to drive the reaction [25,26,27], which not only causes a large waste of energy but may also trigger side reactions due to high voltage, further reducing the selectivity and efficiency of the reaction. At the same time, the stability of the electrode deteriorates further under high voltage, accelerating the electrode’s wear and tear. These problems seriously restrict the practical application of metal electrodes in the field of CO₂ reduction [26]. Effective eCO₂RR implementation hinges on catalytic systems being optimized across three critical dimensions, namely conversion efficiency under applied potentials, target product selectivity over competing reactions, and long-term structural and functional stability. These properties are intrinsically linked to atomic-scale catalyst architecture, particularly the coordination environment of active sites.

Since the conceptualization of single-atom catalysts (SACs) in 2011, these atomically dispersed metal systems have revolutionized catalytic research through maximum metal utilization efficiency (approaching 100%) [28,29,30,31,32,33], well-defined active site geometries for mechanistic studies [34,35,36], and enhanced selectivity profiles compared to nanoparticle analogues. However, SAC implementation faces two fundamental constraints: low active site density due to synthesis limitations and inadequate multi-intermediate stabilization in complex eCO₂RR pathways [37,38]. This has prompted researchers to turn their attention to bimetallic atomic catalyst (DAC) systems with greater structural flexibility.

DACs exhibit distinct advantages over isolated SACs, combining the inherent merits of SACs with supplementary synergistic benefits: (1) DACs substantially elevate metal loading capacities while expanding the population of accessible reactive centers, a critical factor for scalable catalytic applications [39]; (2) DACs permit dynamic spatial arrangements of active sites, enabling coordinated interactions essential for multi-step CO₂ reduction pathways [40,41]; (3) electronic modulation between dissimilar metal atoms allows precise regulation of intermediate binding strengths, creating tunable platforms for reaction pathway optimization and selectivity control [40,42,43,44,45,46,47]; (4) independent yet coexisting metallic centers enable parallel reaction channels, permitting simultaneous production of distinct value-added compounds through site-specific catalytic processes [48]; (5) and in DACs, one metallic component can modify support interactions that subsequently influence the catalytic behavior of adjacent metal sites, creating cascading activation mechanisms [30,49,50]. It is anticipated that further studies will concentrate on enhancing the performance of bimetallic atomic site catalysts.

Contemporary DACs predominantly utilize two-dimensional nitrogen-doped carbon substrates, as exemplified by Fe-Co [51], Ni-Fe [52], and Co-Pt [53] dual-atom configurations, which have been fabricated with dual-solvent, pyrolysis, and cyclic voltammetry methods, respectively. However, these conventional DACs exhibit inherent limitations in post-synthesis catalytic tunability due to their inability to leverage substrate property modifications for performance enhancement. Recent advancements in ferroelectric material engineering provide a promising solution. Substantial theoretical and experimental evidence demonstrates that polarization direction modulation in ferroelectrics not only governs molecular adsorption/desorption dynamics but also enables precise control over surface catalytic activity and product selectivity [54,55,56]. Capitalizing on this principle, we engineered a novel ferroelectric DAC system by anchoring niobium (Nb) and palladium (Pd) single atoms onto an α-In₂Se₃ monolayer substrate (Nb-Pd@In₂Se₃). The α-In₂Se₃ monolayer is a van der Waals material exhibiting coupled in-plane and out-of-plane ferroelectric polarization at room temperature [56,57,58]. It features a quintuple atomic-layer structure (Se-In-Se-In-Se) with spontaneous polarization arising from asymmetric Se atom displacements, enabling bidirectional electric field control of both polarization axes. This unique architecture allows for the dynamic regulation of metal–support interactions, addressing the static catalytic behavior inherent to traditional carbon-based DACs. The theoretical analysis revealed that the dual-metal atomic configuration significantly enhances CO₂ activation capability during the eCO₂RR process. In the synergistic catalytic mechanism, the Nb atomic sites predominantly function as catalytic centers for carbon reduction, while the adjacent Pd counterparts facilitate oxygen species removal through a complementary catalytic pathway. Notably, polarization switching of the ferroelectric substrate modulates both the energy barriers along the reaction coordinates and the dominant reaction pathways, ultimately dictating the selectivity of terminal products.

2. Results and Discussion

2.1. Geometric Structures of Nb-Pd@In₂Se₃

The 2D ferroelectric α-phase In₂Se₃ monolayer was chosen as the substrate material. Based on our previous work [56], we selected Pd and Nb transition metals as candidates for loaded metallic dual atoms, since they can stably form Pd@In₂Se₃ and Nb@In₂Se₃ SACs. According to the position of the intermediate Se layer offset (see Figure 1a,b), the α-In₂Se₃ monolayer has two stable polarization phases, namely polarization upward (P↑) and downward (P↓). We refer to the configuration where the Pd-Nb dual-atom pair is doped on the outer surface of two layers with a Se spacing of 3.06 Å as the Pd-Nb@P↓-In₂Se₃. Moreover, the configuration where the Pd-Nb dual-atom pair is doped on the outer surface of two layers of Se with a spacing of 3.84 Å is called Pd-Nb@P↑-In₂Se₃. As for the SACs [59,60,61], strong binding strength is essential for the stability of DACs. At the energetically most favorable site, the binding energy of the Nb-Pd dual-atom pair in Pd-Nb@P↓-In₂Se₃ and Pd-Nb@P↑-In₂Se₃ were −15.69 and −12.27 eV/unit, respectively. The low binding energies indicate that there is a strong interaction between the metal atoms and the substrate, as evidenced by the strong covalent Pd–Se and Nb-Se bonds (see Figure 1a,b), which are caused by the strong hybridization of Se p and Pd/Nb d orbitals near the Fermi level (see Figure S1a,b).

To further demonstrate the structural stability of Pd-Nb@In₂Se₃, ab initio molecular dynamics (AIMD) calculations were carried out on these two configuration at a temperature of 1000 K, with a time step of 1 fs and a total time length of 10 ps (see Figure 2a,b). During the AIMD simulations, the geometrical structure did not change significantly, and the total energy of the system tended to be stable, indicating that these configurations have good thermal stability. Overall, both the binding energy and molecular dynamics simulation results show the promising feasibility of fabricating Pd-Nb@In₂Se₃ DACs.

2.2. Activation of CO₂ on Pd-Nb@In₂Se₃ DACs

The effective activation of CO₂ molecules is a key step for the subsequent reduction reaction. The linear structure of CO₂ molecules contributes to their pronounced chemical inertness, primarily due to the symmetry-induced cancellation of dipole moments despite the presence of polar C=O bonds. This linear geometry stabilizes the molecule thermodynamically, as the two C=O bonds exhibit dissociation energies of approximately 750 kJ·mol⁻¹. Additionally, the large energy gap (13.7 eV) between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) creates a significant kinetic barrier to electron transfer, necessitating substantial energy input for chemical transformations. In catalytic systems employing isolated atomic site catalysts (SACs), CO₂ adsorption typically occurs via either oxygen– or carbon–metal (O-M or C-M) interactions at the active metal centers. However, the limited electron donating capacity and geometric constraints of isolated atomic sites restrict the extent of CO₂ activation. Consequently, SACs often require elevated temperatures and pressures to achieve moderate reaction rates, further reducing reaction efficiency and selectivity toward multi-carbon products.

Dual-site catalysts can demonstrate enhanced CO₂ adsorption via coordination involving both metallic dual atoms and support atoms, requiring lower activation energy than the SAC to activate CO₂ [62]. As shown in Table S1, by separately comparing the adsorption energy of CO₂ on the Pd and Nb sites of Pd-Nb@In₂Se₃ DACs (see Figure S2), we conclude that the adsorption of CO₂ on the Pd site had more negative adsorption energy in both P↑ and P↓ configurations, which means the CO₂ tends to adsorb on the Pd site of Pd-Nb@In₂Se₃ DACs. The ∠OCO values of CO₂ adsorbed on Pd-Nb@P↓-In₂Se₃ and Pd-Nb@P↑-In₂Se₃ were significantly reduced to 131.38° and 125.18° from an initial value of 180°, respectively. Based on the structural analysis, it could be stated that the Pd-Nb@In₂Se₃ catalyst could effectively activate CO₂ molecules. Moreover, according to our previous report [56] that the ∠OCO values of CO₂ adsorbed on Pd@P↓-In₂Se₃ and Pd@P↑-In₂Se₃ were 149.2° and 151.2°, respectively, it can be concluded that the synergistic effect of a bimetallic atomic site causes a more obvious deformation of adsorbed CO₂ molecules (17.82° and 26.02° for P↓ and P↑, respectively), indicating a higher activation of CO₂. The similar synergistic effects in the Pt-Ni@CeO₂ bimetallic system were extensively validated through comprehensive characterization and computational studies [62]. Temperature-programmed reduction (TPR) and desorption (TPD) analyses revealed that Pt-Ni synergy significantly enhances the generation of reactive oxygen intermediates (e.g., surface peroxides and hydroxyl radicals) and strengthens metal–support interactions via charge transfer mechanisms. These modifications collectively optimize CO₂ chemisorption capacity, as evidenced by the higher adsorption efficiency compared to the monometallic counterparts (Pt@CeO₂ and Ni@CeO₂). Density functional theory (DFT) simulations further demonstrated a 35–40% reduction in CO₂ activation energy (E_a = 10.1 kcal mol⁻¹ for Pt-Ni@CeO₂ vs. 32.9 and 36.5 kcal mol⁻¹ for Ni@CeO₂ and Pt@CeO₂, respectively), which is attributed to electronic structure modulation at Pt-Ni-CeO₂ interfacial sites.

In order to explore the activation mechanism, we employed a charge density difference calculation, which demonstrated that there is both a loss and gain of electrons on the adsorbed CO₂ molecule and the bimetallic atomic sites (see Figure 3a,b). This is because the empty Pd/Nb d orbital can accept electrons from the highest occupied molecular orbitals (1π_g orbital) of the CO₂ molecule, while the occupied Pd/Nb d orbital can back-donate electrons to the lowest unoccupied molecular orbitals (2π_u orbital) of the CO₂ molecule (see Figure 3c). The synergy of electron donation and backdonation-dependent d orbital occupation ensures that CO₂ can be efficiently activated [56].

As mentioned before, the CO₂ adsorbed on Pd-Nb@P↑-In₂Se₃ (∠OCO = 125.18°) had a more obvious deformation than that absorbed on Pd-Nb@P↓-In₂Se₃ (∠OCO = 131.38°), which means Pd-Nb@P↑-In₂Se₃ has higher CO₂ activation. In order to investigate the reason for this, we calculated the Pd and Nb d orbitals in Pd-Nb@P↑-In₂Se₃ and Pd-Nb@P↓-In₂Se₃ DACs, respectively. Then, based on the partial electronic orbitals (see Figure 4a), we obtained the d band center of the Pd and Nb atoms for both kinds of Pd-Nb@In₂Se₃ DACs. As displayed in Figure 4b, both d band centers of the Pd (−2.09 eV) and Nb (0.11 eV) atoms in Pd-Nb@P↑-In₂Se₃ were closer to the Fermi level than the ones of Pd (−2.68 eV) and Nb (0.44 eV) atoms in Pd-Nb@P↓-In₂Se₃. And it has been reported that the exceptional electrocatalytic performance of Co₂ anchored graphdiyne in nitrogen fixation originates from the presence of localized electronic states adjacent to the Fermi level, which optimize charge transfer dynamics during the reaction [63]. Therefore, in the case of P↑, the proximity of the d band center of Pd and Nb atoms to the Fermi level induces a high CO₂ activation performance. Note that the different d band centers of bimetallic atomic sites in Pd-Nb@In₂Se₃ under different polarization states implies that both the reaction path and the limiting potential of the subsequent CO₂ hydrogenation process may be affected by the polarization switch.

2.3. eCO₂RR on Pd-Nb@In₂Se₃ DACs

Considering the complexity of the CO₂ reaction (see Figure S3), we have summarized the minimum-energy reaction paths of the CO₂RR over Pd-Nb@In₂Se₃ catalysts (see Figure 5). The CO₂RR pathways over Pd-Nb@In₂Se₃ catalysts exhibit stark polarization-dependent selectivity, governed by the structural and electronic asymmetry induced by the ferroelectric In₂Se₃ substrate’s polarization orientation (P↓ and P↑). The CO₂ reduction reaction begins with the adsorption of CO₂ onto the Pd-Nb@P↓-In₂Se₃ catalyst surface, forming a CO₂ intermediate (CO₂ + * → CO₂*). This adsorbed CO₂ undergoes a proton-coupled electron transfer (PCET) step, where one hydrogen atom binds to an O atom (CO₂* + H⁺ + e⁻ → OCHO*), leading to the formation of an OCHO intermediate (bent configuration with O–CH–O bonding). Subsequently, a second protonation occurs at the adjacent oxygen atom (OCHO* + H⁺ + e⁻ → HOCHO*), stabilizing the HOCHO intermediate (adsorbed formate-like structure). Finally, the HOCHO intermediate desorbs from the catalyst surface (HOCHO* → HOCHO + *), releasing formic acid (HOCHO) as the end product. Due to the high energy barrier associated with stabilizing the second protonation step, the rate-determining step (PDS) is identified as the transformation of OCHO* → HOCHO*, requiring an applied potential of −0.45 V vs. RHE. In contrast, in the CO₂RR on a Pd-Nb@P↑-In₂Se₃ catalyst, the reaction course is significantly different from that on Pd-Nb@P↓-In₂Se₃, which undergoes an alternative protonation pathway. The first PCET step preferentially protonates the carbon atom, forming the OCOH intermediate (CO₂* + H⁺ + e⁻ → OCOH*) (linear configuration with O–C–O–H bonding). Further reduction cleaves the C–O bond. A second protonation occurs at the hydroxyl group of OCOH intermediate. The hydroxyl group binds a hydrogen ion to generate H₂O and desorb (OCOH* + H⁺ + e⁻ → CO* + H₂O), producing a CO intermediate adsorbed on the Pd site of the catalyst. Sequential hydrogenation steps follow: CO* + H⁺ + e⁻ → CHO* (formyl), CHO* + H⁺ + e⁻ → CH₂O* (formaldehyde-like) and CH₂O* + H⁺ + e⁻ → CH_2* + OH* via C–O bond scission. The critical C–O bond scission step (CH₂O* + H⁺ + e⁻ → CH₂* + OH*) in the methane production pathway over the Pd-Nb@P↓-In₂Se₃ catalyst is driven by the synergistic interplay between the Pd and Nb dual active sites. The CH₂ intermediate absorbs the Pd site, and the OH intermediate absorbs the Nb site. CH₂* undergoes progressive hydrogenation (CH₂* + OH* + H⁺ + e⁻ → CH₃* + OH*), followed by a critical step where CH₃ reacts with a co-adsorbed OH group to form CH₃ and H₂O (CH₃* + OH* + H⁺ + e⁻ → CH₃* + H₂O*). Then, the H₂O molecule desorbs from the Nb site (CH₃* + H₂O* → CH₃* + H₂O). This step is identified as the PDS, with a limiting potential of −0.66 V vs. RHE, reflecting the substantial energy required for H₂O dissociation. The final hydrogenation of CH₃ yields methane (CH₄) (CH₃* + H⁺ + e⁻ → CH₄*), which desorbs from the catalyst surface (CH₄* → CH₄ + *). Consequently, the U_l, catalytic pathway, and the ultimate products during the eCO₂RR, are governed by polarization orientation and are adjustable via ferroelectric switching. Moreover, compared to the U_l of Pd@In₂Se₃ SACs for the eCO₂RR (−0.77 V under the P↓ state and −0.87 V under the P↑ state) [56], each corresponding Pd-Nb@In₂Se₃ DAC for the eCO₂RR has a smaller U_l, indicating that the synergistic effect of the bimetallic atomic site could effectively lower the eCO₂RR barrier. According to the reduction reaction path of CH₂O* → CH₂* + OH* → CH₃* + OH* → CH₃*, we found that carbon-containing intermediates (e.g., CH*, CH₂*) tend to undergo hydrogenation reduction at Pd atomic sites, while oxygen-containing intermediates (e.g., OH*) prefer to be hydrogenated and reduced into water at Nb atomic sites (see Figure S4). Therefore, the synergistic effect of Nb-Pd dual-site metal atoms can be described as such: Pd sites act as functional sites for carbon reduction, whereas Nb sites serve as functional sites for oxygen removal. Notably, the U_l of Pd@In₂Se₃ SACs for the eCO₂RR (−0.45 V under the P↓ state and −0.66 V under the P↑ state) are markedly superior to those of conventional eCO₂RR catalysts, such as Cu (211) (−0.8 V) [64], Co@Cu (−0.87 V) [65], and WC (0001) (−1.0 V) [66]. Since the equilibrium potential (E°) for the formation of HCOOH and CH₄ from CO₂, respectively, are −0.25 V vs. RHE and 0.17 V vs. RHE at pH = 0 [67], the corresponding overpotentials are −0.2 V vs. RHE and −0.83 V vs. RHE, which are lower than the ones of many eCO₂RR electrocatalysts synthesized experimentally, such as Pd₂ (−0.85 V vs. RHE for generating CO) [68], NiCu-NC (−1.07 V vs. RHE for generating CO) [69], FeNi-NSC (−1.0 V vs. RHE for generating CO) [70], Cu/Ni-NC (−0.9 V vs. RHE for generating CO) [71], and Cu-N₂ (−0.84 V vs. RHE for generating CH₄) [72]. Therefore, the Pd-Nb@In₂Se₃ DAC is a promising candidate for a tunable and efficient eCO₂RR, particularly in achieving high selectivity for final products through controlled polarization modulation.

2.4. Selectivity for HER vs. eCO₂RR on Pd-Nb@In₂Se₃ DACs

The HER is a prevalent parasitic process in electrochemical systems. It poses a significant challenge to the Faradaic efficiency of the eCO₂RR by diverting critical proton and electron resources from the electrolyte. This competition arises through the HER’s multi-step mechanisms—Volmer adsorption, Heyrovsky/Tafel recombination, and H₂ desorption—which operate synergistically to deplete reactive intermediates (H*) and impose additional energy barriers for CO₂ reduction pathways. Particularly in acidic media, the HER’s thermodynamic favorability and low activation overpotential exacerbate its dominance over the eCO₂RR, resulting in difficulty in achieving an efficiency of the eCO₂RR that meets the needs of industrial production [73,74]. To check if the eCO₂RR is more favorable, we calculated the Gibbs free energy changes (ΔG) at the first hydrogenation step of the eCO₂RR (* + CO₂ → CO₂*) and the HER (* + H⁺ + e⁻ → H*). As displayed in Figure 6, on the Pd-Nb@P↓-In₂Se₃ DAC, the ΔG for the formation of H* is 0.61 eV, while that of CO₂* is −0.22 eV. As for the case of the Pd-Nb@P↑-In₂Se₃ DAC, the ΔG for the formation of H* is −0.11 eV, while that of CO₂* is −1.04 eV. According to the Brønsted–Evans–Polanyi relation, reactions with lower ΔG have smaller reaction barriers and consequently are kinetically more favorable. The Gibbs free energy changes indicate that the Pd-Nb@In₂Se₃ DACs have a higher selectivity toward the CO₂RR, instead of the HER. These results demonstrate the feasibility of using Pd-Nb@In₂Se₃ catalysts as cathodes for the eCO₂RR with a high Faradaic efficiency.

3. Methods

All density functional theory (DFT) calculations were performed using the Vienna Ab Initio Simulation Package (VASP) (Hanger team, University of Vienna, version 5.3) [75,76]. The calculations were based on the electron exchange correlation of the PBE generalized function calculation under the generalized gradient approximation (GGA) [77,78,79]. The van der Waals (vdW) interactions were described by applying Grimme’s DFT-D3 method [80], with the colinear spin turned off, the truncation energy set to 500 eV, and the convergence thresholds for force and total energy set to 10⁻² eV/Å and 10⁻⁵ eV. The catalytic system was constructed by distributing one Pd atom and one Nb atom on adjacent hexagonal hollow sites of an 4 × 4 α-In₂Se₃ supercell. For the sampling of the dimensional Brillouin zone, 1 × 1 × 1 gamma-centered Monkhorst-pack k-mesh was chosen for performing structural relaxation and frequency calculations. To minimize periodic image interactions, a vacuum layer exceeding 20 Å was introduced along the non-periodic direction. For Gibbs free energy calculations of the eCO₂RR, solvent effects were accounted for by using the implicit water model in VASPsol (version 5.3) [55,81]. Charge transfer analysis was performed using the Bader charge partitioning method.

The binding energy for the Nb-Pd dual-atom pair (E_b-(Nb-Pd)) added onto the substrate was calculated using the following equation [63,82]:

$$E_{\mathrm{b}\text{-}\left(\mathrm{N}\mathrm{b}\text{-}\mathrm{P}\mathrm{d}\right)}=E_{\mathrm{t}\mathrm{o}\mathrm{t}}-E_{\mathrm{s}\mathrm{u}\mathrm{b}}-E_{\mathrm{N}\mathrm{b}}-E_{\mathrm{P}\mathrm{d}}$$

(1)

where $E_{\mathrm{s}\mathrm{u}\mathrm{b}}$ and $E_{\mathrm{t}\mathrm{o}\mathrm{t}}$ are the total energies of the substrate without and with the added Nb-Pd dual-atom pair, respectively. $E_{\mathrm{N}\mathrm{b}}$ and $E_{\mathrm{P}\mathrm{d}}$ are the total energy of the isolated Nb and Pd atoms.

The charge density difference ($∆\rho$) for the CO₂ molecule adsorbed on Pd-Nb@P↓-In₂Se₃ and Pd-Nb@P↑-In₂Se₃ was calculated using the following equation:

$$∆\rho ={\rho }_{{CO}_2\text{-}Pd\text{-}Nb\text{-}sub}-{\rho }_{{CO}_2}-{\rho }_{Pd\text{-}Nb\text{-}sub}$$

(2)

where ${\rho }_{{CO}_2\text{-}Pd\text{-}Nb\text{-}sub}$ and ${\rho }_{Pd\text{-}Nb\text{-}sub}$ are the charge density of Pd-Nb@In₂Se₃ with and without CO₂ molecules, respectively. ${\rho }_{{CO}_2}$ is the charge density of the CO₂ molecule.

In order to obtain the individual orbital components, we employed a code named “splitdos.dos” to process the output file of density of states (DOS). The average d band (d band center) shifts were calculated for the surface metal atoms for both the total d partial DOS and the orbital-resolved d partial DOS. The d band center (${\epsilon }_d$) was calculated as [83]

$${\epsilon }_d={\displaystyle \frac{\int n_d\left(\epsilon \right)\epsilon ds}{\int n_d\left(\epsilon \right)d\epsilon }}$$

(3)

where $\epsilon$ is the electronic energy of states, and $n_d$($\epsilon$) is the electronic density of states.

4. Conclusions

Our study presents a theoretical investigation of a novel Pd-Nb@In₂Se₃ DAC for the eCO₂RR, leveraging DFT calculations to elucidate its structural, electronic, and catalytic properties. The Pd-Nb@In₂Se₃ system, anchored on a ferroelectric α-In₂Se₃ monolayer, combines Nb and Pd single atoms to exploit synergistic interactions, while the substrate’s switchable polarization enables dynamic control over catalytic activity and selectivity. Structural analyses confirm the stability of Pd-Nb@In₂Se₃, with binding energies of −15.69 eV/unit (P↓ polarization) and −12.27 eV/unit (P↑ polarization) and ab initio molecular dynamics simulations demonstrating thermal stability at 1000 K. The CO₂ adsorption studies revealed enhanced activation on Pd sites, where the linear CO₂ molecule bends significantly, which is attributed to electron donation/backdonation between CO₂ π orbitals and the Pd/Nb d orbitals. The d band centers of Pd and Nb atoms, which are closer to the Fermi level in the P↑ configuration, correlate with stronger CO₂ activation, emphasizing the role of electronic structure in catalytic performance. Reaction pathway analyses showed polarization-dependent product selectivity. The P↓ polarization favors formic acid production via a U_l of −0.45 V vs. RHE, while the P↑ polarization directs the reaction toward methane with a U_l of −0.66 V vs. RHE. The dual-site mechanism involves Pd atoms driving carbon reduction and Nb atoms facilitating oxygen removal, synergistically lowering energy barriers compared to their SAC counterparts. Additionally, Gibbs free energy calculations indicate superior selectivity for the CO₂RR over the HER, with CO₂ adsorption energies significantly more favorable than H* formation. The ferroelectric substrate’s polarization switching dynamically modulates metal–support interactions, adjusting d orbital occupancy and intermediate binding strengths, thereby controlling reaction pathways and product outcomes. This work not only advances the understanding of dual-metal catalysis and polarization–catalysis coupling but also provides a strategy to design tunable electrocatalysts for sustainable energy conversion and CO₂ utilization.