Controllable Photocatalytic-to-Electrocatalytic Conversion in Pd-C₃N₄@In₂Se₃ Heterostructures Through Polarization Engineering for Hydrogen Evolution Reaction

Abstract

Facing the dual challenges of energy shortage and environmental degradation, photocatalysis and electrocatalysis have emerged as key technologies for converting small molecules into value-added chemicals, yet their conflicting requirements on the electronic structure of catalysts prevent a single material from freely switching between the two modes. Here, we demonstrate a feasible strategy for achieving on-demand switching between these catalytic functions in a single ferroelectric heterojunction, Pd-C₃N₄@In₂Se₃, through polarization engineering. Using first-principles density functional theory calculations, we show that reversing the polarization direction of the α-In2Se3 layer induces a nonvolatile electronic phase transition. The downward polarization (P↓) configuration exhibits metallic behavior, whereas the upward polarization (P↑) state becomes semiconducting with a type-II band alignment. This transition arises from polarization-dependent interfacial built-in electric fields and charge transfer differences. Notably, the metallicity of the P↓ configuration is localized predominantly within the In₂Se₃ layer rather than delocalized over the entire heterostructure. This arises because the enhanced interfacial charge transfer, driven by the larger work-function difference, selectively populates the conduction band of In₂Se₃, pushing its band edge across the Fermi level, while the Pd-C₃N₄ layer remains semiconducting due to charge depletion and the absence of gap-closing hybridization at the interface. In the P↑ state, the heterojunction acts as an efficient photocatalyst for overall water splitting, with band edges straddling the redox potentials. Under illumination, photogenerated electrons and holes make the hydrogen evolution reaction and oxygen evolution reaction thermodynamically spontaneous. In contrast, the metallic P↓ state serves as an excellent electrocatalyst for hydrogen evolution, delivering a limiting potential as low as −0.11 V, attributed to strengthened N 2p and H 1s orbital hybridization. These findings resolve the conflicting electronic requirements of photocatalysis and electrocatalysis and offer a new paradigm for designing smart, dual-functional catalysts adaptable to varying energy inputs, providing valuable theoretical guidance for future experimental realization of switchable catalytic systems.

1. Introduction

Against the backdrop of accelerated global industrialization in the 21st century, fossil fuels have been over-exploited, leading to a range of issues such as energy shortages, massive greenhouse gas emissions, and ecological degradation [1,2]. Therefore, fundamentally transforming the energy structure and developing efficient, clean, and sustainable technologies for energy conversion and utilization has become an urgent task shared by the global scientific and industrial communities [3]. In recent years, photocatalysis [4,5] and electrocatalysis [6,7] have attracted widespread attention due to their great potential in the fields of energy and environmental sustainability. These two approaches are capable of upgrading small molecules into high-value-added chemicals and have been extensively utilized in hydrogen production, ammonia synthesis, hydrocarbon formation, and pollutant abatement [8,9,10,11].

The photocatalytic and electrocatalytic reaction mechanisms and processes differ fundamentally, and thus each exhibits distinct advantages and limitations. In photocatalysis, renewable solar energy sources excite the catalyst to generate photogenerated electron–hole pairs, thereby initiating chemical reactions. The key to efficient photocatalysis lies in the effective generation and separation of charge carriers, as well as suppressing their recombination [12,13]. Therefore, an ideal photocatalyst should possess a suitable band gap for efficient light absorption, and its band edge positions must match the redox potentials of the reactants. In contrast, electrocatalysis is powered by conventional electricity and typically demands highly conductive metallic catalysts to ensure rapid electron exchange between the reactants and the electrode. Achieving outstanding electrocatalytic performance requires high electrical conductivity, high charge-carrier mobility, and a large population of active sites. Therefore, while photocatalysis utilizes renewable energy, its efficiency is limited by light intensity, whereas electrocatalysis is widely used for efficient chemical production in industrial settings but suffers from high energy consumption. Combining photocatalysis and electrocatalysis to enable automatic switching of working modes according to light conditions (e.g., day/night), thereby maximizing the utilization of environmental energy and ensuring continuous reactions, is also an effective way to improve catalytic efficiency.

The distinct electronic property requirements of photocatalysis and electrocatalysis conflict with the fixed electronic structure of conventional catalysts, preventing them from freely switching between catalytic modes. Zhao et al. reported in their study on the CrI₃/Sc₂CO₂ multiferroic heterojunction that the reversal of the polarization direction of the ferroelectric material Sc₂CO₂ could induce a phase transition in the supported CrI₃ from semiconductor to half-metal [14]. This suggests that utilizing polarization reversal holds promise for achieving photo-electrocatalytic conversion in ferroelectric heterojunctions. Inspired by this strategy, selecting appropriate catalyst platforms that can synergize with ferroelectric control becomes crucial.

Graphitic carbon nitride (g-C₃N₄) stands out as a prominent photocatalyst among the diverse array of promising catalyst systems. In 1989, Liu and Cohen first theoretically confirmed the existence of carbon nitride and deduced the crystal structure of this novel material through calculations [15]. Since then, carbon nitride has gained worldwide attention due to its outstanding performance in many aspects. Carbon nitride has five crystal structures, namely α-C₃N₄, β-C₃N₄, c-C₃N₄ (cubic), p-C₃N₄ (pseudocubic), and g-C₃N₄ (graphitic-like), among which graphitic carbon nitride (g-C₃N₄) with a 3-s-triazine basic structural unit is the most stable at room temperature. Meanwhile, g-C₃N₄ possesses a narrow band gap (2.7 eV) [16], a unique electronic structure, excellent photocatalytic performance, non-toxicity, and good water stability, which has attracted extensive attention in fields such as solar energy conversion, environmental remediation, and photocatalytic reactions in recent years [17]. However, g-C₃N₄ has an obvious drawback that, the short lifetime of photogenerated charge carriers and their easy recombination lead to low quantum efficiency. To address this drawback, various modification methods such as doping (B [18], S [19], and F [20]), noble metal surface modification (Pt [21], Au [22], and Ag [23]), and formation of heterostructures with other semiconductors (WO₃ [24], Fe₃O₄ [25], ZnO [26], Cu₂O [27], TiO₂ [28], and MoO₃ [29]) have been employed to improve the electron–hole separation efficiency of g-C₃N₄.

Beyond these conventional modifications, two-dimensional ferroelectric materials exhibit unique advantages in photocatalysis due to their inherent depolarization fields arising from spontaneous polarization and dynamically switchable polarization states [30,31]. These properties enable precise modulation of band structures and carrier dynamics through polarization reversal. Leveraging this mechanism, studies have shown that ferroelectric heterojunctions achieve unprecedented charge transport efficiency by synergistically integrating spontaneous polarization fields with dynamic modulation capabilities, thereby overcoming the intrinsic limitations of conventional heterojunctions in photocatalytic water-splitting applications [30,31,32]. Two-dimensional α-In₂Se₃ is an experimentally realized ferroelectric material with a band gap of approximately 1.3 eV [33,34]. The polarization direction (P↑ or P↓) of its monolayer can be reversed by shifting the middle Se layer, demonstrating promising potential for photocatalytic applications. Theoretical and experimental results have confirmed that the polarization direction can be reversed with a low energy barrier through the application of an external electric field [35,36,37].

Based on the considerations above, we construct the ferroelectric heterojunction (M-C₃N₄@In₂Se₃) by combining the ferroelectric material α-In₂Se₃ with metal atom-doped g-C₃N₄. By computing the electronic band structures using the HSE06 hybrid functional, evaluating the interfacial work-function differences, and performing both charge-density-difference analysis and Bader charge quantification for the P↑ and P↓ states, we explore the spatial localization of the polarization-induced metallicity and its dependence on the direction of the ferroelectric polarization, thereby clarifying the underlying mechanism by which the ferroelectric layer governs the electronic phase behavior of the heterojunction. Moreover, through analyzing the optical absorption spectra, solar-to-hydrogen (STH) efficiency, and Gibbs free energy changes in reaction pathways under different polarization directions, we investigate the regulatory effect of switching the polarization direction of the α-In₂Se₃ ferroelectric layer on the hydrogen evolution reaction (HER). Notably, we systematically investigate the orbital hybridization between the active site and the adsorbate under the P↑ and P↓ polarization states, and further analyze the electronic origin of the polarization-dependent reaction energy barrier, which has been scarcely addressed in previous studies.

2. Results and Discussion

2.1. Electronic Structure of M-C₃N₄@In₂Se₃ Heterojunction

To enable a nonvolatile phase transition between semiconducting and metallic states during polarization reversal upon heterojunction formation with In₂Se₃, suitable metal dopants for g-C₃N₄ were systematically evaluated. The prior literature has established that transition metals such as Fe [38] and Co [39] effectively enhance oxygen evolution reaction (OER) activity and modulate electronic structures, while noble metals including Pd [40], Ag [41], and Pt [42] can be stably incorporated into the catalytic system to augment activity. Additionally, Mo doping has been shown to improve catalytic performance through the modulation of electronic structures and interfacial charge transfer [43]. Guided by these findings, twelve metal atoms, namely V, Cr, Mn, Fe, Co, Cu, Zn, Mo, Pd, Ag, Ce, and Pt, were preliminarily selected as doping candidates. These atoms were subsequently introduced into the C₃N₄ framework and combined with In₂Se₃ under P↓ and P↑ states to construct two heterostructural configurations, designated M-C₃N₄@P↓-In₂Se₃ and M-C₃N₄@P↑-In₂Se₃ (Figure 1a).

Based on the projected density of states (DOS) calculated via the Perdew–Burke–Ernzerhof (PBE) method for the M-C₃N₄@P↓-In₂Se₃ systems under both P↑ and P↓ polarization states (Figure 1b), a screening of suitable dopants was performed to identify those capable of inducing an electronic phase transition upon reversal of the In₂Se₃ polarization. The DOS plots reveal that doping with V, Mn, Fe, Co, Cu, Zn, Mo, Ag, Ce, and Pt atoms imparts metallic character to the M-C₃N₄@P↓-In₂Se₃ heterostructures in both spin channels (Figure S1a,c,d,f–h,j–l). In contrast, Cr doping results in semiconducting behavior in both spin channels (Figure S1b). Notably, Pd doping is found to enable an electronic phase transition in the heterostructure when the polarization orientation of In₂Se₃ is reversed. Specifically, as illustrated in Figure S1i, the Pd-C₃N₄@P↑-In₂Se₃ configuration exhibits semiconducting character, whereas the Pd-C₃N₄@P↓-In₂Se₃ configuration shows metallic behavior.

2.2. Structural and Electronic Properties of the Pd-C₃N₄@In₂Se₃ Heterojunction

As shown in Figure S2, the interlayer distances of Pd-C₃N₄@P↑-In₂Se₃ and Pd-C₃N₄@P↓-In₂Se₃ are 3.41 Å and 3.39 Å, respectively, indicating that the heterojunction layers are primarily bonded by van der Waals forces. The formation energies of Pd-C₃N₄@P↑-In₂Se₃ and Pd-C₃N₄@P↓-In₂Se₃ were derived from Equation (1) as −0.044 eV/Ų and −0.083 eV/Ų, respectively. These negative values confirm the energetic favorability of the ferroelectric heterojunction. In addition, the ab initio molecular dynamics (AIMD) simulations (Figure 2a,b) reveal that the structures remain intact and the total energy converges toward a stable plateau, further attesting to the excellent thermodynamic stability of the Pd-C₃N₄@In₂Se₃ heterojunction.

As mentioned before, the DOS results at PBE state that the Pd-C₃N₄@In₂Se₃ heterostructure undergoes an electronic phase transition upon the reversal of the polarization orientation of In₂Se₃. As displayed in Figure 3, the HSE06 results of the electronic band structures further confirm this point. When the polarization state of In₂Se₃ switches to the P↓ state, the heterojunction exhibits MS, with the conduction band of In₂Se₃ component crossing the Fermi level (Figure 3a). When the polarization state of In₂Se₃ switches to the P↑ state, the heterojunction becomes SS (Figure 3b). In this case, the CBM of In₂Se₃ component is lower than that of Pd-C₃N₄ component but higher than the VBM of Pd-C₃N₄ component, whereas the VBM of In₂Se₃ component is lower than that of Pd-C₃N₄ component, indicating that, the Pd-C₃N₄@P↑-In₂Se₃ heterojunction has a typical type-II band alignment structure. The band offsets for CBM and VBM are 0.37 eV and 0.64 eV, respectively.

The physical origin of the MS-SS phase transition can be attributed to the reversal of the interfacial built-in electric field direction and the difference in the interfacial electron transfer, induced by the polarization reversal of the α-In₂Se₃ ferroelectric layer. The symmetry breaking in In₂Se₃ layer leads to differences in the in-plane averaged electrostatic potentials on the opposite sides. The work function of the top surface is 5.21 eV, while that of the bottom surface is 6.65 eV (Figure S3); therefore, the potential difference (∆Φ) for the In₂Se₃ layer is 1.44 eV. As to the case of Pd-C₃N₄ layer, as shown in Figure S4, due to its asymmetric structure, the work functions of its top and bottom surfaces are not equal. Given the configurational variation in Pd-C₃N₄ layer between the Pd-C₃N₄@P↓-In₂Se₃ and Pd-C₃N₄@P↑-In₂Se₃ heterostructures, the resulting potential differences are disparate. Therefore, when determining the potential difference at the interfaces of Pd-C₃N₄@P↓-In₂Se₃ and Pd-C₃N₄@P↑-In₂Se₃ heterostructures, the potential difference derived from the configuration of Pd-C₃N₄ layer in the relevant heterostructure was taken as the reference benchmark (Figure S4a,b).

As shown in Figures S3 and S4, before the formation of the Pd-C₃N₄@P↓-In₂Se₃ heterostructure, the work function on the Pd-C₃N₄ side (3.88 eV) is 2.77 eV lower than that on the In₂Se₃ side (6.65 eV). This work-function difference provides the driving force for electron transfer from the Pd-C₃N₄ side to the In₂Se₃ side during the mutual contact for the formation of the Pd-C₃N₄@P↓-In₂Se₃ heterostructure. For the case of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure, the work function on the Pd-C₃N₄ side (3.99 eV) is also lower than that on the In₂Se₃ side (5.21 eV), but by only 1.22 eV. Since the work-function difference between the Pd-C₃N₄ side and the In₂Se₃ side in the Pd-C₃N₄@P↑-In₂Se₃ heterostructure is smaller than that in the Pd-C₃N₄@P↓-In₂Se₃ heterostructure, the driving effect for electron transfer from the Pd-C₃N₄ side to the In₂Se₃ side at the interface of the Pd-C₃N₄@P↓-In₂Se₃ heterostructure is greater than that at the interface of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure. This is confirmed by charge density difference analysis, which shows more pronounced electron transfer at the Pd-C₃N₄@P↓-In₂Se₃ interface (as shown in Figure 4c,d). Moreover, the Bader charge analysis also states that the number of transferred electrons in Pd-C₃N₄@P↓-In₂Se₃ interface is larger than that in the Pd-C₃N₄@P↑-In₂Se₃ interface by 0.11 e.

In the semiconducting phase of Pd-C₃N₄@P↑-In₂Se₃ heterostructure, a built-in electric field (E_int) oriented from Pd-C₃N₄ region to In₂Se₃ region is established at the interface, arising from the work-function-difference-driven charge transfer during the contact process. As shown in Figure 4b, upon formation of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure, the work-function difference at the interface is reduced to 0.52 eV owing to the built-in electric field. The strength of the built-in electric field could be characterized by the change in the work-function difference at the interface (0.70 eV). Under light illumination, the flow of photogenerated carriers at the interface of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure is simultaneously affected by both the band offset and the built-in electric field, and these two effects act in opposite directions. As shown in Figure 3b, the band offset causes photoelectrons and photogenerated holes to accumulate on the In₂Se₃ and the Pd-C₃N₄ sides, respectively. However, the built-in electric field at the interface drives photoelectrons and photogenerated holes to accumulate on the Pd-C₃N₄ and the In₂Se₃ sides, respectively. Since the driving voltage provided by the built-in electric field (0.7 V) is larger than that provided by the band offset (0.37 V for electrons and 0.64 V for holes), the migration trajectory of photogenerated carriers is dominated by the effect of the built-in electric field. As shown in Figure 5a, upon photoexcitation, the photogenerated electrons at the interface are driven toward the Pd-C₃N₄ layer, whereas the photogenerated holes are correspondingly driven toward In₂Se₃ layer, and arrive at its surface with the help of the intrinsic built-in electric field (E_p) in the In₂Se₃ regions. As a consequence, the Pd-C₃N₄ layer enriched with photogenerated electrons can serve as an active site for the HER, while the In₂Se₃ layer enriched with photogenerated holes acts as an active site for the OER. The band-edge potentials of Pd-C₃N₄@P↑-In₂Se₃ heterojunction were also evaluated to determine whether it exhibits adequate redox strength to enable overall water splitting. The band-edge potentials presented in Figure 5a reveal that the CBM of the Pd-C₃N₄ moiety lies at −3.39 eV (vs. vacuum), which is more positive than the H⁺/H₂ reduction potential. In contrast, the VBM of the In₂Se₃ moiety lies at −6.91 eV (vs. vacuum), which is more negative than the H₂O/O₂ oxidation potential. On the basis of these thermodynamic criteria, the Pd-C₃N₄ component is identified as the HER-active photocatalyst with sufficient reduction capacity to transform H⁺ into H₂, while the In₂Se₃ component functions as the OER-active counterpart meeting the energy requirement for efficient oxidation of water molecules to O₂. Accordingly, the two sides of Pd-C₃N₄@P↑-In₂Se₃ heterostructure are favorable for the HER and OER, respectively, thereby providing a promising catalytic interface for achieving efficient overall water splitting.

As shown in Figure 5b, the Pd-C₃N₄@P↑-In₂Se₃ heterostructure exhibits a pronounced light absorption coefficient peak of 1.20 × 10⁶ cm⁻¹ at 140.26 nm, substantially higher than that of pristine In₂Se₃ (9.99 × 10⁵ cm⁻¹ at 131.03 nm, blue line) and Pd-C₃N₄ (1.65 × 10⁵ cm⁻¹ at 82.08 nm, green line) monolayers. Moreover, the initial optical absorption peak of Pd-C₃N₄@P↑-In₂Se₃ heterostructure redshifts significantly, relative to the ones from both component materials. The significant increase in both the maximum absorption peak intensity and the optical absorption spectral range, observed for Pd-C₃N₄@P↑-In₂Se₃ heterojunction compared with its constituent materials, indicates that the heterojunction configuration contributes to an enhanced light-harvesting capacity and improved photocatalytic performance.

In order to further verify this point, we calculate the light absorption efficiency (η_abs), carrier utilization efficiency (η_cu), STH efficiency (η_STH), and the corrected solar-to-hydrogen efficiency (η′_STH) of the Pd-C₃N₄ monolayer, In₂Se₃ monolayer, and Pd-C₃N₄@P↑-In₂Se₃ heterostructure with the previous method [44], using their band gaps, over-potential for hydrogen evolution reaction (χ(H₂)) and oxygen evolution reaction (χ(O₂)), and ΔΦ, which have been listed in Table S1. An enhancement in the light absorption efficiency η_abs is observed for the heterostructure design in Table S2, attributable to the reduced band gap, which aligns well with the foregoing absorption analyses. Specifically, the η_abs of Pd-C₃N₄@P↑-In₂Se₃ heterostructure is 13.68% higher than that of Pd-C₃N₄ component and 28.53% higher than that of In₂Se₃ component. Since Pd-C₃N₄ component does not possess sufficient oxidation ability to oxidize H₂O into O₂ (χ(O₂) < 0, as listed Table S1), its η_cu and η_STH are not considered here. Compared with the In₂Se₃ component, the heterostructure configuration further increases η_cu, as the substantial ΔΦ markedly boosts the reduction potential of the photogenerated electrons. Consequently, the η_STH of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure attains 65.46%, far surpassing that of the bare In₂Se₃ component (35.65%). After accounting for the ΔΦ effect, the η′_STH of this heterostructure still reaches 34.18%, which exceeds the commercial viability threshold (>10%) [45].

2.3. Adsorption of Water Molecules

The strength of H₂O adsorption is widely regarded as a critical descriptor for evaluating the catalytic activity of HER catalysts [46,47]. In this work, the semiconducting phase of material Pd-C₃N₄@In₂Se₃ (Pd-C₃N₄@P↑-In₂Se₃), which exhibits relatively poor electrical conductivity, was chosen to assess its hydrophilicity according to the adsorption energy (E_ads) for water molecules.

We separately studied the adsorption behavior of H₂O molecules at the surfaces of the Pd-C₃N₄ and In₂Se₃ components. The E_ads was defined using the following equation:

$$E_{\mathrm{ads}}=E_{\mathrm{total}}-E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@\mathrm{P}\uparrow \text{-}{\mathrm{In}}_2{\mathrm{Se}}_3}-E_{{\mathrm{H}}_2\mathrm{O}}$$

where E_total is the total energy of the whole H₂O adsorption system, $E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@\mathrm{P}\uparrow \text{-}{\mathrm{In}}_2{\mathrm{Se}}_3}$ is the energy of the pristine Pd-C₃N₄@P↑-In₂Se₃ heterostructure, and $E_{{\mathrm{H}}_2\mathrm{O}}$ is the energy of an isolated H₂O molecule. For the Pd-C₃N₄ layer, the most energetically favorable configuration corresponds to the O atom of H₂O binding to the N site adjacent to the Pd atom, yielding the E_ads of −0.21 eV. For the surface of the ferroelectric In₂Se₃ layer, various possible adsorption sites were systematically evaluated via geometric optimization (Figure S5) to determine the most stable configuration. As listed in Table S3, the calculated E_ads values for H₂O on the In, Se₁, and Se₂ sites are −0.16, −0.19, and −0.11 eV, respectively, establishing Se₁ as the most favorable adsorption site on the In₂Se₃ surface (Figure 6). Collectively, these results demonstrate that H₂O molecules can be stably co-adsorbed on both the upper and lower surfaces of the Pd-C₃N₄@P↑-In₂Se₃ heterostructure. Such dual-surface adsorption behavior ensures an adequate supply of reactant molecules for the subsequent catalytic reactions.

2.4. The HER on Pd-C₃N₄@In₂Se₃

The metallic-state Pd-C₃N₄@P↓-In₂Se₃ can serve as an HER electrocatalyst (Figure 7a), where the N sites in Pd-C₃N₄ act as the active sites for HER (Figure S6), exhibiting a limiting potential of only −0.11 V (Figure 7b), and the formation of H* is the rate-determining step. We also examined H adsorption on the embedded single Pd atom site. Interestingly, upon full structural relaxation, the H atom initially placed on the Pd site spontaneously migrated to the adjacent N site in both the P↓ and P↑ polarization states, indicating that the N site is energetically more favorable for H* adsorption than the Pd site, regardless of the polarization direction. This confirms that the N sites, rather than the Pd atoms, serve as the primary active centers for HER in the metallic Pd-C₃N₄@P↓-In₂Se₃ state, while in the semiconducting P↑ state, the N sites remain the active sites for photocatalytic HER. Meanwhile, for the photocatalytic HER performance on the semiconducting Pd-C₃N₄@P↑-In₂Se₃, the ΔG_H* is 0.39 eV according to the Gibbs free energy calculations at pH = 0 (Figure 7d). This is superior to many theoretically predicted HER photocatalysts, such as the Janus WSSe monolayer (ΔG_H* = 0.41 eV) [46] and the PdSeO₃ monolayer (ΔG_H* = 0.57 eV) [48]. Under an external potential provided by photogenerated electrons of U_e = 1.05 V, both hydrogenation steps of the HER on the Pd-C₃N₄@P↑-In₂Se₃ heterojunction are downhill (Figure 7d). This indicates that the driving potential provided by the photogenerated electrons enables the complete reaction pathway of the HER to proceed spontaneously.

Our computational results reveal that the metallic Pd-C₃N₄@P↓-In₂Se₃ surface delivers a substantially lower HER limiting potential (−0.11 V) than its upward-polarized counterpart (Pd-C₃N₄@P↑-In₂Se₃). To elucidate the electronic origin of this performance difference, we systematically investigated the effect of polarization direction on H* adsorption. As shown in Figure 8a,b, the N 2p orbitals in the σ-bonding region of the downward-polarized configuration exhibit markedly enhanced delocalization relative to the upward-polarized case. This enhanced delocalization promotes more pronounced orbital overlap between the N 2p and H 1s states, which strengthens H* adsorption, leading to significant improvement in HER activity.

2.5. The Photocatalytic OER on Pd-C₃N₄@P↑-In₂Se₃

To consume accumulated photogenerated holes and produce H⁺ for the HER, this study further considers the OER on the bottom surface of the In₂Se₃ component in Pd-C₃N₄@P↑-In₂Se₃. Specifically, the OER at this site follows a classical four-electron pathway involving four proton-coupled electron transfer steps. As shown in Figure S7, based on the calculations of the free energies of the reaction intermediates, we screened out the optimal OER pathway from the two reaction pathways. The selected OER pathway could be expressed as: * + H₂O → OH* + H⁺ + e⁻, OH* → O* + H⁺ + e⁻, O* + H₂O → O*OH* + H⁺ + e⁻, O*OH* → * + O₂(g) + H⁺ + e⁻, with OH, O, and O*OH* as intermediates (Figure 9a). Under dark conditions at pH = 0, the limiting potential corresponding to the maximum thermodynamic barrier that needs to be overcome to complete this OER is calculated to be 1.48 V (Figure 9b). And the first hydrogenation step (* + H₂O → OH* + H⁺ + e⁻) is the rate-determining step. However, under illumination, when the external potential (U_h = 2.47 V) is provided by photogenerated holes, the rate-determining step becomes a downhill reaction (Figure 9b), indicating that this reaction can proceed spontaneously under illumination.

3. Computational Details

All calculations were carried out using spin-polarized density functional theory (DFT) simulations as implemented in the Vienna Ab initio Simulation Program (VASP) code [49,50]. Exchange-correlation effects were treated with the spin-polarized generalized gradient approximation (GGA) in the PBE parametrization, while electron–ion interactions were described via the frozen-core projector augmented wave (PAW) method [51,52,53]. Van der Waals (vdW) forces were accounted for through Grimme’s DFT-D3 dispersion correction scheme [54]. To construct the metal-doped C₃N₄ (M-C₃N₄) model, a single metal atom was placed at the center of the N-ring in a 1 × 1 C₃N₄ supercell. The Pd-C₃N₄@In₂Se₃ heterostructure was built by vertically stacking a $\sqrt{3}\times \sqrt{3}$ In₂Se₃ layer (lattice constants a = b = 7.05 Å) onto a 1 × 1 Pd-C₃N₄ layer (lattice constants a = b = 7.14 Å). Given that the polarization state of In₂Se₃ layer depends sensitively on the lattice constant [55], the lattice constant of In₂Se₃ layer is chosen for the construction of Pd-C₃N₄@In₂Se₃ heterostructure. Under this configuration, the lattice mismatch of Pd-C₃N₄ layer is merely 1.26% along both X and Y axes (Table S6). A vacuum spacing exceeding 30 Å was introduced along the out-of-plane direction to eliminate interactions between periodic images, and dipole corrections were applied to all asymmetric structures [56]. Brillouin-zone integration employed a 3 × 3 × 1 Monkhorst-Pack k-mesh for the two-dimensional system. Site-specific charge populations were derived from Bader analysis. To remedy the band-gap underestimation typical of PBE, the electronic structure was further evaluated with the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional [57]. The plane-wave cutoff energy was set to 500 eV, and convergence criteria for forces and total energy were 10⁻² eV/Å and 10⁻⁵ eV, respectively. Gibbs free energies were obtained using the computational hydrogen electrode (CHE) model [58]. For the free-energy calculations of HER and OER, solvent effects were accounted for by the implicit solvation model implemented in the VASPsol software (version VASP 6.4.1) [47,59], with a relative dielectric constant of 80.0 for water. Additional simulation details can be found in the Supporting Information.

Formation energy (E_f) is a fundamental metric to assess the stability of materials, and it has been calculated as:

$$E_{\mathrm{f}}=(E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@{\mathrm{In}}_2{\mathrm{Se}}_3}-E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4}-E_{{\mathrm{In}}_2{\mathrm{Se}}_3})/\mathrm{S}$$

(1)

where $E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@{\mathrm{In}}_2{\mathrm{Se}}_3}$ represents the total energy of the Pd-C₃N₄@In₂Se₃ heterostructure, $E_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4}$ is the energy of Pd-C₃N₄ monolayer, $E_{{\mathrm{In}}_2{\mathrm{Se}}_3}$ is the energy of In₂Se₃ monolayer, and S denotes the interfacial area of the Pd-C₃N₄@In₂Se₃ heterostructures.

The charge density difference for the Pd-C₃N₄@In₂Se₃ ($∆\rho *$) is calculated by the following equation:

$$∆\rho *={\rho }_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@{\mathrm{In}}_2{\mathrm{Se}}_3}-{\rho }_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4}-{\rho }_{{\mathrm{In}}_2{\mathrm{Se}}_3}$$

(2)

where ${\rho }_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4@{\mathrm{In}}_2{\mathrm{Se}}_3}$ is the charge density of the Pd-C₃N₄@In₂Se₃ heterostructures. ${\rho }_{\text{Pd-}{\mathrm{C}}_3{\mathrm{N}}_4}$ and ${\rho }_{{\mathrm{In}}_2{\mathrm{Se}}_3}$ are the charge densities of the Pd-C₃N₄ and In₂Se₃ monolayers, respectively.

To extract the orbital-resolved components, we used the “splittos.dos” code to analyze the DOS output file. The average d-band center shifts in the surface metal atoms were computed from both the total and orbital-resolved d partial densities of states. The d-band center (E_d) was then evaluated using the following expression [60]:

$$E_d={\displaystyle \frac{\int n_d\left(E\right)\mathit{Eds}}{\int n_d\left(E\right)\mathit{ds}}}$$

(3)

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

The light-harvesting capability was evaluated by the absorption coefficient α(ω), which was computed using the following formula [61]:

$$\alpha (\omega )=\sqrt{2}{\displaystyle \frac{\omega }{\mathrm{c}}}(\sqrt{{\epsilon }_1{(\omega )}^2+{\epsilon }_2({\omega }^2)}-{\epsilon }_1(\omega ){)}^{{\displaystyle \frac{1}{2}}}$$

(4)

where the real and imaginary components of a frequency-dependent dielectric function are denoted by ε₁ and ε₂, respectively, while the vacuum speed of light is denoted by c.

4. Conclusions

Our work systematically investigates the ferroelectric heterojunction Pd-C₃N₄@In₂Se₃ using first-principles DFT calculations. The electronic structure, optical absorption, and catalytic performance are examined under two opposite polarization states, namely P↑ and P↓. Reversing the polarization direction of the α-In₂Se₃ ferroelectric layer induces a nonvolatile electronic phase transition. The P↓ configuration exhibits metallic behavior, while the P↑ configuration becomes semiconducting with a typical type-II band alignment. This transition originates from the polarization-dependent interfacial built-in electric field and the consequent difference in charge transfer magnitude, as confirmed by work-function analysis and Bader charge quantification. In the semiconducting P↑ state, the heterojunction functions as an efficient photocatalyst, and its band edges straddle the water-redox potentials. Electrons accumulate on the Pd-C₃N₄ side for HER, and holes migrate to the In₂Se₃ side for OER. The Pd-C₃N₄@P↑-In₂Se₃ heterostructure shows a significantly enhanced optical absorption coefficient of 1.20 × 10⁶ cm⁻¹ at approximately 140 nm and a broadened spectral response compared to its constituents, confirming superior light-harvesting capability. Gibbs free energy calculations reveal that under illumination, both the HER with ΔG_H* of 0.39 eV at pH = 0 and the OER with a limiting potential of 1.48 V become thermodynamically spontaneous when driven by photogenerated electrons (U_e = 1.05 V) and holes (U_h = 2.47 V), respectively. In contrast, the metallic P↓ state serves as an excellent electrocatalyst for HER, with a limiting potential as low as −0.11 V. More importantly, the present work provides an in-depth investigation into the microscopic mechanism of HER, revealing at the orbital level the intrinsic correlation between the ferroelectric polarization direction and the N 2p–H 1s hybridization strength, thereby further enriching the ferroelectric heterojunction catalytic system. Collectively, these results establish a feasible strategy to achieve on-demand switching between photocatalytic and electrocatalytic functions within a single heterostructure by simply tuning the ferroelectric polarization. This polarization-driven electronic phase transition not only resolves the conflicting electronic requirements of the two catalytic modes but also offers a new paradigm for designing smart, dual-functional catalysts that can adapt to varying energy inputs, such as sunlight or electricity. This work provides valuable theoretical guidance for experimental realization of switchable catalysis and paves the way toward more flexible and sustainable energy-conversion systems.