Carbon-Rich Selenide Monolayers as Metal-Free Catalysts for Oxygen Reduction Reactions: A First-Principles Investigation

Abstract

Carbon-based materials have garnered significant attention for electrocatalysis applications in fuel cells due to their unique structural and electronic properties, but rapid oxygen reduction reaction (ORR) at the cathode of fuel cells is challenging. Dopants are typically used as active sites for ORR, and increasing the number of active sites for carbon-based catalysts remains a challenge. Here, we carried out first-principles calculations for the electrocatalytic ORR performance of the recently reported monolayer superconductors of carbon-rich selenides. Remarkably, the abundant C atoms serve as the active centers instead of the foreign atoms (Se). All the free energy changes during the ORR process are downhill, suggesting that these carbon-rich selenides hold promise as metal-free electrocatalysts for ORR. Note that the promising electrocatalytic performance of carbon-rich selenides is theoretically predicted; validation is encouraged for experimental efforts.

1. Introduction

Energy plays the most important role in the development of society and industry. As the storage of fossil fuels is limited, the search for renewable and sustainable clean energy is increasingly urgent. Proton exchange membrane fuel cells (PEMFCs) converting the chemical energy from hydrogen into electrical energy through an electrochemical reaction provide a very attractive alternative [1]. However, the reaction in which oxygen reacts with protons and electrons to produce water (oxygen reduction reaction, ORR) at the cathode is kinetically sluggish and has a significant energy barrier, requiring efficient catalysts to facilitate the reaction [2]. Pt-based catalysts have long been the leading ORR catalysts, but the high cost and scarcity of Pt have severely hindered their large-scale commercial application [3]. Therefore, it is of paramount importance to develop low-cost, highly durable, and highly active ORR electrocatalysts for the large-scale application of PEMFCs, and seeking efficient and inexpensive metal-free ORR catalysts has become a hot topic in recent years [4].

Carbon-based materials are a new class of metal-free ORR catalysts that are expected to replace platinum for efficiently catalyzing the ORR in fuel cells due to their large surface area, good electrical conductivity, tunable morphology, simple and economically feasible preparation, etc. [5]. Among them, N-doped graphene and graphitic flakes have been extensively synthesized, and most reported samples can efficiently electrocatalyze the ORR via a four-electron pathway in fuel cells, showing high catalytic activity, stability, and tolerance to methanol crossover effects [6,7,8,9,10,11]. Moreover, various carbon materials doped with heteroatoms, such as B-doped carbon nanotubes (CNTs) or grapheme [12,13], sulfur-doped graphene [14], phosphorus-doped graphite layers [15], iodine-doped graphene [16], and graphene nanosheets with edge halogenation (Cl, Br, or I), have also been investigated [17]. In addition, the binary or ternary doping of carbon materials with different heteroatoms was found to be more electrocatalytically active toward ORR than the single-doped counterparts [5]. Typically, dopants serve as the primary active sites but are constrained by low doping concentrations in the carbon matrix. This limitation hinders further improvements in catalytic efficiency. Therefore, developing strategies to fully utilize the abundant intrinsic carbon atoms as active sites is crucial for enhancing catalytic performance. Given that the synthesized selenium-doped carbon materials are utilized in a range of sustainable technologies [18], we would like to know whether the large number of intrinsic C atoms in carbon-rich selenide monolayers can serve as the active sites for ORR. This consideration is based on the large surface-to-volume ratio in two-dimensional (2D) materials facilitating tremendous contact with reactants and intermediates.

In this work, we examined the ORR performance of three 2D carbon-rich selenide monolayers, namely C₄Se, C₅Se, and C₆Se, which were recently reported to be the global minima and to exhibit superconductivity [19], by means of first-principles calculations. Our calculations revealed that carbon atoms (C) are the active centers that boost ORR, largely because of the electron transfer from Se to C. Moreover, both C₄Se and C₅Se superconductors are promising candidates for metal-free electrocatalysts for ORR, as all elementary reaction steps are downhill in free energy. Though the carbon-rich selenide monolayers are not experimentally available yet, these lowest-energy and highly stable structures suggest they are highly promising for experimental synthesis. There are many predictions realized by experimentalists. For example, our predicted Cu₂N global minimum in 2D space [20] was successfully synthesized by Wu’s group [21], and the promising ORR performance of the iron phthalocyanine moiety [22] was experimentally validated [23]. Our theoretical work provides guidelines for developing 2D metal-free electrocatalysts with carbon atoms serving as active sites.

2. Computational Methodology

All the spin-polarized density functional theory (DFT) calculations were carried out in the Vienna Ab initio Simulation Package (VASP) [24]. Electron exchange and correlation interactions were treated by the generalized gradient approximation (GGA) method with the Perdew–Burke–Ernzerhof (PBE) functional, whereas the interactions between ion nuclei and valence electrons were described using the projector-augmented wave (PAW) method [25]. D2 dispersion corrections were employed for calculations [26]. The wavefunction for valence electrons was expanded by the Kohn–Sham plane-wave basis set with an energy cutoff of 500 eV. All the structures were fully relaxed until the convergence tolerances for the energy and force on each atom were less than 1.0 × 10⁻⁴ eV and −0.01 eV/Å, respectively. The three monolayers, C₄Se, C₅Se, and C₆Se, were sampled in the Brillouin zone at k points using a scheme of a 3 × 3 × 1 k-point Monkhorst-Pack grid [27]. To avoid image interaction, 2 × 5 × 1, 3 × 3 × 1, and 2 × 4 × 1 supercells were used in the calculations for C₄Se, C₅Se, and C₆Se monolayers, respectively, and a vacuum layer of ~20 Å was applied in the z-direction. The free energy was calculated according to the computational hydrogen electrode (CHE) proposed by Nørskov et al. [28]. The zero-point energy (ZPE) and entropic corrections were obtained from DFT calculations. Bader charge analysis was used to assess charge transfer [29]. The crystal orbit Hamilton population (COHP) analysis was performed by using LOBSTER-5.0.0 software [30,31].

The overall reaction of four-electron ORR is

$${\mathrm{O}}_2\left(\mathrm{g}\right)+{4\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2\mathrm{O}(l)$$

(1)

The four elementary reaction steps during ORR in acidic media are as follows:

$${\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}+* \to {}^{*}\mathrm{OOH}$$

(2)

$${}^{*}\mathrm{OOH}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {}^{*}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}(l)$$

(3)

$${}^{*}\mathrm{O} +{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {}^{\mathrm{*}}\mathrm{O}\mathrm{H}$$

(4)

$${}^{*}\mathrm{OH}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {\mathrm{H}}_2\mathrm{O}\left(l\right)+*$$

(5)

where “$*$” denotes the adsorption site. The adsorbed energy is calculated by the following equations [32]:

$$\Delta E(*\mathrm{O})=E(*\mathrm{O})-E(*)-(E_{{\mathrm{H}}_2\mathrm{O} }-E_{{\mathrm{H}}_2})$$

(6)

$$\Delta E(*\mathrm{OH})=E(*\mathrm{OH})-E(*)-(E_{{\mathrm{H}}_2\mathrm{O}}-{\displaystyle \frac{1}{2}}{E}_{{\mathrm{H}}_2})$$

(7)

$$\Delta E(*\mathrm{OOH})=E(*\mathrm{OOH})-E(*)-(2E_{{\mathrm{H}}_2\mathrm{O}}-{\displaystyle \frac{3}{2}}{E}_{{\mathrm{H}}_2})$$

(8)

where E($*$) is the ground state energy of the catalyst. $\Delta E(*\mathrm{O} )$, $\Delta E(*\mathrm{OH} ) ,$ and $\Delta E(*\mathrm{OOH} )$ represent the energies of the intermediates O, OH, and OOH adsorbed onto the catalysts, respectively. $E_{{\mathrm{H}}_2\mathrm{O}}$ and $E_{{\mathrm{H}}_2}$ are the calculated energies of the gas-phase water and hydrogen molecules, respectively, in a 15 Å × 15 Å × 15 Å cube.

The free energy of each reaction step is determined by the following equation:

$$\Delta G=\Delta E_{\mathit{DFT}}+\Delta \mathit{ZPE}-T\Delta S+\Delta G_{U_0}-\Delta G_{\mathrm{pH}}$$

(9)

where $\Delta E_{DFT}$ is the reaction energy directly from the DFT calculation. $\Delta ZPE$ and $T\Delta S$ are the zero-point energy and entropy contributions, respectively [33]. The term related to pH is $\Delta G_{\mathrm{p}\mathrm{H}}$, determined by $\Delta G_{\mathrm{p}\mathrm{H}}=k_{B }T$ × ln10 × pH, where “k_B” is Boltzmann’s constant. In this paper, pH is set to 0; therefore, $\Delta G_{\mathrm{p}\mathrm{H}}$= 0 eV. U₀ is the potential relative to the standard hydrogen electrode (SHE) under standard conditions (U₀ = 0 V, pH = 0, P = 1 bar, T = 298.15 K). In this paper, the free energy of a free O₂ is determined by the following equation [34]:

$$G_{{\mathrm{O}}_2}=2G_{{\mathrm{H}}_2\mathrm{O}}-2G_{{\mathrm{H}}_2}+4.92 \mathrm{e}\mathrm{V}$$

(10)

where $G_{{\mathrm{H}}_2\mathrm{O}}$ and $G_{{\mathrm{H}}_2}$ are the free energies of H₂ and H₂O, respectively. The $\Delta G_1~\Delta G_4$ of each ORR step can be obtained by the following expressions.

$$\Delta G_1=\Delta G(*\mathrm{OOH})-4.92 \mathrm{eV}$$

(11)

$$\Delta G_2=\Delta G(*\mathrm{O}) - \Delta G(*\mathrm{OOH})$$

(12)

$$\Delta G_3=\Delta G(*\mathrm{OH}) - \Delta G(*\mathrm{O})$$

(13)

$$\Delta G_4=-\Delta G(*\mathrm{OH})$$

(14)

where 4.92 eV is the total reaction energy. The limiting potential ($U_L$) is used to evaluate the catalytic performance [35], representing the maximum free energy change in the four steps of (11)–(14) and having the expression:

$$U_L=-{\displaystyle \frac{\mathit{max} (\Delta G_1, \Delta G_2, \Delta G_3, \Delta G_4)}{e}}$$

(15)

The overpotential (${\eta }_{\mathit{ORR}}$) for the whole process of the oxygen reduction reaction can be obtained via the following formula:

$${\eta }_{\mathit{ORR}}=1.23-UL$$

(16)

3. Results and Discussion

The optimized structures of the three carbon-rich selenides are shown in Figure 1. The lattice parameters are a = 6.16 Å and b = 2.55 Å in C₄Se, a = b = 4.55 Å in C₅Se, and a = 9.69 Å and b = 4.54 Å in C₆Se. The corresponding space group symmetries are Pmm2, P31m, and P2₁2₁2, respectively, where the lattice constant c was fixed at 20 Å. The C−Se bond lengths of the three monolayers were measured to be 1.94, 1.91, and 1.98~2.00 Å for C₄Se, C₅Se, and C₆Se, respectively. These structural parameters are in good agreement with the results reported in the literature [19].

3.1. Stability

The three C-Se monolayers (C₄Se, C₅Se, and C₆Se) represent the global minimum of the same stoichiometry in the two-dimensional space. Their stabilities were confirmed through multiple criteria, including formation energy, ab initio molecular dynamics simulations, phonon dispersion curves, and elastic constants [19], indicating a high likelihood of experimental realization. In addition, we calculated the integrated crystal orbital Hamilton population (ICOHP) of Se−C bonding (Se−C_I, Se−C_II, and Se−C_III in C₄Se, C₅Se, and C₆Se, respectively, as exemplified and illustrated in Figure 1). The ICOHP values for the three monolayers are −6.13, −6.35, and −5.64 eV, respectively (Figure 2). The negative ICOHP values further indicate the excellent structural stability of these C-Se monolayers.

3.2. O₂ Adsorption

To investigate the ORR performance, we first examined the adsorption behavior of O₂. Both Se and C sites were considered, and O₂ prefers to adsorb at C sites on all three carbon-rich selenides. The O−O bond length of the adsorbed O₂ is elongated to 1.38 Å on C₄Se, compared to the calculated value of 1.25 Å for free O₂. Interestingly, O₂ dissociates spontaneously on C₅Se and C₆Se, and with O−O bond distances of 2.57 and 2.20 Å, respectively. Among them, the adsorption energies of oxygen on the three systems are −0.80, −3.08, and −3.60 eV, respectively. We found that oxygen molecules and subsequent intermediates are adsorbed on the C atoms that surround the Se atoms, with the C atoms serving as active sites, which significantly increases the number of available active sites.

3.3. Gibbs Free Energy

We calculated the Gibbs free energy change (ΔG) of each elemental step during the four-electron ORR process. The free energy profile and the side view of each intermediate are shown in Figure 3. The rate-determining step (RDS) is the formation of the second water molecule (*OH → *H₂O) on C₄Se, the formation of the intermediate (*O → *OH) on C₅Se, and the formation of the first water molecule (*O + *OH → *O + H₂O) on C₆Se, with values for the vales of limiting potential $U_L$ of 0.09, 0.08, and −0.34 V and values for the overpotential ${\eta }_{\mathit{ORR}}$ of 1.14, 1.15, and 1.57 V for C₄Se, C₅Se, and C₆Se, respectively. As a metal-free catalyst, the ${\eta }_{\mathit{ORR}}$ values of C₄Se and C₅Se are both lower than that of the 2D carbon materials of the Haeckelite and N-doped Haeckelite structures (1.26 and 1.20 eV) [36]. Notably, the free energies are downhilled during the four-electron process on both C₄Se and C₅Se, suggesting their high ORR activity.

3.4. Origin of ORR Performance

Furthermore, we compared the charge transfer between C and Se atoms to gain insight into the origin of the ORR activity of abundant C sites. Bader charge analysis revealed that Se atoms transfer electrons to C (Figure 1), in line with the higher electronegativity of C compared to Se, and the extra electrons on C activate O₂, facilitating ORR. Note that C atoms have more extra electrons on average in both C₄Se and C₅Se than those of C₆Se, since each Se has fewer coordinates with C (two and three) in the former two monolayers than that (four) in the latter one. In addition, the projected density of states (PDOS) was analyzed to further investigate the electronic structure. As shown in Figure 4, the electronic density of states diagrams reveal that C₄Se, C₅Se, and C₆Se exhibit metallic properties, indicating that all of these materials are suitable for use as electrocatalysts to promote the oxygen reduction reaction. From the analysis of PDOS, the electronic states are primarily contributed by the p orbitals of carbon and selenium, and the p-band center of the C atoms in the monolayers of C₄Se, C₅Se, and C₆Se is closer to the Fermi energy level compared to that of the Se atoms (0.57 vs. 0.62, 0.11 vs. 1.34, and −0.20 vs. −0.65 eV, respectively). It is further confirmed that the adsorption capacity of carbon atoms toward O₂ and intermediates is stronger than that of Se atoms, leading to C atoms being the active sites and to the increase in the number of active sites.

4. Conclusions

In summary, we performed DFT calculations to investigate the electrocatalytic performance of superconducting C₄Se, C₅Se, and C₆Se monolayers for an oxygen reduction reaction (ORR). O₂ was effectively activated on all three monolayers, as evidenced by the elongated or dissociated O−O bonds. It is noteworthy that the free energy changes for the four-electron process on both C₄Se and C₅Se are downhill, indicating excellent catalytic activity. Specifically, carbon atoms serve as active sites, benefiting from the electron transfer from Se to the adjacent C atoms, which effectively addresses the issue of insufficient active sites and enhances the overall reaction efficiency. Though our theoretical study provides valuable insights for the development of metal-free electrocatalysts with intrinsic carbon atoms as active centers for oxygen reduction reactions, our predictions require experimental validation. Given the superconductivity and global stability of these carbon-rich selenide monolayers, our findings are of broad interest to both theoretical and experimental research communities.