The regulatory function of the d-orbital structure in TM@g-t-C₄N₃ for bifunctional catalysis of the oxygen evolution/reduction reaction

Abstract

Highly efficient catalysts for the oxygen evolution/reduction reaction (OER/ORR) have attracted great attention in research for energy devices with high conversion efficiency. Herein, systematic first-principles investigations are performed to explore the catalytic performance of graphitic C₄N₃ loaded with single transition metal atoms (TM@g-t-C₄N₃) for the OER/ORR. The results show that Fe, Co, Ni and Rh@g-t-C₄N₃ exhibit fascinating bifunctional catalytic activities for both the OER and ORR. Moreover, it is observed that better activities are easily achieved when the valence d orbitals of doped TM atoms are nearly fully occupied. Further analysis reveals the volcano relationship between the OER/ORR performance and the adsorption Gibbs free energy. The adsorption free energy of intermediates in the OER/ORR process is also found to highly correlate with the electronic structures of TM@g-t-C₄N₃, which are mainly characterized by two quantities, one is the descriptor φ related to the electronegativity and the number of valence electrons in d orbitals, and the other is the projected d band center. The results indicate that it is possible to predict the catalytic performance of TM@g-t-C₄N₃ by a detailed examination of the electronic properties of the doped TM atoms to some extent. This research not only provides several highly active g-t-C₄N₃-based single-atom catalysts (SACs) for the OER/ORR, but also reveals some potential regularities of SAC systems.

---

1. Introduction

The energy issue has drawn widespread concerns because of massive consumption of fossil fuels and ever-increasing power demands.^1,2 Developing energy devices with high conversion efficiency is a promising strategy to deal with the energy crisis. Among various devices, water splitting cells and fuel cells are paid close attention as water splitting cells can produce clean and high-energy-density hydrogen by using renewable energy and fuel cells are able to efficiently utilize hydrogen energy.^3–5 Unfortunately, their commercial applications are hindered by the sluggish electrode reactions, i.e., the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR).^6–8 Therefore, catalysts with high activities are desired to accelerate the sluggish reactions. Currently, noble metal-based materials are commonly used as effective catalysts for the OER and ORR.^9–14 However, the low reserves and high price restrict the large-scale application of these precious materials. As a consequence, developing alternative catalysts with high activity and low cost becomes more and more urgent in practice.^15,16

Single-atom catalysts (SACs) have been considered to have broad prospects in catalysis owing to the maximized utilization of loaded metal atoms and the excellent catalytic activity.^17,18 Numerous studies have revealed the commendable catalytic ability of SACs for a series of reactions, such as the OER,^19–21 ORR,^22–24 hydrogen evolution reaction (HER),^25–28 nitrogen reduction reaction (NRR),^29,30 carbon dioxide reduction reaction (CO₂RR),^31,32etc. In order to acquire a SAC structure with sufficiently dispersed transition metal (TM) atoms, a suitable substrate is firstly required, which should restrain the aggregation of loaded TM atoms.³³ Two-dimensional (2D) carbonaceous materials have shown promising prospects as substrates to anchor TM atoms due to their porous structures and large surface area.^34–39 Particularly, graphene (Gr),^22–24,34 graphyne (Gy)^35,36 and graphitic carbon nitride (g-C_xN_y)^37–39 have been widely reported as appropriate substrates for the anchoring of TM atoms. Among various g-C_xN_y species, g-C₄N₃ has received widespread interest due to its unique geometric and electronic structures.^40–44 Many reports have already shown that the single-ring g-C₄N₃ (g-s-C₄N₃) is appropriate to provide support for SACs, which can efficiently catalyze many reaction processes, such as the NRR,⁴⁵ OER/ORR⁴⁶ and oxidation reaction of formaldehyde (HCHO).⁴⁷ On the other side, another structure of g-C₄N₃ with tri-ring units ((g-t-C₄N₃) was reported theoretically in 2013.⁴¹ Furthermore, Sakshi Agarwal et al. found that the g-t-C₄N₃ doped with single TM atoms can catalyze the NRR process with high performance,⁴⁸ clarifying that the g-t-C₄N₃ has broad prospects in catalysis. However, relevant studies for the application of g-t-C₄N₃ for the OER and ORR are rare and need to be further conducted. Therefore, in this work, a series of TM-doped g-t-C₄N₃ SACs (TM@g-t-C₄N₃) are designed so as to investigate the potential ability for catalyzing the OER and ORR.

Herein, 26 TMs (Fig. 1) are selected to be embedded into the g-t-C₄N₃ sheet to form TM@g-t-C₄N₃ whose stability and electronic properties are explored firstly. Then the catalytic performance of TM@g-t-C₄N₃ for the OER/ORR is evaluated by investigating the reaction process. The relationship between adsorption Gibbs free energy and OER/ORR activity is revealed from the volcano curve. Furthermore, the catalytic origins of TM@g-t-C₄N₃ are analyzed using the introduced descriptor φ and the projected d-band center, where the former is determined from Pauling's electronegativity and the number of valence electrons in d orbitals of TM atoms while the latter directly represents the electronic properties of doped-TM atoms. Meanwhile, the electronic structures of typical adsorbed systems are analyzed to gain a deeper insight into the physical image of catalytic activity.

Fig. 1 (a) Schematic diagram of g-t-C₄N₃ with anchored TM atoms, and (b) 26 TM atoms considered in this work.

2. Computational methods

Spin-polarized density functional theory (DFT) calculations are performed using the Vienna ab initio simulation package (VASP),^49,50 with the DFT-D3 van der Waals (vdW) corrections.⁵¹ The interactions between ions and electrons are treated by the project-augmented wave (PAW) method⁵² with a cut-off energy of 500 eV. The Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) is adopted to describe the exchange–correlation interaction.⁵³ A 3 × 3 × 1 gamma-centered k-point grid is employed in the structural optimization, while a denser grid of 6 × 6 × 1 is used for the calculation of density of states (DOS). Besides, the thermodynamic stability of TM@g-t-C₄N₃ is assessed via ab initio molecular dynamics (AIMD) simulations.⁵⁴ The convergence criteria of energy and force are set as 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively. A vacuum region of 20 Å is created to preclude the influence between adjacent layers.

The changes of Gibbs free energy (ΔG) are calculated based on the computational hydrogen electrode (CHE) model¹⁰via the equation:

ΔG = ΔE + ΔE_ZPE − TΔS (1)

where ΔE is the change of total energy obtained from DFT calculations, and ΔE_ZPE and ΔS are the differences of zero-point energy and entropy, respectively. T is the room temperature. More computational details are presented in the ESI.†

3. Results and discussion

3.1. Construction and stability of TM@g-t-C₄N₃

A steady substrate is a prerequisite for the construction of SACs. Herein, a 2 × 2 × 1 supercell of g-t-C₄N₃ is selected to construct TM@g-t-C₄N₃ systems. As shown in Fig. S1 (ESI†), the optimized structure of g-t-C₄N₃ possesses planar properties with net pores encircled by six sp²-bonded N atoms, which could be beneficial to the anchoring of TM atoms. The AIMD simulations indicate the good thermodynamic stability of g-t-C₄N₃ as the total energy oscillates around the equilibrium value. In addition, the insets of Fig. S1 (ESI†) demonstrate that the structure of g-t-C₄N₃ is robust due to the little deformation after a 5 ps evolution.

Fig. 1 shows the construction process and structural prototype of TM@g-t-C₄N₃. There are 26 TMs that are chosen to be embedded in the g-t-C₄N₃ sheet to obtain initial models of TM@g-t-C₄N₃. Then, all these configurations are optimized and the final structures are shown in Fig. S3 (ESI†). It can be seen that most TM atoms locate at the pore center, while Fe, Co, Ni, Cu and Zn prefer to stay at off-center positions, which may be owing to their smaller atomic radii. Furthermore, crinkles appear around the TM sites in the structures of Fe, Ni, Cu and Zn@g-t-C₄N₃. The asymmetric position of TM might be the primary reason for the slight deformation of the structure. The energy stability of TM@g-t-C₄N₃ is evaluated by calculating the binding energy (E_b) defined as:

E_b = E_TM@g-t-C4N3 − E_g-t-C4N3 − E_TM (2)

where E_TM@g-t-C4N3 and E_g-t-C4N3 are the total energies of g-t-C₄N₃ with and without TM atoms, and E_TM is the energy of a free TM atom. According to this definition, the more negative the E_b is, the more stable the TM@g-t-C₄N₃ is. As presented in Fig. 2(a), all the TM@g-t-C₄N₃ possess negative E_b ranging from −12.95 to −3.63 eV, indicating the energy stability of TM@g-t-C₄N₃. Interestingly, the increasing number of valence d electrons can result in the decrease of binding strength between TM atoms and the substrate. This may be due to the less unoccupied d orbitals of TM atoms having less capacity to interact with electrons in bordering N atoms, thus leading to their weaker interactions and less negative E_b. This can be partially evidenced by the charge density difference (CDD) presented in Fig. S4 (ESI†), which is calculated using the formula: Δρ = ρ_TM@g-t-C4N3 − ρ_g-t-C4N3 − ρ_TM, where the ρ_TM@g-t-C4N3, ρ_g-t-C4N3 and ρ_TM represent the charge densities of TM@g-t-C₄N₃, g-t-C₄N₃ and TM atoms, respectively. Comparison of Fig. 2(a) and (b) shows that the Bader charge⁵⁵ displays contrary tendency with the E_b of various doped TM atoms. This indicates that the stronger the interactions between the TM and the substrate, the more stable the TM@g-t-C₄N₃ is, which is consistent with the analysis of CDDs.

Fig. 2 (a) The binding energy of TM@g-t-C₄N₃. (b) The Bader charge transferred from the metal atom to the substrate in the TM@g-t-C₄N₃. (c) The formation energy (left label) and dissolution potential (right label) of TM@g-t-C₄N₃. The dashed line marks the zero value of dissolution potential.

The formation energy (E_f) is used to investigate the thermodynamic feasibility for construction of TM@g-t-C₄N₃, which is computed using the formula:

where E_c is the cohesive energy of the TM and E_TM,bulk is the energy of the TM bulk unit cell with n atoms.⁵⁶ Generally speaking, a negative E_f can provide an argument for the spontaneous formation of SACs rather than metal clusters,⁵⁷ which means that the TM atoms tend to be dispersedly bound in the g-t-C₄N₃ rather than remain aggregated to form metal clusters. As shown in Fig. 2(c), the E_f values are negative for all TM@g-t-C₄N₃ except Os@g-t-C₄N₃, which indicates that Os is more likely to accumulate into metal clusters while the other TMs prefer to be anchored dispersedly on the substrate. Another point to consider is the electrochemical stability of the TM@g-t-C₄N₃ due to the fact that the metal atoms may be dissolved into ions in aqueous environments. The electrochemical stability against electrochemical dissolution can be estimated by calculating the dissolution potential (U_dis):where U_TM,bulk⁰ is the standard dissolution potential of the bulk metal and n_e is the number of electrons involved in the dissolution.^58,59 As shown in Fig. 2(c), all the TM@g-t-C₄N₃ have positive U_dis, suggesting their electrochemical stability in aqueous environments. In short, the Os@g-t-C₄N₃ whose E_f is positive is not considered as a SAC candidate while other TM@g-t-C₄N₃ are further studied in following discussions on the catalysis of the OER and ORR.

3.2. Catalytic performances of TM@g-t-C₄N₃

The adsorption properties of intermediates in the OER/ORR process (*OH, *O and *OOH) are studied to investigate the catalytic performances of TM@g-t-C₄N₃. According to the Sabatier principle,²⁵ the adsorption strength of the intermediate should not be too strong or too weak, otherwise the reaction progress would be restrained somehow. Fig. 3 depicts the ΔG values of oxygen containing adsorbates with the data summarized in Table S2 (ESI†). It is seen that the ΔG of different intermediates vary in a similar trend. Particularly, the changing of ΔG_*OH and ΔG_*OOH is almost synchronous, which indicates that there exists a strong correlation between these two quantities and it will be further proved in Section 3.3. The Ti, V, Zr, Nb, Mo, Hf, Ta and W@g-t-C₄N₃ systems possess low ΔG_*O with the value in the range of −2.16 to −0.56 eV, indicating too strong adsorption of *O. It could be related to the obvious d states near the Fermi level in the spin-up channel as presented in Fig. S5 (ESI†). Hence, these SAC candidates probably display poor activity for the OER/ORR.

Fig. 3 The adsorption Gibbs free energies of *OH, *O and *OOH on TM@g-t-C₄N₃. The ΔG_*OOH of Ta@g-t-C₄N₃ is marked with hollow triangles because the adsorption of *OOH on Ta@g-t-C₄N₃ is not stable. The *OOH group will automatically separate into *O + OH after structural optimization, and the optimized structure is shown in Fig. S6 (ESI†).

In order to clarify the OER and ORR performances of TM@g-t-C₄N₃, the reaction Gibbs free energy of each fundamental step is calculated whose value is summarized in Table S4 (ESI†). Besides, the theoretical overpotential (η) is also computed from the reaction Gibbs free energy in the potential-determining step (PDS) for the OER/ORR, which is listed in Table S5 (ESI†). For the OER, it can be seen from Fig. 4(a)–(d) that the Fe, Co, Ni and Rh@g-t-C₄N₃ possess low η^OER values of 0.63, 0.54, 0.44 and 0.56 V, respectively, which shows comparable catalytic ability to the previous IrO₂ (η^OER = 0.56 V),¹⁰ while other TM@g-t-C₄N₃ have relatively poor OER activity due to their large η^OER. Specifically, for example, the Ni@g-t-C₄N₃ possesses lowest η^OER of 0.44 V among all candidates, indicating that when the equilibrium potential of 1.23 V is applied, the OER still proceeds non-spontaneously owing to the uphill steps of both *OH to *O and *O to *OOH. An external potential of 1.67 V is required at least to fully inverse the upward trend of the steps and to make the OER process occur spontaneously. For the ORR, Ni@g-t-C₄N₃ is also the best catalyst due to the lowest η^OER (0.41 V) among all the TM@g-t-C₄N₃, and it presents comparable catalytic activity to the Pt catalyst (η^ORR = 0.45 V).⁶⁰ In addition, the doped systems with Mn (0.60 V), Fe (0.70 V), Co (0.61 V), Cu (0.70 V), Zn (0.78 V), Ru (0.75 V), Rh (0.75 V) and Ir (0.74 V) also exhibit relatively good ORR activity.

Fig. 4 The Gibbs free energy diagrams of (a) Fe@g-t-C₄N₃, (b) Co@g-t-C₄N₃, (c) Ni@g-t-C₄N₃ and (d) Rh@g-t-C₄N₃ under different external potentials. (e) and (f) show the heat maps of overpotentials of the OER and ORR for TM@g-t-C₄N₃, respectively.

Interestingly, it is found that the active SACs for the OER and ORR are those catalysts doped with TM atoms at the upper center-right area of the d-block in the periodic table as shown in Fig. 4(e) and (f). The preferable performances of the OER and ORR are achieved when the valence d orbitals of TM atoms are nearly full in each period, and among that, the overpotential tends to be lower with the decrease of the electron shell number (following the reduction of atomic radius). Therefore, the lowest value for both the OER and ORR in the TM@g-t-C₄N₃ system is found in Ni@g-t-C₄N₃. A similar trend has been also observed in some other SAC studies.^5,16,36,61 This may partly originate from the moderate electronegativity and partly from the over half occupation of valence d orbitals of corresponding TM atoms, which enables the TMs’ middle affinity for electrons and appropriate adsorption strength of the intermediates. Quantitative analysis will be described in Section 3.4 with the introduced φ-descriptor.

Based on the aforementioned analysis, the promising bifunctional catalysts for the OER and ORR can be further examined. It is noted that the Ni@g-t-C₄N₃ (η^OER/η^ORR = 0.44/0.41 V) exhibits best catalytic activity for both the OER and ORR among all TM@g-t-C₄N₃ candidates. Thus Ni@g-t-C₄N₃ is the most promising bifunctional catalyst for the OER and ORR, followed by Co@g-t-C₄N₃ (η^OER/η^ORR = 0.54/0.61 V), Rh@g-t-C₄N₃ (η^OER/η^ORR = 0.56/0.75 V) and Fe@g-t-C₄N₃ (η^OER/η^ORR = 0.63/0.70 V). It can be inferred from the above results that the screened TM@g-t-C₄N₃ candidates are potential candidates for application as highly efficient catalysts for the OER and ORR.

3.3. Relationship between adsorption and activity

As intrinsic quantities in the OER/ORR process, the adsorption Gibbs free energies of intermediates (ΔG_*OH, ΔG_*O and ΔG_*OOH) are customarily used to characterize the catalytic activity of catalysts. Hence it is important to identify the relationships between the adsorption Gibbs free energies of intermediates and the overpotentials of the OER and ORR.⁶² For TM@g-t-C₄N₃ systems, a strong linear relationship between ΔG_*OH and ΔG_*OOH is discovered. As depicted in Fig. 5(a), the ΔG_*OOH can be expressed as a function of ΔG_*OH: ΔG_*OOH = 0.93ΔG_*OH + 3.15 eV with a large coefficient of determination (R² = 0.93). This result is consistent with other studies on metals and their oxides as well as SACs.^5,6,35,62 Another linear equation between ΔG_*O and ΔG_*OOH is also revealed: ΔG_*OOH = 0.60ΔG_*O + 2.71 eV with an R² of 0.77 as shown in Fig. 5(b). The difference of linearity can be attributed to the fact that *OH and *OOH require one electron to be adsorbed on active sites,^5,6 while *O requires two electrons.

Fig. 5 The scaling relationships of (a) ΔG_*OOHversus ΔG_*OH and (b) ΔG_*OOHversus ΔG_*O. The volcano plots of (c) η^OER against ΔG_*OOH–ΔG_*O and (d) η^ORR against ΔG_*OH, respectively.

As listed in Table S4 (ESI†), the PDSs of the OER for TM@g-t-C₄N₃ systems appear mostly in the third step (*O to *OOH), thus ΔG_*OOH–ΔG_*O can be applied as a solid indicator to delineate the η^OER. As shown in Fig. 5(c), the η^OERversus ΔG_*OOH–ΔG_*O exhibits universal volcano characteristics. Ni@g-t-C₄N₃ is the closest to the peak of volcano and exhibits best catalytic activity. Besides, it is noticed that most TM@g-t-C₄N₃ tend to stay in the right branch of the volcano curve where the values of ΔG_*OOH–ΔG_*O are larger than the left ones, which implies that the relatively weak adsorption of *OOH or the relatively strong adsorption of *O are the main limiting factors to the OER activity of TM@g-t-C₄N₃. Table S4 (ESI†) also shows that the PDSs of the ORR for TM@g-t-C₄N₃ occur at the desorption step of *OH or the formation of *OOH (*OH). Considering the strong linearity between ΔG_*OOH and ΔG_*OH, the ΔG_*OH can be employed as a sufficient descriptor for the η^ORR. As shown in Fig. 5(d), a volcano curve between η^ORR and ΔG_*OH is obtained. Among all TM@g-t-C₄N₃ candidates, the Ni@g-t-C₄N₃ nearly locates at the peak of the volcano, indicating its best ORR activity. Moreover, the ORR activity of TM@g-t-C₄N₃ will increase at first and then decrease with the decreasing of ΔG_*OH, and reaches its maximum when ΔG_*OH equals 0.79 eV, which indicates that moderate adsorption strength of *OH will be beneficial to the ORR activity of TM@g-t-C₄N₃.

3.4. Origin of the catalytic activity

In order to uncover the origin of catalytic activity of TM@g-t-C₄N₃, the descriptor (φ) based on intrinsic properties of TM atoms is introduced,⁶³ which is calculated using the formula:

φ = θ_d × χ_TM (5)

where θ_d represents the number of valence electrons in d orbitals of TM atoms and χ_TM is the Pauling's electronegativity. The definition of φ suggests that φ is a comprehensive quantity to estimate the ability of TM atoms to accommodate and gain electrons. As mentioned in Section 3.2, the middle affinity of TM atom for electrons is more appropriate for the moderate adsorption of intermediates and the good OER/ORR performance. Thereby a quantitative analysis is conducted to further investigate the relationships between φ and adsorption Gibbs free energies of reaction species. As shown in Fig. 6(a), the φ is positively correlated with the ΔG_*OH (ΔG_*OOH) with a large Pearson correlation coefficient of 0.87 (0.82). Furthermore, the values of ΔG_*OH and ΔG_*OOH can be evaluated approximately by the fitting lines presented in Fig. 6(b) and (c), respectively. These results suggest that a medium φ is beneficial to the moderate adsorption of intermediates, which will be good for the reaction process according to the Sabatier principle. Therefore, φ can be a sufficient descriptor to predict the adsorption strength of intermediates, and thus an appropriate descriptor for the OER/ORR performance.

Fig. 6 (a) Heat map of Pearson correlation matrix of φ, ΔG_*OH, ΔG_*O and ΔG_*OOH. The color bar represents the value of Pearson correlation coefficient. (b) and (c) show the fitting lines of (b) ΔG_*OH and (c) ΔG_*OOHversus φ, respectively.

The d-band center (ε_d) is then applied to gain a deeper insight into the catalytic activity of TM@g-t-C₄N₃, which is calculated using the formula:

where ε is the energy and D(ε) is the density of states of d orbitals along the variation of ε. The computed results are depicted in Fig. 7(a) and the data are summarized in Table S6 (ESI†). In general, the value of each projected d-band center decreases with the increasing of the number of valence electrons in d orbitals in each period. The d_xz- and d_yz-band centers of each TM atom have nearly the same values in each spin channel, and so do the d_xy- and d_x²−y²-band centers. Moreover, as shown in Table S7 (ESI†), the fitting equations of d_xz- and d_yz- (d_xy- and d_x²−y²-) band centers versus d_z²-band center exhibit nearly same slopes and intercepts. This characteristic is attributed to the spatial distribution of different d orbitals in TM atoms and the quasi-symmetric structures around TM sites in most TM@g-t-C₄N₃. Therefore, d_xz and d_yz (d_xy and d_x²−y²) orbitals can be treated as a group. As shown in Fig. 7(b) and (c), the relative order of group d_xy–d_x²−y² will upshift with the increasing of d_z²-band center especially for the spin-up channel. Considering the fact that the d_z², d_xz and d_yz orbitals are mainly involved in the interactions between TM and the adsorbates,^8,64 this kind of order changing will impel the d_z², d_xz and d_yz orbitals to locate at relatively deeper energy levels and to be good electrons donors, which will strengthen the binding strength of oxygen containing intermediates as depicted in Fig. S10–S12 (ESI†). Therefore, the intermediates adsorbed on early-TM-doped g-t-C₄N₃ usually are more negative ΔG as shown in Fig. 3.

Fig. 7 (a) The spin-up (UP) and spin-down (DW) projected d-band centers of anchored TM atoms. The fitting lines of projected d-band centers of group d_xz–d_yz and group d_xy–d_x²−y²versus d_z²-band center for (b) UP and (c) DW channels, respectively. The insets show the relative order of projected d-orbitals in each region.

The electronic structures of *OH adsorbed on Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃ are further analyzed to reveal the specific images of activity. It is found from Fig. 8(a) and (b) that electrons are transferred from the TM to the *OH, which is also consistent with the result obtained from Bader charge analysis. Furthermore, based on the analysis of crystal orbital Hamilton population (COHP) and projected density of states (PDOS), it is indicated that when *OH is adsorbed on Ni@g-t-C₄N₃, the p orbitals of O and the d orbitals of Ni will strongly hybridize and form bonding and anti-bonding orbitals as shown in Fig. 8(c). The hybridization includes inert d_xy and d_x²−y² orbitals. It is mainly attributed to the asymmetric and crinkling structure of the Ni@g-t-C₄N₃ especially near the active Ni site, which can be helpful to break out the symmetry conservation and make inert orbitals (d_xy and d_x²−y²) participate in orbital interactions.⁶⁴ In addition, for *OH adsorbed on Rh@g-t-C₄N₃, strong hybridizations also occur between p orbitals of O and d orbitals of Rh as seen in Fig. 8(d). However, the participation of d_xy and d_x²−y² orbitals in hybridization is negligible. It is due to the quasi-symmetric structure of Rh@g-t-C₄N₃ around Rh atom that keeps the restriction of orbital symmetry in orbital interactions.⁶⁴ The results indicate that the concrete electronic structures of TM@g-t-C₄N₃ can be used to predict the adsorption behavior of intermediates in the OER and ORR, thus be effectual to investigate the origin of catalytic activity.

Fig. 8 The CDDs of *OH adsorbed on (a) Ni@g-t-C₄N₃ and (b) Rh@g-t-C₄N₃, respectively. The yellow represents accumulation of electrons while the cyan represents depletion of electrons. The isovalue is set to 0.009 e Bohr⁻³. (c) and (d) show the COHP (PDOS) of *OH adsorbed on Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃, respectively. The Fermi level is set to zero. (e) and (f) are the results of AIMD simulations (300 K) of Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃, respectively. The insets show corresponding atomic structures after a 5 ps evolution.

To further ensure the thermodynamic stability of Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃, the AIMD simulations are carried out. As shown in Fig. 8(e) and (f), the total energies of Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃ are fluctuating near the equilibrium states. For Ni@g-t-C₄N₃, the energy oscillation is smaller than 1.2 eV, and for Rh@g-t-C₄N₃, the energy oscillation is no more than 1.5 eV. Besides, the insets demonstrate that the atomic structures of Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃ are robust and hardly changed after a 5 ps evolution at the temperature of 300 K, indicating their excellent thermodynamic stability.

4. Conclusions

By means of DFT calculations, the catalytic performances of TM@g-t-C₄N₃ (TM = Sc ∼ Au) for the OER and ORR have been studied systematically. The results show that Ni@g-t-C₄N₃ exhibits highest bifunctional catalytic activity for the OER and ORR (η^OER/η^ORR = 0.44/0.41 V) among all TM@g-t-C₄N₃ systems. Meanwhile, Fe, Co and Rh@g-t-C₄N₃ also exhibit excellent bifunctional ability for the OER and ORR. Furthermore, it is discovered that the best OER and ORR activities are easily achieved when the doped TM atoms are located at the upper center-right area of the d-block. The volcano curves are uncovered to present the relationship between adsorption Gibbs free energies of reaction intermediates and catalytic performances.

The electronic structures of TM@g-t-C₄N₃ are investigated to explore the origin of catalytic activity. Firstly, it is found that the ΔG_*OH and ΔG_*OOH can be simply assessed using the intrinsic descriptor φ. Moreover, the analysis based on the projected d-band center reveals that the relative order of different projected d orbitals will affect the adsorption strength of oxygen containing intermediates, thus promoting or inhibiting the catalytic processes of the OER and ORR. The COHP and PDOS show the orbital interactions between *OH and TM active sites (Ni and Rh), which can provide deeper insights for the excellent catalytic activity of Ni@g-t-C₄N₃ and Rh@g-t-C₄N₃. The results manifest the wide prospects of g-t-C₄N₃-based materials for the catalysis of the OER/ORR process. However, some key factors for the TM@g-t-C₄N₃ SACs need to be further studied. On the one hand, the investigation into reaction kinetics of the OER/ORR should be paid attention so as to further determine the actual barrier in the reaction process. On the other hand, the synthesis of TM@g-t-C₄N₃ and their stability under OER/ORR conditions ought to be studied more to evaluate the application of TM@g-t-C₄N₃ as efficient OER/ORR catalysts.

Conflicts of interest

There are no conflicts to declare.

References

1. K. Villa, J. R. Galán-Mascarós, N. López and E. Palomares, Photocatalytic water splitting: advantages and challenges, Sustainable Energy Fuels, 2021, 5, 4560–4569.
2. S. Wang, L. Shi, X. Bai, Q. Li, C. Ling and J. Wang, Highly efficient photo-/electrocatalytic reduction of nitrogen into ammonia by dual-metal sites, ACS Cent. Sci., 2020, 6, 1762–1771.
3. T. Zheng, X. Han, J. Wang and Z. Xia, Role of heteroatom-doping in enhancing catalytic activities and the stability of single-atom catalysts for oxygen reduction and oxygen evolution reactions, Nanoscale, 2022, 14, 16286–16294.
4. J. J. Yang, Y. Zhang, X. Y. Xie, W. H. Fang and G. Cui, Photocatalytic reduction of carbon dioxide to methane at the Pd-supported TiO₂ interface: mechanistic insights from theoretical studies, ACS Catal., 2022, 12, 8558–8571.
5. Y. Wang, M. Wang, Z. Lu, D. Ma and Y. Jia, Enabling multifunctional electrocatalysts by modifying the basal plane of unifunctional 1T'-MoS₂ with anchored transition metal single atoms, Nanoscale, 2021, 13, 13390–13400.
6. J. Xu, Y. Wang, N. Song, S. Luo, B. Xu, J. Zhang and F. Wang, Doping of the Mn vacancy of Mn₂B₂ with a single different transition metal atom as the dual-function electrocatalyst, Phys. Chem. Chem. Phys., 2022, 24, 20988–20997.
7. S. Lu, H. L. Huynh, F. Lou, K. Guo and Z. Yu, Single transition metal atom embedded antimonene monolayers as efficient trifunctional electrocatalysts for the HER, OER and ORR: a density functional theory study, Nanoscale, 2021, 13, 12885–12895.
8. C. Zhang, Y. Dai, Q. Sun, C. Ye, R. Lu, Y. Zhou and Y. Zhao, Strategy to weaken the oxygen adsorption on single-atom catalysts towards oxygen-involved reactions, Mater. Today Adv., 2022, 16, 100280.
9. Y. J. Wang, N. Zhao, B. Fang, H. Li, X. T. Bi and H. Wang, Carbon-supported Pt-based alloy electrocatalysts for the oxygen reduction reaction in polymer electrolyte membrane fuel cells: particle size, shape, and composition manipulation and their impact to activity, Chem. Rev., 2015, 115, 3433–3467.
10. J. Rossmeisl, Z. W. Qu, H. Zhu, G. J. Kroes and J. K. Nørskov, Electrolysis of water on oxide surfaces, J. Electroanal. Chem., 2007, 607, 83–89.
11. N. T. Suen, S. F. Hung, Q. Quan, N. Zhang, Y. J. Xu and H. M. Chen, Electrocatalysis for the oxygen evolution reaction: recent development and future perspectives, Chem. Soc. Rev., 2017, 46, 337–365.
12. A. Mahata, A. S. Nair and B. Pathak, Recent advancements in Pt-nanostructure-based electrocatalysts for the oxygen reduction reaction, Catal. Sci. Technol., 2019, 9, 4835–4863.
13. N. Bhuvanendran, S. Ravichandran, S. S. Jayaseelan, Q. Xu, L. Khotseng and H. Su, Improved bi-functional oxygen electrocatalytic performance of Pt–Ir alloy nanoparticles embedded on MWCNT with Pt-enriched surfaces, Energy, 2020, 211, 118695.
14. R. Wang, X. Cao, S. Sui, B. Li and Q. Li, Study on the growth of platinum nanowires as cathode catalysts in proton exchange membrane fuel cells, Front. Chem. Sci. Eng., 2021, 16, 364–375.
15. S. Qi, J. Wang, X. Song, Y. Fan, W. Li, A. Du and M. Zhao, Synergistic trifunctional electrocatalysis of pyridinic nitrogen and single transition-metal atoms anchored on pyrazine-modified graphdiyne, Sci. Bull., 2020, 65, 995–1002.
16. Z. Qin, Z. Wang and J. Zhao, Computational screening of single-atom catalysts supported by VS₂ monolayers for electrocatalytic oxygen reduction/evolution reactions, Nanoscale, 2022, 14, 6902–6911.
17. X. F. Yang, A. Q. Wang, B. T. Qiao, J. Li, J. Y. Liu and T. Zhang, Single-atom catalysts: a new frontier in heterogeneous catalysis, Acc. Chem. Res., 2013, 46, 1740–1748.
18. H. Xu, D. Cheng, D. Cao and X. C. Zeng, A universal principle for a rational design of single-atom electrocatalysts, Nat. Catal., 2018, 1, 339–348.
19. Q. Wang, E. Yang, R. Liu, M. Lv, W. Zhang, G. Yu and W. Chen, Embedding group VIII elements into a 2D rigid pc-C₃N₂ monolayer to achieve single-atom catalysts with excellent OER activity: a DFT theoretical study, Molecules, 2022, 28, 254.
20. Z. H. Zhou, W. H. Li, Z. Zhang, Q. S. Huang, X. C. Zhao and W. Cao, Ni-O₄ as active sites for efficient oxygen evolution reaction with electronic metal-support interactions, ACS Appl. Mater. Interfaces, 2022, 14, 47542–47548.
21. A. Allangawi, T. Mahmood, K. Ayub and M. A. Gilani, Anchoring the late first row transition metals with B₁₂P₁₂ nanocage to act as single atom catalysts toward oxygen evolution reaction (OER), Mater. Sci. Semicond. Process., 2023, 153, 107164.
22. F. Ge, Q. Qiao, X. Chen and Y. Wu, Probing the catalytic activity of M-N_4−xO_x embedded graphene for the oxygen reduction reaction by density functional theory, Front. Chem. Sci. Eng., 2021, 15, 1206–1216.
23. X. Hu, S. Chen, L. Chen, Y. Tian, S. Yao, Z. Lu, X. Zhang and Z. Zhou, What is the real origin of the activity of Fe-N-C electrocatalysts in the O₂ reduction reaction? Critical roles of coordinating pyrrolic N and axially adsorbing species, J. Am. Chem. Soc., 2022, 144, 18144–18152.
24. W. Zhang, J. K. Pan, Y. F. Yu, X. J. Zhang, J. H. Wang, W. X. Chen and G. L. Zhuang, Correlation of the spin state and catalytic property of M-N₄ single-atom catalysts in oxygen reduction reactions, Phys. Chem. Chem. Phys., 2023, 25, 11673–11683.
25. G. Di Liberto, L. A. Cipriano and G. Pacchioni, Universal principles for the rational design of single atom electrocatalysts? Handle with care, ACS Catal., 2022, 12, 5846–5856.
26. D. Chodvadiya, P. K. Jha and B. Chakraborty, Theoretical inspection of Ni/α-SiX (X = N, P, As, Sb, Bi) single-atom catalyst: ultra-high performance for hydrogen evolution reaction, Int. J. Hydrogen Energy, 2022, 47, 41733–41747.
27. T. Liu, X. Zhao, X. Liu, W. Xiao, Z. Luo, W. Wang, Y. Zhang and J. C. Liu, Understanding the hydrogen evolution reaction activity of doped single-atom catalysts on two-dimensional GaPS₄ by DFT and machine learning, J. Energy Chem., 2023, 81, 93–100.
28. T. L. Wan, J. Liu, X. Tan, T. Liao, Y. Gu, A. Du, S. Smith and L. Kou, Rational design of 2D ferroelectric heterogeneous catalysts for controllable hydrogen evolution reaction, J. Mater. Chem. A, 2022, 10, 22228–22235.
29. T. Bo, S. Cao, N. Mu, R. Xu, Y. Liu and W. Zhou, First principles screening of transition metal single-atom catalysts for nitrogen reduction reaction, Appl. Surf. Sci., 2023, 612, 155916.
30. S. Han, X. Wei, Y. Huang, J. Zhang, J. Yang and Z. Wang, Tuning the activity and selectivity of nitrogen reduction reaction on double-atom catalysts by B doping: a density functional theory study, Nano Energy, 2022, 99, 107363.
31. J. Min, L. Liu, F. Chen, X. Jin, T. Yuan and X. Yao, Theoretical exploration on the activity of copper single-atom catalysts for electrocatalytic reduction of CO₂, J. Mater. Chem. A, 2023, 11, 7735–7745.
32. P. Hou, Y. Huang, F. Ma, X. Wei, R. Du, G. Zhu, J. Zhang and M. Wang, S and N coordinated single-atom catalysts for electrochemical CO₂ reduction with superior activity and selectivity, Appl. Surf. Sci., 2023, 619, 156747.
33. X. Liu, G. Li, J. Liu and J. Zhao, Transition metal atoms anchored on square graphyne as multifunctional electrocatalysts: a computational investigation, Mol. Catal., 2022, 531, 112706.
34. X. Bai, X. Zhao, Y. Zhang, C. Ling, Y. Zhou, J. Wang and Y. Liu, Dynamic stability of copper single-atom catalysts under working conditions, J. Am. Chem. Soc., 2022, 144, 17140–17148.
35. M. Guo, M. Ji and W. Cui, Theoretical investigation of HER/OER/ORR catalytic activity of single atom-decorated graphyne by DFT and comparative DOS analyses, Appl. Surf. Sci., 2022, 592, 153237.
36. Z. Zhang, S. Qi, X. Song, J. Wang, W. Zhang and M. Zhao, Stable multifunctional single-atom catalysts adsorbed on pyrazine-modified graphyne, Appl. Surf. Sci., 2021, 553, 149464.
37. H. Niu, Z. Zhang, X. Wang, X. Wan, C. Shao and Y. Guo, Theoretical insights into the mechanism of selective nitrate-to-ammonia electroreduction on single-atom catalysts, Adv. Funct. Mater., 2020, 31, 2008533.
38. Z. Yang, Y. Li, C. Qi and C. Wang, Single atom catalysts supported on metallic C₅N monolayers for oxygen reduction/evolution reactions with more active sites than loaded metal atoms, Appl. Surf. Sci., 2023, 614, 156048.
39. N. Sathishkumar, S.-Y. Wu and H.-T. Chen, Mechanistic exploring the catalytic activity of single-atom catalysts anchored in graphitic carbon nitride toward electroreduction of nitrate-to-ammonia, Appl. Surf. Sci., 2022, 598, 153829.
40. A. Du, S. Sanvito and S. C. Smith, First-principles prediction of metal-free magnetism and intrinsic half-metallicity in graphitic carbon nitride, Phys. Rev. Lett., 2012, 108, 197207.
41. X. Li, S. Zhang and Q. Wang, Stability and physical properties of a tri-ring based porous g-C₄N₃ sheet, Phys. Chem. Chem. Phys., 2013, 15, 7142–7146.
42. J. Cui, S. Liang and J. Zhang, A multifunctional material of two-dimensional g-C₄N₃/graphene bilayer, Phys. Chem. Chem. Phys., 2016, 18, 25388–25393.
43. M. Mehrdad and A. Moosavi, Novel adjustable monolayer carbon nitride membranes for high-performance saline water desalination, Nanotechnology, 2021, 32, 045706.
44. R. B. Gurung, N. Sharma and H.-F. Wu, White light emission and superior photoelctrochemical response from semi-metallic graphitic carbon nitride analogue: g-C₄N₃, Mater. Sci. Eng. B, 2022, 280, 115663.
45. X. Wang and L.-M. Yang, Unveiling the underlying mechanism of nitrogen fixation by a new class of electrocatalysts two-dimensional TM@g-C₄N₃ monosheets, Appl. Surf. Sci., 2022, 576, 151839.
46. X. Wan, W. Yu, H. Niu, X. Wang, Z. Zhang and Y. Guo, Revealing the oxygen reduction/evolution reaction activity origin of carbon-nitride-related single-atom catalysts: quantum chemistry in artificial intelligence, Chem. Eng. J., 2022, 440, 135946.
47. D. Li, X. Chen, Y. Huang, G. Zhang, D. Zhou and B. Xiao, Selective catalytic oxidation of formaldehyde on single V- and Cr-atom decorated magnetic C₄N₃ substrate: a first principles study, J. Hazard. Mater., 2022, 439, 129608.
48. S. Agarwal, R. Kumar, R. Arya and A. K. Singh, Rational design of single-atom catalysts for enhanced electrocatalytic nitrogen reduction reaction, J. Phys. Chem. C, 2021, 125, 12585–12593.
49. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci., 1996, 6, 15–50.
50. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
51. S. Grimme, S. Ehrlich and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem., 2011, 32, 1456–1465.
52. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
53. J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, 77, 3865–3868.
54. G. J. Martyna, M. L. Klein and M. Tuckerman, Nosé–Hoover chains: the canonical ensemble via continuous dynamics, J. Chem. Phys., 1992, 97, 2635–2643.
55. W. Tang, E. Sanville and G. Henkelman, A grid-based Bader analysis algorithm without lattice bias, J. Phys.: Condens. Matter, 2009, 21, 084204.
56. P. Janthon, S. M. Kozlov, F. Vines, J. Limtrakul and F. Illas, Establishing the accuracy of broadly used density functionals in describing bulk properties of transition metals, J. Chem. Theory Comput., 2013, 9, 1631–1640.
57. P. Hou, Y. Huang, F. Ma, G. Zhu, J. Zhang, X. Wei, P. Du and J. Liu, Computational screening and catalytic origin of transition metal supported on g-t-C₃N₄ as single-atom catalysts for nitrogen reduction reaction, Appl. Surf. Sci., 2022, 599, 153880.
58. X. Guo, J. Gu, S. Lin, S. Zhang, Z. Chen and S. Huang, Tackling the Activity and Selectivity Challenges of Electro-catalysts toward the Nitrogen Reduction Reaction via Atomically Dispersed Biatom Catalysts, J. Am. Chem. Soc., 2020, 142, 5709–5721.
59. CRC Handbook of Chemistry and Physics, Internet Version 2005, ed. David R. Lide, CRC Press, Boca Raton, FL, https://www.hbcpnetbase.com, 2005.
60. J. K. Nørskov, J. Rossmeisl, A. Logadottir and L. Lindqvist, Origin of the overpotential for oxygen reduction at a fuel-cell cathode, J. Phys. Chem. B, 2004, 108, 17886–17892.
61. S. L. Li, Q. Li, Y. Chen, Y. Zhao and L. Y. Gan, Transition metal embedded graphynes as advanced bifunctional single atom catalysts for oxygen reduction and evolution reactions, Appl. Surf. Sci., 2022, 605, 154828.
62. M. Bajdich, M. Garcia-Mota, A. Vojvodic, J. K. Norskov and A. T. Bell, Theoretical investigation of the activity of cobalt oxides for the electrochemical oxidation of water, J. Am. Chem. Soc., 2013, 135, 13521–13530.
63. X. Chen, Q. Liu, H. Zhang and X. Zhao, Exploring high-efficiency electrocatalysts of metal-doped two-dimensional C₄N for oxygen reduction, oxygen evolution, and hydrogen evolution reactions by first-principles screening, Phys. Chem. Chem. Phys., 2022, 24, 26061–26069.
64. Y. Sun, S. Sun, H. Yang, S. Xi, J. Gracia and Z. J. Xu, Spin-related electron transfer and orbital interactions in oxygen electrocatalysis, Adv. Mater., 2020, 32, 2003297.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp04249a

---