Density Functional Theory Study of Oxygen Evolution Reaction Mechanism on Rare Earth Sc-Doped Graphene

Abstract

The development of a stable catalyst with excellent catalytic performance for the oxygen evolution reaction (OER) in alkaline environments is a key reaction in various electrochemical technologies. In this work, single-atom catalysts (SACs) systems in which scandium (Sc), a rare earth metal, with different N/C coordination environments (ScN_xC_3−x@SACs and ScN_xC_4−x@SACs of Sc) were systematically studied with the help of density functional theory (DFT) calculations. The results of the structural thermodynamic stability analysis indicated that the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems are more stable with increasing N atom doping concentration around Sc. The ScN₃, ScN₃C, and ScN₄ with better stability were selected as the objects of subsequent research. However, ScN₃ and ScN₄ form Sc(OH)₂N₃ and Sc(OH)₂N₄ structures with double-hydroxyl groups as ligands because of the strong adsorption of OH species, whereas the strong adsorption of OH species by ScN₃C causes structural instability. Here, the overpotential (η) of Sc(OH)₂N₃ was 1.03 V; Sc(OH)₂N₄ had two reaction paths and the η of path 1 was 0.80 V, which was 0.30 V lower than that of path 2. Therefore, Sc(OH)₂N₄ can be used as a stable and promising OER catalyst with easy desorption of O₂ and good cycle performance. The hydroxyl ligand modification of Sc-N_xC_3−x@SACs and Sc-N_xC_4−x@SACs provides a method for studying the catalytic performance of other rare earth elements.

1. Introduction

The current society is confronted with the challenge of increasing energy demand and the associated environmental problems caused by energy consumption. As a result, the global research community has prioritized the search for pollution-free, sustainable, and efficient energy production/energy conversion technologies [1,2,3]. In this regard, the development of rechargeable fuel cells and metal–air battery technologies has been perceived as a promising clean and sustainable energy technology because of its high energy conversion efficiency and power density [4,5]. In these energy conversion technologies, the anodic half-cell reaction, i.e., oxygen evolution reaction (OER), plays a vital role in the efficiency of regenerative fuel cells and metal–air battery technologies [6,7,8]. Due to the instability of transition-metal-based materials in acidic circumstances, electrocatalytic OER is typically carried out in alkaline conditions [9]. Nonetheless, the OER is often deemed the main obstacle in rechargeable fuel cell and metal–air battery technologies because of the slow and sluggish kinetics of this four-electron transfer reaction, which restricts the high efficiency of these energy conversions [10,11].

Extensive research and a wide range of engineered catalysts have been proposed in an effort to increase OER kinetics [12,13,14,15]. Among them, RuO₂ and IrO₂ have exhibited excellent OER catalytic activities [16,17]. However, both are unstable during the reaction process and are oxidized to form RuO₄ and IrO₃, respectively, which preferentially dissolve in solution [18]. Furthermore, Ru and Ir are precious metals with scarce resources and high costs, making them unsuitable for large-scale, commercial applications [19]. Thus, it is essential to develop excellent alternative electrocatalysts for OER with better stability and to explore affordable OER electrocatalysts with good catalytic activity.

On the other hand, carbon-based catalysts, such as graphene, have advantages such as a large specific surface area, high acid/alkaline stability, and excellent electronic conductivity [20,21]. In recent years, carbon-based catalysts have become the focus of OER research. However, pure graphene is catalytically inert [20,22]. Heteroatom doping, especially N doping of graphene, is found to be the most effective method to improve the intrinsic activity of the catalyst because of the variation in the spin density and charge of the carbon atom next to the doped N atom, together with high specific surface area, excellent conductivity, and outstanding electrochemical properties [23,24,25,26]. Single-atom catalysts (SACs), in which a central single metal atom surrounded by different doping atoms forms coordination and disperses in the supporting material, have gained special interest for various catalytic reactions because of their excellent stability, maximum utilization of the metallic electrochemically active surface area, strong metal–support interactions, and unique properties [27,28,29]. Metal–organic frameworks (MOFs) have proven to be a promising approach for SAC preparation. Carbonization of MOFs can result in N-doped carbon materials with N/C coordination, which provides an abundance of anchor points for the fixation of a single metal atom, resulting in SAC stability [30,31]. Accordingly, the synthesis of single transition metal–nitrogen moiety-supported carbon catalysts (M–N–C, M = Fe/Co, etc.) as OER catalysts has been extensively investigated, and these are the most widely studied SACs [32,33]. Unfortunately, the instability of Fe–N–C SACs limits their further application owing to the high Fenton catalytic activity of Fe [34]. On the other hand, the OER overpotential in the Co-N-Gra system is 0.69 V. In addition, due to cobalt’s toxicity, poisoning can happen during the manufacturing and recycling processes, and cobalt leakage also results in battery damage [35].

Rare earth (RE) elements, such as Sc, Nd, Gd, and Ce, have attracted increasing attention in the field of electrocatalytic applications because of their unique multi-electron properties and electronic structure, high electrical conductivity, good stability, abundant reserves, and excellent electrocatalytic activity [36,37,38,39,40,41,42]. In particular, Sc atoms have the characteristics of a small atomic radius, suitability for single/double atom vacancy doping, and multi-electron properties [43,44,45]. Moreover, it has been well established that SACs with a Sc atom as the active site of the catalytic center have a good catalytic effect on CO oxidation and the reduction of CO₂ and N₂ [46,47,48]. Sc@SACs are synthesized on a carbon support with high yields in the literature. Catalytic activities are observed in Sc₁/NC SACs despite the fact that Sc-based nanomaterials are typically inert to room temperature electrochemical processes. This is because N and C coordination alters the local electronic structure of Sc single atoms. The catalytic properties of rare earth single atoms not only showcase the miraculous impact of SACs, but also advocate for the use of rare earth catalysts in electrochemical reactions that take place at room temperature [46,47,48]. Therefore, Sc@SACs systems with varied N/C coordinations as OER catalysts for increased OER kinetics are worth investigating. However, there has been little research on the use of Sc for OER applications. As a result, we investigated the effect of Sc and its coordination environment on the OER in alkaline media.

In this work, Sc@SACs systems with different N/C coordination ratios (4 ScN_xC_3−x@SACs and 7 ScN_xC_4−x@SACs) were studied in detail by performing density functional theory (DFT) calculations. Based on the calculation of the thermodynamic formation energy, the influence of N/C coordination on ScN_xC_3−x@SACs and ScN_xC_4−x@SACs was studied. Thermodynamic stability screening indicated that the formation energies of the ScN₃, ScN₃C, and ScN₄ structures were negative, making them more stable than other structures. Further, simulation analysis in an alkaline environment found that ScN₃ and ScN₄ can exist as Sc(OH)₂N₃ and Sc(OH)₂N₄, respectively, because of the strong adsorption of OH species. However, the Sc (OH)₂N₃C structure formed by ScN₃C was unstable. The catalytic reactions of Sc(OH)₂N₃ and Sc(OH)₂N₄ structures with double-hydroxyl ligand modification for the OER under alkaline conditions were also studied. Finally, the influence of N atom doping concentration, also known as different N/C coordination and hydroxyl ligand effects, on the catalytic performance of the structure was described.

2. Computational Details

2.1. Methods

Dmol³ [49] is the algorithm used for any calculations involving density functional theory with no restrictions on spin. Electronic exchange and correlation effects were described using the generalized gradient approximation [50] with the Perdew–Burke–Ernzerhof functional. After taking into account the ion–electron interaction in the DFT semi-core pseudopotentials [51] and the double numerical plus polarization [52] basis sets, we proceeded to the core treatment. Grimme’s [53] method was used to calculate the dispersion’s share. Energy convergence tolerances were $1\times {10}^{-5}$ Ha, maximum force tolerances were 0.002 Ha Å−1, and displacement tolerances were 0.005 Å. To hasten the convergence, an orbital occupancy smear of 0.005 Ha was used. The calculations used a cutoff radius for global orbits in actual space that was of fine quality. Electronic structure calculations were performed on a 15 × 15 × 1 k-point grid, whereas geometry optimization and energy calculations were performed on a 5 × 5 × 1 k-point grid in the Brillouin zone. For this exercise, we assumed that water has a dielectric constant of 78.54 and utilized the conductor-like screening model [54] to mimic this environment.

2.2. Models

To begin, a 5 × 5 × 1 periodic graphene supercell was built and separated by a 30 Å vacuum layer to eliminate periodic interactions. By substituting a Sc atom for either one or two carbon atoms, ScN_xC_3−x@SACs and ScN_xC_4−x@SACs were created. In place of the C atoms around the central Sc atom, the extremely electronegative N atoms acted as anchors. There were four structures with three coordinations (Sc-N_xC_3−x@SACs) and seven structures with four coordinations (Sc-N_xC_4−x@SACs). Three distinct architectures of ScN₂C₂ are depicted in Figure 1. ScN₂C₂-h is a hexa-atomic ring composed of two nitrogen atoms, two carbon atoms, and a Sc metal atom, whereas ScN₂C₂-p is a penta-atomic ring composed of two nitrogen atoms, two carbon atoms, and a Sc metal atom. The two N atoms in ScN₂C₂-o are situated on either side of the Sc atom.

2.3. Computational Contents

(1)

Formation energy ($∆E_f$)

The $∆E_f$ of different ScN_xC_3−x@SACs and ScN_xC_4−x@SACs structures can be calculated as follows:

$$∆E_f=E_{\mathrm{Sc}-{\mathrm{N}}_x{C}_{3-x}}+\left(x+1\right){\mu }_C-E_{Graphene}-{\mu }_{Sc}-x{\mu }_N, x=0, 1, 2, 3$$

(1)

$$∆E_f=E_{\mathrm{Sc}-{\mathrm{N}}_x{C}_{4-x}}+\left(x+2\right){\mu }_C-E_{Graphene}-{\mu }_{Sc}-x{\mu }_N, x=0, 1, 2, 3, 4$$

(2)

where $E_{\mathrm{Sc}-{\mathrm{N}}_x{C}_{3-x}}$ and $E_{\mathrm{Sc}-{\mathrm{N}}_x{C}_{4-x}}$ are the total energies of the optimized structures of ScN_xC_3−x@SACs and ScN_xC_4−x@SACs, respectively. $E_{Graphene}$ represents the total energy of a single layer of a 5 × 5 × 1 graphene supercell. ${\mu }_C$, ${\mu }_{Sc}$, and ${\mu }_N$ are the chemical potentials of C, Sc, and N atoms, respectively. ${\mu }_C$ is equal to the energy of each carbon atom in the 5 × 5 × 1 graphene supercell, ${\mu }_N$ is the half energy of the isolation N₂ molecule, and ${\mu }_{Sc}$ is the energy of one Sc atom, which can be obtained from the total energy of the Sc unit cell divided by the number of atoms. x + 1, x + 2 and x are the numbers of C atoms discharged from the original graphene and doped N atoms, respectively.

(2)

Adsorption energy ($∆E_{ads}$)

The $∆E_{ads}$ of intermediates can be calculated as follows:

$$∆E_{ads}=E_{\ast n}-E_{\ast }-E_n$$

(3)

where $E_{\ast n}$, $E_{\ast }$, and $E_n$ are the total energies of the ScN_xC_3−x@SACs/ScN_xC_4−x@SACs with n adsorbed species, the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs, and the isolated n species, respectively.

(3)

Gibbs free energy variation ($∆G$)

The $∆G$ of each reaction step can be calculated as follows [55]:

$$∆G=∆E+∆ZPE-T∆S+∆G_U+∆G_{pH}$$

(4)

where $∆E$, $∆ZPE$, and $∆S$ represent the variation in the reaction energy, zero-point energy (ZPE), and entropy, respectively. T is 298.15 K, which represents the room temperature. $∆G_U=-neU$, where $n$ is the number of electron transfers during these elementary reactions, U is the electrode potential, and $∆G_U$ is the free energy contribution related to the applied electrode potential U. $∆G_{pH}=K_{B}T\times ln10\times pH$, where $K_B$ is the Boltzmann constant, and the value of pH is 14 in an alkaline environment.

(4)

Reaction steps of the OER in an alkaline environment

OH + *→OH* + e

(5)

OH* + OH→O* + H₂O (l) + e

(6)

O* + OH→OOH* + e

(7)

OOH* + OH→O₂ (g) + * + H₂O + e

(8)

* represents the adsorption sites on the catalyst surface. *OOH, *O, and *OH are the oxygen-containing intermediate products of the OER process. g and l represent the gas and liquid phases, respectively.

The overpotential of the OER is defined as follows (ƞ^OER):

ƞ^OER = [∆G₁, ∆G₂, ∆G₃, ∆G₄]_max/e − 0.402 V

(9)

3. Results and Discussion

3.1. Stability of Sc and N Co-Doped Graphene

First, the constructed structures (ScN_xC_3−x@SACs and ScN_xC_4−x@SACs) were optimized to obtain the formation energies ($∆E_f$) of different Sc and N co-doped graphene structures, which can be used to analyze the influence of the N atom doping concentration and different coordination environments on structural stability. The formation energies of the different structures are shown in Figure 2, and the detailed values are listed in Table S1. The results showed that the structures of ScN₃, ScN₃C, and ScN₄ were more stable than the other structures because of the negative value of the formation energy. In general, lower $∆E_f$ values indicate higher structural stability. Furthermore, with the increase in the N atom doping concentration, the $∆E_f$ values of the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems with three and four coordinations, respectively, decreased, and the structures were more stable, which is consistent with the phenomena of other systems studied by predecessors [56,57]. Figure 2 shows a close to negative correlation between the concentration of N atoms and formation energy, regardless of the structure of ScN_xC_3−x@SACs and ScN_xC_4−x@SACs. Moreover, in the four-coordination ScN_xC_4−x@SACs system, although the structures of the three kinds of ScN₂C₂ catalysts were different, their formation energies were similar, which is consistent with previous results [57]. However, Sc was not in the same horizontal plane as the underlying graphene in either optimized structures of ScN_xC_3−x@SACs or ScN_xC_4−x@SACs. The reason for this is that the atomic radius of Sc is larger, and the Sc atom bulges on the surface, making some structures with less N atom doping concentration more unstable. However, the bulge of the Sc atom in the stable structure is more favorable for the adsorption of reactants. Because the incorporation of N atoms can alter the structure’s electronegativity, the charge of C and N atoms coupled to Sc is higher, which results in the structures exhibiting increased levels of stability. Moreover, we demonstrated that the structures of ScN₃ with three coordinations and ScN₄ with four coordinations were more stable. Above all, different N/C coordination affected the stability of ScN_xC_3−x@SACs and ScN_xC_4−x@SACs, with more N atoms resulting in a more stable structure.

The partial densities of states (PDOS) of the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems are shown in Figure 3. The analysis of Figure 3 shows that all the models passed through the Fermi level, indicating that all the structures had excellent conductivity. Furthermore, an effective overlap of the s, p, and d orbitals was observed, indicating that Sc formed bonds with the neighboring N and C atoms. In addition, the PDOS of the central part connected to Sc was studied. The overlap of the s, p, and d orbitals in the PDOS of the central part was more obvious, indicating that the Sc atom formed a bond with the base. The peak value of the d orbital rose with the increase of N atom doping concentration, which is similar to the law of formation energy in the ScN_xC_3−x@SACs system. However, in the ScN_xC_4−x@SACs system, although the peak value of the d orbital of ScN₃C was equivalent to three types of ScN₂C₂ structures, it still showed an overall upward trend. Hence, different N/C coordination can significantly affect the electron distribution of the structure. The higher the concentration of N atoms is, the higher the peak value of the d orbital.

Based on Mulliken charge analysis, charge transfer occurred between the Sc, N, and C atoms. The electron transfer number is shown in Table S2, which indicates that the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs structures formed chemical bonds, and the stability of the structure was explained from the side. In addition, different coordination structures followed the same law: with an increase in the N atom doping concentration, more electrons are lost by the Sc atom and gained by the N atoms, and the structure becomes more stable, which is consistent with the law of formation energy. Mulliken charge analysis for three-coordination ScN₃ and four-coordination ScN₄ with more stable and more negative values of the formation energy is further discussed, as shown in Figure 4. The charge distribution was symmetrical, corresponding to a symmetrical structure, which is consistent with the conclusion reached by other scholars on the charge distribution of symmetrical graphene-based materials [58,59]. The darker the color was, the more the charges on the structures gain or lose.

3.2. Adsorption Properties of the Intermediates

The adsorption capacity of the intermediates on the catalysts reflects their catalytic performance. Therefore, a series of adsorption configurations was obtained by constructing different intermediates and optimizing them in an alkaline environment. The adsorption of OH species was the first priority, and it indicated the availability of the reaction. In an alkaline environment, owing to the existence of a large amount of OH species and H₂O in the solution, the adsorption of OH species occurs as the first step in the OER. The detailed adsorption structures for different numbers of OH species and H₂O molecules are shown in Table S3. Therefore, calculation of the adsorption energy of ScN_xC_3−x@SACs and ScN_xC_4−x@SACs for OH species and H₂O and the comparison of adsorption capacity are prerequisites for subsequent work. As shown in Table S4, the value of the adsorption energy of different structures for OH species was greater than that for water, which also indicates that during the follow-up of the reaction process, H₂O can be desorbed in the structure to facilitate the reaction cycle. Moreover, with an increase in the concentration of doped N atoms, the adsorption capacity of the ScN_xC_3−x@SACs structures for OH species also increased. Although the rule of the ScN_xC_4−x@SACs system was not obvious, it still showed a similar general rule. Among them, N/C coordination in all N environments had the strongest adsorption capacity for OH species in ScN_xC_3−x@SACs and ScN_xC_4−x@SACs. The results are shown in Figure 5.

However, based on the structures of the model, we found that the structures had a strong adsorption capacity for OH species. As the amount of OH species adsorption increased, some structures in addition to ScN₃ and ScN₄ in the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems became increasingly unstable, as illustrated in Table S3. This structural instability resulted in structural deformation, which is not conducive to the study of the reaction and increases the experimental difficulty. However, after absorbing sufficient OH species, the structures of ScN₃ and ScN₄ could exist stably as Sc(OH)₂N₃ and Sc(OH)₂N₄. When the structure adsorbed enough OH species, further adsorption of OH species no longer occurred on the Sc atom, and they reacted with the ligand OH to generate intermediate products, as shown in Table S3. The detailed results are as follows: through structural optimization and DFT calculations, we found that three-coordination ScN₃ could adsorb up to three OH species, whereas four-coordination ScN₄ could adsorb up to four. When ScN₄ adsorbed a fifth OH species, it no longer adsorbed it on the Sc atom as a ligand but formed an OOH structure with a hydroxyl ligand and generated H₂O. While the ScN₃ structure with three coordination groups adsorbed a fourth OH species, it no longer adsorbed it on the Sc atom. As the number of adsorbed OH species increased, the adsorption capacity of both for OH species decreased, as shown in Figure 6. Hence, modification of the hydroxyl ligand weakened the adsorption strength of the structure to OH species.

Therefore, ScN₃ and ScN₄ structures are two types of bases that can stably exist with two hydroxyl ligands modified in an alkaline environment and can be regarded as Sc(OH)₂N₃ and Sc(OH)₂N₄, respectively. A structural diagram of both is shown in Figure 7. Owing to the modification of the two hydroxyl ligands, the OH species adsorption capacity of the structure was reduced, which is beneficial for promoting the next reaction. Catalysts modified with hydroxyl ligand clusters displayed excellent OER performance [60,61]. Therefore, follow-up studies should be conducted.

The cyclicity of the OER is highly dependent on the desorption of the product O₂, and as the reverse process of adsorption, the degree of desorption is determined by the adsorption energy. The more positive the value of the adsorption energy is, the easier the product desorption. Next, the adsorption energies of O₂ on two bases with different numbers of OH ligands were calculated, and the adsorption configurations are listed in Table S5. Among them, the desorption of O₂ occurred in two forms: one was side-on (both oxygen atoms formed bonds with Sc atoms), and the other was end-on (only one oxygen atom formed a bond with the Sc atom). As shown in Figure 8, the ScN₃ and ScN₄ structures with double-hydroxyl ligands effectively desorbed O₂ so that the catalytic reaction was repeated. Moreover, both were more favorable for O₂ desorption with an increase in the number of hydroxyl ligands, and the value of the adsorption energy of O₂ adsorbed by Sc(OH)₂N₄ was positive, as shown in Table S6. In addition, an adsorption model of the intermediates was constructed, as shown in Table S7. It can be seen from the optimized structures (Table S7) that the adsorption configurations of Sc(OH)₂N₃ and Sc(OH)₂N₄ for O₂ all existed in end-on model. With the modification of two hydroxyl ligands, the adsorption capacity of the base for the next OH species was greater than that for water. The adsorption energies of Sc(OH)₂N₄ and Sc(OH)₂N₃ structures for intermediate products (OOH, O, and OH) are shown in Table S8. The values expressed that the intermediate products (OOH, O, and OH) could be effectively adsorbed on the base. The stability of Sc atoms with multiple adsorbates is shown in

Table 1. Formation energy data ($∆E_f$, eV) of reactive species on Sc(OH)₂N₃ and Sc(OH)₂N₄.

	$∆{\mathit{E}}_{\mathit{f}*\mathbf{O}\mathbf{H}}$	$∆{\mathit{E}}_{\mathit{f}*\mathbf{O}}$	$∆{\mathit{E}}_{\mathit{f}*\mathbf{O}\mathbf{O}\mathbf{H}}$	$∆{\mathit{E}}_{\mathit{f}*{\mathbf{O}}_{2\left(\mathrm{end}\mathrm{on}\right)}}$	$∆{\mathit{E}}_{\mathit{f}*{\mathbf{H}}_2\mathbf{O}}$
Sc(OH)2N3	−2.44	−2.98	−1.21	−0.05	−0.70
Sc(OH)2N4	−1.89	−2.67	−0.94	0.25	−0.51

. This shows that the catalytic process of the formation of intermediate products (O, OH, and OOH) was stable, and the formation energy was negative.

3.3. The Catalytic Activity of Sc(OH)₂N₃ and Sc(OH)₂N₄

To further investigate the catalytic performance of the Sc(OH)₂N₃ and Sc(OH)₂N₄ catalysts for the OER process, the Gibbs free energy change ($∆G$) and overpotential (η) of each step of the reaction were calculated. First, $∆G$_*+OH→*OH and $∆G$_{*OH+OH→*2OH} were calculated, and the results are listed in Table S9. These values clearly indicated that ScN₃ and ScN₄ spontaneously generated Sc(OH)₂N₃ and Sc(OH)₂N₄, respectively, with two hydroxyl groups as ligands in an alkaline environment. It was further proven that ScN₃ and ScN₄ have a strong adsorption capacity for OH species. Figure 9 lists the $∆G$ and ⴄ of Sc(OH)₂N₃ and Sc(OH)₂N₄ catalysts for each step of reaction in the OER, and the detailed data are shown in Table S10. The potential determining step (PDS) of the reaction with Sc(OH)₂N₃ as the catalyst was *OH + OH→*O, and the overpotential was 1.03 V. This could be related to the strong adsorption of OH species on the catalyst. Because of the strong adsorption of OH species, formation of *O became more difficult, resulting in a higher overpotential. Two reaction paths were found when Sc(OH)₂N₄ was used as the catalyst. In the second step, there were two reaction pathways: *OH + OH→*O and *OH + OH→*2OH. The first reaction path was the same as that of the Sc(OH)₂N₃ catalyst, and the second reaction path changed to *2OH + OH→*OOH in the third step. The potential determining step of both reaction paths was the second step: path 1: *OH + OH→*O, path 2: *OH + OH→*2OH. The overpotentials were 0.80 V and 1.10 V, respectively. Additionally, because the ΔG₂ of path 1 was 1.20 eV, which was 0.3 eV smaller than that of path 2, the reaction tended to proceed to the first reaction path when Sc(OH)₂N₄ was used as the catalyst. It can be concluded that Sc(OH)₂N₄ with the reaction path *→*OH→*O→*O + *OH→*OOH + *OH→* is a suitable catalyst for the OER.

In addition, the possibility of producing H₂O₂ via side reactions was analyzed. For Sc(OH)₂N₃, the *OOH + OH→*O + H₂O₂ reaction ($∆G$ = 3.58 eV) was endothermic and required more energy than the *OOH→*($∆G$ = −0.00 eV) reaction, which was exothermic. For Sc(OH)₂N₄, the product of H₂O₂ was *OOH + OH→*O + H₂O₂ ($∆G$ = 3.56 eV) and *2OH + OH→*OH + H₂O₂ ($∆G$ = 2.23 eV), nor is it greater than the energy needed for *OOH→* ($∆G$ = −0.34 eV) and *2OH + OH→*OOH ($∆G$ = 0.17 eV). The specific $∆G$ values are listed in Table S11. Hence, the likelihood of side reactions forming H₂O₂ was very low. Therefore, Sc(OH)₂N₄ is a promising catalyst for the OER in alkaline environment.

3.4. The Origin of Catalytic Activity of Sc(OH)₂N₃ and Sc(OH)₂N₄

The PDOS of Sc(OH)₂N₃ and Sc(OH)₂N₄ and that of other atoms connected to Sc are shown in Figure 10. The two structures passed the Fermi level, proving the electrical conductivity of Sc(OH)₂N₃ and Sc(OH)₂N₄. In addition, by studying the PDOS of s, p, and d orbitals, it is found that there is a certain degree of overlap between p and d energies, indicating that the two hydroxyl ligands formed bonds with the Sc atoms. By comparing the PDOS in the central region of Sc(OH)₂N₃ and Sc(OH)₂N₄, the peak shape of the p orbital of Sc(OH)₂N₃ was found to be sharper than that of Sc(OH)₂N₄. This is because the coordination number of Sc(OH)₂N₄ and the number of doped N atoms are greater. The number of electrons obtained by the N atom was higher in the Sc(OH)₂N₄ structure, which is consistent with the structure obtained by Mulliken charge analysis, as shown in Figure S1.

Moreover, by comparing the PDOS of Sc(OH)₂N₃ and Sc(OH)₂N₄ with ScN₃ and ScN₄, we found that the number of electrons in the p orbital of the structure decreased with the modification of the two hydroxyl ligands, which can be obtained by comparing the area of the PDOS of the two structures. The peak deformation of the p orbital was sharper with the double-hydroxyl ligand modification. Second, the analysis of the PDOS comparison of Sc(OH)₂N₄ with ScN₄ and Sc(OH)₂N₃ with ScN₃ shows that the peaks of the 3d orbitals of Sc(OH)₂N₃ and Sc(OH)₂N₄ moved to the right, and the peak value dropped by almost three times. The structure without double-hydroxyl ligands had sharper 3d orbital peaks. This indicates that the presence of hydroxyl ligands can effectively change the properties of the structure and enhance its catalytic activity. In addition, a charge chromatic difference diagram was created by analyzing the Mulliken charges of Sc(OH)₂N₃ and Sc(OH)₂N₄, as shown in Figure S1. Compared with the results of Mulliken charge analysis of ScN₄ and ScN₃, the symmetry of the electron gain and loss distributions of Sc(OH)₂N₃ and Sc(OH)₂N₄ decreased under the modification of double-hydroxyl ligands. Compared with the Mulliken charge analysis structures of Sc(OH)₂N₃ and Sc(OH)₂N₄, the gain and loss charges of the main atoms were similar. Each N atom in the structure lost approximately the same amount of charge, but the N atom in Sc(OH)₂N₄ gained charge by a factor of three compared to the N atom in Sc(OH)₂N₃. All these conclusions can be drawn from Table S12.

4. Conclusions

In this study, we explored the potential of Sc as an OER catalyst. Through DFT calculations, the structures of the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems were optimized. We concluded that the structures of both the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems were more stable with increasing N concentration. Hence, the concentration of N atoms can significantly affect the structural stability. In consideration of the N/C coordination in all N environments of ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems, ScN₃ and ScN₄ were the most stable structures. Moreover, the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems exhibited a strong adsorption capacity for OH species in alkaline environments, and Sc(OH)₂N₃ and Sc(OH)₂N₄ structures with double-hydroxyl ligands could exist stably in alkaline environments. Sc(OH)₂N₃ and Sc(OH)₂N₄ could effectively desorb O₂ and H₂O to ensure a repeated catalytic sequence for the OER. The potential determining step (PDS) of Sc(OH)₂N₃ was *OH + OH→*O, and its overpotential (η) was 1.03 V. Sc(OH)₂N₄ had two reaction paths, and the potential determining steps of the two paths were as follows: path 1: *OH + OH→*O; path 2: *OH + OH→*2OH (η₁ = 0.80 V; η₂ = 1.10 V). In conclusion, Sc(OH)₂N₄ can be used as an effective catalyst for the OER because of its reasonable overpotential and structural stability. Meanwhile, PDOS and charge transfer analysis showed that double-hydroxyl ligands, as special modified ligands, could improve the catalytic activity of the reaction. Furthermore, different coordination structures affect catalytic activity. The method of preparing SACs based on metal–organic frameworks makes possible the experimental study of Sc@SACs. It is expected that our research will promote the development of rare earth catalysis.