Heteroatom-Doped Nickel Sulfide for Efficient Electrochemical Oxygen Evolution Reaction

Abstract

Heteroatom doping is an effective strategy to regulate electrocatalysts for the oxygen evolution reaction (OER). Nonmetal heteroatoms can effectively engineer geometric and electronic structures and activating surface sites of catalysts due to their unique radius and the electronegativity of nonmetal atoms. Hence, the surface geometric and electronic structure and activity of nonmetal atoms (X, X = B, C, N, O, P)-doped Ni₃S₂ (X-Ni₃S₂) were studied to screen high-performance Ni₃S₂-based OER electrocatalysts through density functional theory calculation. Theoretical results demonstrated that dopants in X-Ni₃S₂ can alter bond length and charge of surface, modify active sites for intermediates adsorption, and adjust the theoretical overpotential. Among all dopants, C can effectively modulate surface structure, activate surface sites, weaken the adsorption of key intermediates, decrease theoretical overpotential, and enable C-Ni₃S₂ with the best theoretical OER activity among all X-Ni₃S₂ with the lowest theoretical overpotential (0.46 eV). Further experimental results verified that the synthesized C-Ni₃S₂ performed an improved OER activity in the alkaline condition with a considerably enhanced overpotential of 261 mV at 10 mA cm⁻² as well as a Tafel slope of 95 mV dec⁻¹ compared to pristine Ni₃S₂.

1. Introduction

Electrochemical water splitting is identified as a promising technology for renewable energy conversion [1,2]. Due to the relatively high energy barrier and the inertia involved in the four electron processes, the oxygen evolution reaction (OER), the anode reaction of water splitting exhibits slow kinetics, large reaction overpotential, and high energy consumption, which impede the efficiency of the hydrogen evolution reaction (HER) on the cathode of water splitting. Efficient electrocatalysts are crucial for facilitating the sluggish and energy-intensive OER. Up to now, Ru- and Ir-based oxides are the most prevalent and efficient catalysts for OER [3]. However, their inadequacy and high cost stymie their large-scale commercial applications. Therefore, designing highly active, durable, and nonprecious materials as alternative OER electrocatalysts is the key to overcoming the technical obstacles of hydrogen production and an intensively challenge for extensive commercial application of water splitting technology [4,5,6].

Ni-based nonprecious materials, such as sulfides [7,8,9], nitrides [10,11], oxides [12,13], and phosphides [9,14], have been extensively explored for OER in recent years. Among them, Ni₃S₂ has been regarded as a latent catalyst to replace Ru- and Ir-based noble OER catalysts due to its facile synthesis and inherent metal Ni–Ni connecting network, giving it decent conductivity and praiseworthy catalytic activity. Nevertheless, the intrinsic activity of Ni₃S₂ is still inferior to the Ru and Ir oxides catalysts [15]. Strategies such as heteroatom doping, heterojunction, and morphology engineering have been devoted to promote the OER performance of catalysts [16]. Among these, heteroatom doping serves as an extremely effective method, and has been widely used to tune the structure and catalytic activity of Ni₃S₂. For example, introducing transition metal atoms (Fe, Co, Mn, V, etc.) into the catalysts’ lattice can change lattice structure [8,16], modulate electronic structure [17,18], as well as increase the number of active sites [19,20] of catalysts resulting in improved catalytic activities for Ni₃S₂ materials. Similar to metal heteroatom regulation, nonmetal heteroatoms can also engineer geometric and electronic structures and activate surface sites of catalysts. Moreover, as the radius and electronegativity of nonmetal atoms (especially the second and third period nonmetal atom) usually differ greatly from that of transition-metal atoms, nonmetal atoms are more likely bringing about changes in the local coordinate environment and cause changes in the local geometric and electronic structures of active sites of catalysts [21]. This makes nonmetal heteroatoms more attractive in adjusting the electrocatalytic activity of materials. For example, the N heteroatom can significantly modify the electronic structure and morphology of Ni₃S₂, which brings high exposure of active sites, enhances conductivity, and optimizes HER activity [22]. Previous studies also proved that some nonmetal atoms (X, such as O, C, N) can adjust the electronic structure and increase the number of active sites in terms of HER study [23,24]. In this regard, nonmetal doping would be a more promising way to regulate the electronic structure and OER activity of Ni₃S₂. Even though some studies focused on improving the HER activity of Ni₃S₂ by nonmetal atoms doping [22,25,26], up to now, there are fewer investigations on modulating the OER activity of Ni₃S₂ by doping nonmetal atoms. Therefore, systematically investigating and rationally screening the nonmetal-atoms-doped Ni₃S₂ catalysts are needed to develop high performance OER electrocatalysts. Generally, it is time-consuming and of high cost to systematically screen the superior OER catalysts in experiments. Fortunately, with the help of high-performance computers and advanced theories of computational chemistry, we can screen the promising electrocatalysts at atomic scale by calculating the adsorption of intermediates, as well as reaction overpotentials, and further prepare the excellent catalysts by advanced experimental methods [1,23,24,25]. Thus, exploring the potential of nonmetal-atoms-doped Ni₃S₂ catalysts by combining theoretical prediction and experimental preparation to improve OER’s catalytic activity can further develop the strategy for designing and constructing OER electrocatalysts.

Inspired by the above considerations, we systematically investigated the OER performances of five kinds of nonmetal-atoms (X, X = B, C, N, O, P)-doped Ni₃S₂ (X-Ni₃S₂) electrocatalysts and screened out the most promising X-Ni₃S₂ OER catalysts. The geometric and electronic structures of X-Ni₃S₂, intermediates adsorption, potential determining step (PDS), and theoretical overpotentials of OER were studied using the density functional theory (DFT) calculations. As a result, C can effectively disturb the local geometric and electronic structure of Ni₃S_2, thus adjusting the adsorption of key intermediates among all dopants, consequently enabling Ni₃S₂ to exhibit excellent OER performance with more active sites and much lower theoretical overpotentials. Additionally, C dopants can also improve the OER activity of nickel hydroxides when C-Ni₃S₂ incurs surface oxidation during the OER process. Guided by theoretical results, the C-Ni₃S₂ and Ni₃S₂ electrocatalysts with similar structure and morphology are synthesized in this work. C-Ni₃S₂ was verified to exhibit more optimized OER performance than Ni₃S₂ by means of electrochemical tests. Our theoretical prediction joins with experiment verification results provide a guide to designing promising catalysts for OER through nonmetal heteroatom doping engineering.

2. Computational Details

The periodic DFT calculations were carried out by employing the Vienna ab initio simulation package (VASP) [27]. The projector augmented wave (PAW) potentials [28] and the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional [29] were used to describe electronic-ion interactions and model the electron exchange-correlation, respectively. A cutoff energy of 450 eV for plane-wave basis set, Monkhorst–Pack grid k-points of 3 × 3 × 1, energy convergence criterion of 10⁻⁵ eV, and force convergence criterion of 0.02 eV/Å were employed for all slab models. When calculating the adsorption energy of intermediates, dipole corrections along the surface were considered, Van der Waals interactions were corrected by using Grimme’s DFT-D3 method [30], and the solvent effect was included by using VASPsol [31].

The optimized Ni₃S₂ bulk [23] with rhombohedral crystal structure, lattice constant of 4.07 Å, Ni-S, and Ni-Ni bond lengths of 2.27 Å and 2.52 Å, respectively, all of which are very close to the experimental values [32]. As the (100) surface has the same atomic arrangement as that of the (001) and (010) surfaces and is the most studied and regarded as the most stable low-index surface with the lowest surface energy (Figure S1), the (100) surface was selected as the catalyst surface of Ni₃S₂ in the following investigations. The catalyst surface was simulated using a (2 × 2) Ni₃S₂(100) slab cleaved from a Ni₃S₂ bulk cell. The dopant X includes B, C, N, O, and P, and all these X-Ni₃S₂ with 2.5 at% doping content (one of the S atoms in (2 × 2) Ni₃S₂(100) slab containing 48 atoms was replaced by X atom) materials were validated with the possibility to be prepared in practice [23]. Furthermore, two types of X-Ni₃S₂(100) surface models were constructed due to their similar surface stability, as our previous research mentioned [23]. They are X_out-Ni₃S₂(100) and X_in-Ni₃S₂(100), in which X substitutes one of the top-layer S atoms (X_out) and one of the sublayer S atoms (X_in) of Ni₃S₂(100), respectively. Considering the surface oxidation and phase transition of Ni₃S₂ during the OER process [17,33], the (2 × 2) Ni(OH)₂(100) and (2 × 2) NiOOH(100) surfaces were also constructed using the same method to verify the most effective dopant among those mentioned above. For all slab models, a 15 Å vacuum layer on the vertical direction of slab was added.

The key OER steps include the following:

$$H_{2}O+\ast \to \ast OH+H^{+}+e^{-}$$

(1)

$$\ast OH\to \ast O+H^{+}+e^{-}$$

(2)

$$\ast O+H_{2}O\to \ast OOH+H^{+}+e^{-}$$

(3)

$$\ast OOH\to \ast +O_2+H^{+}+e^{-}$$

(4)

The free energies of each species were calculated according to the equation

$$G=E+ZPE-TS$$

(5)

where G, E, ZPE, and TS are the free energy, total energy, zero-point energy, and entropic contributions (T was set to be 300 K), respectively. ZPE and TS were calculated after obtaining the vibrational frequencies ($v_i$) [20]:

$$ZPE=\frac{1}{2}\sum h{v}_i$$

(6)

$$TS=k_{B}T[\sum \mathit{ln}\left(\frac{1}{1-e^{-h{v}_i/k_{B}T}}\right)+\sum \frac{h{v}_i}{k_{B}T}\frac{1}{\left(e^{h{v}_i/k_{B}T}-1\right)}+1]$$

(7)

Here, the free energy of $H^{+}$ ($G_{H^{+}}$) can be regarded as $G_{H^{+}}=\frac{1}{2}{G}_{H_2}$, and the electrochemical potential of electron ($G_e$) is equal to −$eU$, where $U$ is electrode potential relative to the reversible hydrogen electrode (RHE). Due to the inaccuracy of DFT in estimating the energy of O₂, the free energy of O₂ was derived according to $G_{O_2}=2G_{H_{2}O}-2G_{H_2}+4.92 \mathrm{eV}$ [34]. The adsorption Gibbs free energy of main intermediates were calculated as follows:

$$\mathsf{\Delta }{G}_{\ast OH}=G_{\ast OH}+\frac{1}{2}{G}_{H_2}-G_{\ast }-G_{\ast H_{2}O}$$

(8)

$$\mathsf{\Delta }{G}_{\ast O}=G_{\ast O}+G_{H_2}-G_{\ast }-G_{\ast H_{2}O}$$

(9)

$$\mathsf{\Delta }{G}_{\ast OOH}=G_{\ast OOH}+\frac{3}{2}{G}_{H_2}-G_{\ast }-2G_{\ast H_{2}O}$$

(10)

Correspondingly, the Gibbs free energy of Equations (1)–(4) were calculated as follow:

$$\mathsf{\Delta }G=\mathsf{\Delta }E+\mathsf{\Delta }ZPE-T\mathsf{\Delta }S-eU$$

(11)

To evaluate the OER performance, the theoretical overpotential (η) is defined as

$$\mathsf{\eta }=\left(\mathsf{\Delta }{G}_{max}\right)/\mathrm{e}-1.23\mathrm{V}$$

(12)

where $\mathsf{\Delta }{G}_{max}$ is the most positive value from $\mathsf{\Delta }{G}_1$ to $\mathsf{\Delta }{G}_4$.

Experimental details can be found in Supplementary Materials.

3. Results and Discussion

3.1. The Local Geometric Environment and Electronic Structure of X-Ni₃S₂

Our previous work has validated that X-Ni₃S₂ can be prepared in experimental conditions, and the topmost layer and sublayer doping on Ni₃S₂(100) (X_out-Ni₃S₂(100) and X_in-Ni₃S₂(100), respectively) show good surface stability and might coexist due to the small difference in surface energy between them [23]. In addition, X-Ni₃S₂ shows good electronic conductivity because the orbitals cross the Fermi level shown in the density of states (DOS) of Ni₃S₂ with 2.5 at% X doping content (Figure S2). X-Ni₃S₂ can be a candidate for OER electrocatalysts, which can benefit the charge transfer between the surface and the intermediates during electrocatalysis [35].

In Figure 1a, the stable top-most Ni-nonmetal atomic arrangement of each surface denotes that X doping can well maintain the original ordered crystal structure of Ni₃S₂(100). While due to the radius (R_x) and electronegativity(χ_x) of X are different from those of S, X doping induces disturbance on local structure of surface. Clearly, the distance between X and Ni1 atoms (d_X-Ni1, Ni1 represents the nearest Ni atoms and labeled in Figure 1a) is different from the original d_S-Ni1. As shown in Figure 1b, except for the P-Ni1 bond, the other X-Ni1 bonds are shorter than the S-Ni1 bond. Additionally, C- and N-Ni₃S₂(100) surfaces have the shortest d_X-Ni1 than other X-Ni₃S₂(100) surfaces due to C and N having larger χ_x and smaller R_x. Interestingly, though the O atom has the smallest Rx and largest χ_x, the O-Ni1 bond is longer than the C-Ni1 and N-Ni1 bonds. This may be because O tends to form lone pair electrons when it bonds with the nearest metal atoms [24], which keeps it from getting any closer to Ni atoms. Moreover, the Ni1-Ni5 bonds (both Ni1 and Ni5 connect with X, Figure 1a) are also shorter than those on the pristine Ni₃S₂(100) surface (Table S1) due to the change of X-Ni1 bond. The change of X-Ni1 bond directly induces the change of adjacent Ni-Ni bond length, which further affects the bond length of adjacent Ni-S and distance between top-most Ni atoms. For example, the shorter C/N-Ni1 bond causes obviously shrinkage in the Ni1-Ni5 bond, which further elongates the Ni1-S3 and Ni5-S2 bonds, finally causing the slight displacement of topmost Ni atoms. Especially, among all X atoms, C and N cause more obvious changes in local Ni-Ni and Ni-S bond lengths, denoting that they can trigger prominent local structure disturbance on the Ni₃S₂(100) surface.

The local geometric structure was disturbed by the change of local coordination environment, which could be accompanied by changes in local electronic structure. Following this, the charges of surface atoms were calculated by Bader charge analysis [36] to examine the alteration of X on the electronic structure of the surface. As shown in Figure 1c, for all surfaces, the Ni1 atom which was directly affected by X possesses a positive charge (Q_Ni1), while X shows a negative charge (Q_X), denoting the Ni atoms deliver the charge to X atoms. Notably, compared with Q_Ni1 of pristine Ni₃S₂(100), Q_Ni1 is altered by X, and X with larger χ_x results in a more positive Q_Ni1. This charge transfer between X and Ni and the above-mentioned local structure change further affect the charge of adjacent S atoms (Figure 1d). For example, after C_out doping, a shorter C-Ni1 bond than the pristine S-Ni1 bond combines with more charge transfer between C and Ni1 than S and Ni1, resulting in the adjacent S (S3 atom in Figure 1a) atom bonding more strongly with sublayer Ni atoms (Figure S3); thus, it has slightly more charge than the corresponding S atom on Ni₃S₂(100). Furthermore, the charges of surface Ni sites (i.e., top-most four Ni atoms, Ni1, Ni2, Ni3, and Ni4 in Figure 1a) are also disturbed by the change of local coordination environment. As shown in Figure 1d, on one X-Ni₃S₂(100) surface, Q_Ni1 and Q_Ni3 sites are intensely altered, accompanied by Q_Ni2 and Q_Ni4 being slightly altered by X, resulting in the four Ni sites having different charges. For example, Q_Ni1, Q_Ni2, Q_Ni3, and Q_Ni4 of C_out-Ni₃S₂(100) are 0.46e, 0.48e, 0.43e, and 0.39e respectively, which are about 0.01~0.07e more positive than Q_Ni1 of Ni₃S₂(100), indicating C dopants play a major role in alteration of electronic structure of Ni sites. Thus, according to above analysis, X dopants on Ni₃S₂(100) surface can disturb local geometric structure, change the charge distribution of surface, and modify the charge of Ni sites to varying degrees, which could further affect the OER intermediates’ adsorption performance and consequently modify the OER activity on Ni₃S₂(100).

3.2. The OER Activity of X-Ni₃S₂(100)

We further probe into the OER activity of X-Ni₃S₂(100) to screen the promising X-Ni₃S₂ catalysts. For OER, the *OH, *O, and *OOH are key intermediates for elementary reactions (Equations (1)–(4)) on nickel-based sulfide [37]. To evaluate the OER activity of the pristine Ni₃S₂ surface, the adsorption of the above intermediates and free energy change ($\mathsf{\Delta }G$) of each elementary step on the pristine Ni₃S₂(100) surface were calculated, respectively, to recognize the adsorption site and the potential determining step (PDS) of OER. On pristine Ni₃S₂(100), *OH and *OOH tend to be absorbed on the Ni top site, while *O is likely to be absorbed on the Ni1-Ni2 bridge site as shown in Table S2; thus, the metal sites should be the reaction sites for OER. Accordingly, the OER pathway is illustrated in Figure 2a, and the free energy diagram is shown in Figure 2b. Apparently, all steps run uphill at U = 0 V vs. NHE and the third step, i.e., the *OOH formation (Equation (4)), is the PDS. This generates the highest $\mathsf{\Delta }G$ of about 1.95 eV among four steps, corresponding to a theoretical overpotential (η) value of 0.72 V (or an onset potential value of 1.95 V), which is needed to make all steps of the free energy diagram go downhill. It means that the pristine Ni₃S₂(100) surface has a strong interaction with *OH and *O or too weak binding with *OOH. This is consistent with how the metal usually possesses a strong bonding interaction with *OH and *O [38]. Thus, it is deduced that properly weakening *O or OH* adsorption or strengthening *OOH binding would reduce the η and enhance the OER performance.

Further, we calculated the OER activity on X-Ni₃S₂. We first focused on the OER activity of Ni1 site, as it is directly bonded with X. Similar to the intermediate adsorption on the pristine Ni₃S₂(100) surface, the *OH, *O, and *OOH adsorbed on the Ni1 top, Ni1-Ni2 bridge, and Ni1 top sites, respectively. The free energy diagrams of the OER steps on the Ni1 site of X_out and X_in-Ni₃S₂(100) are shown in Figure 2c,d, respectively. For X_out-Ni₃S₂(100), all X dopants enhanced the *OH and *OOH adsorption, and B, C, and N enhanced the O adsorption, while O and P doping slightly weakened the O adsorption. This maintains the third step as the PDS, and the $\mathsf{\Delta }G$ of PDS follows the trend of O > B > C > P > S > N (S represents pristine Ni₃S₂(100)), with the η trend of O (0.56 V) > B (0.61 V) > C (0.66 V) > P (0.67 V) > S (0.72 V) > N (0.80 V). Thus, except for N, all other X_out doping can enhance the OER activity on the Ni1 site of Ni₃S₂(100), especially the O_out doping, which almost enhances the OER activity on the Ni1 site by reducing η by 0.16 V compared with Ni₃S₂(100).

For X_in-Ni₃S₂(100), except B and P which weakened OH and OOH adsorption, all other X dopants enhanced the OH and OOH adsorption, and except C which weakened O adsorption, all other X dopants strengthened O adsorption. The PDS on the Ni1 site of X_in-Ni₃S₂(100) is still the *OOH formation step. The $\mathsf{\Delta }G$ of PDS follows the trend of C > S > P > N > O > B, with the overpotential trend of C (0.49 V) > S (0.72 V) > P (0.96 V) > N (1.00 V) > O (1.03 V) > B (1.09 V). Thus, only C_in doping can enhance the OER activity on Ni1 site by reducing η by 0.23 V compared with Ni₃S₂(100), while other X_in doping may hinder the OER activity on the Ni1 site. According to the OER activity on the Ni1 site of both X_out- and X_in-Ni₃S₂(100), C dopant is beneficial for improving the OER activity of its neighbor Ni site, while other X atoms enhance the OER activity of their neighbor Ni site only when doped at the topmost S site. As X_in and X_out may coexist in physical catalysts, the promising X-Ni₃S₂ catalysts should satisfy that both X_in-doped Ni₃S₂ and X_out-doped Ni₃S₂ have better OER activity than pristine Ni₃S₂. In this condition, the C dopant should be a good candidate for doping on the Ni₃S₂(100) surface due to how both C_in and C_out can enhance the OER activity of their adjacent Ni sites.

On both X_out- and X_in-Ni₃S₂(100) surfaces, Ni1 sites are directly affected by X, exhibiting different OER activity from that on pristine Ni₃S₂(100). Considering that the surface geometric and electronic structure are disturbed by X dopants as discussed in Section 3.1, the intermediates’ adsorption, and hence OER activity, on other Ni sites (Ni2, Ni3, and Ni4) may also be affected by X. Correspondingly, other Ni sites have the potential be more efficient OER active sites. Thus, OER activity on other Ni sites of each surface should be calculated and the number of efficient active sites needs to be counted to better screen out the most effective X dopants. Nevertheless, the adsorption of *O tends to coordinate with more metal atoms and has more complicated adsorption sites than *OH and *OOH (Figure S4 and Table S3), which make the calculation and screening of the effective adsorption site for OER intermediates too complex and high-cost. Usually, the adsorption free energy of *OH ($\mathsf{\Delta }{G}_{\ast OH}$) can be scaled, correlated with that of *OOH ($\mathsf{\Delta }{G}_{\ast OOH}$) on the same site [39,40]. Thus, it is possible to conveniently estimate the OER activity of different sites on X-Ni₃S₂(100) by calculating the difference between the adsorption energy of *OOH or *OH and *O ($\mathsf{\Delta }{G}_{\ast O}$). Based on this, the relationship between $\mathsf{\Delta }{G}_{\ast OH}$ and $\mathsf{\Delta }{G}_{\ast OOH}$ on Ni1 sites of all X-Ni₃S₂(100) were tested. As shown in Figure 3a, the larger $\mathsf{\Delta }{G}_{\ast OH}$ corresponds to larger $\mathsf{\Delta }{G}_{\ast OOH}$, validating the linear scaling relation between $\mathsf{\Delta }{G}_{\ast OH}$ and $\mathsf{\Delta }{G}_{\ast OOH}$, which follows the equation of

$$\mathsf{\Delta }{G}_{\ast OOH}=\mathsf{\Delta }{G}_{\ast OH}+3.02\mathrm{eV}$$

(13)

Thus, the sum free energy change of the second and third steps is fixed, that is

$$\mathsf{\Delta }{G}_5+\mathsf{\Delta }{G}_6=\mathsf{\Delta }{G}_{\ast OOH}-\mathsf{\Delta }{G}_{\ast OH}=3.02\mathrm{eV}$$

(14)

Hence, we can deduce that when $\mathsf{\Delta }{G}_{\ast O}$ is in the middle of these two adsorption energies, that is, $\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}$ or $\mathsf{\Delta }{G}_{\ast OOH}-\mathsf{\Delta }{G}_{\ast O}$ equals to the critical value of 1.51 eV, the lowest η of about 0.28 V for OER is obtained. Therefore, it suggests that the value of $\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}$ or $\mathsf{\Delta }{G}_{\ast OOH}-\mathsf{\Delta }{G}_{\ast O}$ could be used as a descriptor to evaluate the OER activity. If the difference value of $\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}$ is smaller than the critical value, the formation of *OOH is the PDS, such as that on pristine Ni₃S₂(100), and the η at standard conditions is

$$\mathsf{\eta }=\left(\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}\right)/e-1.23\mathrm{V}$$

(15)

Conversely, if the difference value of $\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}$ is larger than the critical value, the formation of *O (the second step) becomes the PDS, and the theoretical overpotential at standard conditions is

$$\mathsf{\eta }=\left[3.02-\left(\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}\right)\right]/e-1.23\mathrm{V}$$

(16)

Accordingly, all possible $\mathsf{\Delta }{G}_{\ast OH}$ and corresponding $\mathsf{\Delta }{G}_{\ast O}$ on X-Ni₃S₂(100) were calculated thoroughly (*OH on top sites, and *O on bridge sites shown in Figure S4) to evaluate the OER activity more accurately. The corresponding $\mathsf{\Delta }{G}_{\ast OOH}$ was calculated using the linear scaling equation of $\mathsf{\Delta }{G}_{\ast OH}$. Figure 3b presents the location of $\mathsf{\Delta }{G}_{\ast O}$, and the difference value between $\mathsf{\Delta }{G}_{\ast O}$ and $\mathsf{\Delta }{G}_{\ast OH}$. All $\mathsf{\Delta }{G}_{\ast O}$ on X-Ni₃S₂(100) are close to the $\mathsf{\Delta }{G}_{\ast OH}$, denoting that the *OOH formation is still the PDS on pristine Ni₃S₂(100). Though the *O adsorption strength on X-Ni₃S₂(100) is a little stronger compared to the ideal *O adsorption strength, there are still many active sites showing weaker $\mathsf{\Delta }{G}_{\ast O}$ on X-Ni₃S₂(100) than on pristine Ni₃S₂(100), indicating a possible higher OER activity of the former. The relationship between $\mathsf{\Delta }{G}_{\ast O}-\mathsf{\Delta }{G}_{\ast OH}$ and η is further plotted to confirm how many active sites of X-Ni₃S₂(100) have higher OER activity than pristine Ni₃S₂(100). In Figure 3c, there are 1, 5, 2, 2, and 4 of 8 sites on B-, C-, N, O-, and P-Ni₃S₂(100), respectively that have lower η than that of pristine Ni₃S₂(100), meaning that all X dopants can activate at least one surface Ni site, and C dopant contributes to the most active sites among five dopants. Moreover, the proportion of improved active site (n_site) and change value of η ($\mathsf{\Delta }$η, more negative value means better activity than pristine Ni₃S₂(100)) on the best active site of each X-Ni₃S₂(100) are listed in Figure 3d. The n_site follow the sequence of C (62.5%) > P (50.0%) > O = N (25%) > B (12.5%), and $\mathsf{\Delta }$η follows P_out (−0.05 V) > N_out (−0.06 V) > B_out (−0.11 V) > O_out (−0.16 V) > C_out (−0.26 V), and O_in (0.11 V) > B_in (0.06 V) > N_in (0.02 V) > P_in (−0.16 V) > C_in (−0.23 V) for X_out-Ni₃S₂(100) and X_out-Ni₃S₂(100), respectively. These values indicate that C is prominent among all dopants, can efficiently alter the OER active site and activate 62.5% of the surface Ni sites, and enable best active sites of both C_out- and C_in-Ni₃S₂(100) which have a much lower η relative to η of Ni₃S₂(100). Especially, C_out doping endows the surface with the lowest η of 0.46 V (Figure 3c), which is even comparable to 0.37 V of RuO₂ [41] and 0.51 V of IrO₂ [42]. Thus, considering both the number of active sites and activity of the Ni site, the C dopant can effectively activate the surface OER active site and can be selected as most effective dopant for X-Ni₃S₂ OER catalysts among all X dopants.

Furthermore, considering the surface oxidation and phase transition of Ni₃S₂ to exist as Ni-based hydroxides (such as Ni(OH)₂ and NiOOH) during OER processes [17,33], and to further verify the efficiency of the promising C dopant, we evaluated the OER activity of C-doped Ni-based hydroxides (the adsorption structures are shown in Figure S5). As shown in Figure S6a,b, when C is doped on both Ni(OH)₂ and NiOOH, it can enhance the adsorption of OER intermediates, which is especially beneficial to the O adsorption. Consequently, the decrease the free energy of the PDS generates the η of 0.07 and 0.13 V lower than those of pristine Ni(OH)₂ and NiOOH, respectively. Thus, C dopants not only help to improve the OER activity of pristine Ni₃S₂ but also contribute to the OER activity of Ni-based hydroxides, denoting that C-Ni₃S₂ can serve as a promising OER electrocatalyst.

Based on these theoretical prediction results, the C-doped Ni₃S₂ nanosheets (C-Ni₃S₂ NSs), as well as Ni₃S₂ nanosheets (Ni₃S₂ NSs), were synthesized in the same way used in previous study [23] (also see Supplementary Matrials for more detail) to verify its application in OER. Our previous work has demonstrated that C-Ni₃S₂ NSs and pristine Ni₃S₂ NSs have similar nanosheet morphology and the same crystal structure and uniform elemental distribution. Thus, we mainly focused on studying the OER performance of these two samples in this study. The OER activities of samples were evaluated in 1 M KOH. Figure 4a,b shows the LSV of the above samples and a comparison of their catalytic activities for OER, respectively. The C-Ni₃S₂ NSs exhibit higher OER activity than pristine Ni₃S₂ NSs, needing a lower overpotential of 261 mV and 480 mV to reach current density of 10 mA cm⁻² and 900 mA cm⁻², respectively, compared with Ni₃S₂ NSs (310 mV, 590 mV, respectively). The corresponding Tafel slope (Figure S7a) of C-Ni₃S₂ NSs (96.18 mV dec⁻¹) is lower than that of pristine Ni₃S₂ NSs (109.35 mV dec⁻¹), indicating the favorable reaction kinetics of C-Ni₃S₂ NSs. Nyquist plots in Figure S7b illustrate that C-Ni₃S₂ NSs have faster charge transfers between electrolyte and electrode. Furthermore, C-Ni₃S₂ NSs also show higher exchange current density (J₀) (Figure 4b and Figure S7c) and average turnover frequency (TOF) of 0.02 mA cm⁻² and 0.31, respectively, than those of Ni₃S₂ NSs (0.02 mA cm⁻² and 0.06, respectively). Additionally, C-Ni₃S₂ NSs exhibits similar electrochemical double-layer capacitance with that of Ni₃S₂ NSs (Figure S7d). Moreover, the OER activity of the as-prepared catalyst is comparable to that of most reported nickel-based OER catalysts (Table S4).These experimental results validate that the C-Ni₃S₂ NSs have improved OER performance compared with pristine Ni₃S₂ NSs, which is in line with the above DFT results, highlighting the effectiveness of C dopant modification in the OER activity of Ni₃S₂.

3.3. The Origin of Improved OER Activity of C-Doped Ni₃S₂(100)

For further insight into the improved OER activity of C-doped Ni₃S₂(100), the geometric and electronic structure of key OER intermediates on the most effective site, i.e., the Ni3 site of C_out-Ni₃S₂(100), were discussed as an example. As shown in Figure S8, for OH and OOH, they both adsorbed on the Ni3 top site to form a single O-Ni bond, and the bond length of all O-Ni bonds on C_out-Ni₃S₂(100) are longer than that on Ni₃S₂(100). The charge density difference displayed in Figure 5a shows O of *OH or *OOH can acquire charge through O-Ni bods, due to how charge can transfer from Ni to O and some charge can also transfer from C and S to O through Ni. The Bader charge in Figure 5a indicates that O of *OH or *OOH acquires less charge from the Ni3 site of C_out-Ni₃S₂(100) than from the Ni site of Ni₃S₂(100). Furthermore, the DOS of the O-Ni atoms pair in *OH shown in Figure 4b display that the main states below fermi level (−3.0~−4.5 eV) of the O atom on C_out-Ni₃S₂(100) are slightly less than that of the O atom on Ni₃S₂(100), verifying less charge transfer from the Ni3 site of C_out-Ni₃S₂(100) to *OH/*OOH. Thus, the C dopant can slightly elongate the O-Ni3 bond and decrease the charge transfer from Ni3 to O, consequently helping to impair the O-Ni3 interaction and weaken the OH and OOH adsorption (Figure 4c). For *O adsorption on Ni3 of C_out-Ni₃S₂(100), it tends to bond with Ni3 and the sublayer Ni atom (Ni7 in Figure 1a), forming two Ni-O bonds after optimization, which are different from those of *O bonds with the topmost two Ni atoms (Ni3 and Ni4) on Ni₃S₂(100). This makes the average Ni-O bond of *O on C_out-Ni₃S₂(100) longer than that of *O on Ni₃S₂(100), and *O acquires less charge from Ni (Ni3 and Ni7) of C_out-Ni₃S₂(100) than from Ni (Ni3 and Ni4) of Ni₃S₂(100) (Figure 5a). Furthermore, the states below Fermi level of O on C_out-Ni₃S₂(100) are less than that of *O on Ni₃S₂(100), manifesting the lower charge transfer between O-Ni. More importantly, the electronic states interaction between O and Ni of C_out-Ni₃S₂(100) occur at a higher energy level than that of Ni₃S₂(100), confirming the weaker O-Ni interaction, and consequently, the weaker *O adsorption on the Ni3 site of C_out-Ni₃S₂(100) than that on the Ni site of Ni₃S₂(100).

The weakened OER intermediate adsorption on the Ni3 site of C_out-Ni₃S₂(100) mainly results from an electronic structure alerted by C dopants. C dopant makes the charge of Ni3 site more positive and the d band center of Ni3 site negatively shift when compared with those of the Ni site on Ni₃S₂(100) (Table S5). Consequently, this decreases the charge transferred from Ni to O and weakens the O-Ni bonds. Moreover, the surface structure also contributes to weakening the O adsorption. Specifically, the disturbance on local structure caused by C_out makes the Ni3-Ni4 distance (4.68 Å) longer than the pristine Ni3-Ni4 distance (4.07 Å), which leads O to prefer bonding with Ni3 and the Ni7 atoms rather than Ni4 atom. Due to the more saturated coordination and lower position in the Z direction of the Ni4 atom, O forms a longer and weaker Ni-O bond with the Ni atom. Thus, the special surface geometric and electronic structure induced by C doping can weaken OER intermediates’ (especially O) adsorption on the Ni3 site of C_out-Ni₃S₂(100) and reduce the $\mathsf{\Delta }G$ of the PDS ($\mathsf{\Delta }{G}_{\ast OOH}-\mathsf{\Delta }{G}_{\ast O}$), consequently yielding a better OER activity with η as low as 0.46 V (Figure 5c).

4. Conclusions

In summary, the geometric structure, charge transfer, and OER activity of nonmetal atoms X (X = B, C, N, O, P)-doped Ni₃S₂ were studied systematically using DFT calculations. This demonstrated that the geometric structure and electronic structure, hence OER activity, are disturbed by the introduction of X dopants. Among all X dopants, C can be a promising dopant for Ni₃S₂ materials due to the way it can efficiently alter the local geometric structure and electronic structure of the Ni site, hence adjusting the key intermediates adsorption. This consequently enables the modified Ni₃S₂(100) surface to have the most effective active sites and exhibits the best OER activity, with the lowest theoretical overpotential of 0.46 V, which is 0.26 V lower than that of pristine Ni₃S₂(100). Further electrochemical experiments verified that C-doped Ni₃S₂ indeed presents higher intrinsic OER activity than pristine Ni₃S₂, which needs the 49 mV lower overpotential than that of pristine Ni₃S₂ to deliver a geometrical current density of 10 mA cm⁻² in 1 M KOH. Above all, the DFT calculation and experimental results jointly highlight the promising C dopant in promoting the OER performance of Ni₃S₂. Our study offers guidance for screening and fabricating promising OER catalysts through nonmetal doping engineering, which can inspire more exploration of nonmetal doping of other electrocatalysts.