NH₃, as one of the key chemicals for human production and life, plays a vital role in promoting human society through its application in agricultural production, chemical fuel, etc. Currently, the Haber-Bosch process is an industrial direct synthesis of ammonia from N₂ and H₂ under high temperature (300–500 ℃) and high pressure (15,000–30,000 kPa) conditions. To meet the demanding conditions of high temperature and pressure in synthesis, large amounts of fossil fuels are consumed, so nearly 12% of the energy consumed in industrial ammonia synthesis is used annually, emitting over 300 million tons of carbon dioxide (CO₂), causing an energy resource crisis and global greenhouse effect. Therefore, in order to solve the problems of high energy consumption, high pollution and complex plant facilities in the Haber-Bosch process, there is an urgent need to develop a new process to replace the existing ammonia production method. Electrochemical nitrogen reduction (NRR) is a more environmentally friendly and economical method for synthesis. An increasing number of researchers have explored a variety of materials for catalytic nitrogen reduction reactions, providing theoretical guidance for the exploration of novel catalytic materials [1-10]. For example, Liu et al. [2] designed dual-dot metal-free atom catalysts anchored on g-CN. Based on DFT calculations, the limiting potential of the B and P co-doped g-CN system is as low as −0.18 V, which exhibits excellent NRR performance. Ma et al. [3] have discovered that the B dopant in InSe can effectively reduce N₂ to NH₃ under ambient conditions, because of the empty orbitals of B ions and the favorable carrier mobility of InSe. However, the strong bonding strength of the non-polar N≡N bond is extremely difficult to be destroyed at room temperature, leading to low reactivity in the process of ammonia synthesis. Compared to N₂, the NO molecule manifests a single unpaired electron in the π* (π*2py) orbital, leading to a relatively weaker binding strength of N—O bond. Therefore, it is easier to activate NO to synthesis ammonia, compared to the situation of N₂. Therefore, many pioneering studies have focused on the study of NO electroreduction (NORR), which is assumed to achieve higher reactivity compared to NRR.

Nitric oxide (NO) is a polluting gas produced by vehicle emissions and the burning of fossil fuels. Its large emission will not only pollute the environment but also threaten human health. At the same time, NO, as another nitrogen-containing gas molecule, acts as a free radical and can be used as a nitrogen source for catalytic reactions. In recent years, some scholars have tried to use NO as a nitrogen source to synthesize ammonia by electrocatalysis, which is called electrocatalytic nitric oxide electroreduction reaction (NORR). NORR not only solves the problem that NO in the atmosphere is harmful to the environment and human health, but also provides a green synthesis method for NH₃ needed for industrial production [11-22]. For example, The experiments of Li et al. [17] revealed that the oxygen vacancy (VO) in MnO₂ nanowire arrays can efficiently activate NO and further reduce NO to NH₃, with a NH₃ yield of 27.51 × 10⁻¹⁰ mol s⁻¹ cm⁻² and a Faraday efficiency of 82.8%. Ji et al. [18] investigated the potential of boron-doped graphene (BG) as a metal-free catalyst for the catalytic reduction of ammonia by NO. Calculations, based on density functional theory (DFT), have showed that the introduction of B dopants into graphene can enhance its interactions with HNO* intermediates and effectively facilitates the subsequent reduction steps along the NH₂O*, NH₂OH*, and NH₂* intermediates, with a low limiting potential of −0.35 V. Chen et al. [21] designed the Co-N₄/graphene (The Co atom is anchored on porphyrin-like N-doped graphene) structure to study its catalytic performance. The results of DFT calculations show that the limiting potential of NORR on Co-N₄/graphene is −0.12 V, which is comparable (or even better) than that of metal Pt. Therefore, Co-N₄/graphene can be treated as a highly promising catalyst. These results have indicated that it is feasible to use NO as a nitrogen source in the process of ammonia synthesis, from both theoretical and experimental aspects.

In recent years, two-dimensional materials, such as graphene, hexagonal boron nitride, transition metal compounds, have been investigated extensively in the areas of energy and catalysis, due to their unique structures and excellent physical and chemical properties [23-38]. Among them, the unique layered structure of transition metal sulfides is often used as catalytic materials, benefiting from the unique configuration: The transition metal layer is sandwiched between two layers of sulfur atoms. For example, Ma et al. [4] have systematically investigated WS₂ nanosheet based single metal atoms as NRR catalysts. The results of DFT calculations show that WS₂ nanosheets with sulfur vacancies are good platforms for anchoring individual transition metal atoms. Among them, the Ni system (Ni-WS₂) has prominent NRR catalytic activity, and the NRR process on the Ni-WS₂ surface is more inclined to occur with the alternating hydrogenation-binding pathway and generates ammonia without energy input. Li et al. [39] designed two-dimensional transition metal disulfides, including MoS₂, WS₂, VS₂, NbS₂, TiS₂ and TaS₂, to study their NRR process. DFT-based calculations of energy barriers for each step show that VS₂ has 0.16 eV in the distal path, which endows it with favorable catalytic activity among the candidates investigated. In addition, the author has also demonstrated that charge transfer is crucial for the reactivity of NRR. Many researchers have also focused their studies on CrS₂, which is a novel metal disulfide. Chen et al. [40] studied disulfides based on transition metals in all groups, including Ⅳ, Ⅴ and Ⅵ, and found that CrS₂ manifests the most diverse electronic and magnetic properties. Gabriela et al. [41] have also found that CrS₂ has the highest charge transfer efficiency, compared with MoS₂ and WS₂. Qin et al. [42] designed heteroatom-doped CrS₂ catalysts (X@CrS₂, X = B, C, N, O, Si, P, Cl, As, Se, and Br) to study their catalytic properties. Based on energy calculations, N@CrS₂ has the lowest overpotential (0.41 V) of NRR, which is even lower than that of Pt (0.45 V). Therefore, CrS₂ can be used as a promising catalyst.

As we know, some catalysts can be flexibly modulated via some strategies, which is beneficial for the improvement of reactivity. Among numerous methods, introducing vacancy defects and doping heterogeneous atoms are widely used [43-45]. For example, Tursun [19] have attempted to introduce S vacancies in MoS₂ to explore their NO catalytic reduction properties. The results of DFT calculations showed that the S vacancies can effectively activate NO with an extended N—O bond, which is beneficial for NO-catalyzed reduction. The high reactivity mainly originates from the strong interaction between NO and the catalyst, induced by the vacancy defects. Besides, the heteroatom doping can accelerate the NO-catalyzed process by modulating the electron-donating ability of the MoS₂ substrate. Among them, the onset potential of NH₃ production was −0.06 V on the Pt-doped MoS₂ catalyst with S vacancies. Therefore, the Pt-MoS₂@Vs catalysts have a great potential for catalyzing the reduction of ammonia from NO; Liu et al. [1] have systematically designed graphene based catalysts with various kinds of defects for NRR. The results have demonstrated that graphene containing one vacancy (GR1) and two vacancy (GR2) defects had higher reactivity and better adsorption stability than pristine graphene (GR). For elemental doped graphene, both N and S dopants can significantly improve the adsorption strength of NRR intermediates and further improve the NRR reactivity. Among numerous dopants, Ti can be treated as a promising candidate with cheap and easily obtained characters, which has been investigated extensively in pioneering works. For instance, Wang et al. [36] have performed DFT calculations on Ti doped two-dimensional (2D) boron nitride (BN). The Ti dopant can effectively reduce the energy barrier of ammonia synthesis from 1.20 eV (on pristine BN) to 0.96 eV, suggestion that Ti doped 2D materials have the potential to be new catalysts for electrocatalytic ammonia synthesis. Kalwar et al. [46] have also investigated hydrogen adsorption on Ti doped vacancy silicene (SV-SL) via first-principles density-functional theory (DFT). The results have demonstrated that the adsorption energies of H₂ ranges from −0.481 eV to −0.201 eV, with a hydrogen storage capacity of 6.3 wt%. This study suggests that the Ti doped 2D materials could also be a promising candidate for hydrogen storage applications. Liu et al. [47] designed a Ti doped BP monolayer with B vacancy (Ti@BP) for the application of NORR. Ti@BP is proved to manifest excellent NORR selectivity for NH₃, which is similar to that of the Pt-based catalysts. The above experimental calculations proved that both doping and manufacturing vacancies can significantly improve the catalytic performance of the catalyst. Above all, The Ti doped two-dimensional materials have achieved superior performance in the catalysis area due to moderate adsorption strength of intermediates. We therefore treat Ti as a promising dopant for two-dimensional catalysts.

Inspired by the pioneering studies, we have herein investigated catalysts for electrocatalytic reduction of NO, including pristine CrS₂, CrS₂ with one S vacancy (v-CrS₂), and Ti doped CrS₂ (Ti@CrS₂). The results have shown that the pristine CrS₂ exhibits inert character for NO activation. However, v-CrS₂ and Ti@CrS₂ can exhibit enhanced interaction with NO, due to increased charge transfer between NO and substrates (0.52–0.75 e) and enhanced adsorption of NO on the catalysts (−0.96~−1.64 eV), compared to the situation of CrS₂ (0.065 e/−0.30 eV). The results, including adsorption energies and reaction pathways, have demonstrated that v-CrS₂ and Ti@CrS₂ can both be treated as promising catalysts for NORR, with ultralow limiting potentials of −0.03~−0.47 V. Therefore, the strategies, including introducing vacancy and doping, are proved as effective methods to improve the reactivity of NORR. This study has provided a theoretical basis for the search of sulfide catalysts in the area of NO electroreduction.

In this work, the spin density functional theory is implemented by using the Vienna Ab initio Simulation Package (VASP). Projection enhanced wave (PAW) method is used to describe the interaction between ions and electrons. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional is used to describe the exchange correlation. A 3 × 3 × 1 CrS₂ supercell with S vacancy containing 9 Cr atoms and 18 S atoms was used for calculation. The cutoff energy was set as 450 eV. The vacuum layer was set as 15 Å to avoid periodic repetition effects. The Monk-horst Pack k-point grid of 5 × 5 × 1 was chosen to sample the Brillouin zone for geometric optimization. The convergence criterion for the residual force and energy was set to 0.02 eV/Å and 10⁻⁵ eV, respectively.

The adsorption energy was calculated by Eq. 1:

where the E_slab/NO, E_slab and E_NO are energies of catalyst with NO adsorbed on it, pure catalyst, and NO molecule in vacuum, respectively.

The reaction free energy (ΔG) of every reaction step was modified with the zero-point energy and entropy of DFT. The calculation formula follows Eq. 2:

ΔE is obtained from DFT calculations, ΔZPE is zero-point energy, T is 298.15 K and ΔS is entropy change.

Charge transfer indicates a change in the electronic structure of each adsorption system. The charge transfer is calculated as follows Eq. 3:

ΔQ_c represents the charge transfer between NO and CrS₂, Q_N represents the charge of the N atom in NO after adsorption, and Qo represents the charge of the O atom in NO after adsorption. If the calculated ΔQ_c is negative, NO gains electrons and CrS₂ loses electrons during adsorption. On the contrary, if ΔQ_c is positive, electrons are transferred from NO to CrS₂. In general, the amount of charge transfer indicates the adsorption capacity of the adsorbent for the adsorbate.

For v-CrS₂, the calculation of vacancy formation energy follows Eq. 4:

where N is the total number of particles, E_prefect is the total energy of the optimized cell, and E_defect is the total energy of the optimized cell containing vacancies.

For Ti@CrS₂, the calculation of formation energy follows Eq. 5:

E_Ti@CrS represents the energy of Ti@CrS₂, E_v@CrS represents the energy of CrS₂ containing S vacancies, and E_Ti represents the energy of Ti atom in vacuum.

For Ti the cohesive energy is calculated as follows Eq. 6:

In this work, we first analyze the geometric properties of CrS₂ based catalysts to demonstrate the potential application of CrS₂ based catalyst in NO electroreduction. We focus on the research of pristine CrS₂ (001), CrS₂ with S vacancy (denoted as v-CrS₂) and CrS₂ with Ti atom doped in the S vacancy (denoted as Ti@CrS₂), as shown in Fig. 1. The structure presents two atomic layers in a unit cell containing a total of 9 Cr atoms and 18 S atoms. The layer of Cr atoms in each of these cells is placed between two layers of S atoms, forming a pincer structure. In order to illustrate the stability of catalysts designed, we have also calculated the vacancy-formation energy (E_f) of v-CrS₂, and the binding energy (E_b) of Ti in Ti@CrS₂.

The formation energy of S vacancies in CrS₂ was calculated as −1.51 eV according to Eq. 4. The negative value of E_f indicates that S vacancy defects are easily formed in the crystal structure of CrS₂ in practical experiments; The binding energy of Ti atom in Ti@CrS₂ was calculated to be −7.17 eV according to Eq. 5. The ultra-negative value of E_b suggests that the S in the pristine CrS₂ can be easily substituted by the Ti atom in the real experimental work. As we know, the Ti single atoms are likely to aggregate into clusters due to a large surface energy. We therefore demonstrate the stability via comparison of binding energy and cohesive energies. The binding energy of Ti atoms in CrS₂ is −7.17 eV, which is significantly larger than the cohesive energy of Ti (−4.90 eV). Therefore, the binding strength of Ti atom is big enough to inhibit the aggregation of Ti atoms into clusters. In other words, the formation of titanium atoms is thermodynamically more favorable than that of clusters. These results have demonstrated that our designed catalysts are advisable for the application in the real electrochemical condition.

In addition, there are negligible structure deformation after introducing defects, including S vacancy and Ti dopant. This can further illustrate that CrS₂ is a stable substrate, which can effectively sustain the defect sites to avoid the deformation. To further determine the stability of v-CrS₂ and Ti@CrS₂, we performed calculations of phonon dispersion spectrum (Fig. S1 in Supporting information), the absence of imaginary frequencies in the phonon spectrum indicates that v-CrS₂ and Ti@CrS₂ manifest thermodynamic stability.

As we know, the prerequisite of NORR is the effective capture and activation of inert NO. We therefore focus on the discussion of NO adsorption on CrS₂. As shown in Fig. S2 (Supporting information), NO can be adsorbed on v-CrS₂ and Ti@CrS₂ spontaneously after full geometric optimization. Therefore, there exists no transition states in the process of NO adsorption. Based on the characters of the adsorbate and substrate, the NO can bind with CrS₂ vertically via both N (CrS₂-S1) and O (CrS₂-S2) atoms (Fig. 2a). According to Table 1 and Fig. 2a, NO prefers to be adsorbed on CrS₂ via CrS₂-S2 behavior with a low adsorption energy of −0.3 eV, indicating a physical adsorption character. This can also be reflected from the charge transfer, which is only −0.065 e between NO and CrS₂. Therefore, the interaction between NO and CrS₂ is extremely weak and NO cannot be effectively activated on CrS₂. We therefore attempt to modify the CrS₂ with various defects, including vacancy and Ti dopant, to study further.

For v-CrS₂, we have also discussed various adsorption behaviors of NO on it, as pristine CrS₂. Based on the configuration of v-CrS₂, NO can be adsorbed on the S-vacancy vertically via N atom (v-CrS₂-S1) or parallelly via both N and O atoms (v-CrS₂-S2). As shown in Fig. 2b and Table 1, NO prefers to be adsorbed on v-CrS₂ via v-CrS₂-S1 behavior with an adsorption energy of −1.64 eV, which is significantly higher than that on pristine CrS₂ (−0.3 eV). Therefore, we can conclude that introducing S vacancy in CrS₂ is an effective strategy, which can dramatically enhance the interaction between NO and the catalyst. Similar conclusion can also be obtained from the aspect of charge transfer and change of N—O bond: The charge transfer between NO and v-CrS₂ ranges from 0.52 e to 0.75 e, which is remarkably larger than the situation of CrS₂ (−0.065 e). This may indicate that there exists a strong chemisorption between NO and CrS₂ surfaces. The adsorption energy of NO is −0.981 eV via v-CrS₂-S2 behavior on v-CrS₂, which also demonstrates a strong binding strength between NO and v-CrS₂.

Therefore, we can assume that the two adsorption behaviors of NO on v-CrS₂ are all likely to occur in the real electrochemical condition. In addition, the N—O bonds of adsorbed NO molecules are elongated by 0.026 and 0.097 Å respectively compared to the pristine state. This may further indicate that CrS₂ can effectively activate NO, which is beneficial for NO electroreduction. Above all, the v-CrS₂-S1 behavior is more beneficial for the capture NO due to a higher adsorption energy (−1.64 eV). In comparison, the v-CrS₂-S2 behavior can active NO more efficiently due to larger elongation of N—O bond (0.097 Å).

In order to demonstrate the phenomenon from the aspect of binding properties, we have calculated the crystal orbital Hamiltonian population (COHP) of N—O bond in adsorbed NO (Figs. 3a and b). To quantitatively analysis the occupation degree of NO's antibonding, we have also calculated the integrated COHP (ICOHP). The ICOHP values can reflect how much this bond contributes to the band-structure energy. ICOHP refers to the numerical integral from the lowest energy peak to 0 eV on the COHP. In general, the bonding (anti-bonding) state is defined as negative (positive) in COHP. Therefore, ICOHP can quantitatively indicate the occupation degree of anti-bonding states: A less negative ICOHP corresponds to a higher occupation degree of antibonding orbitals, leading to a more activated degree of NO. The ICOHP of adsorbed NO via v-CrS₂-S2 behavior is −7.96, which is more positive than the situation of v-CrS₂-S1 behavior (−9.22). We therefore assumed that the bidentate character of adsorbed NO via v-CrS₂-S2 is beneficial for the charge transfer between NO and v-CrS2 (0.75 e), which can further fill the antibonding orbitals of NO dramatically. This can effectively activate the adsorbed NO, leading to a significantly elongate N—O bond (0.097 Å). However, the occupation of NO antibonding states in v-CrS₂-S2 behavior will also lead to a destabilization of the system, leading to a decreased adsorption energy of NO (−0.981 eV), compared to the situation of v-CrS₂-S1 behavior (−1.64 eV). We have discussed the activation degree of NO from the aspect of N—O bond length, as mentioned above. However, the change of N—O bond length is not the only factor to determine the activation capacity. We therefore attempt to correlate the bond length with ICOHP to demonstrate the activation degree of NO. Among them, The ICOHP of NO adsorbed on v-CrS₂-S1 (v-CrS₂-S2, Ti@CrS₂-S1, and Ti@CrS₂-side) is −9.22 (−7.69, −9.07, and −7.02) with a N—O bond length of 0.026 Å (0.097 Å, 0.07 Å, and 0.139 Å). In general, a positive ICOHP corresponds to a more occupation degree of antibonding orbitals, which can lead to a more enlongation of N—O bond.

In order to further study the interaction between NO and v-CrS₂ (001) form the aspect of charge distribution, we have also calculated the charge differential density (CDD) (Figs. 4a and b). It can be clearly seen that both charge depletion and accumulation can be observed between NO and CrS₂, which is accordance with the well-known "accept-donate" mechanism as mentioned in pioneering works. In other words, the S vacancy not only transfers electrons to NO antibonding orbital, but also accepts lone pair electrons from NO molecule during NO activation. In general, the substrate is more capable of missing electrons, leading to the electron accumulation on NO. This is accordance with the bader charge analysis: The NO adsorbed on v-CrS₂ is negatively charged with −0.52~−0.75 e. To further analyze the effect of S vacancies on the NO activation, we calculated the density of states (DOS) as shown in Fig. 5. Compared to pristine CrS₂, the upward and downward spin states of v-CrS₂ turn into asymmetric tendency near the Fermi energy level, indicating enhanced magnetism. This property can facilitate the transfer of electrons from v-CrS₂ to the empty orbitals of NO, filling the antibonding orbitals and favoring the activation of NO.

For Ti@CrS₂, we have considered three adsorption behaviors for NO: NO can be adsorbed on Ti@CrS₂ vertically with N (Ti@CrS₂-S1) or O (Ti@CrS₂-S2) atom. In addition, NO can also bond with Ti@CrS₂ parallelly with both N and O atoms (Ti@CrS₂-Side). As shown in Table 1 and Fig. 2c, the NO adsorbed via Ti@CrS₂-S1 and Ti@CrS₂-Side behaviors manifest higher adsorption energy of −0.963~−1.178 eV, compared to the situation of Ti@CrS₂-S2 (−0.694 eV). From this phenomenon, we can deduce that the binding strength of N atom is stronger than the O atom for NO on Ti@CrS₂. Therefore, NO is preferred to be captured via Ti@CrS₂-S1 or Ti@CrS₂-Side behavior in the real electrochemical environment. The adsorption energy of NO on Ti@CrS₂ is significantly improved compared to that on CrS₂ (−0.3 eV), which is similar to the situation on v-CrS₂. Moreover, the charge transfer between NO and Ti@CrS₂ ranges from 0.536 e to 0.726 e for Ti@CrS2-S1 and Ti@CrS2-Side behaviors, which is significantly larger than that for CrS₂ (Figs. 4c and d). This may indicate a strong chemisorption between NO and Ti@CrS₂ surface, similar to the situation of v-CrS₂. Therefore, introducing Ti dopant is also a promising modification strategy for CrS₂ to activate NO. This can also be reflected from the N—O bond lengths for the adsorbed NO molecules, which are elongate by 0.07 Å (Ti@CrS₂-S1), 0.054 Å (Ti@CrS₂-S2), and 0.139 Å (Ti@CrS₂-Side), respectively, compared with the pristine state. This can further demonstrate that Ti@CrS₂ can effectively activate NO, which is favorable for the electroreduction of NO. Through comparison between Ti@CrS₂-S1 and Ti@CrS₂-Side behaviors of NO adsorbed on Ti@CrS₂, we can find that the Ti@CrS₂-S1 (Ti@CrS₂-Side) behavior is more favorable for the capture (activation) of NO, due to a larger adsorption energy (N—O elongation) of −1.178 eV (0.139 Å), compared to that of Ti@CrS₂-Side (Ti@CrS₂-S1). This phenomenon can also be analyzed from COHP calculation (Figs. 3c and d). The N—O bond of NO adsorbed via Ti@CrS₂-Side behavior possesses more positive ICOHP of −7.02, compared to the situation of Ti@CrS₂-S1 behavior. This can reflect that the antibonding orbitals of NO adsorbed via Ti@CrS₂-Side behavior have been dramatically filled, which can also be illustrated from the coordination aspect as the situation of v-CrS₂. As shown in Fig. 2c, the NO binds with Ti@CrS₂ bidentate (monodentate) with Ti@CrS₂ via Ti@CrS₂-Side (Ti@CrS₂-S1) behavior. The larger coordination number between Ti@CrS₂ and NO adsorbed via Ti@CrS₂-Side behavior can facilitate the charge transfer, as mentioned above. This will eventually lead to the significant occupation of NO's antibonding orbitals and weaken the N—O bond, corresponding to a larger N—O bond length. To further investigate the interaction between NO and Ti@CrS₂ from the aspect of charge distribution, we have also calculated the charge density difference (CDD), as shown in Figs. 4c and d. The interaction between NO and Ti@CrS₂ also follows the "accept-donate" mechanism, as analyzed above. The Ti doped in CrS₂ can transfer electrons to the antibonding orbitals of adsorbed NO, and simultaneously accept lone pair electrons from NO. This character eventually leads to efficient activation of NO during the interaction between the catalyst and NO. In general, the doped Ti atom is positively charged, consuming 1.41 e electrons to NO. In contrast, NO is negatively charged, accumulating 0.536 e electrons on it. Similar as the situation of v-CrS₂, the DOS of Ti@CrS₂ also exhibits an asymmetry tendency between upward and downward spin states, indicating an enhanced magnetism (Fig. 5). Therefore, the antibonding orbitals of NO adsorbed on Ti@CrS₂ can also be effectively filled, which can eventually facilitate the activation of NO.

As discussed above, the v-CrS₂ and Ti@CrS₂ are screened as promising catalysts for NO capture and activation, which has satisfied the prerequisite for ammonia synthesis. To analyze the reactivity quantitatively, we herein begin to discuss the hydrogenation process of NO to NH₃ (denoted as NORR). As discussed above, NO can be adsorbed on v-CrS₂ and Ti@CrS₂ via various behaviors due to similar adsorption strength. For v-CrS₂ (Ti@CrS₂), the v-CrS₂-S1 and v-CrS₂-S2 (Ti@CrS₂-S1 and Ti@CrS₂-side) behaviors of NO adsorption are all likely to occur in the real electrochemical condition, with high adsorption energies of −0.981~−1.643 eV (−0.963~−0.178 eV). In comparison, the coverage of N₂ with v-CrS₂-S2 (Ti@CrS₂-side) behavior is somewhat lower than that of v-CrS₂-S1 (Ti@CrS₂-S1) on v-CrS₂ (Ti@CrS₂), due to relative lower adsorption strength. Therefore, we focus our research on four systems, including v-CrS₂-S1, v-CrS₂-S2, Ti@CrS₂-S1, and Ti@CrS₂-side, to study the reaction pathway of NORR to NH₃.

As shown in Scheme 1, the adsorbed NO could be reduced to NH₃ via consumption of five hydrogen protons and electrons (H⁺ + e⁻) (NO(g) + 5H⁺ + 5e⁻ = NH₃(g) + H₂O(l)) [18]. At each step of protonation, the proton-electron pair can selectively combine with the N- or O-terminal of NO, leading to various of mechanisms. The first protonation of NO is essential for the subsequent NORR process. *NO can be protonated into two different intermediates: HNO* and *NOH. Therefore, there are two possible reaction pathways for NORR: HNO* pathway and *NOH pathway. For v-CrS₂-S1 and Ti@CrS₂-S1 systems, the adsorbed *NO is unlikely to be protonated to *HNO, because the *NO is adsorbed on the substrate vertically with N atom binding on it. In comparison, the *NO is adsorbed on the substrate with parallel configurations in systems of v-CrS₂-S2 and Ti@CrS₂-side. Therefore, the *NOH and *HNO intermediates are all treated as possible intermediates for v-CrS₂-S2 and Ti@CrS₂-side systems. We first compare the free energy changes of the initial protonation steps: The reaction energy of *NO → *NOH is −0.66 eV/0.53 eV for v-CrS₂-S2/Ti@CrS₂-side system, which is much more negative (positive) than that of *NO → *HNO (0.16 eV/−0.82 eV). In summary, we eventually ignore *HNO (*NOH) and treat *NOH (*HNO) as the favorable intermediate in the subsequent research for the systems (system) of v-CrS₂-S1, v-CrS₂-S2, and Ti@CrS₂-S1 (Ti@CrS₂-side).

About *NOH pathway, the following protonation of *NOH can generate different intermediates, including *N and *HNOH, due to the selective combination with the N- or O-terminal. For *N intermediate, three proton-electron pairs are consumed successively until NH₃ is formed, which is defined as Path 1. In contrast, the further hydrogenation of *NHOH intermediate is still selective. As *NH is formed, it will experience two successive protonation steps to NH₃, which is defined as Path 2. When the intermediate is *H₂NOH, further protonation will lead to water generation to produce *NH₂ and NH₃, which is defined as Path 3. About *HNO pathway, *HNO can also be hydrogenated to various intermediates, including *H₂NO and *HNOH, due to the selective combination with the N- or O-terminal. The further hydrogenation of *H₂NO intermediate is still selective. As *H₃NO is formed, it will be protonated first to produce NH₃ and *OH and further to H₂O, which is defined as Path 4. As the intermediate is H₂NOH*, it can be protonated to produce NH₃ and *OH as defined in Path 5. In addition, H₂NOH* can also be hydrogenated first to produce H₂O and *NH₂ further protonated to produce NH₃ as shown in Path 6. For the *HNOH intermediate, the formation of *NH followed by the consumption of two proton electron pairs to produce NH₃ is defined as Path 7. We next considered the further protonation of *NOH and *HNO by evaluating free energies of further reduction intermediates, and treat the reactions with lower free energies are more selective.

For v-CrS₂-S1 and v-CrS₂-S2 system, the minimum energy pathway can be demonstrated as follows: *NO → *NOH → *N → *NH → *NH₂ → *NH₃ (Figs. S3a and b in Supporting information). It is noteworthy that the intermediates, including *HNOH, *H₂NOH are all energetically unfavorable. For v-CrS₂-S1 (v-CrS₂-S2) system, the rate controlling step (RCS) of NORR is *NO + H⁺ + e⁻ →*NOH (*NH₂ + H⁺ + e⁻ →*NH₃) with a reaction energy of 0.13 eV (0.37 eV), as shown in Figs. 6a and b. This reaction energy can be easily overcome at an ultralow limiting potential of −0.13 V (−0.37 V).

For Ti@CrS₂-S1 system, the minimum energy pathway is demonstrated as follows: *NO → *NOH→ *HNOH → *NH → *NH₂ →*NH₃ (Figs. S3c in Supporting information). The intermediates of *N and *H₂NOH are energetically unfavorable. The rate controlling step (RCS) of NORR *NH₃→NH₃(g) with a reaction energy of 0.47 eV, as shown in Fig. 6c. This reaction energy can be easily overcome at a limiting potential of −0.47 V.

For Ti@CrS₂-Side system, the favorable pathway can be described as: *NO → *HNO→ *H₂NO → *H₂NOH →*NH₃ + *OH →*H₂O (Fig. S3d in Supporting information). The intermediates, including *HNOH, *H₂NO, and *NH, are unfavorable from energetic aspect. As shown in Fig. 6d, the rate controlling step (RCS) of NORR is *OH + H⁺ + e⁻ →*H₂O with a reaction energy of 0.03 eV, which can be easily overcome at an ultralow limiting potential of −0.03 V.

Above all, the free energy profiles have demonstrated that both v-CrS₂ and Ti@CrS₂ can effectively activate NO to produce NH₃ at the limiting potentials of −0.03 ~ −0.47 V, with different reaction mechanisms. The configurations of intermediates of rate-controlling steps are demonstrated in Fig. S4 (Supporting information).

As we know, *H may also adsorbe on the catalysts by consuming the proton-electron pair and undergo a potential unwanted hydrogen evolution reaction (HER) side reaction. We thus calculated HER as an important side reaction in the process of NORR on v-CrS₂ and Ti@CrS₂. The *H adsorption free energy (ΔG_H) is a commonly used reactivity measure for HER, which is 1.10 eV and −0.63 eV on v-CrS₂ and Ti@CrS₂ respectively. Through the comparison of the limiting potentials between the NORR (−0.03 ~ −0.47 V) and HER (−0.63 ~ −1.10 V) (Fig. S5 in Supporting information), we find that our designed catalysts all prefer NORR to the HER, indicating a perfect selectivity.

In summary, we have herein investigated the electrocatalytic reduction of NO on catalysts, including CrS₂, v-CrS₂, and Ti@CrS₂ surfaces. The results have shown that the pristine CrS₂ exhibits inert character for NO activation. However, v-CrS₂ and Ti@CrS₂ can exhibit enhanced interaction with NO, due to increased charge transfer between NO and substrates (0.52~0.75 e) and enhanced adsorption of NO on the catalysts (−0.96~−1.64 eV), compared to the situation of CrS₂ (0.065 e/−0.30 eV). Based on the adsorption energies and ICOHP values, we eventually screen the systems, including v-CrS₂-S1 (E_ads[NO] = −1.64; ICOHP = −9.22), v-CrS₂-S2 (E_ads[NO] = −0.98 eV; ICOHP = −7.69), Ti@CrS₂-S1 (E_ads[NO] = −1.18 eV; ICOHP = −9.07), and Ti@CrS₂-side (E_ads[NO] = −0.96 eV; ICOHP = −7.02), as the favorable candidates, which are all likely to occur in the real electrochemical condition. From the free energy profiles of NO electro-reduction to NH₃, we can see that the systems of v-CrS₂-S1, v-CrS₂-S2, and Ti@CrS₂-S1 (Ti@CrS₂-Side) follow the *NOH (*NHO) mechanism, with ultralow limiting potentials of −0.03~−0.47 V. We therefore assume that the methods, including introducing vacancy and doping, can be treated as promising modification strategies of CrS₂ for NO activation to synthesis NH₃. This study has provided a theoretical basis for the search of sulfide catalysts in the area of NO electro-reduction.

All authors declared that there are no competing interests.

Yiwen Xu: Data curation. Chaozheng He: Supervision. Chenxu Zhao: Investigation. Ling Fu: Investigation.

This study was funded by the Natural Science Foundation of China (No. 21603109), the Henan Joint Fund of the National Natural Science Foundation of China (No. U1404216), the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 20JK0676). This work was also supported by Natural Science Basic Research Program of Shanxi (Nos. 2022JQ-108, 2022JQ-096).

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.109797.