Ammonia (NH₃), as a future carrier of renewable energy and a source of fertilizer in agriculture, is the key aspects and anticipated stages in promising technologies for decades, which is provided with large hydrogen content and high energy density [1-3]. Although electrosynthesis of NH₃ from N₂ composing of 78% of the atmosphere, which is a fertile source for synthetic ammonia, it exists in chemically and biologically unusable gaseous form. Haber, who break through the triple bond of dinitrogen with hydrogen in the presence of the Fe and discovered the process by high temperatures and pressures, explained that his main motivation for the study of synthesizing ammonia was the growing demand for food, and is awarded a Nobel Prize in 1931 [4]. Recently, more and more researchers are paying attention to the approach to replace the Haber-Bosch process by searching for the befitting catalyst support of ceria under ambient conditions. Doping single metals of chromium (Cr), copper (Cu), iron (Fe), molybdenum (Mo) and rubidium (Ru) can enhance the performance of electrocatalytic N₂ to NH₃ in comparison to the pure CeO₂(111) surfaces efficiently, which the single Mo atoms in Mo-N₃C are also reported for the reason of the best capability of N₂ adsorption for further electrochemical N₂ reduction [5-9]. Lee and co-workers explored the new way called the reticular chemistry approach which exploiting MOFs water-repelling and molecular-concentrating effects to overcome HER-imposed bottlenecks to accelerate synthesis yield of ammonia in theory [10]. Also, Guo et al. focus on the atomically dispersed Bi-catalysts for nitrogen reduction reaction to tackle the activity and selectivity [11]. As well as Mxene-based materials, which have been noticed as highlighted catalysts for electrochemical N₂ reduction recently, are investigated rapidly due to satisfactory catalytic activity [12]. Analogously, the process of Ammonia borane (AB) hydrolysis generates H₂ and NH₃ on the transition metal Fe@Co core-shell structure has been obtained [13, 14].

However, we will have to admit and should not ignore that the difficulty of a strong N-N bond is the biggest problem in the synthesis of ammonia. In a word, it makes us provide the ideas for seeking another supplementary scheme. As a nitrogen supplement, nitric oxide (NO) has the advantage of bond energy over nitrogen molecules, which consumes much less energy to synthesize ammonia. Especially on the surfaces of CeO₂ (111), oxygen vacancies play an important role in good catalytic performance, which comes from the interconversion between Ce(III) and Ce(IV) oxidation states with the storage and release of 4f electronic orbits [14-19]. In this work, our study demonstrates that we built a 3 × 3 × 1 supercell of CeO₂ (111) surface by doping La atom with oxygen vacancy for adsorbing NO molecules to study geometry, electronic structures, and NO reduction reaction coordinate to propose a new idea of N-element reduction reaction (NORR):

(1)

The calculations were performed by a spin-polarized DFT + U approach using the Vienna ad initio simulation package (VASP) [20], which employing the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerh of (PBE) function. Also, we use DFT-D2 to describe the van der Waals bonds. For guaranteeing a good convergence of total energies, the plane-wave cutoff was 400 eV, which uses the Brillouin zone sampled with 5 × 5 × 1 of k-points with allowing the convergence of total energy to set 0.01 eV, and the Part valence-electron configurations include Ce (5s, 5p, 6p, 5d, 4f), La (5d, 6s) and O (2s, 2p). And we consider the 4f states of the reduced cerium and doped-La atoms, where the value of the Hubbard U terms was used as 5.0 eV and 7.5 eV effectively [21], and we first predicted bulk lattice constant of the pure CeO₂ is 5.42 Å, which compared it and the agreement with the experimental value (5.41 Å) and the theoretical results (5.43 Å) [22, 23]. For the surface selection, we studied only the surface (111) among the low-index surfaces of CeO₂ (111), (110) and (100), which surface (111) is the most stable [24, 25]. As depicted in Fig. S1 (Supporting information), the circular area of the dotted line represents the possible NO adsorption sites of Ce-top, O-top, Ce-O-bridge and hollow sites.

For purpose of better understanding the transition metal (TMs) doped CeO₂ (111) surfaces the formation energies of each surface slab by using the following equation:

(2)

where E_M−CeO2 and E_CeO2 are total energies of TMs doped and stoichiometric CeO₂ (111) surface, respectively. E_Ce and E_M are the energies of single Ce atom and the selected metal atom (M = K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, Cs, Ba, La, Pr, Nd and Sm), respectively. Clearly, the negative value presents the exothermic process, leading to the stable structure. When the values were calculated to be positive, it explained that doping process is thermodynamically unfavorable.

As shown in Fig. S2 (Supporting information), all the formation energies of the metal-doped CeO₂ (111) surfaces are plotted, we actually see that except Cs elements, the dopant formation energies of K to Ba atoms (> 2 eV) are higher than those (< 1.5 eV) which doped with rare metals (La, Pr, Nd and Sm). To further compare with rare metals, La-doped CeO₂ (111) surface with the lowest formation energy of 0.67 eV indicating that the syntheses of La-doped-CeO₂ (111) systems are relatively easy in the experiment. Our results are completely consistent with the radii between the M and Ce atoms, that the larger the size difference is, the larger the formation energy is [26].

Generally, oxygen vacancy (OV) plays an important role in good catalytic performance, which coming from the interconversion between Ce(III) and Ce(IV) oxidation states with the storage and release of 4f electronic orbits. Thus, for investigating the formation energy of oxygen vacancies (OVs) on the CeO₂ (111) surface, the defect energy E_vac is defined as following [27, 28]:

(3)

where E_{Ce1−xMxO2−δ}, E_O2 and E_Ce1−xMxO2 are the energy of the bulk in the presence of one oxygen vacancy, the energy of a gas-phase O₂ and the bulk of surface Ce_1-xM_xO₂, respectively. The definition shows that a positive value indicates an endothermic-formation and a negative value indicates an exothermic formation. We use the same level to gain the formation energy of OVs in this work. As shown in Fig. S1, the formation energy of an oxygen vacancy on the TMs and rare metals doped surface is lower value, compared with the pure surface of 3.01 and 2.85 eV [29, 30], and this fully demonstrated the doping ways can promote the formation of oxygen vacancies, which are in agreement with the calculation by Xue et al. [31, 32].

The adsorption energy (E_ads) is defined as [33, 36]:

(4)

where E_{adsorbate/sub}, E_adsorbate and E_sub are the total energies of adsorbate-substrate, isolated adsorbate and substrate system, respectively. And the negative value of E_ads indicates the better stable configuration and exothermic process.

As shown in Fig. 1a and Fig. S1, in order to further elucidate and study the nature of the CeO₂ systems for NO activation, we have tested E_ads of and bond length of NO, the x-axis coordinates indicate the possible adsorption locations, which are Ce-top, O-top, bridge, hollow and OV sites and the y-axis is the energy of adsorption. Also, we can see that red and black lines, which show NO molecule can be adsorbed over different sites through its O and N atom, respectively. The bar chart shows the bond length of NO after adsorption through N atom, and the date by O atom is listed in Table S1 (Supporting information) due to the minor change. Our computations demonstrated that NO chemisorption occurs on the N site preferably, which the value of N-site shows better adsorption than O-site with E_ads under −0.40 eV in general. Moreover, when the OV occurs on the surface, the adsorption energy is significantly reduced, and the bond length is also increased of 1.211 Å. In all, the results indicate that the existence of OV can well improve the ability of NO activation. Especially, adsorption energy and bond length are significantly improved when metals are doped with oxygen vacancy. By comparison of different adsorption energy E_ads of NO and bond length after different metals doping on M_xCe_1-xO_2-δ surfaces (M = K, Ca, Sc, Ti, V, Cr, Mn, Fe, Cu, Zn, Mo, Cs, Ba, La, Pr, Nd and Sm), what is noteworthy is that the bond length of NO molecule increased to 1.245 Å from its original length of 1.117 Å and the adsorption energy decreased to −1.12 eV by activating over La-doping with OV surface (Fig. 1b).

In a word, according to Fig. 1, Tables S1 and S2 (Supporting information), we found that direct generation of OV can also achieve the result of NO activation (the formation energy of oxygen vacancy (E_ads) is 3.01 eV, the bond length of NO is 1.211 Å and the E_ads is –0.85 eV), except the system of low formation energy doping La atom with OV (the formation energy of oxygen vacancy (E_ads) is 2.85 eV, the bond length of NO is 1.245 Å and the E_ads is –1.12 eV). As shown in Fig. S4 (Supporting information), NO molecule prefers to adopt an end-on way with Ce-N bonding distance of 2.491 Å on the OV surface and a side-on mode with Ce-O, Ce-N and La-N bonding distances of 2.703, 2.542 and 2.661 Å. It is obvious that the defect area is large, the distance of Ce³⁺-O is too far to bond on pure OV surface. Conversely, duo to the La ion is bigger that the Ce and the defect area is smaller, N and O atom can contact with more reductive active sites at the same time to pull the NO bond. Therefore, in order to further study the difference between them for NORR, we carried out the HER study over La doped CeO₂ (111) surface with an oxygen vacancy and CeO₂ (111) surface only with OV, respectively (Fig. S5 in Supporting information), which is an important side reaction to hinder the process of NORR. Ulteriorly, we can see that the first hydrogen is adsorbed on the La doped CeO₂(111) surface with an oxygen vacancy and CeO₂(111) surface only with Vo with the free energy change of −0.73 and −0.81 eV, respectively, which the calculated equation is ΔG_H = E_ads + 0.24 [36]. In other words, the results reveal the practical free energies change of *H are −0.97 eV over La-doped CeO₂ with Vo, which is smaller than that of *NO (−1.12 eV) and the E_ads of *H are −1.05 eV over pure CeO₂ with Vo, which is bigger than that of *NO (−0.85 eV). The calculation indicates that the La-doped CeO₂ (111) with OV can dominantly attract more NO than H, where the defected surface can expose more active sites for NORR.

To speculate the mechanism of the adsorption sites of the NO-molecule, it is necessary to calculate the difference charge density after doping La atom and forming an oxygen vacancy. We thus investigate the electronic structures of interaction between NO and defected species and densities of states (DOS) of N and O atoms which guiding us to determine the location of the reduction sites [37]. According to the Fig. 2a, the charge transference from OV site to La²⁺ (Bader charge of 1.71|e|) and Ce³⁺ (Bader charge of 2.81|e|) sites, respectively. Now therefore, the existence of chemical adsorptive sites may at the position of Ce³⁺ and La²⁺.

For defected systems containing a single metal atom doping and an oxygen vacancy, only the lanthanide element is used, which the value of E_ads is lowest and degree of NO bond activation shows the best performance of 1.245 Å, giving smaller to the volume of dopant hole, where is enclosed by i, ii and iii in Fig. S1, which considering the reason of the similar ion radius sizes between Ce and La atom. Thus, the combination of Ce³⁺ and La²⁺ active reduced sites together can accelerate NO molecules activation, were reacting on a finite scale. As shown in Fig. 2b, the red and blue patterns indicate the distances of neighboring atoms each other on the pure surface and defective surfaces, respectively. The distances between M and O_x (x = I, II and III) atoms (M = Ce and La) are 2.371, 2.369, 2.339 and 2.241 Å as shown in Fig. S1 and Fig. 2b, which are closed to the distance of pure surface (2.348 Å) [38-40]. To better describe the situation of the active sites, it is worth mentioning that the density of states (DOS) to study the influence of doping La atom with an oxygen vacancy on the electronic structure of defected CeO₂ surface. Fig. 2c shows that the orbital electronics of Ce(f) contributed between −0.2 eV and 0 eV, and La(d) orbital electronics contributed between −1.85 eV and 0 eV apparently with both VB occupied by states in spin up closed to the Fermi level, that the result is well consistent with the value [41].

For further understanding activation of NO molecule, we make the Bader charge analysis that N atom accepts the charge of 0.53|e| from the Ce and La cation and O atom receives the charge of 0.17|e| (Fig. 2b). The evidence of chemical adsorption can be confirmed by the charge density difference and is calculated using the expression [42-46]:

(5)

where ρ_total, ρ_sur and ρ_NO are the charge densities of the NO adsorption on the OV site with metal-La doping, the charge density of the pure surface, and the charge density of studied gas molecule-NO, respectively [33].

The Gibbs free energy change (ΔG) for each elementary step was obtained using the computational hydrogen electrode (CHE) model by the following equation [45]:

(6)

where ΔE, ΔE_ZPE and ΔS are the reaction energy by the DFT calculation and the changes in zero-point energy and entropy, respectively. T is the temperature (298.15 K).

In a word, the adsorption energy of NO on the OV site indicates that the CeO₂ (111) surface is modified by metal La and vacancy of O atom with a synergistic effect. Charge density difference plots (Figs. 3a and b) show that adsorbed NO can interact with these active and occupied orbitals of La and Ce atoms, in which the lone pair electrons from the Ce³⁺ and La²⁺ are injecting into the electrons from the Ce³⁺ and La²⁺ are injecting into the antibonding orbitals of NO via N and O atoms by the so-called as the "push" hypothesis. The more interaction is thus for the lower dissociation barrier than NO adsorption on the pure surface. Our calculation is further performed to provide more details of such chemical change between isolated La and NO by fragment orbital analysis as shown in Figs. 3c–g [11, 46-52]. Also, the projected densities of states (PDOS) of NO adsorption on defected species show that α-, β- and αβ-spin states represent pure substrate surface, a gaseous NO molecule, and the adsorption configuration for comparison (Figs. 3f and g) [53].

For the interaction between the two main states of 4f-5d for Ce³⁺ atom and O_2p states for O atoms, we present in Figs. 3c, e and g that the energy levels of Ce³⁺ majority f spin states involved in the interaction with p-spin orbitals of O atom with the energy of αβ-states lower which becoming more stable. Obviously, the f_x3 orbitals electrons are donated to the O_2p orbitals, which proving up to the hilt that surface generated an OV possess the capability of redox. Also, for interaction between Ce³⁺, La²⁺ and O atoms, we present in Figs. 3d–f the spin densities are strongly localized on Ce_{4f, 5d}, La_5d and 2p of N states, the energy levels of Ce³⁺ majority 4f spin states and La²⁺ 5d-states involved in the interaction with 2p-spin orbitals of N atom with the energy of αβ-states lower which becoming more stable, too. Similarly, as our previous analysis, the 4f_x3 orbitals of Ce and 5d_z3 orbitals of La electrons are donated to the 2p orbitals of N indicates that surface-anchored La also owns the capability of redox.

Critically, the investigation into the mechanism of ammonia synthesis over the defected surface with the raw material (NO) is essential. Hence, to explore the reaction path of NORR on La-doped CeO₂ catalysts, the associative hydrogenation of pathways, which the proton-electron pair (H⁺ + e⁻) attacks the N atom firstly and then O atom continuously until the NH₃ is generated, was considered according to the analysis of the degree of activation mechanism between N and O atom and the horizontal adsorption configuration, thus the barrier of NO direct dissociation greater than associative hydrogenation. And the Gibbs free energy of each reaction intermediate was calculated as shown in Fig. 4a.

Different from the value on the O site, ΔG(*NHO) of −0.62 eV is lower than the ΔG(*NOH) of 0.59 eV as shown in Fig. 4a which comparing with other theoretical calculation of positive value and showing the excellent performance [54, 55]. We further examine the "enzymatic" pathway that the applied potential for U = 0 V and T = 298.15 K to study the true condition [56, 57]. And the detailed thermodynamic date we calculated the Gibbs free energy of all the adsorption and desorption structures are considered as shown in Fig. 4b, which the length of NO bond changes of 1.244, 1.334, 1.487 and 2.863 Å in the process of hydrogenation until breaking. Remarkably, due to the degree of NO activation and its own activity, whose *N_xO_y (x = 1, 2 and 3; y = 1, 2) intermediate is substantially low, resulting in a smaller energy barrier of −0.62 eV for the first hydrogenation of *NO into *NHO, which is an exothermic reaction. For the second and third step of *NHOH and *NH₂OH, the reactions are both exothermic energies of −0.09 and −0.26 eV to promote the dissociation of NO, that the third step (*NH₃ + *OH with the NO bond splitting up) is also downhill. It is presented in Fig. 4a that Vo with La doping favors the *NH₃ + *H₂O stabilization with −1.85 eV downhill for *HH₂ + *OH → *NH₃ + *OH substantially. By the step of fifth for *NH₃ + *H₂O, we also found that NORR activity of La-CeO₂-OV over surface (111) can construct H₂O. For the last step, the reason that we ignored the consideration for NORR process is its form of NH₄⁺. Thus, the NORR process we conclude is thermodynamically spontaneous.

Based on the theoretical findings, the NORR performance of La-CeO₂-OV on the associative hydrogenation reaction coordinate can be described as illustrated in Fig. 4. Firstly, the direction of alternation is determined by the activation mechanisms between N and O atoms and the horizontal adsorption configuration. Second, the situations of La-dopants and OV will effectively push the orbitals electrons of the sites of Ce and La to the NO molecular orbitals, resulting in the accelerated transmission of proton-coupled electrons and the spontaneous reaction that synthesis of the ammonia and water.

Subsequently, we find that the effect of atomic radii is a critical factor for altering and ensuring the appropriate size of the NO molecule adsorption. We have also recorded that the most active reduction surface predicted is OV site, and investigated the CeO₂(111) with doping the La metals from the ab initio DFT calculations by studying geometric and electronic structure properties. The results show that E_ads is of −1.12 eV with relative horizontal adsorption, the Bader charge analysis of N atom accepting the charge of 0.53|e| from the Ce and La cation and O atom receiving the charge of 0.17|e|. Importantly, ΔG is less than zero of NORR (NO + 5(H⁺ + e⁻) → NH₃ + H₂O), which indicating thermodynamically spontaneous reaction to synthesize ammonia and water under ambient conditions.

In summary, we have demonstrated the good structural engineering of reduction surface by ceria when La-doping with Vo. Comparing with NRR coordinates, NORR has lower energy consumption as confirmed by the theoretical results [46]. And thus, we anticipate that such metals-La including oxygen vacancies can be extended over new ideas for efficient electrocatalytic NO to ammonia as a feedstock of nitrogen supplement.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

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) and the Special Fund of Tianshui Normal University, China (No. CXJ2020-08).

Appendix Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2021.05.072.