Si3C Monolayer as an Efficient Metal-Free Catalyst for Nitrate Electrochemical Reduction: A Computational Study

Nitrate electroreduction reaction to ammonia (NO3ER) holds great promise for both nitrogen pollution removal and valuable ammonia synthesis, which are still dependent on transition-metal-based catalysts at present. However, metal-free catalysts with multiple advantages for such processes have been rarely reported. Herein, by means of density functional theory (DFT) computations, in which the Perdew–Burke–Ernzerhof (PBE) functional is obtained by considering the possible van der Waals (vdW) interaction using the DFT+D3 method, we explored the potential of several two-dimensional (2D) silicon carbide monolayers as metal-free NO3ER catalysts. Our results revealed that the excellent synergistic effect between the three Si active sites within the Si3C monolayer enables the sufficient activation of NO3− and promotes its further hydrogenation into NO2*, NO*, and NH3, making the Si3C monolayer exhibit high NO3ER activity with a low limiting potential of −0.43 V. In particular, such an electrochemical process is highly dependent on the pH value of the electrolytes, in which acidic conditions are more favorable for NO3ER. Moreover, ab initio molecular dynamics (AIMD) simulations demonstrated the high stability of the Si3C monolayer. In addition, the Si3C monolayer shows a low formation energy, excellent electronic properties, a superior suppression effect on competing reactions, and high stability, offering significant advantages for its experimental synthesis and practical applications in electrocatalysis. Thus, a Si3C monolayer can perform as a promising NO3ER catalyst, which would open a new avenue to further develop novel metal-free catalysts for NO3ER.


Introduction
The ever-increasing discharge of nitrate (NO 3 − )-containing agricultural and industrial sewage causes severe contamination of the soil and water resources, thus posing great threats to global food safety and human health [1,2].At present, state-of-the-art nitrate treatment of wastewater typically involves the biological and physical strategies of denitrification, which have shown some intrinsic drawbacks [3][4][5].For example, biological methods require denitrifying bacteria to convert NO 3 − into nitrogen, which would be ineffective under extreme conditions, and the biomass materials would need to be post-treated [6].As for the physical approaches, such as reverse osmosis and ion exchange, they are still focused on displacement rather than elimination, which requires further processing [7].Chemical reduction is an interesting way to convert NO 3 − into some desirable products, which can be driven using heat, light, and electrical energy [8].Among them, the electrochemical reduction of NO 3 − to ammonia reaction (NO 3 ER) has recently emerged as a most promising strategy for water denitrification due to the use of renewable electric energy, mild operation conditions under room temperature and pressure, and without secondary electroreduction into a NH 3 product is of great significance [31,32].
With these advantages of 2D Si x C y materials in mind, here, we investigated the feasibility of several Si x C y materials (including SiC, SiC 2 , SiC 3 , SiC 5 , SiC 7 , and Si 3 C monolayers) as catalysts for NO 3 ER into NH 3 by means of density functional theory (DFT) computations.The results demonstrated that, among these Si x C y candidates, the Si 3 C monolayer can be identified as the best NO 3 ER catalyst due to its lowest limiting potential of −0.43 V, which stems from the synergic effect of its three adjacent Si active sites to boost the efficient activation of NO 3 − and the subsequent hydrogenation step.Moreover, the positive charge on Si active sites in the Si 3 C monolayer greatly hinders H + attacking, guaranteeing its high selectivity toward NO 3 ER by suppressing the competing HER.In addition, the high stability of the Si 3 C monolayer can be verified from a thermal and electrochemical perspective to meet its realistic applications in NO 3 ER.

Computational Methods and Models
All spin-polarized DFT computations were carried out by using a plane-wave basis set, as implemented in the Vienna Ab Initio Simulation Package (VASP 5.4.1)[54,55], in which the projector augmented wave (PAW) potential was adopted for the interactions between electrons and ions [56,57], and the Perdew-Burke-Ernzerhof (PBE) functional [58] within the generalized gradient approximation (GGA) was employed to determine the exchange-correlation interactions with a cutoff energy of 550 eV.The convergence criteria were set to 0.01 eV/Å and 10 −5 eV, respectively, for the residual force and the energy on each atom during structure formation.The possible van der Waals (vdW) interaction was treated using the empirical correction in Grimme's method (DFT+D3) [59].
A supercell consisting of 3 × 3 × 1 Si x C y unit cells was built with a vacuum space of 20 Å to minimize the interaction between two adjacent images.During the structural relaxation, a 3 × 3 × 1 k-point mesh was employed to sample the 2D Brillouin zone.Ab initio molecular dynamics (AIMD) simulations based on the NVT ensemble [60] were performed to evaluate the thermodynamic stability.To explore the catalytic activity of these Si x C y monolayers for NO 3 ER, the computational electrode model (CHE) method [61,62] was employed to compute the free energy diagrams and the corresponding limiting potentials (U L ).Specially, the free energy change (∆G) of each elementary step can be determined by ∆G = ∆E + ∆ZPE − T∆S + eU, where ∆E is the reaction energy of the reactant and product species adsorbed on the catalyst, directly obtained from DFT computations, and ∆ZPE and ∆S (see Table S1 in Supporting Information) represent the differences in the zero-point energy and entropy of the adsorbed species and the gas phase molecules at 298.15 K, respectively, which can be calculated from the vibrational frequencies.Specially, the entropies of the free molecules (H 2 , H 2 O, and NH 3 ) were taken from the NIST database [63], whereas the energy contribution from the configurational entropy in the adsorbed intermediate was neglected.U represents the applied potential, which can be determined as U = −∆G/e.Thus, U L corresponds to the applied limiting potential, which can be obtained using the maximum free energy change (∆G max ) to overcome in the NO 3 ER process: UL = −∆Gmax/e, well consistent with previous studies [64,65].To avoid directly computing the energy of NO 3 − , the gaseous HNO 3 was chosen as a reference.The Gibbs adsorption free energy of NO 3

Structures and Properties of 2D Si x C y Nanomaterials
The optimized structures of these considered 2D Si x C y nanomaterials are presented in Figures 1a and S1, while some key parameters are summarized in Table S2.Clearly, all Si x C y monolayers have a graphene-like planar structure, which is unlike the puckered structure of silicene.Moreover, the optimized lattice parameters of their unit cells are in the range of 3.09 (SiC) to 7.02 Å (Si 3 C), and the lengths of the Si-C bonds range from 1.69 Å (SiC 7 ) to 1.81 Å (SiC 3 and Si 3 C).In particular, within the frameworks of the SiC 2 , SiC 3 , SiC 5 , and SiC 7 monolayers, some C-C bonds can be formed with shortest lengths of about 1.44 Å.However, in the Si 3 C monolayer, the Si-Si bonds can be formed with lengths of 2.45 Å. Notably, the above results on the optimized configurations of these Si x C y nanomaterials are in good agreement with previous studies [41,45,74] as shown in Table S3, thus ensuring the accuracy of the employed models and methods.Remarkably, the planar configurations of these Si x C y monolayers could be related to the ionic-binding features of the Si-C bonds, as shown by the computed charge density distribution in Figures 1b and S1.As expected, due to the larger electronegativity of the C atom than that of the Si atom, there is a significant amount of charge transfer (0.74~2.51|e -|) from the Si atom to the C atom.As a result, the Si atom carries the positive charge, making it exhibit similar electronic properties to the transition metal and thus holding great potential for efficiently activating NO 3 -in NO 3 ER.To estimate the experimental feasibility of these 2D Si x C y materials, we computed their formation energies (E f ) under C-rich and Si-rich conditions according to the following definition: , where E total is the total elec- tronic energy of a Si x C y monolayer, and n C and n Si are the number of C and Si atoms in the supercell of the Si x C y monolayer according to previous theoretical studies [40].Moreover, µ C and µ Si represent the chemical potentials of the C and Si atoms, which greatly depend on the environment conditions.Under C-rich conditions, µ C was computed from the graphene, and then the chemical potential of the Si atoms was determined by µ Si = µ SiC − µ C , where µ SiC denotes the chemical potential of a SiC unit cell in bulk SiC crystal.On the contrary, the cubic silicon crystal was adopted as the source of Si atoms, and µ C can be obtained as follows: µ C = µ SiC − µ Si .Based on the above definitions, the computed E f values of these 2D Si x C y systems were summarized in Table S2.Our DFT results showed that the E f of the SiC monolayer is 0.67 eV, which is independent of the growth conditions due to the same ratio between the Si and C atoms.In contrast, the SiC 2 , SiC 3 , SiC 5 , and SiC 7 candidates exhibit lower formation energies (0.52~0.66 eV) in C-rich environments than those in Si-rich ones (0.86~1.04 eV), suggesting that such conditions can boost their formation.On the contrary, the Si 3 C monolayer prefers to grow in Si-rich conditions due to its smaller E f value of 0.89 eV.These positive formation energies suggest the synthesis of these Si x C y materials still remains challenging in the experiments.Fortunately, rapid progress in the growth of 2D materials on metal-based surfaces by using chemical vapor deposition has been made in recent years [75,76].For example, Polley et al. reported the synthesis of monolayer honeycomb SiC on ultrathin metal carbide films [77], and Gao et al. synthesized a Si 9 C 15 monolayer on Ru substrates [78].In addition, the reaction between graphene and a Si source is another promising synthetic strategy for 2D Si x C y materials, such as a quasi-2D SiC 2 monolayer [79].
Nanomaterials 2023, 13, x FOR PEER REVIEW 4 of 14 Si atoms, and µC can be obtained as follows: µC = µSiC − µSi.Based on the above definitions, the computed Ef values of these 2D SixCy systems were summarized in Table S2.Our DFT results showed that the Ef of the SiC monolayer is 0.67 eV, which is independent of the growth conditions due to the same ratio between the Si and C atoms.In contrast, the SiC2, SiC3, SiC5, and SiC7 candidates exhibit lower formation energies (0.52~0.66 eV) in C-rich environments than those in Si-rich ones (0.86~1.04 eV), suggesting that such conditions can boost their formation.On the contrary, the Si3C monolayer prefers to grow in Si-rich conditions due to its smaller Ef value of 0.89 eV.These positive formation energies suggest the synthesis of these SixCy materials still remains challenging in the experiments.Fortunately, rapid progress in the growth of 2D materials on metal-based surfaces by using chemical vapor deposition has been made in recent years [75,76].For example, Polley et al. reported the synthesis of monolayer honeycomb SiC on ultrathin metal carbide films [77], and Gao et al. synthesized a Si9C15 monolayer on Ru substrates [78].In addition, the reaction between graphene and a Si source is another promising synthetic strategy for 2D SixCy materials, such as a quasi-2D SiC2 monolayer [79].The electrical conductivity of a given catalyst has been revealed as an important indicator to evaluate its electrocatalytic activity.In general, excellent electrical conductivity normally facilitates rapid charge transfer for an efficient electrochemical process.Therefore, the band structures of these 2D SixCy candidates were computed to estimate their electrical conductivity.We found that the SiC, SiC2, or SiC7 monolayers are semiconductors with large band gaps of 2.55, 0.61, and 0.76 eV (Figure S1), respectively, which would be unfavorable for charge transfer for electrocatalytic reactions.On the (d) The electrical conductivity of a given catalyst has been revealed as an important indicator to evaluate its electrocatalytic activity.In general, excellent electrical conductivity normally facilitates rapid charge transfer for an efficient electrochemical process.Therefore, the band structures of these 2D Si x C y candidates were computed to estimate their electrical conductivity.We found that the SiC, SiC 2 , or SiC 7 monolayers are semiconductors with large band gaps of 2.55, 0.61, and 0.76 eV (Figure S1), respectively, which would be unfavorable for charge transfer for electrocatalytic reactions.On the contrary, analysis of the band structure shows that SiC 3 (Figure S1) and Si 3 C monolayers (Figure 1c) are semi-metallic with the conduction band minimum (CBM) and VBM contacting each other at the point of Γ(k = 0) to form a Dirac cone, implying their good electrical conductivity to boost their applications in electrocatalysis, which mainly originates from the contributions of Si-3p orbitals, as shown by the computed projected density of states (PDOSs, Figure 1d).

Adsorption and Activation of NO 3 − on Si x C y Monolayers
During the process of NO 3 − electroreduction, it is well established that the first step is the adsorption of the nitrate species, which often affects and even determines the whole catalytic reaction pathway.To this end, we next examined the adsorption behavior of the Here, a more negative ICOHP value implies a less activated NO3 * species.As displayed in Figure S3, for the Si3C monolayer, there is a strong orbital interaction with NO3 * due to the fully occupied bonding orbitals and nearly unoccupied antibonding orbitals, inducing weaker N=O bonding and more sufficient NO3 * activation, which can be also confirmed by its less negative ICOHP.Interestingly, a good linear correlation can be observed between the ICOHP and the N-O bond lengths of the adsorbed NO3 * species (Figure 2d), well accounting for the NO3 − adsorption trend in these SixCy catalysts, because their different Si active sites determine different bonding/anti-bonding orbital populations.The results showed that NO 3 − is preferable to be adsorbed on SiC, SiC 2 , SiC 3 , SiC 5 , and SiC 7 systems via the 1-O pattern, in which one Si-O bond is formed with a length ranging from 1.74 to 1.79 Å.On a Si 3 C monolayer, however, we found that the three O atoms of NO 3 − species can be adsorbed on three Si sites of this catalyst, forming three Si-O bonds with lengths of 1.74 Å (Figure 2a).Notably, to the best of our knowledge, there is no prior study on such a NO 3 − adsorption configuration via the 3-O pattern, which mainly stems from the unique geometric ensemble effect in the Si 3 C monolayer: its three adjacent Si active sites can promote synergistically the sufficient activation of the NO 3 − species.Based on these aforementioned adsorption configurations, we then evaluated the binding strength of NO 3 − on these 2D Si x C y catalysts by computing their corresponding ∆G NO * 3 values.Unfortunately, NO 3 − physisorption can be observed on the SiC, SiC 2 , and SiC 5 monolayers due to their computed positive ∆G NO * 3 values (0.99 eV, 0.65 eV, and 0.41 eV, respectively, Figure 2b), suggesting that NO 3 − cannot be effectively captured by these three Si x C y materials, let alone effectively activated.We thus excluded them as promising NO 3 ER catalysts from further studies in this work.Conversely, the spontaneous chemisorption of NO 3 − can be achieved on the SiC 3 , SiC 7 , and Si 3 C monolayers with ∆G NO * 3 values of −0.21, −0.62, and −0.26 eV, respectively.Moreover, to suppress the unwanted hydrogen evolution reaction (HER) for achieving a high selectivity, the ∆G NO * 3 value should be more negative than that of the H + species (∆G H * ), since the H + in the electrolytes will block the active sites when H + binds too strongly with a given catalyst.Notably, a comparison between ∆G H * and ∆G NO * 3 has been extensively employed to estimate the selectivity of a given catalyst for NO 3 ER [65][66][67][68][69][70][71][72][73].To this end, the values of ∆G NO * 3 and ∆G H * on the SiC 3 , SiC 7 , and Si 3 C surfaces are presented in Figure 2b for comparison.Clearly, the ∆G NO * 3 values are more negative than the corresponding ∆G H * in the three candidates, especially for the Si 3 C monolayer (−0.26 eV for ∆G NO * 3 vs.0.27 eV for ∆G H * ), indicating the good suppressing effect on the undesirable HER and thus ensuring a high selectivity toward the NO 3 ER process.Understandably, the positive charges on the Si active sites can greatly hamper H + approaching and H * formation due to the electrostatic repulsion between the positively charged Si sites and H + .
To gain a deep insight into the NO 3 − chemisorption, we took the Si 3 C monolayer as an example to compute the corresponding charge density differences (Figure 2c).The results show that a considerable amount of negative charge is accumulating between the adsorbed O atoms of the NO 3 * species and Si active sites.According to Bader charge analysis, about 2.30 electrons are transferred from the p-orbitals of the three Si active sites to the empty π * -orbital of the NO 3 − species, resulting in the sufficient activation of the adsorbed NO 3 − species via the p-π * interaction, which normally helps trigger the subsequent hydrogenation reaction.In addition, to explain the remarkable difference in the adsorption strength of NO 3 − in these 2D Si x C y materials, integrated crystal orbital Hamilton population (ICOHP) analyses of the adsorbed NO 3 * species were computed.Here, a more negative ICOHP value implies a less activated NO 3 * species.As displayed in Figure S3, for the Si 3 C monolayer, there is a strong orbital interaction with NO 3 * due to the fully occupied bonding orbitals and nearly unoccupied antibonding orbitals, inducing weaker N=O bonding and more sufficient NO 3 * activation, which can be also confirmed by its less negative ICOHP.Interestingly, a good linear correlation can be observed between the ICOHP and the N-O bond lengths of the adsorbed NO 3 * species (Figure 2d), well accounting for the NO 3 − adsorption trend in these Si x C y catalysts, because their different Si active sites determine different bonding/anti-bonding orbital populations.-activation has been confirmed on the SiC 3 , SiC 7 , and Si 3 C monolayers, we further evaluated their NO 3 ER catalytic performance by computing the free energy changes (∆G) of all possible elemental steps, which was presented in Figure 3 according to a summary of previous studies on NO 3 ER [65][66][67][68][69][70][71][72][73].Specially, by computing the ∆G values, we can identify the reaction pathway with the lowest positive free energy change between any two elementary steps, namely, the most favorable reaction pathway.
Since sufficient NO3 -activation has been confirmed on the SiC3, SiC7, and Si3C monolayers, we further evaluated their NO3ER catalytic performance by computing the free energy changes (ΔG) of all possible elemental steps, which was presented in Figure 3 according to a summary of previous studies on NO3ER [65][66][67][68][69][70][71][72][73].Specially, by computing the ΔG values, we can identify the reaction pathway with the lowest positive free energy change between any two elementary steps, namely, the most favorable reaction pathway.For simplicity, we again chose the Si3C monolayer as an example to elaborate the whole NO3ER process.The obtained most favorable reaction pathway and the involved configurations are shown in Figures 4 and S4, while the computed ΔG values of other possible elementary steps are summarized in Table S4.It can be seen from Figure 4 that NO3 − can be stably adsorbed on three Si sites by forming three Si-O bonds with a ΔG value of −0.26 eV.Interestingly, the approach of the first (H + + e − ) pair leads to the dissociation of one N-O bond of NO3 * to generate (NO2 * + OH * ) species, which is highly downhill by 1.12 eV in the free energy profile.Kinetically, however, this step of NO3 * → NO2 * + OH * requires crossing an energy barrier of 0.95 eV (Figure S5).Subsequently, a H2O molecule can be released via OH * hydrogenation, which is slightly endothermic by 0.32 eV.After the formation of H2O, the remaining NO2 * , bound to two Si sites with Si-O lengths of 1.79 Å, can react with another (H + + e − ).Due to the synergistic effect of the Si active sites, the hydrogenation of the NO2 * intermediate also induces the cleavage of one N-O bond spontaneously, forming a (NO * + OH * ) group.Remarkably, this step of (NO2 * + H + + e − → NO * + OH * ) is highly exothermic by 1.90 eV.Next, an endothermal process for NO * formation and H2O desorption is observed with the free energy increased by 0.37 eV.Again, when the H proton attacks the remaining NO * intermediate, its N-O bond is split into (N * + OH * ) with a considerable negative ΔG of −2.54 eV, in which the N atom is adsorbed on the Si-Si bridge site with a length of 1.65 Å.In the subsequent steps, the H proton consecutively attacks the N * intermediates to generate (NH * + OH * ) and (NH2 * + OH * ) with ΔG values of −0.62 and −0.07 eV, respectively.Moreover, the NH2 * species continues to be hydrogenated to achieve a NH3 product, and this step is slightly exothermic by 0.16 eV.Eventually, the residual OH * species is reduced to H2O, and the corresponding energy rises by 0.43 eV.
Overall, the most energetically favorable conversion process from NO3 − into NH3 product on the surface of the Si3C monolayer can be summarized as follows: NO3 − → NO3 * → NO2 * + OH * → NO2 * → NO * + OH * → NO * → N * + OH * → NH * + OH * → NH2 * + OH * → OH * →H2O (Figure 4), in which the reduction of OH * into H2O can be identified as the For simplicity, we again chose the Si 3 C monolayer as an example to elaborate the whole NO 3 ER process.The obtained most favorable reaction pathway and the involved configurations are shown in Figures 4 and S4, while the computed ∆G values of other possible elementary steps are summarized in Table S4.It can be seen from Figure 4 that NO 3 − can be stably adsorbed on three Si sites by forming three Si-O bonds with a ∆G value of −0.26 eV.Interestingly, the approach of the first (H + + e − ) pair leads to the dissociation of one N-O bond of NO 3 * to generate (NO 2 * + OH * ) species, which is highly downhill by 1.12 eV in the free energy profile.Kinetically, however, this step of species continues to be hydrogenated to achieve a NH 3 product, and this step is slightly exothermic by 0.16 eV.Eventually, the residual OH * species is reduced to H 2 O, and the corresponding energy rises by 0.43 eV.
Overall, the most energetically favorable conversion process from NO 3 − into NH 3 product on the surface of the Si 3 C monolayer can be summarized as follows: NO 3 4), in which the reduction of OH * into H 2 O can be identified as the potential-determining step (PDS) due to its maximum ∆G value of 0.43 eV.Thus, the U L of NO 3 ER on the Si 3 C monolayer is computed to be −0.43V, which is comparable (even less negative) to some transition metal-based catalysts (-0.34 to -0.53 V) [63][64][65][66][67][68][69], suggesting the high NO 3 ER catalytic activity of the Si 3 C monolayer.In addition to the Si 3 C monolayer, we also estimated the activity of the SiC 3 and SiC 7 monolayers for NO 3 ER.We found that the NO 3 ER process on the two materials is also hampered by OH * desorption (Figure S6), which requires a high energy input of 0.79 and 1.23 eV, respectively, corresponding to more negative U L values of −0.79 and −1.23 V than that of Si 3 C system (−0.43V).Of note, to examine the accuracy of the employed PBE function in predicting the catalytic activity, we re-computed the free energy profile of NO 3 ER by using the revised PBE functional (rPBE), in which Si 3 C was chosen as an example.Fortunately, we found that the difference in the limiting potential between the two methods is nearly negligible (0.01 V, Figure S7), thus validating the high activity of the Si 3 C monolayer toward NO 3 ER.
less negative) to some transition metal-based catalysts (-0.34 to -0.53 V) [63][64][65][66][67][68][69], suggesting the high NO3ER catalytic activity of the Si3C monolayer.In addition to the Si3C monolayer, we also estimated the activity of the SiC3 and SiC7 monolayers for NO3ER.We found that the NO3ER process on the two materials is also hampered by OH * desorption (Figure S6), which requires a high energy input of 0.79 and 1.23 eV, respectively, corresponding to more negative UL values of −0.79 and −1.23 V than that of Si3C system (−0.43V).Of note, to examine the accuracy of the employed PBE function in predicting the catalytic activity, we re-computed the free energy profile of NO3ER by using the revised PBE functional (rPBE), in which Si3C was chosen as an example.Fortunately, we found that the difference in the limiting potential between the two methods is nearly negligible (0.01 V, Figure S7), thus validating the high activity of the Si3C monolayer toward NO3ER.Another important issue is the selectivity of the Si3C monolayer toward NO3ER.We thus examined the reaction pathways to form some N-containing byproducts, including NO2, NO, and N2.It can be seen from Figures 4 and S8 that the free energy barriers for the release of NO2, NO, and N2 are 0.52, 0.77, and 0.54 eV, respectively, which are much larger than that of NH3 desorption (0.16 eV).Thus, it is rather difficult to generate these N-based byproducts on the Si3C monolayer, indicative of its high selectivity toward NH3 production from NO3ER.In addition, the HER can be well suppressed due to the weaker H* adsorption on the Si active sites than NO3 − (−0.26 eV for ∆ * vs. 0.27 eV for ∆ * ) as in the above discussion (Figure 2b).

pH-Dependent NO3ER Activity
It should be noted that NO3ER generally proceeds in aqueous conditions, which could induce pH-dependent activity in a given electrocatalyst.To examine this concern, the constant potential method (CPM; more computational details can be seen in ESI) developed by Duan et al. [80][81][82][83][84] was employed to explore the pH effects on the NO3ER catalytic activity on the Si3C monolayer.The variations of the total electronic energies of the Si3C monolayer with and without the adsorbed NO3ER intermediates with the applied electrode potential (standard hydrogen electrode, SHE) are presented in Figure 5a, while the corresponding fitted data are summarized in Table S5, from which a good quadratic relation for all these energy potential points can be observed.Moreover, the adsorption energies (Eads; more computational details are provided in Supporting Information) of these reaction intermediates at various applied potentials were computed as shown in Another important issue is the selectivity of the Si 3 C monolayer toward NO 3 ER.We thus examined the reaction pathways to form some N-containing byproducts, including NO 2 , NO, and N 2 .It can be seen from Figures 4 and S8 that the free energy barriers for the release of NO 2 , NO, and N 2 are 0.52, 0.77, and 0.54 eV, respectively, which are much larger than that of NH 3 desorption (0.16 eV).Thus, it is rather difficult to generate these N-based byproducts on the Si 3 C monolayer, indicative of its high selectivity toward NH 3 production from NO 3 ER.In addition, the HER can be well suppressed due to the weaker H* adsorption on the Si active sites than NO 3 − (−0.26 eV for ∆G NO * 3 vs.0.27 eV for ∆G H * ) as in the above discussion (Figure 2b).

pH-Dependent NO 3 ER Activity
It should be noted that NO 3 ER generally proceeds in aqueous conditions, which could induce pH-dependent activity in a given electrocatalyst.To examine this concern, the constant potential method (CPM; more computational details can be seen in ESI) developed by Duan et al. [80][81][82][83][84] was employed to explore the pH effects on the NO 3 ER catalytic activity on the Si 3 C monolayer.The variations of the total electronic energies of the Si 3 C monolayer with and without the adsorbed NO 3 ER intermediates with the applied electrode potential (standard hydrogen electrode, SHE) are presented in Figure 5a, while the corresponding fitted data are summarized in Table S5, from which a good quadratic relation for all these energy potential points can be observed.Moreover, the adsorption energies (E ads ; more computational details are provided in Supporting Information) of these reaction intermediates at various applied potentials were computed as shown in Figure 5b.As the OH * desorption was identified as the potential-determining step in NO 3 ER, its binding strength with the Si 3 C monolayer at different pHs and applied potentials is crucial to determine its pH-and potential-dependent activity.The computed E ads values of the OH * species as function pHs and applied potentials are plotted in Figure 5c.The results indicated that alkaline conditions undoubtedly hinder the PDS process due to the stronger OH * adsorption strength on the Si 3 C monolayer, suggesting the obvious pHdependent NO 3 ER activity of the Si 3 C monolayer.As a result, the Si 3 C monolayer always exhibits a higher catalytic activity in acidic solutions (reflected by a lower limiting potential) than that in alkaline ones (Figure 5d).In particular, when the pH is about 2.90, the OH * adsorption is optimal, thus achieving the highest NO 3 ER activity with the lowest limiting potential of −0.61 V vs. the reverse hydrogen electrode (RHE) and the involved free energy profile presented in Figure S9.Noteworthily, highly efficient NO 3 ER can be usually achieved in neutral and alkaline media so far.Yet, there are only a few reports on efficient NO 3 ER in acidic NO 3 − -containing wastewater [85], which can meet the requirements of industrial processes such as mining, metallurgy, metal processing, and petrochemical and fiber engineering.Especially as compared with neutral/alkaline conditions, NO 3 ER in acidic conditions is more beneficial for directly generating fertilizers (such as ammonium sulphate, ammonium chloride, etc.) from a chemical perspective and meanwhile avoiding the volatilization of NH 3 gas from aqueous ammonia in neutral/alkaline products [86,87].
5c.The results indicated that alkaline conditions undoubtedly hinder the PDS process due to the stronger OH * adsorption strength on the Si3C monolayer, suggesting the obvious pH-dependent NO3ER activity of the Si3C monolayer.As a result, the Si3C monolayer always exhibits a higher catalytic activity in acidic solutions (reflected by a lower limiting potential) than that in alkaline ones (Figure 5d).In particular, when the pH is about 2.90, the OH * adsorption is optimal, thus achieving the highest NO3ER activity with the lowest limiting potential of −0.61 V vs. the reverse hydrogen electrode (RHE) and the involved free energy profile presented in Figure S9.Noteworthily, highly efficient NO3ER can be usually achieved in neutral and alkaline media so far.Yet, there are only a few reports on efficient NO3ER in acidic NO3 − -containing wastewater [85], which can meet the requirements of industrial processes such as mining, metallurgy, metal processing, and petrochemical and fiber engineering.Especially as compared with neutral/alkaline conditions, NO3ER in acidic conditions is more beneficial for directly generating fertilizers (such as ammonium sulphate, ammonium chloride, etc.) from a chemical perspective and meanwhile avoiding the volatilization of NH3 gas from aqueous ammonia in neutral/alkaline products [86,87].

Stability of Si 3 C Monolayer
Stability is a prerequisite for the practical applications of a catalyst.As a result, we evaluated the durability of the Si 3 C monolayer by performing ab initio molecular dynamics (AIMD) simulations.The results demonstrated that the geometric structure of the Si 3 C monolayer can be well preserved at 500 K after 10 ps (Figure S10a), suggesting its excellent thermal stability.In addition, we also examined the Poisson probability of the bare surfaces of the Si 3 C monolayer using the O * /OH * species stemming from the aqueous solution under working conditions.Thus, we constructed the surface Pourbaix profile [88][89][90] of the Si 3 C monolayer to examine its surface configurations under different equilibrium potentials and pH values.As shown in Figure S10b, when the electrode potential is 0 V vs. SHE, the basal plane of the Si 3 C monolayer is only covered by OH * species in an alkaline condition.Moreover, the minimum potential required to remove the surface OH * group on the Si 3 C monolayer at pH = 14 (U R ) is −0.39 V, which is less negative than the U L of NO 3 ER (−0.43 V), indicating the superior electrochemical stability of the Si 3 C monolayer against surface oxidation under working conditions.

Conclusions
In summary, the potential of several 2D Si x C y monolayers as metal-free NO 3 ER catalysts for NH 3 synthesis was evaluated by performing comprehensive density functional theory computations.Our results showed that the unique structure of the Si 3 C monolayer can sufficiently activate the NO 3 − reactant by forming a "3−O" adsorption configuration.Moreover, the adsorbed * NO 3 intermediate can be easily hydrogenated into a NH 3 product due to the excellent synergistic effect of the three Si active sites with a low limiting potential of −0.43 V.Meanwhile, the high free energy barriers hinder the formation of NO 2 , NO, and N 2 byproducts, and the considerable positive charges on the Si active sites result in weaker H adsorption than NO 3 − , ensuring more favorable NO 3 ER than the competitive HER.In addition, the Si 3 C monolayer exhibits a low formation energy in Si-rich conditions and good stability, providing great potential for its experimental synthesis and practical application.Remarkably, acidic conditions are beneficial to promote the NO 3 − -to-NH 3 conversion.The low limiting potential, high selectivity, great promise for synthesis, and high stability render the Si 3 C monolayer as a very compelling electrocatalyst for NO 3 − electrochemical reduction, which may offer new opportunities for efficient nitrate removal and NH 3 synthesis by using metal−free catalysts.

Supplementary Materials:
The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano13212890/s1, Figure S1 S1.The correction of zero-point energy (ZPE, eV) and entropy (TS, eV) of molecules involved in NO 3 ER.T is set to 298.15 K; Table S2.The optimized lattice parameters of unit cells (l, Å), lengths of Si-C bonds (d Si-C , Å), C-C bonds (d C-C , Å), and Si-Si bonds (d Si-Si , Å), formation energies under C-rich (E f-C , eV) and Si-rich conditions (E Si-C , eV), the charge transfer (Q, e) from Si atoms to C atoms, and the band gaps (Egap, eV) of 2D SixCy monolayers; Table S3.The data on the optimized structure of Si 3 C nanomaterial were compared with those in the literature; Table S4.The all computed free energy changes (∆G, eV) of each elementary step of Si3C monolayer.The ∆G values of the selected steps are remarked in red; Table S5.The quadratic relation between the energy (E) of the reaction intermediates and de-pendence of applied electrochemical potential U.

Figure 1 .
Figure 1.(a) Optimized structure of Si3C; (b) charge density distribution of Si3C monolayer (the purple and green areas represent positive and negative charges, respectively); (c) band structure of Si3C; (d) projected density of states (PDOSs) of Si3C monolayer.The Fermi level was set to zero for red dotted lines.

Figure 1 .
Figure 1.(a) Optimized structure of Si 3 C; (b) charge density distribution of Si 3 C monolayer (the purple and green areas represent positive and negative charges, respectively); (c) band structure of Si 3 C; (d) projected density of states (PDOSs) of Si 3 C monolayer.The Fermi level was set to zero for red dotted lines.

NO 3 −
species on these 2D Si x C y candidates.To obtain the most stable adsorption structure, three possible initial configurations were taken into account, including 1-O, 2-O, and 3-O patterns, in which the NO 3 − species is adsorbed on the Si or C active sites via its one, two, or three O atoms.After full structural relaxation, the obtained most stable NO 3 − adsorption configurations for these Si x C y candidates are shown in Figures 2a and S2, and the computed Gibbs adsorption free energies are summarized in Figure 2b.Nanomaterials 2023, 13, x FOR PEER REVIEW 6 of 14 subsequent hydrogenation reaction.In addition, to explain the remarkable difference in the adsorption strength of NO3 − in these 2D SixCy materials, integrated crystal orbital Hamilton population (ICOHP) analyses of the adsorbed NO3 * species were computed.

Figure 2 .
Figure 2. (a) Optimized NO3 − adsorption structure on Si3C monolayer; (b) the computed free adsorption energies of NO3 − and H + on SixCy monolayers ; (c) charge density differences (∆ρ) of NO3 − adsorption on Si3C monolayer with an isosurface of 0.003 e Å −3 (cyan and yellow bubbles denote charge depletion and accumulation, where ∆ρ = ρNO3* − ρ* − ρNO3, in which ρ represents the charge density of a given material); (d) the correlation between ICOHP and the distance of N-O bond in the adsorbed NO3 * (dN-O).

Figure 2 .
Figure 2. (a) Optimized NO 3 − adsorption structure on Si 3 C monolayer; (b) the computed free adsorption energies of NO 3 − and H + on Si x C y monolayers; (c) charge density differences (∆ρ) of NO 3 − adsorption on Si 3 C monolayer with an isosurface of 0.003 e Å −3 (cyan and yellow bubbles denote charge depletion and accumulation, where ∆ρ = ρ NO3* − ρ * − ρ NO3 , in which ρ represents the charge density of a given material); (d) the correlation between ICOHP and the distance of N-O bond in the adsorbed NO 3 * (d N-O ).

3. 3 .
Catalytic Performance of SiC 3 , SiC 7 , and Si 3 C Monolayers for NO 3 ER Since sufficient NO 3

Figure 3 .
Figure 3.The considered possible reaction pathways for NH3 synthesis from NO3ER on Si3C monolayer.

Figure 3 .
Figure 3.The considered possible reaction pathways for NH 3 synthesis from NO 3 ER on Si 3 C monolayer.

NO 3 *
→ NO 2 * + OH * requires crossing an energy barrier of 0.95 eV (Figure S5).Subsequently, a H 2 O molecule can be released via OH * hydrogenation, which is slightly endothermic by 0.32 eV.After the formation of H 2 O, the remaining NO 2 * , bound to two Si sites with Si-O lengths of 1.79 Å, can react with another (H + + e − ).Due to the synergistic effect of the Si active sites, the hydrogenation of the NO 2 * intermediate also induces the cleavage of one N-O bond spontaneously, forming a (NO * + OH * ) group.Remarkably, this step of (NO 2 * + H + + e − → NO * + OH * ) is highly exothermic by 1.90 eV.Next, an endothermal process for NO * formation and H 2 O desorption is observed with the free energy increased by 0.37 eV.Again, when the H proton attacks the remaining NO * intermediate, its N-O bond is split into (N * + OH * ) with a considerable negative ∆G of −2.54 eV, in which the N atom is adsorbed on the Si-Si bridge site with a length of 1.65 Å.In the subsequent steps, the H proton consecutively attacks the N * intermediates to generate (NH * + OH * ) and (NH 2 * + OH * ) with ∆G values of −0.62 and −0.07 eV, respectively.Moreover, the NH 2 *

Figure 4 .
Figure 4.The computed free energy profile for NH3 synthesis from NO3ER on Si3C monolayer.

Figure 4 .
Figure 4.The computed free energy profile for NH 3 synthesis from NO 3 ER on Si 3 C monolayer.

Figure 5 .
Figure 5. (a) Electronic energies of Si3C monolayer with and without the adsorbed NO3ER intermediates as a function of the applied electrode potential; (b) adsorption energies of various NO3ER intermediates as a function of the applied electrode potential; (c) pH-dependent and potential-dependent contour plot of adsorption energies of OH * on Si3C monolayer; (d) the limiting potentials (UL) of NO3ER as a function of pH value.

Figure 5 .
Figure 5. (a) Electronic energies of Si 3 C monolayer with and without the adsorbed NO 3 ER intermediates as a function of the applied electrode potential; (b) adsorption energies of various NO 3 ER intermediates as a function of the applied electrode potential; (c) pH-dependent and potentialdependent contour plot of adsorption energies of OH * on Si 3 C monolayer; (d) the limiting potentials (U L ) of NO 3 ER as a function of pH value.
. The optimized structures, charge density distribution, and the band structures of (a) SiC, (b) SiC 2 , (c) SiC 3 , (d) SiC 5 , and (e) SiC 7 monolayers.The isovalue was set to 0.003 e Å −3 , and yellow and red bubbles represent positive and negative charges, respectively.The Fermi level was set to zero in red dotted lines; Figure S2.The most stable NO 3 * adsorption configurations were viewed from the top and side of these catalysts of (a) SiC, (b) SiC 2 , (c) SiC 3 , (d) SiC 5 , and (e) SiC 7 monolayers; Figure S3.The integrated-crystal orbital Hamilton population (ICOHP) about N-O which from NO 3 * is adsorbed species on (a) SiC, (b) SiC 2 , (c) SiC 3 , (d) SiC 5 , (e) SiC 7 and (f) Si 3 C monolayers; Figure S4.The involved configurations of intermediates for NO3ER on Si 3 C monolayer; Figure S5.The kinetic process for the dissociation of NO 3 * with the help of H + to NO 2 * + OH * on Si 3 C monolayer; Figure S6.The obtained free energy diagrams of NO 3 ER on (a) SiC 3 and (b) SiC 7 catalysts; Figure S7.The free energy diagram of NO 3 ER on Si 3 C obtained by rPBE method; Figure S8.The obtained free energy diagram of N 2 formation on Si 3 C monolayer.; Figure S9.The involved free energy profile for NO 3 -to-NH 3 electrocatalytic reduction on Si 3 C monolayer at pH = 2.90; Figure S10.(a) Variations of temperature and energy as a function of the time for AIMD simulations and (b) Pourbaix profile of Si 3 C monolayer; Table

Author Contributions:
Conceptualization, writing-original draft preparation, W.G.; validation, writing-review and editing, formal analysis, T.Z.; data curation, F.L.; writing-review and editing, Q.C.; Supervision, project administration, J.Z.All authors have read and agreed to the published version of the manuscript.Funding: This work was financially supported in China by the Natural Science Foundation of Heilongjiang Province of China (TD2020B001) and the Natural Science Funds for Distinguished Young Scholars of Heilongjiang Province (No. JC2018004); and the "Grassland Talents" project of Inner Mongolia autonomous region (12000-12102613), and the young science and technology talents cultivation project of Inner Mongolia University (21200-5223708).