Removal of NO with silicene: a DFT investigation

Abstract

Removing or reducing NO is meaningful for environment protection. Herein, the investigation of the probability of NO reduction on silicene is presented utilizing DFT calculations. Two mechanisms for NO reduction on silicene are provided: a direct dissociation mechanism and a dimer mechanism. The direct dissociation mechanism is characterized as the direct breaking of the N–O bond. The calculated potential energy surfaces show that the total energy barrier in the favored direct dissociation pathway is 0.466 eV. On the other hand, the dimer mechanism is identified to undergo a (NO)₂ dimer formation on silicene, which then decomposes into N₂O + O_ad or N₂ + 2O_ad. The (NO)₂ dimer formation on silicene is found to be feasible both in thermodynamics and kinetics. The formation energy barriers for (NO)₂ dimer are lower than 0.231 eV. The calculation results indicate that the (NO)₂ dimers can be readily reduced into N₂O or N₂. The energy barriers in the favored decomposition pathways to produce N₂O are quite low (<0.032 eV). The energy barrier for the release of N₂ is calculated to be 0.156 eV. The further reduction of N₂O to N₂ on silicene is also investigated. The results indicate it is easy to reduce N₂O to N₂ with an energy barrier of only 0.445 eV. NO reduction on silicene hence prefers to generate N₂ via the dimer mechanism when compared to the direct dissociation. NO reduction on silicene with silicane as substrate is further proved to proceed via the same reduction mechanism as compared with the free-standing model. Hence, our results presented here suggest that silicene can be a potential material in NO removal, which will reduce NO into environmentally-friendly gases.

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1. Introduction

Nitrogen oxide (NO) is one of the most prominent pollutants in the atmosphere which mainly originates from the emission of pollutants by mobile sources. It causes environment problems such as acid rain, photochemical smog and ozone depletion.¹ It is hence very important to remove or reduce NO with the aim of cleaning air and protecting the environment. Extensive research has been encouraged in this area.^1–24 Previous investigations have suggested that CO oxidation, precious metals, alkaline earth metal oxides and some reductants like NH₃, urea, hydrocarbons and H₂, are common in removal of NO.^{3–5,7–9,11–13,17,19,25–27} Recent theoretical researches have also found the silicon or nitrogen doped graphene can be an ideal sensor in detecting NO and NO₂ and an kind of metal-free catalyst for the reduction of NO and N₂O.^21,23,24,28 It has been shown that the formation of dimer (NO)₂ plays an important role in NO reduction to N₂O + O_ad on both the silicon-doped and the nitrogen doped graphene.^21,23 In previous theoretical and experimental studies, NO dimer, (NO)₂, has also been proposed to play an important role in the reactions involving NO.^{2,20,21,23,29–32} For example, the reduction of NO to N₂O on Ag{111} surface at very low temperature (∼80 K) was found to go through a dimer intermediate by RAIRS² and STM³¹ in experiments and further a mechanism via an inverted (NO)₂ dimer was identified by theoretical investigations.²⁵ (NO)₂ dimer was also detected inside single-walled carbon nanotubes²⁹ and in the process of NO adsorption on Au 3D hemispherical crystals.³⁰ In this type of reaction, it is proposed that two 2π*–2π* ON–NO bonding orbitals are formed along with the formation of (NO)₂ and the SOMO of (NO)₂ is lying lower than the singly occupied degenerate 2π* orbital of the monomer, providing a better electron transfer from the electron donor to the dimer. The occupation of the LUMO of (NO)₂ increased the N–N bonding and decreased the N–O bonding and finally facilitated the decomposition of the dimer.^20,21,25,32 Since only physisorption is found on pristine graphene, doping Si in graphene is proposed to be an active site for NO capture and reduction. Considering the role of doping Si atom in graphene, silicene comes into view of us for investigating the behavior of NO together with considering the dimerization of NO on silicene.

Silicene is the Si counterparts of graphene and has attracted great attention as a potential material to replace graphene in recent years. Silicene is initially predicted to have unique two-dimensional buckled honeycomb structure consisting of silicon atoms as semimetal by theoretical calculations^33,34 and then was successfully synthesized on various substrates such as Ag(111),^35,36 Ir(111),³⁷ and diboride thin film.³⁸ It has been predicted that free-standing silicene has similar physical properties to graphene such as Dirac cone and linear electronic band dispersion around K point.³³ The silicon atoms in silicene are sp²-/sp³-hybridized and the π bonds in silicene are derived from the overlapping of 3p_z orbital of the Si atoms. Compared to the overlapping of 2p_z orbital of C atoms in graphene, the π bonds of silicene are relatively weaker, which provides silicene an unique bulked structure and a very reactive surface on which chemical bonds can be readily formed between silicene and chemical species.³⁹ It is also the reason why free-standing silicene has not been observed in reality and the substrates are required to stabilize silicene. It is proved in theory that hydrogenation is much easier in silicene^39–41 and the interactions between alkali, alkaline-earth, transition-metal atoms, B, N, Al, or P atoms and silicene are quite strong.^42–45 Silicene has also been further suggested to be a good sensor for NO and NH₃ and disposable molecule sensor for NO₂, O₂, and SO₂ due to the adsorption energies of NO or NH₃ on silicene are no larger than 0.60 eV while the adsorption energies of NO₂, O₂, and SO₂ on silicene are larger than 1.0 eV.^46,47 However, it is known to us only the chemisorption of NO has been investigated but no further researches on the probability of NO reduction on silicene are reported. Silicene is known to be active due to the sp²/sp³ character and the frontier orbitals of NO have been found to be very close to the Dirac point of silicene by Yang et al.,⁴⁸ it hence might exhibit good reactivity with NO. Therefore, an investigation on the probability of NO reduction on silicene is presented in this paper and we will further detail the mechanism of this process since the importance of (NO)₂ dimer formation in NO reduction demonstrated by previous investigations.^{2,20,21,29–32} Moreover, calculations on NO reduction on silicene with silicane as substrate are carried out to interpret the substrate effect since DFT investigation has revealed silicane is promising for producing free-standing silicene due to the successful synthesis of silicane in experiments,^49–51 the preserved chemical reactivity of silicene by the weak interaction between silicene and silicane and the predicted ability for silicane to stabilize silicene.^52,53

2. Computational details

The geometries optimization, charge analysis, transition states searching and vibrational analysis were performed using generalized-gradient approximation (GGA) implemented in DMol³ code,^54,55 where PBE⁵⁶ with long-range dispersion correction via Grimme scheme⁵⁷ was adopted to treat the electronic exchange correlation. The double numerical basis set including polarization function (DNP) basis set⁵⁵ (comparable to 6-31G** Gaussian basis sets) was employed in all-electron calculation. The employed computational method has already been found to be appropriate to describe the interaction in relevant studies involving silicene.^47,58 The threshold is set to be 1.0 × 10⁻⁵ Ha in energy, 2.0 × 10⁻³ Ha Å⁻¹ in force, and 5.0 × 10⁻³ Å in displacement. The real-space global orbital cutoff radius was chosen as high as 4.6 Å and the smearing of electronic occupations was set to be 0.005 Ha to ensure high-quality results. The complete LST (linear synchronous transit)/QST (quadratic synchronous transit) method⁵⁹ was performed to search transition state geometries, and these were further confirmed by minimum-energy pathway (MEP) calculation using the nudged elastic band (NEB) method.⁶⁰

A 5 × 5 silicene supercell containing 50 atoms was chosen as the benchmark model and the minimum distance between the neighboring silicene sheets is greater than 20 Å to avoid the interactions between them. The model is shown in Fig. 1a. The lattice constant of the silicene model in our calculation is 3.860 Å with a bulking value of 0.462 Å. The nearest-neighbor Si–Si bond length is 2.277 Å and the Si bond angle is 115.9°, which is in a good agreement with the previous results.^47,61–63 The letters T and V in blue color respectively represent the Si atom at the top site and valley site. It is obvious that the Si atoms at the T or V site are equivalent to each other. Hence, attention has only been focused on the hexagon ring circled in Fig. 1, in which the possible reactive sites involved in the process of NO reduction on silicene are labeled in red color numbers. The Brillouin zone was sampled by 5 × 5 × 1 special k-points using the Monkhorst–Pack scheme⁶⁴ during the geometry optimization whereas 15 × 15 × 1 special k-points for the calculation of density of states to obtain the electronic properties. The population analysis was performed using the Mulliken population analysis method.^65,66

Fig. 1 Top view and side view of (a) free-standing (5 × 5)silicene and (b) (5 × 5)silicene/(5 × 5)silicane. Golden color denotes Si atom while white color denotes H atom. The atoms in blue color are the reactive sites of silicene for NO adsorption. The distances are in angstrom.

To study the substrate effect on NO reduction on silicene, monolayer silicane are taken as the substrate. Silicane has similar lattice structures with silicene, so that the coherent lattices are built for silicene/silicane bilayers with AB stacking. In silicene/silicane system, the lengths of Si–Si and the bulking for silicene slightly increases to 2.283 and 0.493 Å respectively due to the weak interaction between silicene and silicane, Fig. 1b.

The adsorption energy E_ads is defined by the following equation:

E_ads = E_{[silicene or silicene/silicane+(NO)n]} − [E_{silicene or silicene/silicane} + nE_NO]

where E_{[silicene or silicene/silicane+(NO)n]} is the total energy of the (NO)_n-adsorbed silicene or silicene/silicane bilayer, n = 1 or 2, E_{silicene or silicene/silicane} is the energy of pristine silicene or silicene/silicane bilayer, and E_NO is the energy of an isolated NO molecule. In this definition, E_ads < 0 corresponds to the exothermic adsorption leading to stable minimal energy configurations.

3. Results and discussion

According to the previous researches,^{21,22,25,26,30,31,67} NO reduction occurs via two possible reaction mechanisms: (1) the direct dissociation of NO on silicene, yielding N and O adatoms (NO → N_ad + O_ad); (2) the dimer mechanism for NO reduction on silicene in which two adsorbed NO molecules interact with each other, yielding N₂O or N₂ and atomic oxygen ((NO)₂ → N₂O + O_ad, or (NO)₂ → N₂ + 2O_ad). In order to comprehensively understand the reductive probability of NO on silicene, these two mechanisms will be discussed in detail below.

3.1. Adsorption and direct dissociation mechanism of NO monomer on silicene

3.1.1. Adsorption of NO monomer on silicene. It is known the surface reaction can be greatly affected by the initial adsorption manner of a molecule on the catalyst surface. To better understand the reductive reactivity of silicene towards NO, the adsorption of NO on silicene is presented.

For the adsorption of NO monomer on silicene, we have evaluated N-atom and/or O-atom approach to the silicon atom(s) at T site, the top of the Si–Si bond and the hollow site of the hexagon ring of silicene. After full optimization, four adsorption structures are obtained. The adsorption structures and calculated adsorption energies of monomer NO on silicene are shown in Fig. 2. It is found that N–Si1 bond is formed when N-atom of NO attacking Si1 (see structure M1 in Fig. 2). A four-membered ring is formed in M2 and M3. Noted that N atom in M2 is connected with Si1 and O atom is adjacent to Si2 (N–Si1–Si2–O) while they are in the opposite order in M3 (O–Si1–Si2–N). The adsorption energy of structure M2 are greater than structure M3 (−0.317 eV for M2 vs. −0.259 eV for M3). Structure M4 is originated from the N–O bond approaching to the hollow site of silicene. It features two new-forming N–Si bonds and one new-forming Si–O bond with a N–O bond length of 1.436 Å. The adsorption energy for this configuration is −0.378 eV. But no chemisorption with O atom of NO attacking Si1 is observed and M3 actually does not exist in reality. It is known one unpaired electron is on the N atom of NO molecule. In this case, N atom exhibits a better electrophilicity than O, which leads the weak interaction between O and Si atoms while strong binding between N and Si atoms, resulting the preferred bonding between N and Si atoms rather than O and Si atoms when NO approaches to silicene. When seen from the side of NO approaching to silicene, Si1 is at the T site and Si2 are at the V site. Obviously, the adsorption of NO monomer onto silicene would undergo N atom first attacking the T site Si atom rather than the V site Si atom. Thus, there is no possibility to form M3 with N bonding to the V site Si atom and O bonding to the T site Si atom.

Fig. 2 Optimized adsorption structures and calculated adsorption energies of a single NO molecule on silicene. The bond distances are in angstrom. Golden, red and blue colors denote respectively Si, O, and N atom. The distances are in angstrom.

3.1.2. Direct dissociation mechanism for NO monomer on silicene. The direct dissociation reaction of NO reduction on silicene is described by the equation

NO → N_ad + O_ad (1)

Our calculation results suggest the direct dissociation of NO on silicene would proceed via two different reaction pathways: pathway 1 (Fig. 3a) and pathway 2 (Fig. 3b). It is found that the monoadsorption configurations M1, M2 and M4 are involved in the direct dissociation pathways. Moreover, the two dissociative pathways are both stepwise and require to go through three intermediates (M1, M2 and IM1 in pathway 1 while M1′, IM2 and M4 in pathway 2) to break the N–O bond. Both dissociation pathways would involve in the following steps: (1) form the first N–Si bond, (2) form the Si–O bond, (3) form the second N–Si bond, (4) break the N–O bond.

Fig. 3 The potential energy surface and structures in the direct dissociation of NO on silicene: (a) pathway 1 and (b) pathway 2. Golden, red and blue colors denote respectively Si, O, and N atom. The distances are in angstrom.

Pathway 1 (Fig. 3a) starts from M1 and M1 then goes through TS1 to get M2 along with a decreasing distance between Si2 and O. It is found the formation of M1 is free of barrier. In M2, the distance between Si2 and O is 1.796 Å, indicating a Si–O bond is formed. This step is endothermic by 0.134 eV and requires an energy barrier of 0.493 eV. M2 is not stable and would next turn into IM1 upon forming a second N–Si bond by over passing the transition state TS2 with an energy barrier of 0.282 eV. It is exothermic by 0.145 eV in M2 → IM1. Along with the generation of IM1, the distance between N and Si6 decreases while the bond length of N–O bond increases from 1.375 Å in M2 to 1.395 Å in TS2 and 1.485 Å in IM1. The lengths of the two N–Si bonds in IM1 are 1.848 and 1.859 Å. Finally, IM1 crossovers TS3 to get the dissociative product FS1 with N–O bond breaking. This step requires activation energy of 0.491 eV and it is exothermic by 2.241 eV. In FS1, the N atom inserts into Si1–Si6 and thus penetrated into silicene lattice which is consistent with the investigation of Sivek⁴⁵ while the O atom prefers to form a three-membered ring with Si2 and Si3. Because NO dissociation on silicene releases energy overall pathway 1, the barrier of the highest elementary step should be the overall barrier. From the PESs in Fig. 3a, we found the energy barriers of M1 → M2 and IM1 → FS1 are comparable and hence the both steps will affect the reaction rate of pathway 1.

Pathway 2 (Fig. 3b) starts from M1′, a similar chemisorption configuration to M1. Like M1, it is also a barrier free process to form M1′. The adsorption energy of M1′ is −0.452 eV. In M1′, the distance between N and Si1 is 2.056 Å. The difference between M1 and M1′ is the orientation of the N–O bond after adsorption (Fig. 4a). The N–O bond in M1 is in-plane with Si1–Si2 bond while in M1′ it is almost in-plane with Si1 and Si3 atoms. The O atom in M1′ then approaches Si3 and the conversion from M1′ to IM2 occurs by passing through TS4. This step is endothermic by 0.175 eV and the energy barrier is 0.212 eV. In IM2, the distance between O and Si3 atoms is 1.892 Å, indicating a Si–O bond formed. IM2 next converts into M4 via TS5 with N atom bonding to Si6. A second N–Si bond is formed in this step, similar to M2 → IM1 in pathway 1. As a result, M4 exhibits two N–Si bonds (N–Si1 1.817 Å and N–Si6 1.872 Å) and one Si–O bond (Si3–O 1.798 Å). The energy barrier and the released energy in this step are 0.159 eV and 0.101 eV, respectively. Then M4 climbs over TS6 with an energy barrier of 0.392 eV and achieves IM3 with the N–O bond broken. The N atom is inserted into Si1–Si6 bond in IM3 while the oxygen atom is only bonding to Si3 which is easy to interact with Si4 to form three-membered ring (FS2) by overcoming a small energy barrier of 0.067 eV associated with TS7. The steps of M4 → IM3 and IM3 → FS2 respectively release energy 1.415 and 1.051 eV. In the whole process of pathway 2, it releases energy by 2.392 eV relative to M1′. Hence, pathway 2 is determined by the step of M4 → IM3 which has an energy barrier of 0.392 eV. But M4 is higher in energy than M1′ by 0.074 eV, therefore the overall barrier of pathway 2 is 0.466 eV, that is, the energy difference between M1′ and TS6.

Fig. 4 The topview and sideview of (a) M1 and M1′, (b) D1 and D1′. One of the neighbor hexagon ring adjacent to the labeled ring has been drawn up to clearly show the coordination of the (NO)₂ in the topview of D1 and D1′. The distances are in angstrom.

Comparing the two pathways, we can find similar characters between them, such as the formation of the first N–Si bond in M1′ formation similar to that in M1 formation, the formation of the Si–O bond in M1′ → IM2 similar to that in M1 → M2, the formation of the second N–Si bond in IM2 → M4 similar to that in M2 → IM1, the cleavage of the N–O bond in M4 → IM3 similar to that in IM1 → FS1.

3.2. Adsorption and decomposition mechanism of (NO)₂ dimer on silicene

3.2.1. Adsorption of (NO)₂ dimer on silicene. Due to the importance of (NO)₂ dimer in the reaction involving NO, we next study the coupling of the two NO molecules on silicene into the (NO)₂ dimer. To better understand the formation of the (NO)₂ dimer, we calculate separate (NO)₂ dimer in cis-O=N⋯N=O (C_2v) without silicene which has been proved to be the global minimum in both gas and condensed phases.^68,69 The binding energy of cis-O=N⋯N=O is −0.508 eV relative to the isolated NO molecule in our calculation. In the cis-O=N⋯N=O, the two NO molecules are bonding to each other via the two N atoms. The distance of N–N bond is 2.048 Å (close to that of the gas (NO)₂ in previous investigations),^32,68,69 whereas the two N–O bonds are 1.166 and 1.167 Å which is almost the same as that of the free NO molecule (1.164 Å), as shown in Fig. 5a. Such interaction between the two NO in the cis-O=N⋯N=O would induce the modification of the electronic structure of NO species to some extent. The projected density of states (PDOS) on p orbitals of NO and (NO)₂ in Fig. 5b and c clearly show that more split peaks exhibit in the PDOS of (NO)₂. With comparing to the Fermi level of the free NO (−4.376 eV), the Fermi level of (NO)₂ lies at −4.518 eV and are lifted towards the valence band due to the dimerization. Moreover, the SOMO of (NO)₂ lies a lower energy level comparing with NO.

Fig. 5 (a) The structure and the bond length of NO and (NO)₂ in cis-O=N⋯N=O configuration. The red and blue colors denote O and N atom. The distances are in angstrom. The projected density of states (PDOS) on p orbitals of (b) NO and (c) (NO)₂.

To obtain the adsorption structure of (NO)₂ dimer, we have evaluated various possibilities for the adsorption (NO)₂ on silicene: (1) (NO)₂ binds to one Si atom on silicene via N-η¹, O-η¹, NN-η², OO-η², or NO-η²; (2) (NO)₂ binds simultaneously to two Si atoms on silicene with NN⋯SiSi, NO⋯SiSi, or OO⋯SiSi interactions. After full optimization, six most plausible adsorption configurations of dimers are proposed, shown in Fig. 6. The adsorption energies of the six dimers (−1.308 eV for D1, −2.090 eV for D2, −1.491 eV for D3, −2.165 eV for D4, −1.993 eV for D5, −2.473 eV for D6, and −2.326 eV for D7) are much larger than the twice of that of the NO monomer (M1: E_ads = −0.451 eV) and the dimerization energy of NO (−0.508 eV).

Fig. 6 Optimized adsorption structures and calculated adsorption energies of (NO)₂ dimer on silicene. The bond distances are in angstrom. Golden, red and blue colors denote Si, O, and N atom, respectively.

Structure D1 is characterized by the bonding between N1 and Si1 with N2 and O2 away from Si1 (O1N1_adN2O2, Si1N1_ad). The length of N1–Si1 bond is 1.875 Å and the adsorption energy −1.308 eV. Two possible pathways are proposed to form structure D1 (Fig. 7a). One pathway starts from structure _fIM1 with one NO molecule preadsorbed onto silicene via the interaction between N1 and Si1. N2 of the second NO then attacks N1 to produce D1 with forming N1–N2 bond. The other starts from structure _fIM2 with N1 of (NO)₂ approaching Si1. Both of these two pathways are free of barrier.

Fig. 7 Relative energies along the reaction path for the formation of (NO)₂ dimer on silicene. Golden, red and blue colors denote Si, O, and N atom, respectively. The distances are in angstrom.

Structures D2 and D3 (Fig. 6) correspond to an O1N1_adN2_adO2 species. In structure D2, N1 is bonding to Si1 with N2 bonding to Si2. Hence, a four-membered ring Si1N1_adN2_adSi2 is formed between (NO)₂ and silicene. The two formed N–Si bonds length are 1.899 and 1.912 Å, respectively. D1 could transform to D2 through _fTS1 with an energy barrier of 0.036 eV, Fig. 7b. D2 can also be achieved via two other possible pathways (see Fig. 7b). In the first pathway, two free NO molecules are adsorbed on silicene in order, followed by the formation of structure _fIM3 which lies below the reaction entrance by 0.495 eV. In structure _fIM3, N2 of the second NO molecule gets close to N1 and Si2 while N–N and N–Si distances decrease. Going through _fIM3 finally reaches D2 without any energy barrier. The second pathway starts from structure _fIM4 that is more stable than the free system by 0.636 eV, and only slightly greater in energy than the (NO)₂ dimer formation (−0.508 eV), indicating physisorption of (NO)₂ onto silicene. Once N1 of the dimer (NO)₂ is bonding to Si1, N2 would attack Si2, which leads the system to D2. The process of _fIM4 → D2 is a concerted but very asynchronic process and it is free of barrier. Unlike N2 bonding to Si2 in D2, N2 in D3 is bonding to Si3. The bonding leads Si1 and Si3 pulled out to increase the bulking of silicene. Fig. 7c shows that D1 can also be converted into D3 by overcoming an energy barrier of 0.175 eV involving transition state _fTS2. The formation of D3 can also be originated from the N–N binding between two NO of the monoadsorption configuration (structure _fIM5). The binding energy barrier is 0.048 eV (_fTS3). In _fIM5 → D3, it releases energy by 0.377 eV.

Structure D4 (Fig. 6) is characterized by the bonding between N1 and Si1, O1 and Si2 (O1_adN1_adN2O2) with forming a four-membered ring Si1N1_adO1_adSi2. The new forming bonds N1–Si1 and O1–Si2 between (NO)₂ and silicene are 1.848 and 1.739 Å in length, respectively. Fig. 7d suggests that D4 can be originated from structure D1′ (an isomer of D1) by overcoming an energy barrier of 0.231 eV. The comparison between structure D1 and D1′ are shown in Fig. 4b. D4 can also be formed by the two NO molecules approaching silicene in order. Upon the first NO molecule forming a four-membered ring with Si1 and Si2 to reach M2, the second NO molecule starts to approach N1 (structure _fIM6) and finally D4 is achieved without any barrier. However, the formation of M2 requires an activation energy of 0.493 eV from M1 (Fig. 3a), which means the pathway of D4 formation involving M2 requires an energy barrier of 0.493 eV. Comparing the process involving D1′ to that involving _fIM6, the conversion from D1′ to D4 is more favorable in kinetics.

Structure D5 is characterized by the bonding between N1 and Si1, O1 and Si3 (O1_adN1_adN2O2, Si1N1_adO1_adSi3) (Fig. 6). The new bonds N1–Si1 and O1–Si3 are 1.874 and 1.736 Å. Similar to the formation of D4, D5 can also be formed by the two NO approaching silicene in order (Fig. 7e). IM2 is first formed with the bonding between N1 and Si1, O1 and Si3. N2 of the second NO then starts to approach N1 of the first NO (structure _fIM7) with a decreasing N1–N2 distance. By this, structure _fIM7 is converted into D5 without any barrier. D5 can also start from structure _fIM8 with the dimerization of the two NO molecules before adsorption on silicene. The two N atoms gradually move closer to Si1 at the same time with decreasing distances between N1 and Si1, N2 and Si1 (structure _fIM9). D5 is finally obtained from structure _fIM9 by overcoming an energy barrier (_fTS5) of 0.087 eV. The process of _fIM9 → D5 is along with a decreasing distance between O1 and Si3 and an increasing distance between N2 and Si1. Since IM2 is originated from M1′ by overcoming an energy barrier of 0.212 eV and it is endothermic by 0.175 eV (Fig. 3b), the pathway of D5 which is originated from structure _fIM8 is more favorable in kinetics.

Structure D6 corresponds to a trapezoid O1_adN1N2O2_ad, in which the two O atoms of (NO)₂ dimer are bonding to Si1 atom and a five-membered ring Si1O1_adN1N2O2_ad is formed between (NO)₂ and silicene. The two new-formed Si–O bonds are 1.820 and 1.747 Å. The adsorption energy is −2.473 eV. Because of the weak interaction between O and Si atoms, the (NO)₂ dimer can be only adsorbed onto silicene with the two O atoms attacking the Si1 at the same time. It is found that no barrier is required to form D6 when (NO)₂ approaches to silicene with their O atoms getting close to Si1 (structure _fIM10), shown in Fig. 7f. It should be noted that the bonding of the two O atoms to the different Si atoms such as the bonding of O1 to Si1 and O2 to Si2 or Si3 has been also investigated. However, there is no observation for such configurations according to our calculations due to the weak interaction between O and Si atom.

Structure D7 is characterized by the bonding between N1 and Si1, O2 and Si2 (O1N1_adN2O2_ad) and hence a five-membered ring Si1N1_adN2O2_adSi2 can be observed between (NO)₂ and silicene. Similar to the formation of D1 and D2, D7 can be originated from the two NO approaching silicene in order (Fig. 7f) involving _fIM11 without any barrier.

Overview the formation of (NO)₂ dimer on silicene, it requires zero barrier for D1, D2, D6 and D7 while 0.048, 0.231 and 0.087 eV of energy barriers are respectively required to overcome in the favorite formation pathways of D3, D4 and D5. It should be noted that D2 is more stable than D3 by 0.599 eV. D1 can be readily converted into D2 by overcoming a small energy barrier of 0.036 eV and releasing energy by 0.782 eV while D1 would be turned into D3 which demands an energy barrier of 0.175 eV and releases 0.183 eV energy, shown in Fig. 7b and c. Thus, we propose D3 can be first converted into D1 and then to D2. The conversion energy profile is summarized in Fig. 8. The conversion energy barrier of D3 → D1 is 0.358 eV and it is endothermic by 0.183 eV. In D3 → D1 → D2, the overall energy barrier is 0.358 eV. The process releases energy by 0.599 eV which is the energy difference between D3 and D2. Compared to mono NO molecule on silicene, structure D3 has a larger adsorption energy (−1.491 eV for D3 vs. −0.451 eV for M1) and the conversion energy barrier is smaller than the direct dissociation energy barrier (0.358 eV for the process of D3 → D1 → D2 vs. 0.493 and 0.466 eV for NO direct dissociation shown in Fig. 3). Thus the conversion from D3 to D2 is likely to take place. The decomposition of D1 and D3 therefore would not be included due to the easy conversion from D1 to D2 or D4 and from D3 to D2 according to the kinetic and thermodynamic analysis. Hence, we mainly focus on D2, D4, D5, D6 and D7 in discussions about the dimer decomposition on silicene in this paper.

Fig. 8 Schematic energy profile of the conversion from D3 to D2.

3.2.2. Decomposition mechanism of (NO)₂ dimer on silicene. The decomposition mechanism of (NO)₂ dimer on silicene is proposed to yield N₂O or N₂ and atomic oxygen, which is described by the following eqn (2) and (3).

(NO)₂ → N₂ + 2O_ad (2)

(NO)₂ → N₂O + O_ad (3)

The PESs are presented in Fig. 9. D2, D4, D5, D6, or D7 are taken as the reactants. The results indicate D2, D4, D5 and D7 would decompose into N₂O following eqn (3) while D6 would decompose into N₂ following eqn (2). The decomposition energy barriers of D2 to N₂O (Fig. 9a) are 1.581 and 1.609 eV, while it is 1.000 eV to decompose D7 to N₂O (Fig. 9e). For D4 (Fig. 9b) and D5 (Fig. 9c) to N₂O, the decomposition energy barriers are respectively 0.026 and 0.032 eV. For D6 to N₂ (Fig. 9d), 0.156 eV energy barrier is required. Obviously, the relatively high energy barriers (>1.000 eV) lead to the decomposition of D2 and D7 difficult. However, the very small energy barriers (<0.156 eV) would result in the very fast decomposition of D4 and D5 to N₂O, or D6 to N₂. Moreover, unlike the dimer decomposition products with the dangling Si–O and N–O bond respectively on the Si doped and N doped graphene in the process of (NO)₂ → N₂O + O_ad in which the O should be further removed by CO or NO,^21,23 it is further found the product of atomic O atoms in the dimer decomposition on silicene is facile to form three-membered ring with barely no barrier, hence no consideration for removing the O from silicene in our system.

Fig. 9 The potential energy surfaces of the decomposition of (NO)₂ dimer on silicene: (a) D2, (b) D4, (c) D5, (d) D6, (d) D7 are chosen as the reactants. Golden, red and blue colors denote Si, O, and N atom. The distances are in angstrom.

In order to decompose the dimer to N₂O, the N–O bond is required to break and the N–N bond becomes stronger. In another word, the longer length of N–O bond and the stronger N–N bonding facilitate the decomposition. In D2, the bond length of N1–N2, N1–O1 and N2–O2 bond are 1.401, 1.238 and 1.238 Å, respectively. In D7, the (NO)₂ dimer are bonding to silicene via N1–Si1 and Si1–O2. The bond length of N2–O2 and N1–N2 are 1.388 and 1.293 Å, respectively. The N2–O2 bond is longer than that in D2 while N1–N2 of D7 is shorter than that in D2. N2–O2 bond is more activated in D7 than in D2. Therefore, smaller activation energy is required for D7 (1.000 eV) compared to the decomposition of D2 (1.581 and 1.609 eV). Unlike D7, the (NO)₂ dimer in D4 and D5 are bonding to silicene within one N–O bond. The N1–O1 bond is 1.492 and 1.464 Å while the N1–N2 bond is 1.299 and 1.317 Å for D4 and D5, respectively. Compared to the N2–O2 bond (1.388 Å) of D7, the N1–O1 of D4 and D5 are elongated by 0.104 and 0.076 Å, respectively. The N1–N2 bonding changes slightly. We can clearly see the N1–O1 bond in D4 and D5 are much more activated than D7. Therefore, only much smaller activation energies (<0.032 eV) are required to decompose D4 and D5 to N₂O. In D6, the two N–O bonds are 1.375 and 1.424 Å. The N1–N2 bond is 1.247 Å. Such trapezoid O1_adN1N2O2_ad structure is helpful to decrease N–O bond and increase the N–N bonding, finally facilitate the N–O breaking. So the decomposition energy barrier is only 0.156 eV. Therefore, the dimer mechanism for NO reduction can only take place following the decomposition of D4, D5 and D6.

Since D4 and D5 can be reduced into N₂O, the adsorption and reduction of N₂O on silicene are also considered. For the adsorption of N₂O on silicene, only physisorption is observed; see the structure of PHY in Fig. 10. It is obvious that the interaction between N₂O and silicene is very weak with adsorption energy of 0.159 eV. The N–N and N–O bond lengths are 1.142 and 1.195 Å, respectively. They are unchanged when compared with the isolated N₂O molecule. The PHY structure is then directly decomposed by going through the transition state TS_a and finally PC_a with desorbed N₂ is achieved. The decomposition potential energy surface is depicted in Fig. 10. This process needs to overcome an energy barrier of 0.445 eV and it releases energy by 2.683 eV. In the decomposition of N₂O, the Si1–O is shortened from 3.530 Å (PHY) to 2.305 Å (TS_a) and finally the O atom forms a three-membered ring with two neighboring Si atoms, while the N2–O bond length increases from 1.195 Å (PHY) to 1.241 Å (TS_a) and is ruptured in PC_a. A reaction with an energy barrier of less than 0.500 eV is expected to occur at room temperature, thus the decomposition of N₂O is likely to proceed rapidly at room temperature, which is the reason we can easily observe the decomposition product of N₂O on silicene.⁴⁷ Therefore, N₂ would be the final product in the dimer mechanism for NO reduction.

Fig. 10 The potential energy surfaces of the decomposition of N₂O on silicene. Golden, red and blue colors denote Si, O, and N atom. The distances are in angstrom.

With comparing the direct dissociation and the dimer decomposition mechanism for NO reduction, NO reduction on silicene would like to proceed via the dimer mechanism and prefer the N₂ production. First, the adsorption energies of the (NO)₂ dimer on silicene are larger than that of the NO monomer adsorption. Second, the decomposition energy barriers (0.026, 0.032 and 0.156 eV) for the dimers D4, D5 and D6 are much lower than those (0.493 and 0.466 eV) for the NO direct dissociation. In addition, more electron accumulated on (NO)_n helps the NO reduction. The Mulliken charge analysis showed that the electrons are donated from silicene to the NO species and the order of the accumulated net charge on NO and (NO)₂ are consistent with the adsorption energies of these molecules on silicene: (NO)₂ > NO, listed in Table 1. Moreover, more electron donated by silicene are occupied the 2π*–2π* orbital of (NO)₂, leading to the increasing of the N–N bond distance while the decreasing of the N–O distance and finally facilitating the decomposition of the dimer.^20,21,25,32 Accordingly, the N–N bond is greatly shortened in D4, D5 and D6 compared to 2.048 Å of the gas phase (NO)₂ and the key N–O bond becomes significantly longer in D4, D5 and D6 compared to 1.164 Å of the free NO molecule. The lengths of N–N bond and N–O bond in D4, D5 and D6 have been described in Fig. 6 and Table 1. The projected density of states (PDOS) of silicene and (NO)_n in M1, D4, D5 and D6 (Fig. 11) clearly show that the 2π* orbitals of NO around the Fermi level are partly filled in M1 while 2π*–2π* orbitals of (NO)₂ are almost full filled around the Fermi level in D4, D5 and D6 with the electron density of silicene is depopulated, which is in well agreement with the more electron charge accumulated on the NO species (Table 1).

Table 1 The adsorption energies and the Mulliken charge on NO or (NO)₂ of M1, M1′, D4, D5 and D6, the N–N distance in D4, D5 and D6^a

Adsorption configuration	Eads/eV	Q(NO)n/e	dN–N/Å	dN–O/Å
a n in Q(NO)n indicates the number of NO molecule.
M1	−0.451	−0.171	—	1.192
M1′	−0.452	−0.174	—	1.193
D4	−2.165	−0.711	1.299	1.232, 1.492
D5	−1.993	−0.684	1.317	1.226, 1.464
D6	−2.473	−0.836	1.247	1.375, 1.424

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Fig. 11 The projected density of state (PDOS) of (a) M1, (b) D4, (c) D5 and (d) D6. n of (NO)_n equals to 1 or 2.

It is noted that the calculated direct dissociation barrier of NO on the silicene is 0.466 eV or 0.493 eV and the favorite dimer decomposition energy barrier is no higher than 0.156 eV, which are both much lower than that on the nitrogen doped graphene (1.70 eV for the direct dissociation while 0.70 eV for the dimer mechanism)²³ and that on the silicon doped graphene (3.91 eV for the direct dissociation mechanism while 0.443 eV for the dimer mechanism).²¹ The result indicates the higher reactivity of silicene than graphene to the molecules' adsorption, which is caused by the easy electron transfer from silicene to the adsorbates due to the sp²/sp³ character of silicene.

3.3. The substrate effect on NO reduction on silicene

Noted that Si atom favors sp³ hybridization in nature, free-standing silicene with sp²-/sp³-hybridized Si atoms therefore might exhibit a high chemical reactivity, resulting in the necessary of the substrates to stabilize silicene. As is known to us, silicene has not yet be achieved as free-standing sheet, but it has been successfully deposited on several metallic substrates, such as Ag(111),^35,36 Ir(111),³⁷ and diboride thin film.³⁸ Strong band hybridization are found to exist between silicene and metal substrates, resulting in the significant modification of the electronic properties for silicene.^70–73,77 However, it has been reported that h-BN,^{52,71,74,75,78} SiC(0001) surface,⁷⁴ silicane,^52,53 hydrogen-passivated Si(111)^71,76 and silicene have weak van der Waals interaction with silicene. Thus, these substrates are promising to prevent silicene from undesired bonding and keep the high carrier mobility with Dirac electrons near the Fermi level preserved, providing a possible path for producing free-standing silicene. Encouraged by these investigations, silicane is taken as the substrates for silicene growth to further explore the substrate effect on the behavior of NO on silicene because of the successful synthesis of silicane in experiments,^49–51 the preserved chemical reactivity of silicene by the weak interaction between silicene and silicane and the predicted ability for silicane to stabilize silicene.^52,53 Our theoretical prediction would provide helpful theoretical clues for the experimental development and widen the future application of silicene.

To explore the substrate effect on the chemical reactivity of silicene toward NO, both two direct dissociation pathways of NO on (5 × 5)silicene/(5 × 5)silicane are investigated while only the formation and the decomposition of the (NO)₂ dimer D6 are considered. The PESs for NO reduction on (5 × 5)silicene/(5 × 5)silicane are shown in Fig. 12 and the related structure configurations along the reaction pathways are depicted in Fig. 13. It is found that similar configurations of silicene on silicane are observed along the NO reduction process as compared to those of free-standing silicene. The obtained PESs in Fig. 12 of NO on (5 × 5)silicene/(5 × 5)silicane show the same trends with those of free-standing silicene. For NO direct dissociation on (5 × 5)silicene/(5 × 5)silicane, the energy barriers of M1 → M2 and IM1 → FS1 are with respective to 0.510 and 0.509 eV, both determining the reaction rate of pathway 1; while the overall reaction barrier for pathway 2 is 0.454 eV, which is determined by the N–O broking of M4 → IM3. The dissociation barrier for pathway 2 of NO reduction on silicene/silicane bilayer is lower than pathway 1 and NO direct dissociation on silicene/silicane bilayer thus prefers to proceed along pathway 2 rather than pathway 1, which is the same with the results of free-standing silicene. It is noted that direct dissociation barriers for NO reduction on silicene/silicane bilayer are slightly higher than those for free-standing silicene, which is ascribed to the weak interaction between silicene and silicane. For D6 on silicene/silicane, the formation process for D6 is barrierless and the barrier for D6 decomposition is 0.081 eV. It is clear that the (NO)₂ dimer decomposition mechanism, rather than the direct dissociation mechanism, is preferred for silicene/silicane to give a decomposition product with desorbed N₂. Our theoretical prediction hence suggests that, free-standing silicene and silicene/silicane may be promising materials for NO reduction, which provide helpful theoretical clues for the experimental development and widen the future application of silicene. However, it should be noted that metal substrates may have strong effects on the silicene structure, resulting in different NO reduction features, which need to be further explored in the future.

Fig. 12 The potential energy surfaces of (a) pathway 1 and (b) pathway 2 of NO direct dissociation on (5 × 5)silicene/(5 × 5)silicane, and (c) the formation and decomposition of (NO)₂ dimer D6 on (5 × 5)silicene/(5 × 5)silicane. For simplify the understanding of the related energy along the formation and decomposition process of D6, the energy data in brackets of (c) are relative to two free NO molecule and pristine (5 × 5)silicene/(5 × 5)silicane while those out of the brackets are relative to M1 and one free NO.

Fig. 13 The related structures along the reaction path for (a) pathway 1 and (b) pathway 2 of NO direct dissociation on (5 × 5)silicene/(5 × 5)silicane, and (c) the formation and decomposition of (NO)₂ dimer D6 on (5 × 5)silicene/(5 × 5)silicane. Golden, red, blue and white colors denote Si, O, N and H atom, respectively. The distances are in angstrom.

4. Conclusions

In a summary, a density functional theory using the PBE functional has been employed to investigate the reduction of NO on silicene. Both direct dissociation mechanism of NO and the decomposition of the (NO)₂ dimer mechanism on silicene were explored. The results indicate an activation energy of 0.493 eV or 0.466 eV is required to break the N–O bond in the direct dissociation mechanism. However, easy formation are found for the (NO)₂ dimer on silicene with the formation energy barriers no greater than 0.231 eV. Moreover, the decomposition of the dimers into N₂O or N₂ are calculated to be no higher than 0.156 eV in the kinetically favorite pathways. Together with the ready decomposition of N₂O on silicene with an energy barrier of 0.445 eV, the reduction of NO hence prefers the (NO)₂ dimer decomposition mechanism to give a decomposition product with desorbed N₂ rather than the direct dissociation mechanism. NO reduction on silicene with silicane also proceeds via the same dimer decomposition mechanism to produce N₂, with slight change in the catalytic reactivity. Our theoretical prediction suggests that, free-standing silicene and silicene/non-metal-substrates represented by silicene/silicane may be good candidate materials to reduce NO to environmental-friendly gases at a mild condition, which provide helpful theoretical clues for the experimental development and widen the future application of silicene.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

We gratefully acknowledge the National Natural Science Foundation of China (Grant no. 21173273, 21373277, 21203256, 21473261). The research is also partially supported by the high performance grid computing platform of Sun Yat-Sen University, the Guangdong Province Key Laboratory of Computational Science and the Guangdong Province Computational Science Innovative Research Team.

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