A DFT study on the N₂O reduction by CO molecule over silicon carbide nanotubes and nanosheets

Abstract

In this work, we study the nitrous oxide (N₂O) reduction by CO over zigzag (6,0) silicon carbide nanotubes (SiCNT) and nanosheets (SiCNS) by means of density functional theory calculations. Different N₂O and CO adsorption configurations are examined over these surfaces. The results indicate that the adsorption of N₂O via a [3 + 2]-cycloaddition is the most favorable structure over the SiCNT and SiCNS. For both surfaces, the N₂O reduction proceeds via two different steps: (1) N₂O → N₂ + O*, and (2) O* + CO → CO₂. In addition, the length and curvature effects of the SiCNT on the adsorption of gas molecules are studied in detail. The activation energy (E_act) of the N₂O → N₂ + O* step over (6,0) SiCNT (0.71 eV) is considerably smaller than that of SiCNS (1.12 eV). Also, with the reduction of the tube diameter, the N₂O decomposition reaction proceeds with a smaller E_act.

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1. Introduction

Silicon carbide (SiC) is a semiconducting material with high dielectric strength (2.49 MV cm⁻¹), high thermal conductivity (3.5–4.9 W cm⁻¹ K⁻¹), a high rate of electron drift (∼200 km s⁻¹), and a low density of dislocations (∼1/cm²). Also, it is easily doped forming n- and p-type semiconductors, and the purity level and concentration of defects including the characteristic tubular shells are easily controlled.¹ These perfect characteristics make it to be used as an ideal material for high-voltage, high-frequency, and high-temperature electronic fields, sensing devices, and other electronic instruments.² There are different forms of SiC dependent on its packing formation: (1) the ABAB… type that is the simplest packing which gives a hexagonal (2H) α-SiC with the wurtzite structure.³ (2) The ABCABC… packing which gives the cubic (3C) β-SiC with the sphalerite (zinc blende) structure.^4,5 Other SiC polytypes are 4H-SiC, in which it has a hexagonal lattice with a four-layer repeat structure, and 6H-SiC that have wide band gaps of 3.29 eV and 2.9 eV, respectively.⁶ Approximately, there are about 250 known SiC polytypes that among them, the majority of studies have focused on only three of them, i.e. 3C, 6H and 4H. It is interesting to know that the 4H polytype is the most common form used for electronic devices and sensors. However, their deficiency is that they are indirect band gap semi-conductors with a weak light-emitting. They also have a poor absorption of photons in the visible light region.⁷

It is noteworthy that the zero-dimensional (0D) nanoparticles,⁸ one-dimensional (1D) nanofibers, nanowires, nanowhiskers, nanorods,^9,10 two-dimensional (2D) nanofilms,¹¹ three-dimensional (3D) nanoporous silica¹² and other SiC nanomaterials have been produced from the development of electronics which are motivated the production of other modifications of silica and SiC. Carbon and silicon atoms are both in the fourth group of the periodic table and have a same number of valence electrons but they completely present different bonding characteristics. This can be due to the more stable sp² hybridization of C atoms in comparison with the preferable sp³ hybridization of Si atoms.¹³ Also, in simple clusters, carbon makes linear chains and planar structures, while silicon prefers 3D formation. The main interesting point is that the SiC nanosurfaces are able to provide more active reaction sites than present doped carbon materials. These nanostructures such as nanorods, nanowires and nanocables have been observed by numerous experimental groups.^14–16 For example, Li et al.¹⁷ reported a unique phase SiC₂ silagraphene, in which each Si atom is bonded with four C atoms, while each C atom is bonded with two Si atoms. SiC nanotubes (SiCNTs) which are first experimentally synthesized in 2001 (ref. 18) and SiC nanosheets (SiCNSs) are considered as potential materials for nanodevices operating in high-frequency, high-power, and high-temperature fields.¹⁹ SiCNTs are expected to have advantages over carbon nanotubes (CNTs) due to their high reactivity of exterior surface that facilitate the sidewall decoration and stability at high temperature.^20,21 Also, according to theoretical studies, SiCNTs are meta-stable with respect to the SiC bulk phase.^22,23 Scientists were claimed that despite the weak layer–layer interaction in the SiC layered sheet, its structure is still stronger than that of the cubic SiC sheet; this indicates that the thickness of a synthesized 2D SiCNS is in the range of 0.5–1.5 nm.²⁴ Recent theoretical studies have demonstrated that the reactivity of SiCNTs and SiCNSs are better than CNTs due to the polar nature of Si–C bonds.^25,26 In addition, they are intrinsically appropriate for using as a gas sensor because of their semiconducting characteristic that is not dependant in their chirality or diameter. There are many theoretical and experimental studies performed on the ability of SiCNTs and SiCNSs toward the adsorption of toxic gas molecules. For instance, in a density functional theory (DFT) investigation done by Wang,²⁷ the adsorption of formaldehyde molecule on the SiC sheet is studied. His results revealed that the C atom of the SiC sheet is the active site for the adsorption of the formaldehyde molecule. Additionally, SiCNTs show a better hydrogen storage performance than CNTs in which the hydrogen molecules bind with larger binding energies to the active sites of the tube surface.²⁸ In another DFT study, Gao et al.²⁹ found that NO and N₂O molecules can be chemisorbed on SiCNTs, while this is not the case for CNTs. Moreover, there is a significant charge separation between the silicon and carbon atoms in SiCNTs and SiCNSs which make the silicon atom (electron-deficient) and carbon atom (electron-rich) viewed as Lewis acid and bases, respectively. This provides more active reaction sites than that of CNTs or doped carbon materials, which allow SiCNTs and SiCNSs to serve as efficient metal-free catalysts.^26,30–33

Nowadays, the oxidation/reduction reaction of toxic gas molecules such as carbon monoxide (CO), nitrous oxide (N₂O) or sulfur dioxide (SO₂), emitted from automobiles or industrial processes, plays a critical role in solving the growing environmental pollution problems. N₂O is a greenhouse gas which can cause the acidic rain or photochemical smog, and lead to the depletion of the ozone layer.^34,35 The first cyclic reduction of N₂O by CO molecule in the gas phase, in the presence of atomic metal cations was experimentally explored by Kappes and Staley³⁶ in 1981. According to their findings, the Fe⁺ cation acts as a catalyst for the overall transformation given by the following reactions:

Fe⁺ + N₂O → FeO⁺ + N₂ (1)

FeO⁺ + CO → Fe⁺ + CO₂ (2)

According to other investigations,³⁷ the reduction of N₂O molecule can be performed with another toxic gas pollutant like CO molecule, without using a metal cation such as Fe⁺.^38,39 The mechanism of the N₂O reduction reactions are as the following equations:

N₂O → N₂ + O* (3)

O* + CO → CO₂ (4)

For instance, in our previous study,⁴⁰ the CO oxidation by N₂O molecule over the Si-embedded boron nitride nanotube (Si-BNNT) was investigated. It was found that Si-BNNTs may be considered as a potential candidate for low-temperature N₂O reduction by CO molecule with a high activity. In another work, Wannakao et al.³⁷ studied the catalytic reduction of N₂O molecule by CO over Fe-doped graphene. They found that graphene can induce the positive charge of the Fe atom and, hence, makes it ready to react with the N₂O molecule. They suggested that Fe–graphene is one of the promising candidates for solving the environmentally harmful and toxic gases generated from vehicles and industrial wastes.

However, to the best of our knowledge, neither a theoretical nor an experimental study has thus far been reported to examine the N₂O reduction by CO molecule over the SiCNTs and SiCNSs. Therefore, in this paper, we present the N₂O reduction by CO molecule over the SiCNT and SiCNS, using DFT calculations. For each adsorbate (N₂O and CO), the most stable adsorption configurations, adsorption energies, charge transfers and electron density shift plots are calculated and analyzed. Moreover, the corresponding mechanisms are analyzed via understanding the electronic structures.

2. Computational details

All DFT calculations were performed using the Gaussian 09 package⁴¹ with the M06-2X density functional, which is a global-hybrid meta-GGA functional, with 54% HF exchange, for top-level across-the-board performances in all areas of chemistry. The standard 6-31G* basis set was employed for DFT calculations. Frequency calculations were carried out at the same level to confirm that the structures obtained corresponded to energy minima. To investigate the N₂O reduction reaction mechanisms over the SiCNS, a finite-size monolayer sheet, having 23 Si and 23 C atoms was chosen as the basic model for our calculations. Since the electronic properties of SiCNTs are weakly dependent on the tube diameter and helicity,^42,43 calculations were performed on a truncated single-walled zigzag (6,0) BNNT with 24 B and 24 N atoms, without any loss of generality. Moreover, to investigate the curvature effect, the adsorption of gas molecules and the N₂O reduction mechanisms were studied over the (5,0) SiCNT. An elongated (6,0) SiCNT with the length of about 17 Å was also used to study the effect of increasing the length of the tube on the N₂O/CO adsorption. To avoid boundary effects, the ends of all used SiC nanostructures were capped with hydrogen atoms. All transition state structures were characterized by frequency analysis and intrinsic reaction coordinate (IRC) calculations. The adsorption energy (E_ads) of adsorbate was calculated based on the following equation:

E_ads(A) = E_A–M − E_M − E_A (5)

where E_A–M, E_M and E_A are the total energies of the adsorbate–substrate system, the substrate, and the energy of the adsorbate in the gas phase, respectively. The basis set superposition error correction for the adsorption energies were performed by counterpoise method.⁴⁴ The Mulliken and Hirshfeld charge density analyses were used to evaluate atomic charges and charge transfer values at the M062X/6-31G* level of theory.

3. Results and discussions

3.1 Adsorption of N₂O on the SiCNS and SiCNT surfaces

First of all, before studying the adsorption of N₂O on the SiCNC and SiCNT, it is better to have a look on the geometric structures of these surfaces. We have considered a graphene-like SiCNS and a zigzag (6,0) SiCNT which consist of alternating Si and C atoms, as depicted in Fig. 1. The calculated average Si–C bond length of the SiCNS and SiCNT is about 1.78 and 1.79 Å, respectively, that is almost intermediate between the C–C bond length in graphene (1.42 Å) and the Si–Si distance in silicene (2.28 Å). The obtained Si–C bond lengths are in good agreement with other theoretical studies performed on SiCNSs and SiCNTs,^45–47 but are smaller than those of the β-SiC crystal structure (1.89 Å).¹¹ In addition, the Mulliken charge density analysis indicates that about 0.6 electrons are transferred from the Si atoms to the nearest carbon atoms of both SiCNS and SiCNT, that is larger than those of Si-doped BNNTs.⁴⁰

Fig. 1 Optimized structures of pristine SiCNS and (6,0) SiCNT along with their corresponding Si–C bond lengths. All bond distances are in Å.

Then, we studied the N₂O adsorption over the graphene-like SiCNS, before investigation of the mechanisms of the N₂O reduction in detail. It is found from other related studies^29,48–51 that there are generally three possible configurations for the adsorption of N₂O molecule over nanostructures: (1) adsorption from its O or N atom in which the linear N₂O molecule is attached vertically to the active sites; (2) via a [2 + 2]-cycloaddition and (3) the N₂O adsorption via a [3 + 2]-cycloaddition. These adsorption models along with their corresponding bond lengths over the SiCNS are shown in Fig. 2 (configurations A, B and C). Also, the related adsorption energies (E_ads) and the net charge transfer (q_CT) are listed in Table 1. As Fig. 2 indicates, the N₂O molecule in configuration A is chemisorbed over the surface via a [3 + 2]-cycloaddition, forming a five-member ring. The O–N, N=N and N–C bond lengths are about 1.36, 1.24 and 1.53 Å, respectively. The E_ads for the formation of this complex is calculated to be −0.64 eV at the M062X/6-31G* level, which is larger (more negative) than that of reported for graphene-like BN nanosheet (−0.05 eV),⁵² Fe-ZSM-5 (≈−0.29 eV) and Co-ZSM-5 (≈−0.23 eV)⁵³ surfaces. Note that the inclusion of BSSE correction tends to decrease the E_ads value by about 50%, which should be due to the small size of the 6-31G* basis set. Besides, a smaller adsorption energy (−0.27 eV) is obtained through single point calculations at the M062X/6-311+G(2df,2pd) level. According to the Mulliken charge density analysis, a large charge of about 0.75e is transferred from the tube surface to the π* orbital of N₂O molecule, leading to a large decrease of N–N–O angle. The Hirshfeld method generally gives a similar result, although it exhibits a smaller dependency on the size of the basis set used. The strong adsorption of the N₂O molecule over the SiCNS in configuration A can be also seen from the corresponding electron density difference (EDD) plot as shown in Fig. 2. As evident, there exists a blue region (electron accumulation) around the Si–O and C–N bonds, which may confirm the formation of chemical binding between the N₂O and tube surface. The EDD plot also indicates a sizable electron density rearrangement over the N₂O and SiCNT, which indicates their mutual polarization upon the formation of the complex. Fig. 2 also depicts other two probable N₂O adsorption configurations over the SiCNS (complexes B and C). As it is shown, in complex B, the N₂O molecule is attached to the SiCNT and forms a four-member ring, while in complex C, the N₂O molecule is physically adsorbed over the Si atom of the surface through its N end. However, the positive E_ads values associated with these complexes indicate that the adsorption of N₂O molecule onto the SiCNS surface is unfavorable and should be prevented by an energy barrier. The effect of inclusion of BSSE correction on the calculated E_ads values at the M062X/6-31G* level is also significant. That is, the inclusion of BSSE decreases the E_ads values by 0.55 and 0.25 eV, respectively. Like configuration A, the calculated E_ads values of configurations B and C depend greatly on the size of the basis set used (Table 1). The results of the Mulliken and Hirshfeld charge density analyses clearly show that there is a small charge transfer between the SiCNT and N₂O molecule, especially in configuration C. This can be also evident from the corresponding EDD plots in Fig. 2, where there is a small electron density rearrangement over the interacting molecules.

Fig. 2 The adsorbed configurations of N₂O and CO over SiCNS and (6,0) SiCNT along with their electron density difference (EDD) isosurfaces (±0.001 au). The red and blue colors in the EDD map are related to the charge depletion and accumulation areas, respectively. All bond distances are in Å.

Table 1 Calculated binding distances (R), adsorption energies (E_ads), Mulliken (q_CT,M) and Hirshfeld (q_CT,H) charge-transfer values of adsorbed N₂O and CO molecules over SiCNS and (6,0) SiCNT^a

Configuration	R (Å)	Eads (eV)	qCT,M (e)	qCT,H (e)
a The values within the parenthesis refer to the single point calculations at the M062X/6-311+G(2df,2pd).
SiCNS
A	1.75	−0.59 (−0.27)	0.75 (0.47)	0.26 (0.18)
B	1.57	+2.61 (+1.82)	0.35 (0.18)	0.20 (0.12)
C	3.03	+1.74 (+1.22)	0.03 (0.01)	0.02 (0.01)
G	2.01	−0.18 (−0.08)	0.20 (0.11)	0.23 (0.13)
(6,0) SiCNT
D	1.76	−0.64 (−0.39)	0.74 (0.56)	0.27 (0.12)
E	1.42	+1.14 (+0.92)	0.32 (0.16)	0.34 (0.10)
F	3.31	+1.70 (+1.44)	0.03 (0.01)	0.02 (0.01)
H	2.19	−0.38 (−0.22)	0.16 (0.07)	0.24 (0.10)

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Different N₂O adsorption models were also examined over the cylindrical structure of the (6,0) SiCNT. Fig. 2 shows the optimized configurations, along with their corresponding bond lengths. Here, analogous with the SiCNS, the adsorption of N₂O molecule via a [3 + 2]-cycloaddition (configuration D) is found to be the most favorable structure over the SiCNT surface. The calculated adsorption energy for this configuration is about −0.64 eV, which is larger (more negative) than that of zigzag (6,0) BNNT. Comparing the E_ads of N₂O over SiCNT with metal surfaces such as Pd,^51,54 AuPd₃, Au₃Pd⁵⁵ or Rh⁵⁶ also confirm that the adsorption of this gas molecule is more favorable over the SiCNT than those of metal surfaces. Even though the single point calculations with a larger basis set (6-311+G(2df,2pd)) can provide a less negative E_ads value, however, the results of Table 1 indicate that N₂O adsorption onto the SiCNT is more stronger than that of SiCNS. This is due to the curvature effects in the SiCNT, which will be discussed in the following section. One point which should be noted here is the difference between the calculated charge transfer values using the Mulliken and Hirshfeld methods. As Table 1 indicates, the Mulliken analysis predicts that about 0.74e are transferred from the SiCNT to the N₂O molecule, which should be due to the strong overlap between the donor 2p orbital of the Si atom and the acceptor π* orbital of the N₂O molecule. However, according to the Hirshfeld analysis, there is about 0.27e charge transfer from the SiCNT to the N₂O molecule. However, such a discrepancy between the Mulliken and Hirshfeld charge density analysis schemes is almost popular in other types of the interactions. In addition, both these analyses show a significant dependency to the size of the basis set, which is consistent with those of other studies.⁵⁷ Meanwhile, the blue region in the corresponding EDD map clearly shows that there is a sizable electron density accumulation between the N₂O and SiCNT surface (Fig. 2). In the other two adsorption structures, i.e. configurations E and F, the N₂O molecule is located on the tube surface, with the adsorption energies of +1.14 and +1.70 eV, respectively, which indicates the adsorption process is endothermic and unfavorable. Meanwhile, the calculated E_ads of complexes E and F are in good agreement with that of the N₂O adsorption over Co₃O₄.⁵⁸

Along with studying these adsorption configurations, a question arises whether the adsorption of N₂O depends on the diameter of the nanotube. Therefore, in order to find the answer of this question, we consider the curvature effect on the adsorption of the N₂O molecule over a (5,0) SiCNT. Fig. S1 of ESI† shows the most stable configuration of adsorbed N₂O molecule over the (5,0) SiCNT (complex I) with its corresponding bond length values. It is found that the total geometry of this new configuration is the same as that of (6,0) SiCNT and SiCNS whereas the N₂O molecule adsorbs via its O atom with the Si atom of the tube surface (Si–O = 1.70 Å). Comparing the E_ads of N₂O over (6,0) and (5,0) SiCNTs shows that the adsorption energy of N₂O over the (5,0) SiCNT (−0.86 eV) is increased with the reduction of tube diameter because of the curvature effect (Table S1†). This is due to the enhancement of the sp³-hybridization of surface Si atoms. With the reduction of tube diameter, more p electrons of the tube go out of the surface plane, which facilitates the sp³-hybridization of the surface Si atoms. Also, a net charge of about 0.54e is transferred from the tube surface to the N₂O molecule which confirms the chemisorption.

Furthermore, it seems that the length of (6,0) SiCNT can affect the adsorption of N₂O molecule. So, the adsorption of N₂O molecule over the long-length (6,0) SiCNT is studied for the most stable configuration of adsorbed N₂O over the SiCNT. This configuration is named complex K (Fig. S1†). In this complex, the N₂O molecule forms a five member ring in which the O atom of the N₂O molecule is attached to the Si atom of the surface with a Si–O bond length of 1.72 Å (Table S1†). As a result, the E_ads of this configuration increases to −0.69 eV. Also, a net charge of about 0.55e is transferred from the tube surface to the N₂O molecule. It is noteworthy that because there is not a considerable difference between the N₂O adsorption over the large-length and short-length (6,0) SiCNT, thus, we studied the N₂O reduction mechanism over the short-length nanotube for the simplicity of our calculations.

3.2 Adsorption of CO on the SiCNS and SiCNT surfaces

The adsorption of CO molecule over both SiCNS and SiCNT surfaces is also studied carefully. The complex G in Fig. 2 shows the most suitable configuration of the adsorbed CO over the SiCNS. In this complex, the CO molecule is placed in a tilted position over the SiCNS where its carbon atom is about 2.01 Å far from the Si atom of the sheet (Table 1). The calculated E_ads of this configuration is −0.08 and −0.18 eV with and without the BSSE correction, respectively. Single point calculations at the M062X/6-311+G(2df,2pd) level also confirm that there is a weak interaction between the CO and SiCNT surface. Upon the adsorption process, about 0.20e are transferred from the SiCNS surface to CO, which leads to a negligible C≡O bond elongation. These data together with the corresponding EDD map in Fig. 2 indicates that the CO molecule is physisorbed over the SiCNS and the nanosheet has a small effect on its activity.

Consistent with the previous study about CO adsorption over SiCNT,⁵⁹ in the case of (6,0) SiCNT, the most stable configuration of adsorbed CO molecule over the tube surface is obtained when the CO molecule is physically adsorbed in a vertical position via its C atom. This configuration is named complex H and is shown in Fig. 2. The large Si–C_CO bond length (≈2.19 Å) and the small net charge transferred (about 0.2e) from the SiCNT to CO molecule confirm that there is a weak interaction between the surface and the gas molecule, so, SiCNT surface can not significantly activate the CO molecule. This fact can also be understood from the small E_ads (−0.38 eV) as well as the small electron density shift in the EDD plot which imply that there is no specific interaction between the CO molecule and SiCNT surface (see Table 1 and Fig. 2).

Moreover, studying the curvature effect on the CO adsorption over the (5,0) SiCNT (complex J) reveals that in comparison with complex H, the adsorption energy of complex J is increased (E_ads = −0.48 eV) with the reduction of the tube diameter (Table S1 and Fig. S1†). Also, analogous with other CO adsorbed configurations over (6,0) SiCNT and SiCNS, the CO molecule is physically adsorbed over the (5,0) SiCNT via its C atom with the Si–C bond length of 2.11 Å. Therefore, as it is expected, a small net charge of about 0.17e is transferred from the tube surface to the CO molecule that indicates the weak interaction between the CO molecule and (5,0) SiCNT.

In addition, it is interesting to find out whether the enhancement of the (6,0) SiCNT length can affect the adsorption of CO molecule. Results show that there is an increase in the E_ads and a decrease in the Si–C_CO bond length of the adsorbed CO molecule over a long-length (6,0) SiCNT (complex L) (see Table S1 and Fig. S1†). One can see that herein, the adsorption of CO over large-length (6,0) SiCNT, analogous with complexes G and H, is smaller than the adsorption of N₂O molecule. Therefore, the same as before, it can be proposed that the CO molecule is physisorbed over the tube surface due to the small E_ads and net charge transfer (≈0.16e).

Generally, it can be understood that the N₂O adsorption over the SiCNS and SiCNT surfaces changes its electronic structure properties more significantly than CO due to the larger E_ads and charge-transfer values. Also, the adsorption of N₂O over (6,0) SiCNT is more favorable than over the SiCNS. With the reduction of the tube diameter, the E_ads of the gas molecules is significantly increased. Besides, considering the calculated adsorption energies, the complexes A and D are the most stable and favorable adsorption configuration over the SiCNS and (6,0) SiCNT, respectively. Hence these adsorption configurations are chosen for the rest of our investigation.

3.3 Reaction pathways of N₂O reduction by CO molecule

The reaction mechanisms proposed for the N₂O reduction by CO molecule are as the following reactions:

(a) The adsorption and decomposition of the N₂O molecule:

N₂O → N₂ + O* (6)

(b) The adsorption and oxidation of CO molecule

O* + CO → CO₂ (7)

The related configurations of the initial state (IS), transition state (TS) and final state (FS), along with their corresponding geometric structures and energy profiles are demonstrated in Fig. 3 and 4. Also, the activation energy (E_act), reaction energy (ΔE) as well as the changes in enthalpy (ΔH₂₉₈) and Gibbs free energy (ΔG₂₉₈) of each step are listed in Table 2. In the case of SiCNS, the most stable configuration of the adsorbed N₂O over the surface (complex A) is chosen as IS-1. By overcoming an energy barrier of 1.12 eV and passing from TS-1, the N₂O molecule is decomposed into the N₂ and O* species in FS-1 (Fig. 3). Note that the calculated E_act value for the decomposition of N₂O in this study is in good agreement with those of reported over the MgO (1.6 eV) and CaO (1.06 eV) surfaces,⁶⁰ respectively. Besides, it is much smaller than that of decomposition of N₂O in the absence of the SiCNS (Fig. S2†), which indicates the potential role of this surface for the activation of this gas molecule. In FS-1, the N₂ molecule is about 2.79 Å far from the O* and can be released from the surface with an adsorption energy of 0.56 eV. One can see from Table 2 that the reaction IS-1 → FS-1 is endothermic (ΔH₂₉₈ = 1.03 eV) and a thermodynamically unfavorable reaction at room temperature (ΔG₂₉₈ = 1.0 eV). In the next step, the atomic oxygen reacts with the CO molecule to form IS-2. In this configuration, the CO molecule approaches to the O* while the O*–C bond length is about 2.75 Å. In TS-2, the O*–C distance decreases from 2.75 to 1.89 Å and the Si–O* bond is elongated from 1.67 Å in IS-2 to 1.70 in TS-2 to form the CO₂ molecule. In FS-2, the CO₂ molecule is formed over the SiCNS surface (Si–O = 3.95 Å) and can desorb easily from the SiCNS (E_ads = −0.14 eV). The E_act of the IS-2 → FS-2 reaction is 0.98 eV which is in close agreement with those of Si-,³⁹ Sn-,⁶¹ P-doped graphene,⁶² but smaller than those of noble-metal based catalysts such as Rh(100)⁶³ and Pt(111).⁶⁴ Moreover, the negative ΔH₂₉₈ and ΔG₂₉₈ values clearly show the feasibility of this reaction under ambient conditions.

Fig. 3 Reaction energy profiles and the corresponding optimized structures of these stationary points for the N₂O reduction by CO molecule over the SiCNS. All energy values and distances are in eV and Å, respectively.

Fig. 4 Reaction energy profiles and the corresponding optimized structures of these stationary points for the N₂O reduction by CO molecule over the (6,0) SiCNT. All energy values and distances are in eV and Å, respectively.

Table 2 Calculated activation energy (E_act), reaction energy (ΔE), change of enthalpy (ΔH₂₉₈) and Gibbs free energy (ΔG₂₉₈) for the N₂O reduction by CO molecule over SiCNS and (6,0) SiCNT

Reaction	Eact (eV)	ΔE (eV)	ΔH298 (eV)	ΔG298 (eV)
SiCNS
IS-1 → FS-1	1.12	1.03	1.03	1.00
IS-2 → FS-2	0.98	−1.27	−1.26	−1.18
(6,0) SiCNT
IS-3 → FS-3	0.71	0.39	0.39	0.31
IS-4 → FS-4	1.01	−1.98	−1.98	−1.86

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Continuously, the reduction of N₂O molecule by CO, over the (6,0) SiCNT is also studied. The optimized structures of the IS, TS and FS along with their corresponding bond lengths and reaction energy profile are depicted in Fig. 4. Moreover, the E_act, ΔE, ΔH₂₉₈ and ΔG₂₉₈ values are reported in Table 2. The stable configuration D with the E_ads value of −0.64 eV is chosen as IS-3. As Fig. 4 indicates, the decomposition of the N₂O molecule into the N₂ and O* species over the SiCNT surface takes place passing through TS-3, by overcoming an energy barrier of about 0.7 eV which is in good agreement with those of Pd⁵⁵ and Pt⁶⁵ surfaces. In addition, it is much larger than that of direct oxidation of CO molecule in the absence of catalyst surface (Fig. S2†). In TS-3, the distance between the N₂ and O* is increased from 1.35 in IS-3 to 2.15 Å (see Fig. 4). Then, the N₂ molecule is completely separated from the oxygen atom (O–N = 2.95 Å) and the O* remains over the SiCNT surface while the formed N₂ molecule desorbs from the surface with E_ads of 0.40 eV (Table 2). The reaction energy of the IS-3 → FS-3 step is 0.39 eV which confirms the endothermic process of this route. From the atomic charge point of view, the difference and similarity of partial charges before and after the adsorption of N₂O molecule lead to the attachment and separation of the N₂ molecule to the atomic oxygen. At the next step, the CO molecule is oxidized by attacking toward the O* and forming the CO₂ molecule (Fig. 4). This configuration, in which the CO molecule gets closer to the atomic oxygen (C–O* = 2.7 Å) is chosen as IS-3. In TS-3, the CO molecule reacts with the O* to form the CO₂ molecule. According to the energy profile of this pathway, as shown in Fig. 4, the Si–O* distance is elongated from 1.53 Å in IS-4 to 1.70 Å in the newly formed configuration. Passing over TS-4, the Si–O* bond length increases from 1.53 in IS-4 to 3.48 Å in the FS-4 and the CO₂ molecule desorbs easily from the SiCNT surface. The estimated E_act of this step is 1.01 eV, that is similar to those results of Li et al.⁶⁶ Besides, the relatively large negative ΔH₂₉₈ and ΔG₂₉₈ values for IS-4 → FS-4 step indicate that this reaction is exothermic and may be performed at normal temperatures.

The CO oxidation reaction over the (5,0) SiCNT is also studied. All of the obtained configurations along with their corresponding bond length values are shown in Fig. S3.† The related E_act and ΔE values are also listed in Table S3.† The favorable configuration I is chosen as IS-5. It is noteworthy that the geometric structures of all IS, TS and FS are almost the same as those of (6,0) SiCNT and SiCNS. The IS-5 → FS-5 reaction is proceeded via the E_act of about 0.62 eV, which is smaller than those of (6,0) SiCNT and SiCNS, but similarly, this reaction is endothermic (Table S2†). In FS-5, the N₂O molecule is dissociated into the N₂ and O* species and the N₂ molecule is about 3.00 Å far from the O*. Herein, the formed N₂ molecule can be easily released from the surface with E_ads of 0.53 eV (Fig. S3†). In the next step, the CO molecule gets closer to the O* (C–O* = 3.79 Å) to form the CO₂ molecule. Passing from TS-6, in which the CO molecule gets completely near the O* (C–O* = 1.53 Å), FS-6 is formed. The E_act of this exothermic process is about 1.69 eV and the CO₂ molecule is produced which can be feasibly desorbed from the tube surface. It can be concluded that the N₂O reduction reaction over the (5,0) SiCNT and (6,0) SiCNT is more favorable than that of SiCNS. Also, it is interesting to know that with the reduction of the tube diameter, the oxidation reaction proceeds with a smaller E_act in the first reaction while the second step needs a relatively larger E_act than that of (6,0) SiCNT.

As a final point, there are several concerns that need to be addressed regarding the possibility of using SiCNSs and SiCNTs as a favorable metal-free catalyst for the reduction of N₂O in practical applications. Our results indicate that for the N₂O reduction by the CO molecule, the rate-determining step is the N₂O → N₂ + O* reaction, which is consistent with the results obtained on other surfaces.^67,68 In addition, this reaction needs a larger activation energy over the SiCNS than the (6,0) SiCNT. However, the calculated positive ΔH₂₉₈ and ΔG₂₉₈ values in Table 2 clearly indicate that the decomposition of N₂O over both surfaces is an endothermic and thermodynamically unfavorable reaction at normal temperatures. This suggests that the performance of SiCNSs and SiCNTs as a metal-free catalyst used for the reduction of N₂O may be proceeded at relatively high temperatures. On the other hand, the use of small-diameter SiCNTs can effectively decrease the energy barrier needed for the decomposition of the N₂O. These findings may hold for other finite elongated systems such as armchair and chiral SiCNTs, as well.

4. Conclusion

In summary, this study reported the catalytic reduction of N₂O molecule by CO over the (6,0) SiCNT and SiCNS by means of DFT calculations. Comparing the E_ads values of CO and N₂O molecules showed that the N₂O molecule has a stronger interaction with the SiCNS and SiCNT surfaces. So, it can be proposed that when a mixture of N₂O and CO molecules is injected as the reaction gas, the Si atom of the SiCNT or SiCNS should be covered by N₂O molecule. Additionally, the E_ads of the N₂O molecule over the (6,0) SiCNT is slightly larger (more negative) than that of SiCNS. Then the N₂O reduction mechanism was investigated over both surfaces with their most stable configurations (complexes A and D). It is found that the N₂O reduction by CO molecule proceeds via two following reaction steps: (1) N₂O → N₂ + O*, and (2) O* + CO → CO₂. The E_act of the first step (0.71 eV) is considerably lower than that of SiCNS (1.12 eV). Therefore, it can be estimated that the N₂O reduction reaction over the (6,0) SiCNT is performed better than that of SiCNS. Our results indicated that with the reduction of the tube diameter, the decomposition of the N₂O proceeds with a smaller E_act value. Hence, that small diameter SiCNTs with large curvature would be beneficial for decomposition of N₂O. Generally, it can be suggested that SiCNTs may be considered as a potential candidate for the N₂O reduction reaction by CO molecule with lower cost and high activity.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra07548g

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