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Adsorption and dissociation of NO2 on silicene
Applied Surface Science 498 (2019) 143854
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Full length article
Adsorption and dissociation of NO2 on silicene a,⁎
a
T b
H.N. Fernández-Escamilla , J. Guerrero-Sánchez , E. Martínez-Guerra , N. Takeuchi a b
a
Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, Apartado Postal 14, Ensenada, Baja California Código Postal 22800, Mexico CICFM Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, N.L. 66450, Mexico
A R T I C LE I N FO
A B S T R A C T
Keywords: Silicene Nudge elastic band
Using Density Functional Theory, we have described the full inactivation of NO2 driven by silicene. NO2 is a harmful pollution-generating molecule, causing acid rain. We have studied the minimum energy pathway for the trapping and deactivation of NO2 on silicene substrates. Starting with a configuration in which the molecule and the substrate are not interacting, the NO2 is chemisorbed on silicene, passing through several intermediate states. As the reaction proceeds, the system gains energy, favoring the breaking of the NO2 molecule. In the final state, the molecule is entirely disassociated into N and O atoms, that are incorporated into silicene, forming bonds in bridge positions. The reaction is exothermic, gaining 6.8 eV. These results indicate that silicene is a good substrate to trap NO2 and to completely inactivate it by decomposing it into N and O atoms.
1. Introduction Silicene, a two-dimensional silicon material, was theoretically proposed [1], and its electronic properties were investigated by tightbinding calculations, showing linearly crossing bands at the Fermi level [2]. Since its experimental synthesis [3], both theoretical and experimental research has grown rapidly. In 2016, quasi-freestanding silicene was obtained through oxidization of bilayer silicene on Ag(111) [4]. One of the main reasons for the interest in silicene is the possibility of modulating its properties, with a large number of promising applications in the semiconductor industry. Silicene has a buckled hexagonal honeycomb structure. The hybridization of the silicon atoms in silicene is a combination of sp2 and sp3, with the primary contributions coming from pz, pxy and s orbitals around the Fermi level [5]. The buckling in silicene leads to a simple way to tune its electronic properties, for example by applying an electric field [6], or by organic functionalization [7]. Possible silicene applications can be found in spintronics [8], hydrogen storage [9], or in gas sensing devices [10,11]. The adsorption of NH3, NO, and NO2 on silicene has been investigated, reporting high adsorption energies. The electronic properties of the resulting systems show p-type doping [12]. Adsorption of other molecules such as CO, O2, CO2, and SO2 has been theoretically investigated as well [13]. Silicene cannot be a good sensor for NO2, O2, and SO2 because of their slow desorption rates once they are trapped. The opposite has been reported for NO and NH3, where adsorption energies are lower, facilitating their desorption. CO and CO2 are adsorbed through weak physisorption. Mono-, di-, and tri- vacancies and
⁎
stone-wales defects on silicene increase its surface reactivity. In this way, detection of toxic molecules can be accomplished [14]. Recently, it has been reported that due to the strong interaction between the SO2 and the silicene, once the molecule has been chemically adsorbed, it would not desorb. Instead, the SeO bonds break, incorporating the atoms to silicene in an exothermic process [15]. The silicene reactivity allows breaking the SO2 molecule with a low activation energy. As mentioned before, it is known that NO2 chemically adsorb on silicone with a large adsorption energy. However, the processes that occur after NO2 adsorption have not been investigated in detail. In this article, we theoretically investigate the adsorption of NO2 molecule on silicene. In particular, we are interested to find out if the molecule breaks down, as in the case of SO2. By describing the minimum energy pathway, we have tested the inactivation of the molecule into NO and O. We have also examined the possible decomposing of NO2 into N and two O atoms, as in SO2 [15]. The following sections of our paper are organized as following: in Section 2 we describe the method, Section 3 is devoted to describe and discuss the results. Finally, in Section 4 we conclude the article. 2. Method We have used first-principles calculations based on density functional theory (DFT), as implemented in the Quantum ESPRESSO open source package [16]. For the exchange-correlation (XC) potential, the generalized gradient approximation (GGA), as parametrized by PerdewBurke-Ernzerhof (PBE) has been employed [17]. We have used ultra-
Corresponding author. E-mail address: [email protected] (H.N. Fernández-Escamilla).
https://doi.org/10.1016/j.apsusc.2019.143854 Received 12 June 2019; Received in revised form 6 August 2019; Accepted 1 September 2019 Available online 05 September 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.
Applied Surface Science 498 (2019) 143854
H.N. Fernández-Escamilla, et al.
Fig. 1. Top view of silicene where the molecule is adsorbed/inactivated. (a) In the intermediate state 1, the NO2 molecule chemically adsorbs by forming a SieO covalent bond. (b) In intermediate state 2, all the NO2 atoms bond to silicene. (c) Intermediate state 3, the NO2 breaks down into NO and O subunits, both bonded to silicene, (d) Final state, the NO2 has been fully inactivated into a N atom and two O atoms, all of them incorporated into the monolayer.
pathway to carry out the NO2 inactivation process, through a reaction with different intermediate and transition states, we have used the climbing image nudged elastic band (CI-NEB) method [19]. 3. Results and discussion In this section, we describe the inactivation process of NO2, passing through several intermediate states: zero energy, intermediate 1, intermediate 2, intermediate 3, and final states. The reaction is studied by finding the minimum energy pathway. Analysis of the electronic properties of the fundamental states of the reaction is carried out to understand it. 3.1. Zero energy state (ZS)
Fig. 2. Minimum energy path for the NO2 inactivation reaction driven by silicene. There is no energy barrier for the molecule to attached to the silicene substrate in IS1. From there, the energy barrier needed to desorb the NO2 is 1.63 eV. While the activation energy to take the system from IS1 to FS is around 0.60 eV.
As the reference state, the silicene substrate and the NO2 molecule are separated by 10 Å, in a non-interacting configuration. We call it the zero energy state (ZS) and its total energy is used as the reference to calculate the relative energy of the other states: Erelative = Estate - EZS, where Estate is the total energy of the system, and EZS is the total energy of the ZS. Any configuration (state) with negative relative energy is more stable than the ZS.
soft pseudopotentials and kinetic energy cutoffs of 30 Ry and 240 Ry for the electronic wave functions and charge density, respectively. To analyze the charge transference, we perform a Bader charge analysis. The adsorption of the molecule was made on a 5 × 5 silicene supercell considering a Monkhorst-Pack mesh [18] with a gamma centered kpoints grid of 7 × 7 × 1 in the Brillouin zone for geometrical optimization, for the projected density of states (PDOS), a larger k-point grid of 14 × 14 × 1 was used. The geometry of the structures was optimized, with a convergence criterion that all forces on each atom must be smaller than 1 × 10−3 Ry/a.u. The atomic self-interactions generated by the periodic conditions were avoided by an empty space of 20 Å perpendicular to the monolayer. To calculate the minimum energy
3.2. Intermediate state one (IS1) NO2 can be chemically adsorbed on silicene in several configurations, forming different kind of bonds. When the molecule is adsorbed on top of a Si atom, a covalent single SieO bond is formed, as shown in Fig. 1a. This structural configuration has the lowest energy of the different high symmetry sites in which NO2 can be adsorbed on silicene. The calculated SieO bond length is 1.70 Å, in good agreement with 2
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H.N. Fernández-Escamilla, et al.
Fig. 3. (a) Top view of the relaxed geometry of the ZS. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (cd) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
Fig. 4. (a) Top view of the relaxed geometry of the IS1. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (cd) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
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H.N. Fernández-Escamilla, et al.
Fig. 5. (a) Top view of the relaxed geometry of the IS2. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
Fig. 6. (a) Top view of the relaxed geometry of the IS3. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
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Fig. 7. (a) Top view of the relaxed geometry of the FS. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
this state, the SieN bond length is 1.64 Å, and the SieO bond lengths are 1.64 Å and 1.68 Å. The FS is very stable with a relative energy of −6.80 eV.
previous reports [20]. As a consequence, the two double N]O bonds are no longer equivalent: one of them, decrease is length from 1.23 Å to 1.17 Å, while the other is increased to 1.67 Å (this is the O atom bonded to Si). This increase in the bond length indicates the breaking of the double N]O bond due to the interaction with Si. We call this configuration the intermediate state one (IS1), and its relative energy is −1.63 eV.
3.6. Minimum energy pathway We have calculated the minimum energy pathway of the inactivation of NO2 by silicene, in a reaction that goes from ZE to FS, passing through IS1, IS2 and IS3, as depicted in Fig. 2. We have used a total of 31 images to describe the full reaction. As the NO2 molecule approaches silicene, at a separation of ~4 Å between the molecule and the substrate, an interaction between NO2 and silicene emerges. As NO2 gets closer to the substrate, the system gains energy, reaching IS1 (see Fig. 2). The energy barrier to reach IS2 is 0.59 eV, while the energy for the molecule to desorb and go back to the ZS is 1.63 eV. Therefore, it is more favorable for the system to go forward in the reaction. Once IS2 is reached, the reaction would proceed to the FS state since the required activation energy is low. In order to proceed forward with the reaction, the energy needed to take the system from IS2 to IS3 is 0.21 eV and the activation energy to go to the FS, from IS3, is 0.28 eV. Therefore, once NO2 is adsorbed on silicene, it will go forward to reach the FS, gaining 6.80 eV, in an exothermal process. Experimentally, silicene is usually grown on Ag(111) [3]. Therefore, in a previous work on the adsorption of SO2 on silicene, we have investigated the effects of the substrate during its adsorption and dissociation. We have found that when the substrate effects were included, the silicene surface became more reactive, and the main steps of the reaction were more stable. For the case of the fully inactivation of SO2, the stability of each reaction step increased by ~1 eV, making the reaction even more favorable [15].
3.3. Intermediate state two (IS2) In this configuration, the NO2 is tilted, and the two O atoms are bonded to Si atoms. This configuration is more symmetric and the SieO bond lengths are ~1.74 Å. The NeO bond are also symmetric with bond lengths of 1.52 Å and 1.53 Å. As shown in Fig. 1b, the N atom is positioned at ~1.94 Å above a Si atom. The relative energy of IS2 is −1.20 eV, 0.43 eV less stable than IS1. However, for the reaction to proceed forward, it has to pass through this state. 3.4. Intermediate state three (IS3) In IS3, NO2 breaks down into NO and O subunits, as depicted in Fig.1c. The isolated O atom form bonds with two Si atoms in the bridge position, with SieO bond lengths of 1.73 Å and 1.72 Å. Meanwhile, the NO unit is chemically attached to the substrate forming SieO and NeSi bonds of 1.78 Å and 1.85 Å, respectively. In this configuration, the NeO bond length is ~1.43 Å. IS3 has a relative energy of −2.53 eV, showing that the partial inactivation of NO2 to NO and O on silicene is an exothermic and favorable process. It gains 0.90 eV with respect to IS1. 3.5. Final state (FS) In the FS, the molecule entirely disassociates into N and O atoms. They are attached to silicene in bridge positions, as shown in Fig. 1d. In 5
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Fig. 8. Close view of the system where the reaction is taking place, followed by charge difference isosurfaces for (a) IS1 (isovalue 0.01 eÅ−3), (b) IS2 (isovalue 0.01 eÅ−3), (c) IS3 (isovalue 0.01 eÅ−3) and (e) FS (isovalue 0.1 eÅ−3). The blue and red isosurfaces represents reduction and addition of charge, respectively. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
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Although Si#4 is still bonded to a Si atom (see Fig. 7a), it is also bonded to an O, and a N atom (see Fig. 7c and d). These atoms have a higher electronegativity than Si, and therefore a decrease in the electronic occupied states of Si#4 can be observed (Fig. 7f). Note that Si#5 presents changes in its electronic structure due to the structural distortions generated by the dissociated adsorption of the NO2 molecule (Fig. 7g).
3.7. Electronic properties We have calculated the PDOS of the ZS, IS1, IS2, IS3, and FS to study the evolution of the electronic properties of the system as the reaction proceeds. In addition to the PDOS of the whole system, we also present the PDOS of five specific atoms: the N atom labeled as N#1, the two O atoms (O#2 and O#3), a Si atom labeled as Si#4, which is the first Si atom to be involved in the reaction, and a Si atom labeled as Si#5 that is located far away from where the adsorption is taking place (to compare with the Si atoms involved in the reaction), as shown in Fig. 3a. In the PDOS of the ZS, shown in Fig. 3b, the black line corresponds to the total PDOS. The PDOS of silicene and NO2 are plotted with blue and red lines, respectively. The zero energy corresponds to the energy of the highest occupied state. Note that silicene presents a Dirac-like behavior, whereas the molecule states are highly localized, confirming that there is no interaction between them. The electronic states around the zero energy of atom N#1 are mainly due to s and p orbitals (Fig. 3c), while for the O atoms, the electronic states are mainly composed by p orbitals (Fig. 3d and e). The up and down states of NO2 are different because NO2 is a polar molecule. All Si atoms present the same PDOS (as can be seen for Si#4 and Si#5 in Fig. 3f and g) because NO2 is far from the monolayer and there is no interaction between them. Fig. 4 shows the PDOS of the IS1. As in the previous case, the PDOS of highlighted atoms in Fig. 4a are discussed. In the total PDOS, shown in Fig. 4b, the highest occupied electronic states of silicene decrease their intensity compared with those of the ZS. Due to the interaction with the substrate, the molecule loses its polar character, and the up and down states become symmetric. The PDOS of O#2 and O#3 are no longer equivalent, since atom O#2 bonds to atoms Si#4 and N#1. On the other hand, atom O#3 is bonded to atom N#1 as seen in Fig. 4a. From Fig. 4c and e we can see that O#3 and N#1 presents peaks with similar intensities at energies between −10 eV and −7.5 eV, indicating that they are interacting. A decrease of the NeO bond length mentioned on the previous section is due to the formation of a stronger NeO covalent bond. On the other hand, the broader signal between −3 eV and −4 eV for O#2 (Fig. 4d) coincides with the signal of Si#4 (Fig. 4f), indicating a covalent bond between O#2 and Si#4. The PDOS of Si#5 (Fig. 4g) does not present drastic changes; this is because it is localized far from the adsorption site, without showing structural or electronic changes. Fig. 5a shows the atomic structure of IS2, highlighting the atoms included in the PDOS analysis. In this state, up and down states are clearly symmetric as seen in Fig. 5b. In Fig. 5c-e the formation of NeO bonds can be seen in the PDOS contributions, which are mainly due to the p-orbitals. The PDOS of both O atoms (Fig. 5d and e) are very similar since both form part of the attached molecule, with their contributions mainly due to the p-orbitals. Si#4 experiences changes due to the change of environment (SieO bond formation) (Fig. 5f). Although Si#5 (Fig. 5g) is far from the adsorbed molecule, it shows a slight change in the density of states below the zero energy. This is because silicene has suffered a structural deformation due to the adsorption process. Fig. 6 shows the PDOS of IS3. Compared with pristine silicene, the population of states around the zero energy has increased (Fig. 6b). N#1 and O#3 atoms of the NO subunit show asymmetric spin up and down contributions, recuperating the polar character of the molecule, as seen in Fig. 6c and e. O#2 forms a bond with Si#4 (Fig. 6e and f), with contributions of the p-orbitals of both atoms. Respect to Si#5 (Fig. 6g), its PDOS is slightly modified around the zero energy. These changes are related to the structural distortion induced by the reaction. Fig. 7a shows the atomic structure of the FS, highlighting the atoms included in the PDOS analysis. In the PDOS shown in Fig. 7b, a population of electronic states can be observed at the zero energy. The highest occupied states of O#2 and O#3 atoms (Fig. 7d and e) are displaced to negative values, which gives stability to the system.
3.8. Charge density To gain a better understanding of the adsorption, we have studied the monolayer-molecule charge transfer, as calculated by Δρ = ρXS − ρsilicene − ρNO2, with ρXS the charge density of the XS state (XS = IS1, IS2, IS3, and FS), ρsilicene the charge of the pristine silicene substrate, and ρNO2 the electron density of the molecule. In the IS1, the silicene substrate transfer 0.16e to the NO2 (indicated by a red arrow in Fig. 8a). The Si atom involved in the SieO bond (Si#4) loses 0.10e. The charge transferred to the molecule is localized mainly in the O atom bonded to the monolayer (O#2). When the NO2 attaches to silicene, the difference in electronegativity between oxygen and silicon results in the charge transfer from the monolayer to the O atom. This additional charge weakness the NeO bond resulting in a larger NeO bond length. In IS2, silicene transfers 0.40e to the molecule, 0.20e to the N, and 0.20 distributed between the two O atoms, as shown in Fig. 8b. As the charge in NO2 is distributed uniformly, the molecule becomes symmetric, with similar NeO bond lengths. The Si atoms bonded to O show the large charge deficit. In IS3, silicene transfers 0.26e and 0.23e to the NO and O units, respectively, as shown in Fig. 8c. The results of the FS are shown in Fig. 8d. For this state, O#2 losses 0.70e, while N and O#3 gain 0.42e and 5.77e, respectively. As the reaction proceeds, silicene transfers more charge to the molecule, making the system more stable. 4. Summary In this paper we have proposed a mechanism using silicene, to trap and inactivate NO2, a harmful molecule, responsible of acid rain. Our results show that silicene not just trap the NO2 molecule. Once the molecule and the substrate interact, it is possible to decompose the molecule into N and O isolated atoms, which are incorporated into the monolayer in an exothermic reaction with a gain of energy of 6.80 eV. The highest activation energy in the proposed reaction is 0.58 eV, which indicates that this reaction has a high probability to occur. We hope that our results contribute to the evolution of new devices to sense and inactivate toxic gases. Acknowledgments We thank DGAPA, UNAM project IN101019 and CONACYT grant A1-S-9070 of the Call of Proposals for Basic Scientific Research 2017–2018 for partial financial support. Calculations were performed in the DGCTIC-UNAM Supercomputing Center, project LANCADUNAM-DGTIC-051, and Laboratorio Nacional de Supercómputo del Sureste de México, CONACYT member of the network of national laboratories. References [1] K. Takeda, K. Shiraishi, Phys. Rev. B 50 (1994) 14916. [2] G.G. Guzmán-Verri, L.C. Lew Yan Voon, Phys. Rev. B 76 (2007) 075131. [3] P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M.C. Asensio, A. Resta, B. Ealet, Guy Le Lay, Silicene: compelling experimental evidence for graphene-like two-dimensional silicon, Phys. Rev. Lett. 108 (2012) 155501. [4] Du Yi, Jincheng Zhuang, Jiaou Wang, Zhi Li, Hongsheng Liu, Jijun Zhao, Xu Xun, Haifeng Feng, Lan Chen, Kehui Wu, Xiaolin Wang, Shi Xue Doou, Quasi-freestanding epitaxial silicene on ag(111) by oxygen intercalation, Mater. Eng. 2 (7) (2016) e1600067. [5] W. Wan, Y. Ge, F. Yang, Y. Yao, Phonon-mediated superconductivity in silicene predicted by first-principles density functional calculations, Europhys. Lett. 104 (2013).
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[6] Jia-An Yan, Shang-Peng Gao, Ryan Stein, and Gregory Coard, Tuning the electronic structure of silicene and germanene by biaxial strain and electric field, Phys. Rev. B 91, 245403. [7] Rubí Zarmiento-García, J. Guerrero-Sánchez, Noboru Takeuchi, Functionalization of silicene and silicane with benzaldehyde, J. Mol. Model. 25 (2019) 109. [8] W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, A. Bansil, Gated silicene as a tunable source of nearly 100% spin-polarized electrons, Nat. Commun. 4 (2013) 1–6. [9] Metal-functionalized Silicene for efficient hydrogen storage, Chem. Phys. Chem 14 (2013) 3463–3466. [10] Jariyanee Prasongkit, Rodrigo G. Amorin … highly sensitive and selective gas detection based on silicene. J. Phys. Chem. C 2015, 119, 16934–16940. [11] H.N. Fernández-Escamilla, J. Guerrero-Sánchez, Reyes Garcia-Diaz, E. MartínezGuerra, N. Takeuchi, Adsorption of dimethyl sulfoxide on blue phosphorene, Surf. Sci. 680 (2019) 88–94. [12] Wei Hu, Nan Xia, Xiaojun Wu, Zhenyu Li, Jinlong Yang, Silicene as a highly sensitive molecule sensor for NH3, NO, and NO2, Phys. Chem. Chem. Phys. 16 (2014) 6957. [13] Jing-wen Feng, Yue-jie Liu, Hong-xia Wang, Jing-xiang Zhao, Qing-hai Cai, Xuan-
[14]
[15] [16] [17] [18] [19]
[20]
8
zhang Wang, Gas adsorption on silicene: a theoretical study, Comput. Mater. Sci. 87 (2014) 218–226. Tanveer Hussain, Thanayut Kaewmaraya, Sudip Chakraborty, Rajeev Ahuja, Defect and substitution-induced silicene sensor to probe toxic gases, J. Phys. Chem. C 120 (44) (2016) 25256–25262. J. Guerrero-Sánchez, Dalia M. Munoz-Pizza, Noboru Takeuchi, Silicene as an efficient way to fully inactivate the SO2 pollutant, Appl. Surf. Sci. 479 (2019) 847–851. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, et al., J. Phys. Condens. Matter 21 (2009). J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188. G. Henkelman, B.P. Uberuaga, H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113 (2000) 9901. Wei Hu, Nan Xia, Xiaojun Wu, Zhenyu Li, Jinlong Yang, Silicene as a highly sensitive molecule sensor for NH3, NO and NO2, Phys. Chem. Chem. Phys. 16 (2014) 6957.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Full length article
Adsorption and dissociation of NO2 on silicene a,⁎
a
T b
H.N. Fernández-Escamilla , J. Guerrero-Sánchez , E. Martínez-Guerra , N. Takeuchi a b
a
Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, Apartado Postal 14, Ensenada, Baja California Código Postal 22800, Mexico CICFM Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, N.L. 66450, Mexico
A R T I C LE I N FO
A B S T R A C T
Keywords: Silicene Nudge elastic band
Using Density Functional Theory, we have described the full inactivation of NO2 driven by silicene. NO2 is a harmful pollution-generating molecule, causing acid rain. We have studied the minimum energy pathway for the trapping and deactivation of NO2 on silicene substrates. Starting with a configuration in which the molecule and the substrate are not interacting, the NO2 is chemisorbed on silicene, passing through several intermediate states. As the reaction proceeds, the system gains energy, favoring the breaking of the NO2 molecule. In the final state, the molecule is entirely disassociated into N and O atoms, that are incorporated into silicene, forming bonds in bridge positions. The reaction is exothermic, gaining 6.8 eV. These results indicate that silicene is a good substrate to trap NO2 and to completely inactivate it by decomposing it into N and O atoms.
1. Introduction Silicene, a two-dimensional silicon material, was theoretically proposed [1], and its electronic properties were investigated by tightbinding calculations, showing linearly crossing bands at the Fermi level [2]. Since its experimental synthesis [3], both theoretical and experimental research has grown rapidly. In 2016, quasi-freestanding silicene was obtained through oxidization of bilayer silicene on Ag(111) [4]. One of the main reasons for the interest in silicene is the possibility of modulating its properties, with a large number of promising applications in the semiconductor industry. Silicene has a buckled hexagonal honeycomb structure. The hybridization of the silicon atoms in silicene is a combination of sp2 and sp3, with the primary contributions coming from pz, pxy and s orbitals around the Fermi level [5]. The buckling in silicene leads to a simple way to tune its electronic properties, for example by applying an electric field [6], or by organic functionalization [7]. Possible silicene applications can be found in spintronics [8], hydrogen storage [9], or in gas sensing devices [10,11]. The adsorption of NH3, NO, and NO2 on silicene has been investigated, reporting high adsorption energies. The electronic properties of the resulting systems show p-type doping [12]. Adsorption of other molecules such as CO, O2, CO2, and SO2 has been theoretically investigated as well [13]. Silicene cannot be a good sensor for NO2, O2, and SO2 because of their slow desorption rates once they are trapped. The opposite has been reported for NO and NH3, where adsorption energies are lower, facilitating their desorption. CO and CO2 are adsorbed through weak physisorption. Mono-, di-, and tri- vacancies and
⁎
stone-wales defects on silicene increase its surface reactivity. In this way, detection of toxic molecules can be accomplished [14]. Recently, it has been reported that due to the strong interaction between the SO2 and the silicene, once the molecule has been chemically adsorbed, it would not desorb. Instead, the SeO bonds break, incorporating the atoms to silicene in an exothermic process [15]. The silicene reactivity allows breaking the SO2 molecule with a low activation energy. As mentioned before, it is known that NO2 chemically adsorb on silicone with a large adsorption energy. However, the processes that occur after NO2 adsorption have not been investigated in detail. In this article, we theoretically investigate the adsorption of NO2 molecule on silicene. In particular, we are interested to find out if the molecule breaks down, as in the case of SO2. By describing the minimum energy pathway, we have tested the inactivation of the molecule into NO and O. We have also examined the possible decomposing of NO2 into N and two O atoms, as in SO2 [15]. The following sections of our paper are organized as following: in Section 2 we describe the method, Section 3 is devoted to describe and discuss the results. Finally, in Section 4 we conclude the article. 2. Method We have used first-principles calculations based on density functional theory (DFT), as implemented in the Quantum ESPRESSO open source package [16]. For the exchange-correlation (XC) potential, the generalized gradient approximation (GGA), as parametrized by PerdewBurke-Ernzerhof (PBE) has been employed [17]. We have used ultra-
Corresponding author. E-mail address: [email protected] (H.N. Fernández-Escamilla).
https://doi.org/10.1016/j.apsusc.2019.143854 Received 12 June 2019; Received in revised form 6 August 2019; Accepted 1 September 2019 Available online 05 September 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.
Applied Surface Science 498 (2019) 143854
H.N. Fernández-Escamilla, et al.
Fig. 1. Top view of silicene where the molecule is adsorbed/inactivated. (a) In the intermediate state 1, the NO2 molecule chemically adsorbs by forming a SieO covalent bond. (b) In intermediate state 2, all the NO2 atoms bond to silicene. (c) Intermediate state 3, the NO2 breaks down into NO and O subunits, both bonded to silicene, (d) Final state, the NO2 has been fully inactivated into a N atom and two O atoms, all of them incorporated into the monolayer.
pathway to carry out the NO2 inactivation process, through a reaction with different intermediate and transition states, we have used the climbing image nudged elastic band (CI-NEB) method [19]. 3. Results and discussion In this section, we describe the inactivation process of NO2, passing through several intermediate states: zero energy, intermediate 1, intermediate 2, intermediate 3, and final states. The reaction is studied by finding the minimum energy pathway. Analysis of the electronic properties of the fundamental states of the reaction is carried out to understand it. 3.1. Zero energy state (ZS)
Fig. 2. Minimum energy path for the NO2 inactivation reaction driven by silicene. There is no energy barrier for the molecule to attached to the silicene substrate in IS1. From there, the energy barrier needed to desorb the NO2 is 1.63 eV. While the activation energy to take the system from IS1 to FS is around 0.60 eV.
As the reference state, the silicene substrate and the NO2 molecule are separated by 10 Å, in a non-interacting configuration. We call it the zero energy state (ZS) and its total energy is used as the reference to calculate the relative energy of the other states: Erelative = Estate - EZS, where Estate is the total energy of the system, and EZS is the total energy of the ZS. Any configuration (state) with negative relative energy is more stable than the ZS.
soft pseudopotentials and kinetic energy cutoffs of 30 Ry and 240 Ry for the electronic wave functions and charge density, respectively. To analyze the charge transference, we perform a Bader charge analysis. The adsorption of the molecule was made on a 5 × 5 silicene supercell considering a Monkhorst-Pack mesh [18] with a gamma centered kpoints grid of 7 × 7 × 1 in the Brillouin zone for geometrical optimization, for the projected density of states (PDOS), a larger k-point grid of 14 × 14 × 1 was used. The geometry of the structures was optimized, with a convergence criterion that all forces on each atom must be smaller than 1 × 10−3 Ry/a.u. The atomic self-interactions generated by the periodic conditions were avoided by an empty space of 20 Å perpendicular to the monolayer. To calculate the minimum energy
3.2. Intermediate state one (IS1) NO2 can be chemically adsorbed on silicene in several configurations, forming different kind of bonds. When the molecule is adsorbed on top of a Si atom, a covalent single SieO bond is formed, as shown in Fig. 1a. This structural configuration has the lowest energy of the different high symmetry sites in which NO2 can be adsorbed on silicene. The calculated SieO bond length is 1.70 Å, in good agreement with 2
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Fig. 3. (a) Top view of the relaxed geometry of the ZS. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (cd) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
Fig. 4. (a) Top view of the relaxed geometry of the IS1. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (cd) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
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Fig. 5. (a) Top view of the relaxed geometry of the IS2. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
Fig. 6. (a) Top view of the relaxed geometry of the IS3. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
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Fig. 7. (a) Top view of the relaxed geometry of the FS. Highlighted atoms are the ones included in the PDOS analysis, (b) total, substrate, and molecule PDOS are plotted with black, blue, and red continuous lines, respectively, (c) PDOS of N#1, (d) PDOS of O#2, (e) PDOS of O#3, (f) PDOS of Si#4, and (g) PDOS of Si#5. In (c–d) Total PDOS is plotted with a discontinuous black line, while s and p orbitals are shown with blue and red continuous lines, respectively.
this state, the SieN bond length is 1.64 Å, and the SieO bond lengths are 1.64 Å and 1.68 Å. The FS is very stable with a relative energy of −6.80 eV.
previous reports [20]. As a consequence, the two double N]O bonds are no longer equivalent: one of them, decrease is length from 1.23 Å to 1.17 Å, while the other is increased to 1.67 Å (this is the O atom bonded to Si). This increase in the bond length indicates the breaking of the double N]O bond due to the interaction with Si. We call this configuration the intermediate state one (IS1), and its relative energy is −1.63 eV.
3.6. Minimum energy pathway We have calculated the minimum energy pathway of the inactivation of NO2 by silicene, in a reaction that goes from ZE to FS, passing through IS1, IS2 and IS3, as depicted in Fig. 2. We have used a total of 31 images to describe the full reaction. As the NO2 molecule approaches silicene, at a separation of ~4 Å between the molecule and the substrate, an interaction between NO2 and silicene emerges. As NO2 gets closer to the substrate, the system gains energy, reaching IS1 (see Fig. 2). The energy barrier to reach IS2 is 0.59 eV, while the energy for the molecule to desorb and go back to the ZS is 1.63 eV. Therefore, it is more favorable for the system to go forward in the reaction. Once IS2 is reached, the reaction would proceed to the FS state since the required activation energy is low. In order to proceed forward with the reaction, the energy needed to take the system from IS2 to IS3 is 0.21 eV and the activation energy to go to the FS, from IS3, is 0.28 eV. Therefore, once NO2 is adsorbed on silicene, it will go forward to reach the FS, gaining 6.80 eV, in an exothermal process. Experimentally, silicene is usually grown on Ag(111) [3]. Therefore, in a previous work on the adsorption of SO2 on silicene, we have investigated the effects of the substrate during its adsorption and dissociation. We have found that when the substrate effects were included, the silicene surface became more reactive, and the main steps of the reaction were more stable. For the case of the fully inactivation of SO2, the stability of each reaction step increased by ~1 eV, making the reaction even more favorable [15].
3.3. Intermediate state two (IS2) In this configuration, the NO2 is tilted, and the two O atoms are bonded to Si atoms. This configuration is more symmetric and the SieO bond lengths are ~1.74 Å. The NeO bond are also symmetric with bond lengths of 1.52 Å and 1.53 Å. As shown in Fig. 1b, the N atom is positioned at ~1.94 Å above a Si atom. The relative energy of IS2 is −1.20 eV, 0.43 eV less stable than IS1. However, for the reaction to proceed forward, it has to pass through this state. 3.4. Intermediate state three (IS3) In IS3, NO2 breaks down into NO and O subunits, as depicted in Fig.1c. The isolated O atom form bonds with two Si atoms in the bridge position, with SieO bond lengths of 1.73 Å and 1.72 Å. Meanwhile, the NO unit is chemically attached to the substrate forming SieO and NeSi bonds of 1.78 Å and 1.85 Å, respectively. In this configuration, the NeO bond length is ~1.43 Å. IS3 has a relative energy of −2.53 eV, showing that the partial inactivation of NO2 to NO and O on silicene is an exothermic and favorable process. It gains 0.90 eV with respect to IS1. 3.5. Final state (FS) In the FS, the molecule entirely disassociates into N and O atoms. They are attached to silicene in bridge positions, as shown in Fig. 1d. In 5
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Fig. 8. Close view of the system where the reaction is taking place, followed by charge difference isosurfaces for (a) IS1 (isovalue 0.01 eÅ−3), (b) IS2 (isovalue 0.01 eÅ−3), (c) IS3 (isovalue 0.01 eÅ−3) and (e) FS (isovalue 0.1 eÅ−3). The blue and red isosurfaces represents reduction and addition of charge, respectively. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
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Although Si#4 is still bonded to a Si atom (see Fig. 7a), it is also bonded to an O, and a N atom (see Fig. 7c and d). These atoms have a higher electronegativity than Si, and therefore a decrease in the electronic occupied states of Si#4 can be observed (Fig. 7f). Note that Si#5 presents changes in its electronic structure due to the structural distortions generated by the dissociated adsorption of the NO2 molecule (Fig. 7g).
3.7. Electronic properties We have calculated the PDOS of the ZS, IS1, IS2, IS3, and FS to study the evolution of the electronic properties of the system as the reaction proceeds. In addition to the PDOS of the whole system, we also present the PDOS of five specific atoms: the N atom labeled as N#1, the two O atoms (O#2 and O#3), a Si atom labeled as Si#4, which is the first Si atom to be involved in the reaction, and a Si atom labeled as Si#5 that is located far away from where the adsorption is taking place (to compare with the Si atoms involved in the reaction), as shown in Fig. 3a. In the PDOS of the ZS, shown in Fig. 3b, the black line corresponds to the total PDOS. The PDOS of silicene and NO2 are plotted with blue and red lines, respectively. The zero energy corresponds to the energy of the highest occupied state. Note that silicene presents a Dirac-like behavior, whereas the molecule states are highly localized, confirming that there is no interaction between them. The electronic states around the zero energy of atom N#1 are mainly due to s and p orbitals (Fig. 3c), while for the O atoms, the electronic states are mainly composed by p orbitals (Fig. 3d and e). The up and down states of NO2 are different because NO2 is a polar molecule. All Si atoms present the same PDOS (as can be seen for Si#4 and Si#5 in Fig. 3f and g) because NO2 is far from the monolayer and there is no interaction between them. Fig. 4 shows the PDOS of the IS1. As in the previous case, the PDOS of highlighted atoms in Fig. 4a are discussed. In the total PDOS, shown in Fig. 4b, the highest occupied electronic states of silicene decrease their intensity compared with those of the ZS. Due to the interaction with the substrate, the molecule loses its polar character, and the up and down states become symmetric. The PDOS of O#2 and O#3 are no longer equivalent, since atom O#2 bonds to atoms Si#4 and N#1. On the other hand, atom O#3 is bonded to atom N#1 as seen in Fig. 4a. From Fig. 4c and e we can see that O#3 and N#1 presents peaks with similar intensities at energies between −10 eV and −7.5 eV, indicating that they are interacting. A decrease of the NeO bond length mentioned on the previous section is due to the formation of a stronger NeO covalent bond. On the other hand, the broader signal between −3 eV and −4 eV for O#2 (Fig. 4d) coincides with the signal of Si#4 (Fig. 4f), indicating a covalent bond between O#2 and Si#4. The PDOS of Si#5 (Fig. 4g) does not present drastic changes; this is because it is localized far from the adsorption site, without showing structural or electronic changes. Fig. 5a shows the atomic structure of IS2, highlighting the atoms included in the PDOS analysis. In this state, up and down states are clearly symmetric as seen in Fig. 5b. In Fig. 5c-e the formation of NeO bonds can be seen in the PDOS contributions, which are mainly due to the p-orbitals. The PDOS of both O atoms (Fig. 5d and e) are very similar since both form part of the attached molecule, with their contributions mainly due to the p-orbitals. Si#4 experiences changes due to the change of environment (SieO bond formation) (Fig. 5f). Although Si#5 (Fig. 5g) is far from the adsorbed molecule, it shows a slight change in the density of states below the zero energy. This is because silicene has suffered a structural deformation due to the adsorption process. Fig. 6 shows the PDOS of IS3. Compared with pristine silicene, the population of states around the zero energy has increased (Fig. 6b). N#1 and O#3 atoms of the NO subunit show asymmetric spin up and down contributions, recuperating the polar character of the molecule, as seen in Fig. 6c and e. O#2 forms a bond with Si#4 (Fig. 6e and f), with contributions of the p-orbitals of both atoms. Respect to Si#5 (Fig. 6g), its PDOS is slightly modified around the zero energy. These changes are related to the structural distortion induced by the reaction. Fig. 7a shows the atomic structure of the FS, highlighting the atoms included in the PDOS analysis. In the PDOS shown in Fig. 7b, a population of electronic states can be observed at the zero energy. The highest occupied states of O#2 and O#3 atoms (Fig. 7d and e) are displaced to negative values, which gives stability to the system.
3.8. Charge density To gain a better understanding of the adsorption, we have studied the monolayer-molecule charge transfer, as calculated by Δρ = ρXS − ρsilicene − ρNO2, with ρXS the charge density of the XS state (XS = IS1, IS2, IS3, and FS), ρsilicene the charge of the pristine silicene substrate, and ρNO2 the electron density of the molecule. In the IS1, the silicene substrate transfer 0.16e to the NO2 (indicated by a red arrow in Fig. 8a). The Si atom involved in the SieO bond (Si#4) loses 0.10e. The charge transferred to the molecule is localized mainly in the O atom bonded to the monolayer (O#2). When the NO2 attaches to silicene, the difference in electronegativity between oxygen and silicon results in the charge transfer from the monolayer to the O atom. This additional charge weakness the NeO bond resulting in a larger NeO bond length. In IS2, silicene transfers 0.40e to the molecule, 0.20e to the N, and 0.20 distributed between the two O atoms, as shown in Fig. 8b. As the charge in NO2 is distributed uniformly, the molecule becomes symmetric, with similar NeO bond lengths. The Si atoms bonded to O show the large charge deficit. In IS3, silicene transfers 0.26e and 0.23e to the NO and O units, respectively, as shown in Fig. 8c. The results of the FS are shown in Fig. 8d. For this state, O#2 losses 0.70e, while N and O#3 gain 0.42e and 5.77e, respectively. As the reaction proceeds, silicene transfers more charge to the molecule, making the system more stable. 4. Summary In this paper we have proposed a mechanism using silicene, to trap and inactivate NO2, a harmful molecule, responsible of acid rain. Our results show that silicene not just trap the NO2 molecule. Once the molecule and the substrate interact, it is possible to decompose the molecule into N and O isolated atoms, which are incorporated into the monolayer in an exothermic reaction with a gain of energy of 6.80 eV. The highest activation energy in the proposed reaction is 0.58 eV, which indicates that this reaction has a high probability to occur. We hope that our results contribute to the evolution of new devices to sense and inactivate toxic gases. Acknowledgments We thank DGAPA, UNAM project IN101019 and CONACYT grant A1-S-9070 of the Call of Proposals for Basic Scientific Research 2017–2018 for partial financial support. Calculations were performed in the DGCTIC-UNAM Supercomputing Center, project LANCADUNAM-DGTIC-051, and Laboratorio Nacional de Supercómputo del Sureste de México, CONACYT member of the network of national laboratories. References [1] K. Takeda, K. Shiraishi, Phys. Rev. B 50 (1994) 14916. [2] G.G. Guzmán-Verri, L.C. Lew Yan Voon, Phys. Rev. B 76 (2007) 075131. [3] P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M.C. Asensio, A. Resta, B. Ealet, Guy Le Lay, Silicene: compelling experimental evidence for graphene-like two-dimensional silicon, Phys. Rev. Lett. 108 (2012) 155501. [4] Du Yi, Jincheng Zhuang, Jiaou Wang, Zhi Li, Hongsheng Liu, Jijun Zhao, Xu Xun, Haifeng Feng, Lan Chen, Kehui Wu, Xiaolin Wang, Shi Xue Doou, Quasi-freestanding epitaxial silicene on ag(111) by oxygen intercalation, Mater. Eng. 2 (7) (2016) e1600067. [5] W. Wan, Y. Ge, F. Yang, Y. Yao, Phonon-mediated superconductivity in silicene predicted by first-principles density functional calculations, Europhys. Lett. 104 (2013).
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[6] Jia-An Yan, Shang-Peng Gao, Ryan Stein, and Gregory Coard, Tuning the electronic structure of silicene and germanene by biaxial strain and electric field, Phys. Rev. B 91, 245403. [7] Rubí Zarmiento-García, J. Guerrero-Sánchez, Noboru Takeuchi, Functionalization of silicene and silicane with benzaldehyde, J. Mol. Model. 25 (2019) 109. [8] W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, A. Bansil, Gated silicene as a tunable source of nearly 100% spin-polarized electrons, Nat. Commun. 4 (2013) 1–6. [9] Metal-functionalized Silicene for efficient hydrogen storage, Chem. Phys. Chem 14 (2013) 3463–3466. [10] Jariyanee Prasongkit, Rodrigo G. Amorin … highly sensitive and selective gas detection based on silicene. J. Phys. Chem. C 2015, 119, 16934–16940. [11] H.N. Fernández-Escamilla, J. Guerrero-Sánchez, Reyes Garcia-Diaz, E. MartínezGuerra, N. Takeuchi, Adsorption of dimethyl sulfoxide on blue phosphorene, Surf. Sci. 680 (2019) 88–94. [12] Wei Hu, Nan Xia, Xiaojun Wu, Zhenyu Li, Jinlong Yang, Silicene as a highly sensitive molecule sensor for NH3, NO, and NO2, Phys. Chem. Chem. Phys. 16 (2014) 6957. [13] Jing-wen Feng, Yue-jie Liu, Hong-xia Wang, Jing-xiang Zhao, Qing-hai Cai, Xuan-
[14]
[15] [16] [17] [18] [19]
[20]
8
zhang Wang, Gas adsorption on silicene: a theoretical study, Comput. Mater. Sci. 87 (2014) 218–226. Tanveer Hussain, Thanayut Kaewmaraya, Sudip Chakraborty, Rajeev Ahuja, Defect and substitution-induced silicene sensor to probe toxic gases, J. Phys. Chem. C 120 (44) (2016) 25256–25262. J. Guerrero-Sánchez, Dalia M. Munoz-Pizza, Noboru Takeuchi, Silicene as an efficient way to fully inactivate the SO2 pollutant, Appl. Surf. Sci. 479 (2019) 847–851. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, et al., J. Phys. Condens. Matter 21 (2009). J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188. G. Henkelman, B.P. Uberuaga, H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113 (2000) 9901. Wei Hu, Nan Xia, Xiaojun Wu, Zhenyu Li, Jinlong Yang, Silicene as a highly sensitive molecule sensor for NH3, NO and NO2, Phys. Chem. Chem. Phys. 16 (2014) 6957.