Experimental Sensing and Density Functional Theory Study of H2S and SOF2 Adsorption on Au‐Modified Graphene

A gas sensor is used to detect SF6 decomposed gases, which are related to insulation faults, to accurately assess the insulated status of electrical equipment. Graphene films (GrF) modified with Au nanoparticles are used as an adsorbent for the detection of H2S and SOF2, which are two characteristic products of SF6 decomposed gases. Sensing experiments are conducted at room temperature. Results demonstrate that Au‐modified GrF yields opposite responses to the tested gases and is thus considered a promising material for developing H2S‐ and SOF2‐selective sensors. The first‐principles approach is applied to simulate the interaction between the gases and Au‐modified GrF systems and to interpret experimental data. The observed opposite resistance responses can be attributed to the charge‐transfer differences related to the interfacial interaction between the gases and systems. The density of states and Mulliken population analysis results confirm the apparent charge transfer in Au‐modified GrF chemisorption, whereas the van der Waals effect dominates the pristine graphene adsorption systems. Calculation results can also explicate the significant SOF2 responses on Au‐modified GrF. This work is important in graphene modulation and device design for selective detection.


Introduction
Sulfur hexafl uoride (SF 6 ) is widely used in gas-insulated electrical equipment because it features excellent insulating and arc-extinguishing properties. At the early stages of insulation degradation of electrical equipment, the occurrence of partial www.MaterialsViews.com www.advancedscience.com fabrication to investigate H 2 S and SOF 2 adsorption responses. Based on fi rst-principles calculations, we studied the interaction mechanism of the Au-modifi ed GrF substrate with the gases. To the best of our knowledge, theoretical study combined with experimental data regarding the SOF 2 adsorption effect on Au-modifi ed GrF has not been conducted and a thorough study of H 2 S adsorption effect is rarely reported.

Experimental Sensing Performance
Materials must be thoroughly analyzed before the investigation of sensing performance. The main Au (111) peak suggests the formation of a crystal phase, and the broad Au peaks imply that Au nanoparticles (AuNPs) are highly dispersed in the sample. The particle size of 14 nm was estimated from the main peak width of Au (111) through the Scherrer formula. The broad diffraction peaks at 24.63° and 23.77° for Au-modifi ed GrF and rGO samples, respectively, reveal the carbon structure of graphene.
Raman spectra were determined for structural characterization. [ 23 ] The typical postsubtraction Raman spectra were directly recorded on the sensor substrate and shown in Figure 1 b. As the epoxy layers underlying the fi lms function as insulators, the effect on electron distribution is disregarded. The comparison of the Raman spectra between Au-modifi ed GrF and pure rGO fi lms indicates that low amounts of modifi ed AuNPs do not signifi cantly change the formation of the in-plane sp 2 domains in graphene. The Raman spectra of the fi lms show the representative peaks at ≈1356 (D) and ≈1590 cm −1 (G) and the broad bands between 2400 and 3200 cm −1 . [ 20 ] As the intensity ratios of the D and G peaks are highly sensitive to the quality of material, [ 24 ] we speculate that graphene-based  (3 of 10) 1500101 wileyonlinelibrary.com materials contain multiple layers. Furthermore, the D peak is relatively pronounced, indicating the presence of a signifi cant number of defects and a degree of confusion structure caused by deprivation of oxygen functionalities during hydrogen reduction. [ 25 ] The sample fl akes present a size of tens nanometers based on the D/G ratio of 0.85 and the G peak position. This observation is consistent with the results of XRD analysis. Figure 2 a shows low-and high-resolution SEM images of pure rGO. The clear and bright vision of rGO fi lm sample indicates good electrical conductivity, which is free of metal spraying treatment. The fl imsy, wrinkled, and fl uctuant surface of two-dimensions is the typical morphology of rGO in practice application. Morphological structure, particle size, and metal dispersion of Au-modifi ed GrF were also determined and the results are illustrated in Figure 2 b. The enhanced area caused by highly dispersed AuNPs provides more available active sites on the sensing surface. AuNPs are uniformly embedded and covered on rGO. After analyzing several images, the average diameter of AuNPs is determined as tens of nanometers; this fi nding is in agreement with the results of XRD and Raman studies. Figure 2 c,d shows the TEM morphologies of pure rGO and Au-modifi ed GrF, respectively. The rGO sample is with good light transmittance and obvious fold boundary. These features indicate that the quality of rGO sample is excellent, which owns few carbon layers. The specifi c number regarding these carbon layers is further confi rmed to nine by HRTEM, which is embedded in Figure 2 c. Therefore, our rGO sample is classifi ed as the multilayer graphene. From the TEM image in Figure 2 d, we confi rm that AuNPs with dozen nanometer sizes are homogenously dispersed on the rGO sheet surface. The HRTEM images in the inset in Figure 2 d reveal the well-defi ned lattice fringes of Au (111) with a clear lattice distance ( d 111 = 0.235 nm), indicating that AuNPs exist and are highly crystalline. The EDS spectrum further verifi es that Au is successfully modifi ed in graphene.
XPS spectra are important in valence analysis. Figure 3 shows the XPS spectra of rGO and Au-modifi ed GrF. The results reveal that ≈6% AuNPs are successfully modifi ed on the www.MaterialsViews.com www.advancedscience.com graphene surface, which is in accordance with the XRD, SEM, and TEM results. The high-resolution C 1s XPS spectrum of rGO indicates that numerous heteroatom defects exist on the plane and edges. [ 26 ] Moreover, the C 1s spectrum can be fi tted into four peaks corresponding to C atoms from four functional groups: nonoxygenated ring C at 284.8 eV, C in the C N bond at 285.8 eV, hydroxyl C at 286.8 eV, and carbonyl C at 288.6 eV. After Au was introduced, a new peak appears at 284.2 eV and this peak is attributed to the C N Au bond. [26][27][28] After peakdifferentiation-imitating analysis, the Au 4f doublet deconvolutes into two pairs of peaks, which correspond to the reduced Au (0) at 84.27 eV in Au 4f 7/2 and at 87.94 eV in Au 4f 5/2 , Au (III) ions at 85.02 eV in Au 4f 7/2 and Au (I) ions at 88.37 eV in Au 4f 5/2 , respectively. [ 29 ] Approximately 0.6 eV redshift of the XPS peak of Au (0) ions exists in Au 4f 7/2 . This shift in the bonding energy may be ascribed to the substrate and reduced core-hole screening in metal particles. Furthermore, a dynamic electron transfer from modifi ed AuNPs to the supported graphene fi lms is confi rmed by the existence of positively charged Au (III) and Au (I) ions according to the electrostatic balance principle and theoretical calculation in DFT study. Moreover, according to the N 1s spectra of rGO and Au-modifi ed sample in Figure 3 e,f, modifi ed AuNPs result in a blue shift of binding energy (from 400.03 eV to 399.53 eV), which indicates that Aumodifi ed sample is a covalent hybrid based on the coordination or chemical effects between heteroatoms, such as, N and O, and Au clusters. [ 26,30,31 ] Target gas molecules, namely, H 2 S and SOF 2 , were delivered to the graphene-based sensor device through mass fl ow-controlled dilution with clean, pure, and dry helium. Figure 4 a-d represents the responses of the rGO and Au-modifi ed GrF sensors in terms of resistance changes during exposure to varied concentrations of target gases in an autonomous sealed chamber. Resistance change is defi ned as where R F represents the sensor resistance at the fi nal target gas exposure and R I represents the initial vacuum resistance at the previous rest period. Sensor response [ 32 ] is universally defi ned as Although humidity and temperature signifi cantly affect the sensor response, specifi c operating conditions in electrical equipment may reduce this variation. Figure 4 a-d shows the sensor responses after exposure to 50 and 100 ppm of H 2 S and SOF 2 . Only the responses associated with these two concentrations were analyzed to investigate the sensing mechanism. For rGO under ambient conditions, 100 and 50 ppm H 2 S cause 15.78% and 10.53% reduction in resistance, respectively. SOF 2 is not sensitive to rGO. Moreover, 100 and 50 ppm SOF 2 result in 23.83% and 15.36% reduction in the resistance of Au-modifi ed GrF, respectively. These fi ndings indicate that Au-modifi ed GrF exhibits higher sensitivity to SOF 2 than rGO. Although Au-modifi ed GrF is also sensitive to H 2 S, a positive resistance change was observed. In this system, 100 and 50 ppm H 2 S increase the resistance by 28.15% and 18.73%, respectively. These sensing performances reveal that the Au-modifi ed GrF and pure rGO sensors are promising materials for selective detection. Therefore, the sensing behavior was further analyzed.   Further experiments were performed to determine the response properties under repeated gas pulses. For this, a series of sensing experiments involving H 2 S and SOF 2 were performed at the same setting. Figure 5 a,b shows our rGO sensor's behavior in repeated H 2 S and SOF 2 fl ows, respectively, and Figure 5 c,d illustrates the responses of our Au-modifi ed GrF sensor to target gases. The target gas and pure N 2 were fl own over the sensor sequentially and recurrently, and the changes in resistance were measured. N 2 fl ow expelled the target gas that had already been existed, for the purpose of exploring its recovery property and preparing the next detection round at the same time. Based on the results in Figure 5 , the sensor response presents the similar variation tendency in comparison with the single test result, regardless of the magnitude and response direction. In addition, we have noticed that the transient for H 2 S on rGO sensor is much slower compared to the response behavior on Au-modifi ed GrF. Hence, the response speed of Au-modifi ed GrF is proved to be better than pure rGO.

Au-Modifi ed Graphene
A simulation model was constructed for theoretical calculation to investigate the factors affecting sensor performance and the sensing mechanism. We already discussed the nature of the bonding between decorated Au and graphene. The three possible positions [ 22 ] considered are the top site above a carbon atom (T), bridge site between the C C bond (B), and hollow site at the hexagon center (H), which are illustrated in Figure 6 a. Our calculation results show that the T site model holds the lowest energy, as shown in Figure 6 b. And the detailed calculated energy information has been summarized in Table S1 (Supporting Information). Therefore, our calculation focuses on the T position, in which Au substitutes C. Au atoms in Au-modifi ed GrF adopt a partial sp 3 confi guration and protrude from the graphene plane by 1.87 Å along the Z axis. The bond lengths (2.07 Å) of the three C Au bonds confi rm the partial sp 3 confi guration of Au atoms. A similar bonding geometry was observed in M -modifi ed graphene ( M = Pd, Pt, and Mn) [33][34][35]

Gas Adsorption Effects
Different orientations are required to achieve the most stable adsorption confi guration, which exhibits the lowest total energy and highest adsorption energy. [ 36 ] Figure 8 illustrates the most stable adsorption confi gurations of single and double H 2 S and SOF 2 molecules on Au-modifi ed GrF. Table 1 presents the calculated results of every adsorption system. Figure 9 further shows the spin-polarized DOS for H 2 S and SOF 2 adsorption systems. We focused on the adsorption effects of double molecules on the Au-modifi ed GrF plane according to previous research, which reported that several molecule adsorption cases were inclined to be unstable at room temperature because of signifi cant decreases in their E ad . [ 22 ] Although part of Au concentration was ignored in DFT calculation, we aimed to establish the basic principle by using a simple model. The infl uence of Au concentration on the mechanisms underlying sensing properties was further investigated.
H 2 S Adsorption Cases : In the Au-modifi ed GrF-H 2 S system, H 2 S is adsorbed parallel to the surface with S atoms closest to Au. The geometric structure of H 2 S slightly changes as the H S H bond angle (91.181°) expands to 91.719° and the H S bond angle (1.356°) extends to 1.360 and 1.362 Å. H 2 S molecules also prefer a closer confi guration on the Au-modifi ed GrF plane than that on the pristine graphene, as indicated by the shorter distance between Au-modifi ed graphene and S (2.401 Å) than that between pristine graphene and H 2 S (3.108 Å). Hence, H 2 S molecules are chemisorbed on Au-modifi ed GrF as evidenced by the high adsorption energy (−0.9 eV) and electron transfer (0.348 e ) from H 2 S molecules to Au-modifi ed GrF. This electron transfer leads to electron enrichment on the Au-modifi ed GrF surface. In graphene-H 2 S adsorption case, the obtained electron transfer value (0.011 e ) indicates the presence of few electron interactions. Nevertheless, the adsorption energy of graphene-H 2 S (−0.617 eV) presents a relatively strong intermediate between physisorption and chemisorption, [ 37,38 ] which indicates the prevalence of van der Waals. By comparing the studies on Au-modifi ed GrF-H 2 S and pure Au-modifi ed GrF, we observed an evident difference in DOS near the Fermi level, indicating a decrease in the surrounding DOS. For Au-modifi ed GrF, the Fermi level shifts upward by www.MaterialsViews.com www.advancedscience.com   We found that the two H 2 S molecules exhibiting a similar confi guration are the stable confi guration on Au-modifi ed GrF; in this confi guration, each S atom moves closer to Au. The binding geometry is similar to that of the Au-modifi ed GrF-H 2 S system. The adsorption energy (−1.718 eV) is two times higher than that of Au-modifi ed GrF-H 2 S. Although ≈0.3 electrons per H 2 S molecule transfer to the Au-modifi ed GrF complex in the Au-modifi ed GrF-2H 2 S system, the system still exhibits an n-type sensing nature. The n-type effect introduced by the two H 2 S cases could be attributed to the upward shift of the Fermi level by 0.077 eV. This observation is also consistent with the higher adsorption energy of 2H 2 S on Au-modifi ed GrF than 1H 2 S. In fact, our separate PDOS calculation confi rms that Au prefers to hybridize S atoms in the H 2 S valence band, which contributes to the strong interaction between Au and adsorbed H 2 S. A comparison study using Figure 9 a suggests that 2H 2 S adsorption remains magnetic in the semiconductor system with a magnetic moment of 0.823 µ B .

SOF 2 Adsorption Cases :
In the Au-modifi ed GrF-SOF 2 case, SOF 2 prefers the confi guration in which SOF 2 is located above Au-modifi ed GrF; in this confi guration, S and F atoms bond to Au as indicated by the distance between S and Au (2.508 Å) and F and Au (2.039 Å). The F S bond extends longer (2.894 Å) than that in the gas phase (1.668 Å) because of the charge transfer, indicating SOF 2 rupture. The results of Mulliken population analysis confi rm the occurrence of a signifi cant electron transfer (0.624 e ) from Au-modifi ed GrF to SOF 2 ; this phenomenon features a p-type process with SOF 2 as an acceptor. The adsorption energy (−0.961 eV) is similar to that in the Au-modifi ed GrF-H 2 S case. Our DOS calculation results further reveal that the spin-up and spin-down channels shift downward by 1.05 eV, indicating the strong p-type effect of SOF 2 adsorption. The adsorbed SOF 2 converts the system of Au-modifi ed GrF from magnetic metal into a nonmagnetic system with magnetic moment quenching. This observation differs from that in the H 2 S cases, which maintains the magnetic property.
When two SOF 2 molecules move closer to Au-modifi ed GrF, the most stable confi guration is where one SOF 2 prefers the active state and approaches the Au-modifi ed GrF plane and the other SOF 2 moves away from Au-modifi ed GrF (Figure 8 d).
The inactive SOF 2 does not effectively participate in the interaction process as also confi rmed by the results of Mulliken population analysis. Approximately 0.658 electrons transfer to the active SOF 2 , whereas 0.031 electrons transfer to the inactive site. Minimal change is introduced to the DOS around the Fermi level (the overlapping solid black and red curves) because of the inactive SOF 2 . In the H 2 S case, this observation differs from that in 2H 2 S adsorption, in which one H 2 S exhibits equivalent effect to the other H 2 S. The adsorption energy of the Au-modifi ed GrF-2SOF 2 system (−1.334 eV) is higher than that in Au-modifi ed GrF-SOF 2 (0.961 eV). The small amounts of additional energy can be ascribed to the van der Waals interaction, which is supplemented by electrostatic effect caused by chemically inactive SOF 2 molecules. The results of DOS analysis further indicate that the Fermi level shifts downward by 0.966 eV compared with that of Au-modifi ed GrF; this phenomenon demonstrates a p-type effect. Moreover, Au-modifi ed GrF-2SOF 2 case maintains its nonmagnetic property similar to the Au-modifi ed GrF-SOF 2 system. D denotes the shortest distance between the molecule and the oriented substrate, where d 1 and d 2 represent former and latter molecules, respectively; b) E ad describes the surface interaction Qt represents the net charge transformation, which indicates the redistribution charges in the adsorption system, where Qt 1 and Qt 2 refer to former and latter molecules, respectively.   Figure 4 a,c presents the responses of H 2 S, which is significantly sensitive to rGO and Au-modifi ed GrF but exhibits opposite effect compared with each other. As confi rmed in our DFT calculations, the pronounced chemisorption effect contributes to the H 2 S responses on Au-modifi ed GrF. However, the results also prove that the adsorption interaction with pure graphene is typical physisorption, which contradicts the experimental fi ndings. The factors affecting this discrepancy remain unclear, but we postulate that it could be related to the method used to manufacture pure graphene fi lms. The pure graphene fi lms used in this study were prepared through chemical reduction, which could inevitably harbors heteroatoms, such as N and O. The combined XPS analysis results and Raman spectra reveal the presence of nonoxygenated ring, C N bonds, hydroxyl C, and carbonyl, which may affect the sensing interaction. This phenomenon must be further investigated through theoretical and experimental studies.

Discussion of Sensing Performances Based on DFT Calculations
For SOF 2 , sensing experiments were conducted on pure graphene and Au-modifi ed GrF (Figure 4 b,d) to investigate the infl uence of decorated Au on gas sensing. The sensing performance of SOF 2 on pure graphene is not signifi cant as it only results in 0.7% decrease in resistance. This response is significantly lower than that of Au-modifi ed GrF, which decreases the resistance by a maximum of 23.83%. In DFT calculations, the interaction between SOF 2 and Au-modifi ed GrF is chemisorption as evidenced by the charge transfer from Au-modifi ed GrF to SOF 2 (0.624 e in the Au-modifi ed GrF-SOF 2 system). This fi nding could also be attributed to the higher chemical potentials of Au-modifi ed GrF than the lowest unoccupied molecular orbital of SOF 2 . Nevertheless, as SOF 2 is physisorbed on the pure graphene surface, no charge transfer (Table 1 ) could occur. This physisorption phenomenon, in which only the van der Waals effect dominates, could contribute to the unclear responses of SOF 2 on pure graphene. In addition, the calculated adsorption energy (−0.267 eV) is not signifi cant in the graphene-SOF 2 system compared with that in the Au-modifi ed GrF-2SOF 2 system (−1.334 eV). Therefore, based on our experiment and calculation results, we successfully established an effective approach to manufacture SOF 2 sensors. Figure 4 c,d presents the comparison between the performance of a resistive sensor with H 2 S and the SOF 2 sensing results obtained using Au-modifi ed GrF. Au-modifi ed graphene exhibits a 28.15% increase in resistance for 100 ppm H 2 S and 23.83% decrease in resistance after 12 min of exposure to 100 ppm SOF 2 . The fabricated Au-modifi ed graphene sensor demonstrates a reverse resistance change because of gas species. The n-type and p-type behavior determined through the altered direction of the charge carrier plays a dominant role in the conduction response. [ 39,40 ] Different conductivity types of graphene-based sensors were reported in previous experimental studies, but no specifi c trend was observed. [ 38 ] Based on our DFT calculations, we infer that H 2 S exhibits an n-type behavior with electron depletion on itself. An increase in resistance was further observed in the sensing experiment, indicating the n-type sensing nature of the Au-modifi ed graphene layer. In DFT calculations, SOF 2 presents a p-type behavior with electron withdrawing capability, in which electrons can be removed from the adsorbent surface. This phenomenon results in decreased resistance, thereby confi rming that Au-modifi ed GrF displays a p-type sensing behavior. The corresponding correlation between sensing performance and nature of carriers for Au-modifi ed GrF was obtained under our experiment conditions and illustrated in Figure 10 .

Conclusions
Detection of H 2 S and SOF 2 , which are two types of SF 6 decomposed gases, has gained importance because they are signifi cantly related to insulation faults in power equipment. As current detection methods suffer from online monitoring shortage, electrochemistry sensors could be a promising technology for online detection.
Pure graphene fi lms and graphene fi lms incorporated with AuNPs were fabricated as gas sensors through deposition-precipitation method. Sensing experiments conducted at room temperature demonstrated that Au-modifi ed GrF is a promising material for developing H 2 S and SOF 2 selective sensors because it yields opposite responses for these gases. The interaction between the Au-modifi ed GrF surface and these gases was simulated through fi rst-principles calculations. The results reveal that the opposite responses observed in experiments could be due to the charge-transfer differences related to the interfacial interaction within gases and Au-modifi ed GrF systems. Calculation and experimental fi ndings consistently show n-type H 2 S functions as an electron donor and p-type SOF 2 as an electron acceptor.
The results of sensing experiments further show the strong response of the Au-modifi ed GrF sensor for SOF 2 . This fi nding confi rms the robustness and the ability to adsorb SOF 2 of the sensor compared with the poor performance on pure graphene fi lms. According to the results of DFT calculations, the typical chemisorption effect between decorated Au and SOF 2 could be the main reason for this observation and the adsorption of the pristine graphene corresponds to physisorption dominated by van der Waals.
Our calculation results further show that the H 2 S chemisorption behavior endows Au-modifi ed GrF with a magnetic system, whereas SOF 2 adsorption converts the system into a nonmagnetic one. This result may be utilized in designing novel magnetic sensing or switching devices, but requires further investigation through experimental methods.

Experimental Section
Experimental Details : Carboxylic functionalized graphene and rGO were purchased from XF NANO, Inc. (Nanjing, China). Dimethylformamide (DMF), acetone, and absolute ethyl alcohol were purchased from Huihuang Chemical Reagent Co., Ltd (Chongqing, China). NaBH 4 and HAuCl 4 were purchased from Aladdin Chemistry Co., Ltd. All chemicals in this work were of analytical grade and used without further purifi cation, and double-distilled water was used throughout the experiments.
Au-modifi ed GrF was synthesized through the following chemical reduction procedures. [ 29 ] Carboxyl functionalized graphene (1 mg) was dispersed in HAuCl 4 (5 mL, 1 × 10 −3 M ) solution as a precursor under constant sonication for 40 min to reach a stable colloidal state. Briefl y, NaBH 4 (5 mL, 40 × 10 −3 M ) solution was added dropwise to the colloid solution and the solution was vigorously stirred for 30 min. The solution was then subjected to centrifugal separation, and products were collected and washed with distilled water several times. The washed products were dried in a vacuum oven at 60 °C for 12 h to obtain Au-modifi ed GrF. Au-modifi ed GrF (5 mg) powder was ultrasonically dispersed in DMF solution (200 mL) for 30 min to achieve good dispersibility.
Sensors were fabricated using Au-modifi ed GrF through LBL deposition. [ 41 ] Responses were measured by monitoring surface resistance changes in a pressure-tight system. For the planar sensor depicted in Figure 11 , copper electrodes were inter-digitally etched on epoxy resin with ≈30 µm thick foil and 0.2 mm electrode gap. The prepared Au-modifi ed GrF solution was continuously dispersed on the substrate and then dried until the desired initial surface resistance values, which translate to the formation of uniform, dense, and smooth deposited fi lms, were achieved. The fabricated Au-modifi ed GrF sensor was used for detection. A sensing element was placed in an autonomous sealed chamber connected to an electrochemical analyzer. As the initial vacuum resistance stability is a prerequisite for gas detection experiment, responses were measured at room temperature and repeated several times to obtain reliable results.
X-ray diffraction (XRD) patterns were recorded on a Rigaku D/Max-1200X using Cu Kα radiation ( λ = 0.15418 nm) at 40 kV and 30 mA. Wide-angle XRD patterns were collected at a scanning speed of 10° per minute over the 2 θ range of 5° to 100°. Raman spectra were determined using a Renishaw inVia Raman microscope confi gured with a 532 nm wavelength laser and full-range grating. Scanning electron microscopy (SEM) images were recorded with a Zeiss Auriga Focus Ion Beam/ Field-Emission SEM dual-cross system operated at 30 kV and 2 nA. The samples were directly exfoliated from the planar sensor. High-resolution transmission electron microscopy (HRTEM) combined with energy dispersive spectroscopy (EDS) images was recorded with an FEI Tecnai G2 F20 S-TWIN operated at 200 kV. X-ray photoelectron spectroscopy (XPS) was performed on a Thermo ESCALAB 250Xi spectrometer with Al Kα (1486.6 eV) radiation. All measurements were conducted under ambient condition.
Theoretical Methods : To determine the role of van der Waals, we performed theoretical calculations by using dispersion-corrected DFT (DFT-D) provided by the DMol 3 code. The exchange and correlation energies included were identifi ed through a generalized gradient approximation in revised Perdew-Burke-Ernzerhof (PBE) format. [42][43][44] Core treatment, in which core electrons are replaced by a single effective potential, was conducted with DFT semi-core pseudopods to evaluate relativistic effects. To simulate a 2D graphene sheet, we modeled a supercell comprising 6 × 6 units (consisting of 72 atoms) in the XY plane. A vacuum region of 20 Å in the Z direction was also adopted to prevent the interaction between adjacent layers. The k -point mesh was increased to 6 × 6 × 1 for the Brillouin-zone integration to obtain accurate results. All calculations were performed in a spin-unrestricted manner. The convergence tolerance of energy was set at 1.0 × 10 −6 Ha in geometry optimization.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.