Adsorption Behavior of Toxic Carbon Dichalcogenides (CX2; X = O, S, or Se) on β12 Borophene and Pristine Graphene Sheets: A DFT Study

The adsorption of toxic carbon dichalcogenides (CX2; X = O, S, or Se) on β12 borophene (β12) and pristine graphene (GN) sheets was comparatively investigated. Vertical and parallel configurations of CX2⋯β12/GN complexes were studied herein via density functional theory (DFT) calculations. Energetic quantities confirmed that the adsorption process in the case of the parallel configuration was more desirable than that in the vertical analog and showed values up to −10.96 kcal/mol. The strength of the CX2⋯β12/GN complexes decreased in the order CSe2 > CS2 > CO2, indicating that β12 and GN sheets showed significant selectivity for the CSe2 molecule with superb potentiality for β12 sheets. Bader charge transfer analysis revealed that the CO2⋯β12/GN complexes in the parallel configuration had the maximum negative charge transfer values, up to −0.0304 e, outlining the electron-donating character of CO2. The CS2 and CSe2 molecules frequently exhibited dual behavior as electron donors in the vertical configuration and acceptors in the parallel one. Band structure results addressed some differences observed for the electronic structures of the pure β12 and GN sheets after the adsorption process, especially in the parallel configuration compared with the vertical one. According to the results of the density of states, new peaks were observed after adsorbing CX2 molecules on the studied 2D sheets. These results form a fundamental basis for future studies pertaining to applications of β12 and GN sheets for detecting toxic carbon dichalcogenides.


Introduction
Recently, the emission of greenhouse gases and toxic molecules into the environment has gathered unprecedented attention from the scholarly community. These molecules might cause severe heart and lung conditions and contribute to the greenhouse impact and the destruction of the ozone layer [1][2][3][4]. Among these harmful molecules, carbon dioxide (CO 2 ) is a crucial gas because of its high concentration in the atmosphere as a result of the combustion of petroleum, coal, and other fossil fuels [5]. Carbon disulfide (CS 2 ) is another toxic gas that adversely affects human health. It was documented that exposure to CS 2 gas leads to many problems, including paucity of vitamin B 6 and an increase in heart attack risk [6,7]. In the same vein, the carbon diselenide (CSe 2 ) molecule is well recognized as a highly toxic molecule with unpleasant properties [8,9]. Because of its high toxicity, the CSe 2 molecule must be handled with utmost care [10]. Many researchers have accordingly focused their efforts on developing various effective sensors for monitoring such toxic molecules.

Computational Methods
Geometric optimization and energy calculations of the CX2•••β12/GN complexes (CX2; X = O, S, or Se) were carried out in accordance with density functional theory (DFT) [46,47] via the Quantum ESPRESSO 6.4.1 package [48,49]. To describe the electronic interactions, the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional of the Generalized Gradient Approximation (GGA) was applied [50]. Ultrasoft pseudopotential was adopted for describing the interaction of valence electrons and the atomic cores [51]. The Grimme (DFT-D2) algorithm [52] was applied to correct the dispersion energy of the van der Waals interactions. In all the executed computations, the energy cutoff was set to 50 Ry, and the charge density cutoff was 500 Ry. The structures were optimized at energy and force convergence of 10 −5 eV and 10 −4 eV/Å, respectively. To sample and analyze the first Brillouin Figure 1. CSe 2 · · · GN complex as an illustration for the CX 2 · · · 2D sheet complexes (where CX 2 = CO 2 , CS 2 , or CSe 2 and the 2D sheet = β 12 or GN) within vertical and parallel configurations from the side and top representations.

Computational Methods
Geometric optimization and energy calculations of the CX 2 · · · β 12 /GN complexes (CX 2 ; X = O, S, or Se) were carried out in accordance with density functional theory (DFT) [46,47] via the Quantum ESPRESSO 6.4.1 package [48,49]. To describe the electronic interactions, the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional of the Generalized Gradient Approximation (GGA) was applied [50]. Ultrasoft pseudopotential was adopted for describing the interaction of valence electrons and the atomic cores [51]. The Grimme (DFT-D2) algorithm [52] was applied to correct the dispersion energy of the van der Waals interactions. In all the executed computations, the energy cutoff was set to 50 Ry, and the charge density cutoff was 500 Ry. The structures were optimized at energy and force convergence of 10 −5 eV and 10 −4 eV/Å, respectively. To sample and analyze the first Brillouin zone (BZ), Monkhorst-Pack grids were utilized with 6 × 6 × 1 k-points for geometric optimization and adsorption energy calculations. For the electronic structure calculations, 12 × 12 × 1 k-points were utilized. The Marzari-Vanderbilt smearing technique was performed to speed up the convergence [53]. To avoid interactions between neighboring atoms in the z-direction of the β 12 and GN sheets, a vacuum layer with 20 Å was used. Supercells of 3 × 4 × 1 and 6 × 5 × 1 were modeled to calculate the adsorption energy of β 12 -and GN-containing complexes, respectively, containing 60 atoms in both sheets. For the CX 2 · · · β 12 /GN complexes, both vertical and parallel configurations were considered, as depicted in Figure 1. The adsorption energy (E ads ) of all the studied complexes was computed using Equation (1): where E CX 2 ···2D sheet , E CX 2 , and E 2D sheet represent the energies of complexes, adsorbed CX 2 molecules, and 2D sheets, respectively. The charge density difference (∆ρ) calculations were estimated using Equation (2): where ρ total , ρ CX 2 , and ρ 2D sheet are the charge densities of complexes, adsorbed CX 2 molecules, and 2D sheets, respectively. The Visualization for Electronic and Structural Analysis (VESTA) package was used to generate the ∆ρ maps [54]. Analysis of the Bader charge [55] was utilized to determine the charge transfer (Q t ) to or from the 2D sheets according to Equation (3): where Q combined 2D sheet indicates the total charge of the 2D sheets after the adsorption process, and Q isolated 2D sheet represents the total charge of the 2D sheets before the adsorption process. To elucidate the electronic properties, the electronic band structure and the total and projected density of states (TDOS and PDOS) calculations were determined for the inspected 2D sheets. For the band structure calculations, high-symmetry points-namely, Г (0.0, 0.0, 0.0), Y (0.5, 0.0, 0.0), S (0.5, 0.5, 0.0), and X (0.0, 0.5, 0.0)-were selected, and 50 points were taken between each high-symmetry point.

Geometric Structures
The structures of the β 12 and GN sheets were fully relaxed prior to the adsorption of the CX 2 molecules on their surfaces, and the obtained structures are given in Figure 2.
After the relaxation of the β 12 and GN sheets, the optimized lattice parameters of their primitive cells were a = 5.06 Å and b = 2.93 Å for β 12 sheets (Figure 2), while a and b had a similar value of 2.47 Å in the case of GN sheets. The obtained findings were compatible with experimental and theoretical evidence [33,37,56,57]. primitive cells were a = 5.06 Å and b = 2.93 Å for β12 sheets (Figure 2), while a and b had a similar value of 2.47 Å in the case of GN sheets. The obtained findings were compatible with experimental and theoretical evidence [33,37,56,57].
According to the equilibrium structures displayed in Figure 2, four probable adsorption sites were identified in the β12 sheet-namely, top (T), hollow (H), and two bridge (Br1 and Br2) sites. For GN sheets, the top (T), bridge (Br), and hollow (H) sites were located above the carbon atom, C-C bond, and center of the hexagonal ring, respectively.  According to the equilibrium structures displayed in Figure 2, four probable adsorption sites were identified in the β 12 sheet-namely, top (T), hollow (H), and two bridge (Br1 and Br2) sites. For GN sheets, the top (T), bridge (Br), and hollow (H) sites were located above the carbon atom, C-C bond, and center of the hexagonal ring, respectively.

Adsorption Energy Calculations
The adsorption process within the vertical and parallel configurations of the CX 2 · · · β 12 /GN complexes (where X = O, S, or Se) was unveiled at variant sites ( Figure 2). The CX 2 · · · β 12 /GN complexes were first relaxed, and the obtained structures are given in Figure S1. The adsorption energies (E ads ) for all relaxed complexes were then assessed and are gathered in Table 1. The most desirable relaxed structures of the CX 2 · · · β 12 /GN complexes are provided in Figure 3.
Apparently, the relaxed structures of the CX 2 · · · β 12 /GN complexes showed the ability of the β 12 and GN sheets to adsorb toxic CX 2 molecules ( Figure S1), resulting in significant negative adsorption energies (Table 1). From Figure 3 and Table 1, the CX 2 β 12 and GN equilibrium distances were found to be in the ranges 3.04-3.49 and 3.03-3.55 Å, respectively.
For adsorption of the CX 2 molecules on the β 12 sheet in the vertical configuration, the CS 2 · · · and CSe 2 · · · H@β 12 complexes exhibited the most significant negative adsorption energies with values of −4.25 and −6.73 kcal/mol, respectively. For the CO 2 · · · β 12 complexes, the most favorable adsorption energy value of −2.13 kcal/mol was obtained at the Br2 adsorption site of the β 12 sheet (Table 1). In the parallel configuration, it was observed that the most favorable adsorption site on the β 12 sheet for adsorbing all the CX 2 molecules was the H@β 12 site ( Figure 3). Notably, the CSe 2 · · · H@β 12 complex had the largest negative adsorption energy, followed by the CS 2 · · · H@β 12 and CO 2 · · · H@β 12 complexes, with values of −10.96, −6.53, and −4.42 kcal/mol, respectively (Table 1).
Similar to the CX 2 · · · β 12 complexes, the most considerable negative adsorption energies were generally observed in the case of CSe 2 · · · GN complexes. In the case of the vertical configuration, the E ads values of the studied complexes were noticed to decrease in the order CX 2 · · · H@GN > · · · Br@GN > · · · T@GN, showing the favorability of the H@GN site. Numerically, the E ads values of CS 2 · · · H@GN, CS 2 · · · Br@GN, and CS 2 · · · T@GN were found to be -3.28, -3.14, and -3.13 kcal/mol, respectively. For the parallel configuration, the favorability of the CX 2 · · · GN complexes increased in the order of CX 2 · · · H@GN < CX 2 · · · T@GN < CX 2 · · · Br@GN. It was also observed that the CSe 2 · · · Br@GN complex with an equilibrium distance of 3.47 Å had the most significant E ads , with a value of −6.91 kcal/mol (Table 1).
Ultimately, all the studied carbon dichalcogenides (CX 2 ; X = O, S, or Se) showed negative values of E ads , indicating greater preferentiality of the parallel configuration of the CX 2 · · · β 12 /GN complexes compared with the vertical one. Table 1. Adsorption energies (E ads , kcal/mol) and equilibrium distances (d, Å) for the vertical and parallel configurations of the CX 2 · · · β 12 /GN complexes (where X = O, S, or Se), in addition to the charge transfer differences (Q t , e) for the investigated 2D sheets after adsorbing the CX 2 molecules.

2D Sheet
Adsorption Site a Carbon Dichalcogenides (CX 2 )  Figure 2. b Q t was estimated using Equation (3). c Figure S1 displays all relaxed structures of the CX 2 · · · β 12 /GN complexes. d No favorable adsorption was observed.  Apparently, the relaxed structures of the CX2•••β12/GN complexes showed the ability of the β12 and GN sheets to adsorb toxic CX2 molecules ( Figure S1), resulting in significant

Band Structure Calculations
To trace the influence of the adsorbed CO 2 , CS 2 , and CSe 2 molecules on the electronic features of the β 12 and GN sheets, electronic band structure analysis was performed for the pure and combined 2D sheets. The PBE functional was used to calculate the band structure on the high-symmetry path of the BZ. The Г-Y-S-X-Г and Y-S-X-Г-Y paths were selected for band structures of the β 12 and GN sheets, respectively. Figure S2 illustrates the band structures of the pure β 12 and GN sheets. The electronic band structure calculations of the adsorbed CX 2 molecules at the most favorable adsorption sites on the β 12 and GN sheets were plotted and are shown in Figure 4.
According to Figure S2, the electronic band structure of the pure β 12 surface showed a metallic character that was attributed to the presence of many bands that crossed the Fermi level along the high-symmetry path. In comparison, the Dirac point on the pure GN surface between points X and Г indicated that the GN exhibited a semiconductor amplitude that was consistent with that in previous work [17]. Figure 4 shows that the electronic properties of 2D sheets were marginally affected by the adsorption of the CO 2 molecule in both studied configurations on the surfaces of the β 12 and GN sheets (see Figure S2). Such an observation outlines that β 12 and GN cannot be highly effective CO 2 sensors, which agrees with evidence from previous studies [44,58]. In contrast, the adsorption of the CS 2 and CSe 2 molecules in vertical and parallel configurations on the β 12 and GN sheets resulted in the appearance of many new bands in valence and conduction regions, as illustrated in Figure 4. The band structure plots showed that the bands of β 12 moved far away from each other after adsorbing CS 2 and CSe 2 molecules, confirming the strong adsorption of these molecules on the β 12 sheet. In detail, the resultant band structures after the adsorption of CS 2 molecules on β 12 showed extra conduction bands in the vertical and parallel configurations at around 2.3 and 1.8 eV, respectively. Besides this, new valence bands were noticed at -1.8 and -2.0 in the vertical and parallel configurations, respectively. For CS 2 · · · GN complexes, additional conduction and valence bands in both configurations were found at 1.5 and -2.5 eV, respectively. The band structures of the CSe 2 · · · β 12 complexes strongly affirmed the more evident impact of the adsorbed CSe 2 molecules on the electronic characteristics of the β 12  Conspicuously, the results regarding the band structure demonstrated that the CSe2•••β12 complexes were more favorable than the CS2•••β12 complexes, as revealed by the bands that moved toward the Fermi level. To sum up, the electronic characteristics of the studied 2D sheets after adsorbing CX2 molecules were improved in the order CO2•••β12/GN < CS2•••β12/GN < CSe2•••β12/GN, which is consistent with the results regarding the adsorption energies ( Table 1). The appearance of new valence and conduction bands indicates the interaction of the CX2 molecules with the investigated 2D sheets. In addition, the presence of the Dirac point was not affected by the adsorption of CX2 molecules on the GN sheet, confirming the physical adsorption of CX2 on the GN sheet.

Charge Transfer Calculations
Bader charge analysis is considered an informative method for deducing the charge transfer throughout the adsorption process [55,59]. Thus, the charge transfer (Qt) was calculated for the vertical and parallel configurations of the CX2•••β12/GN complexes at variant sites, and the results are given in Table 1. Negative and positive signs of the Qt values indicate the transference of charge from the CX2 molecules to the 2D sheet and from the 2D sheet to the adsorbed CX2 molecules, respectively. Conspicuously, the results regarding the band structure demonstrated that the CSe 2 · · · β 12 complexes were more favorable than the CS 2 · · · β 12 complexes, as revealed by the bands that moved toward the Fermi level. To sum up, the electronic characteristics of the studied 2D sheets after adsorbing CX 2 molecules were improved in the order CO 2 · · · β 12 /GN < CS 2 · · · β 12 /GN < CSe 2 · · · β 12 /GN, which is consistent with the results regarding the adsorption energies ( Table 1). The appearance of new valence and conduction bands indicates the interaction of the CX 2 molecules with the investigated 2D sheets. In addition, the presence of the Dirac point was not affected by the adsorption of CX 2 molecules on the GN sheet, confirming the physical adsorption of CX 2 on the GN sheet.

Charge Transfer Calculations
Bader charge analysis is considered an informative method for deducing the charge transfer throughout the adsorption process [55,59]. Thus, the charge transfer (Q t ) was calculated for the vertical and parallel configurations of the CX 2 · · · β 12 /GN complexes at variant sites, and the results are given in Table 1. Negative and positive signs of the Q t values indicate the transference of charge from the CX 2 molecules to the 2D sheet and from the 2D sheet to the adsorbed CX 2 molecules, respectively.
According to the Q t values recorded in Table 1, adsorption of the CX 2 molecules in the vertical configuration at different adsorption sites on the β 12 sheet was noticed with negative values of Q t . For instance, the CO 2 · · · , CS 2 · · · , and CSe 2 · · · β 12 complexes at the T site exhibited Q t values of -0.0117, -0.0219, and -0.0127 e, respectively. These negative values demonstrate that the β 12 sheet behaved as an electron acceptor.
The adsorption of the CO 2 molecule on the β 12 sheet, in the case of the parallel configuration, had negative values of Q t , demonstrating the electron donor character of the CO 2 molecule. Moreover, the adsorption of the CS 2 and CSe 2 molecules on the β 12 sheet showed positive Q t values, proposing that the CS 2 and CSe 2 molecules acted as electron acceptors. Numerically, Q t values of 0.0044 and 0.0513 e were shifted from the β 12 sheet toward the CS 2 and CSe 2 molecules at the T@β 12 site, respectively. In line with the adsorption energy results, the CSe 2 · · · H@β 12 complex, the most favorable adsorption system in the parallel configuration, was found to have the largest positive Q t value of 0.0724 e.
For the vertical configuration of the CX 2 · · · GN complexes, the H@GN site showed the highest negative Q t values, consistent with its energetic preferentiality. Notably, all the CX 2 · · · GN complexes showed negative values of Q t , illustrating the potent ability of the GN sheet to accept electrons from the CX 2 molecules.
Negative Q t values were observed for the parallel configuration of the CO 2 · · · T/H/Br@GN complexes, while both negative and positive Q t values were found at the studied adsorption sites in the case of the CS 2 · · · GN complexes. For adsorption of the CSe 2 molecule, it can be seen that the charge was transferred from the GN sheet to the adsorbed CSe 2 , as indicated by the positive Q t values shown in Table 1.
At the most favorable energetic sites, the charge density difference (∆ρ) maps of the CX 2 · · · β 12 /GN complexes were plotted and are depicted in Figure 5.
As seen in Figure 5, the ∆ρ maps of the CX 2 · · · β 12 complexes in the vertical configuration showed that the CX 2 molecules acted as electron donors, as demonstrated by the negative Q t values (Table 1). In the case of the parallel configuration, the charges were shifted from the CO 2 to the β 12 sheet, as seen from the charge accumulation region existing below the CO 2 (cyan region) and corroborated by the negative Q t value in Table 1 (−0.0271 e). A depletion region (i.e., yellow color) was clearly observed above the β 12 sheet in the case of the adsorption of CS 2 and CSe 2 molecules in the parallel configuration, which was consistent with the positive Q t values stated in Table 1. This observation emphasized that CS 2 and CSe 2 molecules have the potential to draw charge from the β 12 sheet.
For the vertical configuration of the CX 2 · · · GN complexes, the existence of regions with accumulated charge ensures the adsorption of CX 2 molecules on the β 12 and GN sheets. The accumulated charge above the GN sheet within the CO 2 · · · and CS 2 · · · GN complexes in the parallel configuration indicated that electrons were transferred from the CO 2 and CS 2 molecules to the GN sheet ( Figure 5). In comparison, the depletion region above the GN sheet in the case of adsorption of the CSe 2 molecule revealed the ability of the molecule to attract charge from the sheet.
To recapitulate, the Bader charge findings revealed that the charge was transferred from the CX 2 molecules to the studied 2D sheets in the vertical configuration, indicating the electron-donating character of the CX 2 molecules. The CO 2 · · · β 12 /GN complexes in the case of parallel configuration had the largest negative Q t values, followed by CS 2 · · · β 12 /GN, then CSe 2 · · · β 12 /GN complexes. The small Q t values confirmed physical adsorption between the CX 2 molecules and the investigated 2D sheets. Consistent with the literature, the electronic properties of the β 12 and GN sheets were changed by transferring electronic charge to or from the adsorbed molecules, indicating their potential for use as sensors [60][61][62]. The isosurface values were determined in (e/Å 3 ) for each complex. Dark green, brown, red, yellow, and pale green balls refer to boron, carbon, oxygen, sulfur, and selenium atoms, respectively.
As seen in Figure 5, the ∆ρ maps of the CX2•••β12 complexes in the vertical configuration showed that the CX2 molecules acted as electron donors, as demonstrated by the negative Qt values (Table 1). In the case of the parallel configuration, the charges were shifted from the CO2 to the β12 sheet, as seen from the charge accumulation region existing below the CO2 (cyan region) and corroborated by the negative Qt value in Table 1 (−0.0271 e). A depletion region (i.e., yellow color) was clearly observed above the β12 sheet in the case of the adsorption of CS2 and CSe2 molecules in the parallel configuration, which was consistent with the positive Qt values stated in Table 1. This observation emphasized that CS2 and CSe2 molecules have the potential to draw charge from the β12 sheet. Dark green, brown, red, yellow, and pale green balls refer to boron, carbon, oxygen, sulfur, and selenium atoms, respectively.

Density of State Calculations
For pure and combined 2D sheets, density of state (DOS) analysis was carried out in terms of total and projected DOS (TDOS and PDOS). The TDOS and PDOS of the pure β 12 and GN surfaces are illustrated in Figure S3.
From the data in Figure S3, the TDOS peaks of the pure β 12 sheet at the Fermi level had high DOS, demonstrating that the β 12 sheet had a metallic property. In the case of the GN surface, the TDOS peaks reached zero at the Fermi level, showing the presence of the Dirac point on the pure GN surface. The DOS results confirmed the band structures in Figure S2. For β 12 and GN surfaces before adsorbing CX 2 molecules, the major contributions to the DOS were ascribed to the PDOS of B p and C p , respectively. Figure 6 shows the TDOS and PDOS for the β 12 and GN sheets within the vertical and parallel configurations of the CX 2 · · · β 12 /GN complexes (where X = O, S, or Se) at the most favorable energetic sites. For adsorption of the CO 2 molecule on the β 12 sheet in both configurations, a significant hybridization between the PDOS of O p and B p peaks was observed in the valence region between −3.9 and −4.5 eV. In addition, the TDOS and PDOS peaks of adsorption of the CO 2 molecule on the GN sheet in both configurations demonstrated the occurrence of a weak physical adsorption process. Hence, the appearance of the PDOS of O p peaks within the CO 2 · · · GN complexes in both configurations was noticed in the valence and conduction regions ranging from -4.5 to -5.6 eV and from 3.5 to 4.0 eV, respectively. Overall, the DOS results outlined that the electronic properties of the β12 and GN sheets were changed after adsorbing the CX2 molecules in vertical and parallel configurations. The appearance of the new DOS peaks indicated the occurrence of adsorption of the CX2 molecules on the investigated 2D sheets. Conspicuously, the PDOS of S p was the major contributor to the adsorption within both modeled configurations of the CS 2 · · · β 12 /GN complexes. For both configurations of CS 2 · · · β 12 and · · · GN complexes, the appearance of the PDOS of S p peaks was observed in the valence region with values from −1.5 to −2.5 eV and from −2.0 to −3.0 eV, respectively.
For both configurations of CSe 2 · · · β 12 /GN complexes, the PDOS of Se p peaks appeared in the valence region in the range from −1.0 to −2.2 eV within the CSe 2 · · · β 12 complexes and from −1.5 to −2.3 eV within the CSe 2 · · · GN complexes.
Overall, the DOS results outlined that the electronic properties of the β 12 and GN sheets were changed after adsorbing the CX 2 molecules in vertical and parallel configurations. The appearance of the new DOS peaks indicated the occurrence of adsorption of the CX 2 molecules on the investigated 2D sheets.

Conclusions
The adsorption of toxic carbon dichalcogenides (CX 2 ; X = O, S, or Se) on β 12 and GN sheets was assessed via DFT calculations. After geometric relaxation, adsorption energy calculations and electronic analyses were carried out for vertical and parallel configurations of all CX 2 · · · β 12 /GN complexes. The favorability of CX 2 · · · β 12 /GN complexes was more obvious in the parallel configuration compared with the vertical one. The CSe 2 · · · H@β 12 complex in the parallel configuration was the most promising complex, with an adsorption energy value of -10.96 kcal/mol. The electronic properties of the β 12 and GN surfaces were notably changed after the adsorption of CS 2 and CSe 2 molecules. In comparison, the electronic characteristics of the β 12 and GN surfaces were slightly changed after adsorbing the CO 2 molecule. Based on Bader charge analysis, an electron-donating character was observed for all the CX 2 molecules in vertical configuration within the CX 2 · · · β 12 /GN complexes. In comparison, the CS 2 and CSe 2 molecules acted as electron acceptors within the parallel configuration of the CS 2 · · · and CSe 2 · · · β 12 /GN complexes. The results of the electronic band structure, TDOS, and PDOS demonstrated that adsorption of the CX 2 molecules on the β 12 and GN sheets boosted their electronic properties. The appearance of new bands and DOS peaks affirmed the interaction of the CX 2 molecules with the investigated 2D sheets. Based on the findings of the present study, it appears promising to use the β 12 and GN sheets as a suitable sensor for CX 2 molecules, particularly CS 2 and CSe 2 molecules.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano12193411/s1, Figure S1: Side and top representations for the relaxed structures of the vertical and parallel configurations of the CX 2 · · · β 12 /GN complexes (where X = O, S, or Se) at all the adsorption sites. Equilibrium distances (d) are given in Å. Figure S2: Band structure plots of β 12 and GN sheets along the high-symmetry points of the Brillouin zone. The Fermi energy is located at zero-energy. Figure S3: Total and projected densities of states (TDOS/PDOS) plot for the pure surfaces of β 12 and GN sheets, assuming the Fermi level as the reference level. The contributions of the p-orbital for boron (B) and carbon (C) atoms are represented by B p and C p , respectively.