Adsorption Features of Tetrahalomethanes (CX4; X = F, Cl, and Br) on β12 Borophene and Pristine Graphene Nanosheets: A Comparative DFT Study

The potentiality of the β12 borophene (β12) and pristine graphene (GN) nanosheets to adsorb tetrahalomethanes (CX4; X = F, Cl, and Br) were investigated using density functional theory (DFT) methods. To provide a thorough understanding of the adsorption process, tetrel (XC-X3∙∙∙β12/GN)- and halogen (X3C-X∙∙∙β12/GN)-oriented configurations were characterized at various adsorption sites. According to the energetic manifestations, the adsorption process of the CX4∙∙∙β12/GN complexes within the tetrel-oriented configuration led to more desirable negative adsorption energy (Eads) values than that within the halogen-oriented analogs. Numerically, Eads values of the CBr4∙∙∙Br1@β12 and T@GN complexes within tetrel-/halogen-oriented configurations were −12.33/−8.91 and −10.03/−6.00 kcal/mol, respectively. Frontier molecular orbital (FMO) results exhibited changes in the EHOMO, ELUMO, and Egap values of the pure β12 and GN nanosheets following the adsorption of CX4 molecules. Bader charge transfer findings outlined the electron-donating property for the CX4 molecules after adsorbing on the β12 and GN nanosheets within the two modeled configurations, except the adsorbed CBr4 molecule on the GN sheet within the tetrel-oriented configuration. Following the adsorption process, new bands and peaks were observed in the band structure and density of state (DOS) plots, respectively, with a larger number in the case of the tetrel-oriented configuration than in the halogen-oriented one. According to the solvent effect affirmations, adsorption energies of the CX4∙∙∙β12/GN complexes increased in the presence of a water medium. The results of this study will serve as a focal point for experimentalists to better comprehend the adsorption behavior of β12 and GN nanosheets toward small toxic molecules.


Geometric Structures
β12 and GN structures were modeled and relaxed before the adsorption process of the tetrahalomethanes. The optimized β12 and GN structures are presented in Figure 2. The obtained equilibrium la ice constants for the primitive cells of the β12 nanosheet were a = 5.06 Å and b = 2.93 Å. For the GN nanosheet, the equilibrium la ice constants were a = b = 2.47 Å. The current findings are consistent with earlier research [30,49,50]. On the β12 optimized structure, six adsorption sites were detected, comprising three top (T1, T2, and T3), two bridge (Br1 and Br2), and one hollow (H) sites ( Figure 2). Looking at the GN surface, three adsorption sites, namely the top (T), bridge (Br), and hollow (H) sites, were noticed ( Figure 2).

Results and Discussion
2.1. Geometric Structures β 12 and GN structures were modeled and relaxed before the adsorption process of the tetrahalomethanes. The optimized β 12 and GN structures are presented in Figure 2. The obtained equilibrium lattice constants for the primitive cells of the β 12 nanosheet were a = 5.06 Å and b = 2.93 Å. For the GN nanosheet, the equilibrium lattice constants were a = b = 2.47 Å. The current findings are consistent with earlier research [30,49,50]. On the β 12 optimized structure, six adsorption sites were detected, comprising three top (T1, T2, and T3), two bridge (Br1 and Br2), and one hollow (H) sites ( Figure 2). Looking at the GN surface, three adsorption sites, namely the top (T), bridge (Br), and hollow (H) sites, were noticed ( Figure 2).

Adsorption Energy Calculations
The adsorption of tetrahalomethanes CX 4 (where X = F, Cl, and Br) on the surfaces of β 12 and GN was investigated at different adsorption sites within the tetrel (XC-X 3 )-and halogen (X 3 C-X)-oriented configurations. The adsorption energies and the corresponding equilibrium distances of all relaxed CX 4 ···β 12 /GN complexes were calculated and are summarized in Table 1. Figure S1 illustrates all relaxed complexes. The relaxed CX 4 ···β 12 /GN complexes at the most energetically preferable adsorption sites are displayed in Figure 3.

Adsorption Energy Calculations
The adsorption of tetrahalomethanes CX4 (where X = F, Cl, and Br) on the surfaces of β12 and GN was investigated at different adsorption sites within the tetrel (XC-X3)-and halogen (X3C-X)-oriented configurations. The adsorption energies and the corresponding equilibrium distances of all relaxed CX4···β12/GN complexes were calculated and are summarized in Table 1. Figure S1 illustrates all relaxed complexes. The relaxed CX4···β12/GN complexes at the most energetically preferable adsorption sites are displayed in Figure 3. Table 1. Adsorption energies (Eads, kcal/mol) and equilibrium distances (d, Å) of the relaxed CX4···β12/GN complexes (where X = F, Cl, and Br) at all possible sites within the tetrel (XC-X3)-and halogen (X3C-X)-oriented configurations. Charge transfer difference (Qt, e) for the 2D nanosheets before and after the adsorption process.  Figure 2. b Q t was calculated based on Equation (3). c Desired configuration was not observed after geometry relaxation (see Figure S1).   For the adsorption process of the CX4 on the β12 nanosheet within the tetrel-oriented configuration, the BrC-Br3···β12 complexes had the most significant Eads values, followed by the ClC-Cl3···β12, then the FC-F3···β12 complexes (Table 1). Numerically, the Eads of the BrC-Br3···, ClC-Cl3···, and FC-F3···Br1@β12 complexes were −12.33, −7.74, and −4.46 kcal/mol, respectively. These findings were in accord with a prior study, indicating that the adsorption For the adsorption process of the CX 4 on the β 12 nanosheet within the tetrel-oriented configuration, the BrC-Br 3 ···β 12 complexes had the most significant E ads values, followed by the ClC-Cl 3 ···β 12 , then the FC-F 3 ···β 12 complexes (Table 1). Numerically, the E ads of the BrC-Br 3 ···, ClC-Cl 3 ···, and FC-F 3 ···Br1@β 12 complexes were −12.33, −7.74, and −4.46 kcal/mol, respectively. These findings were in accord with a prior study, indicating that the adsorption energies increased with the increasing atomic size of the halogen atom (decreasing the electronegativity of the halogen atom) [51]. It is worth noting that the most preferred complex was the BrC-Br 3 ···Br1@β 12 complex, with an E ads value of −12.33 kcal/mol and an equilibrium distance of 4.11 Å. In line with the tetrel-oriented configuration, energetic manifestations of the halogen-oriented complexes (i.e., X 3 C-X···β 12 ) showed the existence of a direct correlation between the adsorption energy and the atomic size of the halogen atom. Apparently, the H@β 12 site was the most appropriate adsorption site for adsorbing the X 3 C-X molecules in the halogen-oriented configuration. Moreover, the Br 3 C-Br···H@β 12 complex had the most prominent E ads with a value of −9.00 kcal/mol at an equilibrium distance of 2.98 Å. The efficiency of the β 12 nanosheet to adsorb the CX 4 molecules was more significant in the tetrel-oriented configuration than in the halogen-oriented one (Table 1). For instance, the E ads values of the adsorption of the CBr 4 at the Br1@β 12 site were −12.33 and −8.91 kcal/mol in the tetrel-and halogen-oriented configurations, respectively.

2D
For the adsorption of CX 4 on the GN nanosheet, all complexes showed negative E ads values, confirming the occurrence of the adsorption process. Similar to the CX 4 ···β 12 complexes, the preferentiality of the adsorption process of the CX 4 molecules on the GN nanosheet increased upon the following order X = F < Cl < Br. Obviously, the T@GN site had the highest tendency for adsorbing the studied tetrahalomethanes on the GN sheet, exhibiting significant E ads values. Numerically, the ClC-Cl 3 ··· and Cl 3 C-Cl···T@GN complexes had E ads values of −7.32 and −4.22 kcal/mol, respectively (Table 1).
For all CX 4 ···β 12 /GN complexes, the obtained E ads values ranged from −2.46 to −12.33 kcal/mol, demonstrating the occurrence of physisorption processes. The latter observation was in line with the literature, which reported the adsorption energy of CH 4 ···, CF 4 ···, and CCl 4 ···GN complexes with values of −1.61, −3.46, and −8.99 kcal/mol, respectively [52]. While the adsorption of the CH 4 molecule on the borophene nanosheet exhibited a small E ads value of −2.54 kcal/mol and was accordingly documented as a physisorption process [53]. For a given type of halogen, the β 12 nanosheet showed more affinity to adsorb the CX 4 molecules than the GN nanosheet, which can be attributed to the lower electronegativity of boron relative to carbon and, hence, a lower electronegativity difference compared with that of the halogen.
Besides, the adsorption of the tetrahalomethanes became more favorable by decreasing the electronegativity of the halogens in the following order CF 4 ··· > CCl 4 ··· > CBr 4 ···β 12 /GN, which was accompanied by a lower electronegativity difference in the case of boron compared with carbon atoms. The favorability of the adsorption process within the tetrel-oriented configuration might be attributed to the contribution of the three halogen atoms of XC-X 3 molecules to the overall interaction.

Frontier Molecular Orbital (FMO) Calculations
In order to comprehend the effect of the adsorption process on the electronic characteristics of the examined systems, the energies of the highest occupied molecular orbitals (E HOMO ), the lowest unoccupied molecular orbitals (E LUMO ), and the energy gap (E gap ) values were assessed. Table 2 shows data of the E HOMO , E LUMO , and E gap values of the investigated systems before and following the adsorption process.
According to the data in Table 2, notable differences in the E HOMO , E LUMO , and E gap values were observed for the studied systems before and following the adsorption process. For instance, in the tetrel-oriented configuration, the E HOMO value of the BrC-Br 3 ···Br1@β 12 complex was −2.544 eV, whereas the pure β 12 nanosheet had an E HOMO value of −2.875 eV (Table 2). Moreover, the E gap values of all CX 4 molecules, β 12 , and GN nanosheets were altered, confirming the occurrence of adsorption processes. For example, the pure β 12 nanosheet had an E gap value of −0.626 eV that was changed to −0.602 eV after the adsorption process within the BrC-Br 3 ···Br1@β 12 complex (Table 2).

Charge Transfer Calculations
The Bader charge method is a reliable appliance for determining the charge transfer over the adsorption process [54,55]. The transferred charge between the CX 4 molecules and the 2D nanosheets within all the studied complexes was evaluated in terms of the charge transfer difference (Q t ) values ( Table 1). The Q t values with negative signs remarked that the charge was shifted from the CX 4 molecules towards the β 12 and GN nanosheets, and vice versa was true for the positive Q t values.  Figure 3. Table 1 shows Q t values with a negative sign for the CX 4 ···β 12 complexes, demonstrating the ability of the inspected tetrahalomethanes to donate electrons to the β 12 nanosheets within the tetrel-and halogen-oriented configurations. Notably, the Q t values of the CX 4 ···β 12 complexes within the halogen-oriented configuration generally decreased as the adsorption energies decreased (i.e., in the order CBr 4 ··· > CC1 4 ··· > CF 4 ···β 12 ). For instance, the Q t values of the Br 3 C-Br···, Cl 3 C-Cl···, and F 3 C-F···T1@β 12 complexes were −0.0654, −0.0410, and −0.0164 e, respectively. The reversed trend was noticed for the complexes within the tetrel-oriented configuration, outlining the noticeable contributions of the three coplanar halogen atoms to the adsorption process. For example, the Q t values for the CF 4 ···, CCl 4 ···, and CBr 4 ···Br1@β 12 complexes within the tetrel-oriented configuration were −0.0313, −0.0283, and −0.0263 e, respectively.
The Q t values of the CX 4 ···GN complexes within the tetrel-and halogen-oriented configurations showed similar trends to the CX 4 ···β 12 complexes, except for the CBr 4 ···GN complexes within the former configuration that had positive Q t values. For the latter complexes, the electronaccepting property increased in the following order, H@GN < Br@GN < T@GN adsorption sites, and was confirmed with positive Q t values of 0.0070, 0.0023, and 0.0036 e, respectively.
Charge density difference (∆ρ) maps were generated in order to investigate the distribution of the charge within the relaxed CX 4 ···β 12 /GN complexes at the most preferable adsorption sites, and the maps are provided in Figure 4. As demonstrated in Figure 4, the electron depletion and accumulation regions (i.e., cyan-and yellow-colored regions, respectively) revealed the distribution of the charge between the tetrahalomethanes and the investigated 2D nanosheets. Apparently, the most remarkable electron-accumulated region was observed for the CBr 4 ···β 12 /GN complexes, demonstrating the further ability of CBr 4 molecules to be adsorbed on the studied 2D nanosheets among tetrahalomethane analogs (Figure 4).
Charge density difference (∆ρ) maps were generated in order to investigate the distribution of the charge within the relaxed CX4···β12/GN complexes at the most preferable adsorption sites, and the maps are provided in Figure 4. As demonstrated in Figure 4, the electron depletion and accumulation regions (i.e., cyan-and yellow-colored regions, respectively) revealed the distribution of the charge between the tetrahalomethanes and the investigated 2D nanosheets. Apparently, the most remarkable electron-accumulated region was observed for the CBr4···β12/GN complexes, demonstrating the further ability of CBr4 molecules to be adsorbed on the studied 2D nanosheets among tetrahalomethane analogs (Figure 4).  Overall, the negative Q t values confirmed that all the CX 4 molecules had an electrondonating character except for the CBr 4 ···GN complexes within the tetrel-oriented configuration. According to the Q t values, the amount of charge transferred from the tetrahalomethanes to the β 12 nanosheet was more significant than that of the GN nanosheet, which was in line with the adsorption energy values. Based on ∆ρ maps, it was observed that the amount of the distribution charge area (colored area) increased as the electronegativity of the halogen atom decreased. For instance, the size of the distribution charge area increased as the atomic size of the halogen atom increased in the order FC-F 3 ··· < ClC-Cl 3 ··· < BrC-Br 3 ···Br1@β 12 complexes.
Given that the Q t values of the CX 4 ···β 12 /GN complexes within the halogen-oriented configuration generally decreased as the adsorption energies decreased, while the reversed trend was noticed for the complexes within the tetrel-oriented configuration. This implies that the halogen orientation relies on a more localized charge transfer and electronegativity difference during the binding mechanism, while the tetrel orientation is accompanied by a more distributed charge transfer binding that is more significant with large-sized bromine atoms.

Band Structure Calculations
To ascertain the impact of the adsorption of the CX 4 molecules on the electronic properties of the β 12 and GN nanosheets, band structure analysis was carried out for the pure and combined 2D nanosheets. Using PBE functional along the high-symmetry paths of the Brillouin zone, band structures were extracted. The Γ-Y-S-X-Γ path was chosen for the β 12 nanosheet, and the Y-S-X-Γ-Y path was selected for the GN nanosheet. The band structures of the pure 2D nanosheets are demonstrated in Figure S2.
Looking at Figure S2, a metallic character of the pure β 12 surface was noted by several bands, which crossed the Fermi level along the high-symmetry path. For the pure GN surface, the existence of the Dirac point at the Fermi level announced its semiconducting property.
Band structures of the relaxed CX 4 ···β 12 /GN complexes at the most preferable adsorption sites are plotted in Figure 5. After the adsorption process, slight differences were noticed in the electronic band structures of the pure nanosheets, outlining the physisorption process of tetrahalomethanes on the pure nanosheets ( Figure 5).
For the adsorption of CF 4 molecules, insignificant changes were denoted in the electronic band structures of the β 12 nanosheet. Upon adsorbing CCl 4 and CBr 4 molecules, further new bands appeared in the band structures of the combined nanosheets compared with the pure analogs. Such new bands remarked the adsorption of the CCl 4 and CBr 4 molecules on the β 12 nanosheet. Illustratively, the CBr 4 ···β 12 complexes displayed a new conduction band at 1.35 eV and new valence bands at −0.60 and −2.00 eV. It was also observed that the bands shifted towards the Fermi level in the case of the complexes within the tetrel-oriented configuration more than the halogen-oriented analog. For instance, the adsorption of CCl 4 at the Br1@β 12 and H@β 12 within the tetrel-and halogen-oriented configurations led to the appearance of a conduction band at around 2.70 and 2.15 eV, respectively. This observation demonstrated the higher favorability of the adsorption process within the former configuration than the latter one.
Similar to the β 12 nanosheet, the CF 4 molecules had a neglected effect on the band structure of the pure GN surface ( Figure 5). Besides, the band structures of the CCl 4 ··· and CBr 4 ···GN complexes showed many new valence and conduction bands, confirming the higher potentiality of the GN nanosheet to adsorb these molecules compared with CF 4 molecules. For instance, in the CBr 4 ···GN complexes, a new conduction band appeared at 0.60 and 0.67 eV, respectively, while in the valence region, many valence bands appeared at −2.40 eV and then ranged from −2.62 to −2.65 eV ( Figure 5). It can be seen that the valence and conduction bands in the CX 4 ···GN complexes shifted towards the Fermi level as the atomic size of the halogen atom increased, demonstrating a favorable adsorption process. For example, the valence band at around −2.55 eV in the FC-F 3 ···T@GN complex shifted to −2.60 eV in the ClC-Cl 3 ···T@GN complex, and then to −2.65 eV in the BrC-Br 3 ···T@GN complex ( Figure 5). For the adsorption of CF4 molecules, insignificant changes were denoted in the electronic band structures of the β12 nanosheet. Upon adsorbing CCl4 and CBr4 molecules, further new bands appeared in the band structures of the combined nanosheets compared with the pure analogs. Such new bands remarked the adsorption of the CCl4 and CBr4 molecules on the β12 nanosheet. Illustratively, the CBr4···β12 complexes displayed a new conduction band at 1.35 eV and new valence bands at −0.60 and −2.00 eV. It was also observed that the bands shifted towards the Fermi level in the case of the complexes within the tetrel-oriented configuration more than the halogen-oriented analog. For instance, the adsorption of CCl4 at the Br1@β12 and H@β12 within the tetrel-and halogen-oriented configurations led to the appearance of a conduction band at around 2.70 and 2.15 eV, respectively. This observation demonstrated the higher favorability of the adsorption process within the former configuration than the la er one.
Similar to the β12 nanosheet, the CF4 molecules had a neglected effect on the band structure of the pure GN surface ( Figure 5). Besides, the band structures of the CCl4··· and CBr4···GN complexes showed many new valence and conduction bands, confirming the higher potentiality of the GN nanosheet to adsorb these molecules compared with CF4 molecules. For instance, in the CBr4···GN complexes, a new conduction band appeared at 0.60 and 0.67 eV, respectively, while in the valence region, many valence bands appeared at −2.40 eV and then ranged from −2.62 to −2.65 eV ( Figure 5). It can be seen that the valence and conduction bands in the CX4···GN complexes shifted towards the Fermi level as Summing up, the band structures of the β 12 nanosheet demonstrated more new bands after adsorbing the CX 4 molecules than those of the GN nanosheet. The latter affirmation indicated the further desirability of the adsorption process on the β 12 nanosheet than the GN nanosheet. The obtained findings were in line with the adsorption energy affirmations. The appearance of the new bands after the adsorption process indicated the overlap of the bands of the adsorbent and substrate, confirming the interaction between the CX 4 molecule and the studied 2D nanosheet. Further, the number of the new bands increased as the electronegativity of the halogen atom decreased. Illustratively, the CBr 4 ···β 12 /GN complexes, which exhibited the highest negative adsorption energy, showed the largest number of new bands among the other complexes ( Figure 5).

Density of State Calculations
The total density of state (TDOS), together with the projected density of state (PDOS), were extracted for pure and combined 2D nanosheets to truly comprehend the impact of the adsorption process on the electronic characteristics of the 2D nanosheets ( Figure S3). TDOS and PDOS plots of the most favorable complexes are shown in Figure 6. , and X . The Fermi energy was set at zero energy.
The PDOS plots with the contribution of the p-orbital of B, C, and X atoms within the studied complexes were plo ed in the energy range from −7.00 to 7.00 eV for β12 and from −8.00 to 8.00 eV for GN.
As shown in Figure 6, intense and feeble peaks were observed for the contributions of the PDOS of the X and C , respectively, to the TDOS of all the studied complexes. Accordingly, the halogens and carbon atoms of the CX4 molecules exhibited major and minor roles within the adsorption process on the 2D nanosheets, respectively. The PDOS plots with the contribution of the p-orbital of B, C, and X atoms within the studied complexes were plotted in the energy range from −7.00 to 7.00 eV for β 12 and from −8.00 to 8.00 eV for GN.
As shown in Figure 6, intense and feeble peaks were observed for the contributions of the PDOS of the X P−CX 4 and C P−CX 4 , respectively, to the TDOS of all the studied complexes. Accordingly, the halogens and carbon atoms of the CX 4 molecules exhibited major and minor roles within the adsorption process on the 2D nanosheets, respectively.
For example, the contribution of Cl p to the CCl 4 ···β 12 and ···GN complexes within the tetrel-oriented configuration were found in the valence region ranging from −2.50 to −4.70 eV and −3.00 to −5.10 eV, respectively. At the same time, the contribution of Cl p also appeared in the conduction regions from 1.70 to 2.30 eV and; 3.00 to 3.60 eV for the adsorption over the β 12 nanosheet and between 2.50 and 3.00 eV for the GN analog. Within the halogen-oriented configuration, the Cl p peaks of the adsorbed CCl 4 molecule on the β 12 and GN nanosheets were noticed in the valence region between −2.40 and −4.50 eV and −3.00 and −5.00 eV, respectively. In the conduction region, the contribution of the Cl p of the adsorbed CCl 4 molecule on the β 12 and GN nanosheets were found in the energy ranges of 1.80-2.50 and 3.00-4.00 eV, and 1.10-1.60 and 2.50-3.10 eV, respectively.
Notably, hybridizations between the p-orbital of the 2D nanosheets and the p-orbital of the CX 4 molecules were also observed, revealing the occurrence of the adsorption process ( Figure 6). For instance, an overlap between the PDOS (Bp) and the PDOS (Clp) appeared in the range from −3.50 to −3.90 eV in the CCl 4 ···Br1@β 12 complex within the tetrel-oriented configuration, affirming the ability of the β 12 nanosheet to adsorb the CCl 4 molecule. The latter observation was consistent with the E ads of the CCl 4 ···Br1@β 12 complex with a value of −7.74 kcal/mol (Table 1). While in the CCl 4 ···H@β 12 complex within the halogenoriented configuration, a small overlap between the PDOS (Bp) of the β 12 nanosheet and the PDOS (Clp) of the CCl 4 molecule was noticed in the conduction region from 1.80 to 2.20 eV. This finding was in agreement with the small E ads value of −5.58 kcal/mol.
From the DOS outlines, halogens had the dominant role in the adsorption of the CX 4 molecules on the β 12 and GN nanosheets within the modeled configurations. In line with the adsorption-energy and band structure findings, the DOS plots revealed the favorability of the β 12 nanosheet over the GN analog to adsorb the tetrahalomethanes.

Solvent Effect Calculations
To speculate the effect of the solvent on the adsorption process within the CX 4 ···β 12 /GN complexes, the adsorption energy was evaluated in the presence of a water solvent. Afterwards, the solvent effect (E solvente f f ect ads ) energy was computed for the most preferable complexes as the difference between the adsorption energies of the water solvent and vacuum (see the Computational Methodology section for details). The obtained E water ads and E solvente f f ect ads values are listed in Table 3. According to the data presented in Table 3, the adsorption energies of the CX 4 ···β 12 /GN complexes in the water medium showed higher negative values compared with those in a vacuum. For instance, the E water ads and E vacuum ads values of the CBr 4 ···Br1@β 12 complex within the tetrel-oriented configuration were −15.99 and −12.33 kcal/mol, respectively (Tables 1 and 3, respectively). Subsequently, E solvent effect ads exhibited negative values, confirming the occurrence of the adsorption process in the water medium. As an illustration, the E solvent effect ads value of the CBr 4 ···Br1@β 12 complex within the tetrel-oriented configuration was −3.66 kcal/mol. Similar to the energetic manifestation obtained in a vacuum, the more prevalent effect of the water solvent on the favorability of the adsorption process was ascribed to the complexes within the tetrel-oriented configuration compared with the halogen-oriented configuration. Numerically, as an example, the E solvent effect ads values of the CBr 4 ···Br1@β 12 and ···H@β 12 complexes within the tetrel-and halogen-oriented configurations were −3.66 and −1.60 kcal/mol, respectively.

Computational Methods
The density functional theory (DFT) method was applied for all calculations [56,57] via the Quantum ESPRESSO 6.4.1 package [58,59]. Based on the Perdew-Burke-Ernzerhof (PBE) scheme, the electron exchange-correlation function was conducted utilizing the generalized gradient approximation (GGA) [60]. To represent the electron-core interaction, the ultrasoft pseudopotential (USPP) was employed [61]. The van der Waals interactions for all the executed computations were taken into account using the Grimme-D2 method [62]. The utilized energy cutoff and charge density cutoff values were 50 and 500 Ry, respectively. The total energy and the atomic force convergence criteria were 1 × 10 −5 eV and 1 × 10 −4 eV/Å, respectively. Based on the Monkhorst-Pack mesh, the 6 × 6 × 1 and 12 × 12 × 1 k-points grids were adopted for the first Brillouin zone sampling within the geometry relaxation and density of state calculations, respectively. The convergence was enhanced using the Marzari-Vanderbilt smearing method [63]. For preventing image-image interaction, a vacuum thickness of 20 Å was added along the z-direction of the β 12 and GN nanosheets.
To model the adsorption of the tetrahalomethanes (CX 4 ; X = F, Cl, and Br) on β 12 and GN nanosheets, 3 × 4 × 1 and 6 × 5 × 1 supercells were constructed for β 12 and GN nanosheets, respectively. Adsorption energies (E ads ) of the CX 4 ···β 12 /GN complexes within tetrel (XC-X 3 )-and halogen (X 3 C-X)-oriented configurations were assessed as follows: where E CX 4 ···2D nanosheet , E CX 4 , and E 2D nanosheet are the energies of complex, tetrahalomethane, and 2D nanosheet, respectively. Frontier molecular orbital (FMO) calculations were carried out to gain a better understanding of the adsorption process of CX 4 molecules on the investigated 2D nanosheets. Within the FMO analyses, the energies of the highest occupied molecular orbitals (E HOMO ) and lowest unoccupied molecular orbitals (E LUMO ) for the most stable relaxed CX 4 ···β 12 /GN complexes were computed. The energy gap (E gap ) was estimated according to the following equation: The charge transfer of the adsorbed CX 4 molecules was determined using the Bader charge method [55,64] based on the following equation: where Q combined 2D nanosheets and Q isolated 2D nanosheets are the charges of the 2D nanosheets after adsorbing tetrahalomethanes and the charge of the isolated 2D nanosheets, respectively. The charge density difference (∆ρ) was plotted according to the following equation: where ρ CX 4 ···2D nanosheet , ρ CX 4 , and ρ 2D nanosheet are the charge densities of complex, tetrahalomethane, and 2D nanosheet, respectively. VESTA 3 visualization software was invoked for generating the charge density plots [65]. To comprehend the influence of the adsorption process of the tetrahalomethanes on the electronic characteristics of the β 12 where E water ads and E vacuum ads are the adsorption energies of the complex in water and vacuum media, respectively.

Conclusions
In the presented work, a DFT study was conducted to comparatively illustrate the adsorption features of tetrahalomethanes (CX 4 , where X = F, Cl, and Br) on β 12 borophene (β 12 ) and GN nanosheets. To attain a thorough investigation, geometry relaxation, adsorption energies, Bader charge, electronic band structures, and DOS computations were conducted for the adsorption of the CX 4 molecules on the studied 2D nanosheets within tetrel (XC-X 3 )-and halogen (X 3 C-X)oriented configurations. From the energetic perspective, the adsorption of the CX 4 model on the β 12 and GN nanosheets within the tetrel-oriented configuration was more desirable than that within the halogen-oriented configuration. Further favorability of the Br1@β 12 and T@GN adsorption sites were announced toward adsorbing the CX 4 molecules within the tetrel-oriented configuration and showed the most significant E ads for the CBr 4 molecule with values of −12.33 and −10.03 kcal/mol, respectively. According to the FMO results, the E HOMO , E LUMO , and E gap values of the β 12 and GN nanosheets were changed following the adsorption process. Based on the Bader charge results, the electron-donating characters for all the CX 4 molecules after adsorbing on the β 12 and GN nanosheets within tetrel-and halogen-oriented configurations were illustrated, except the CBr 4 ···GN complexes within the former configuration. In the latter complexes, the adsorbed CBr 4 molecule showed an electron-accepting property confirmed by the small positive Q t values. From the band structure and DOS plots, new bands and peaks were observed, respectively, after the adsorption of CX 4 molecules on the 2D nanosheets, indicating the occurrence of the adsorption process. The energetic results are pertinent to the solvent effect demonstrated, that the presence of the water solvent led to more observable negative adsorption energies compared with the adsorption in a vacuum. The emerging findings would provide a foundation for any future consideration of β 12 and GN nanosheets to adsorb small molecules.
Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules28145476/s1, Figure S1: Side and top representations for the relaxed structures of the tetrel (XC-X 3 )-and halogen (X 3 C-X)-oriented configurations of the CX 4 ···β 12 /GN complexes (where X = F, Cl, and Br) at all the adsorption sites. Equilibrium distances (d) are given in Å; Figure S2: Electronic band structures of β 12 and GN nanosheets along the high symmetry points of the Brillouin zone. The Fermi energy was set at zero energy, and the Dirac point is defined by the dotted circle; Figure S3: Total and projected density of state (TDOS/PDOS) plots for the pure surfaces of β 12 and GN nanosheets, assuming Fermi level as the reference level. The dotted circle defines the Dirac point. The contributions of the p-orbital for boron (B) and carbon (C) atoms are represented by B p and C p , respectively. Data Availability Statement: Data will be made available on request.