Borophene and Pristine Graphene 2D Sheets as Potential Surfaces for the Adsorption of Electron-Rich and Electron-Deficient π-Systems: A Comparative DFT Study

The versatility of striped borophene (sB), β12 borophene (β12), and pristine graphene (GN) to adsorb π-systems was comparatively assessed using benzene (BNZ) and hexafluorobenzene (HFB) as electron-rich and electron-deficient aromatic π-systems, respectively. Using the density functional theory (DFT) method, the adsorption process of the π-systems on the investigated 2D sheets in the parallel configuration was observed to have proceeded more favorably than those in the vertical configuration. According to the observations of the Bader charge transfer analysis, the π-system∙∙∙sB complexes were generally recorded with the largest contributions of charge transfer, followed by the π-system∙∙∙β12 and ∙∙∙GN complexes. The band structures of the pure sheets signaled the metallic and semiconductor characters of the sB/β12 and GN surfaces, respectively. In the parallel configuration, the adsorption of both BNZ and HFB showed more valence and conduction bands compared to the adsorption in the vertical configuration, revealing the prominent preferentiality of the anterior configuration. The density-of-states (DOSs) results also affirmed that the adsorption process of the BNZ and HFB on the surface of the investigated 2D sheets increased their electrical properties. In all instances, the sB and β12 surfaces demonstrated higher adsorptivity towards the BNZ and HFB than the GN analog. The findings of this work could make a significant contribution to the deep understanding of the adsorption behavior of aromatic π-systems toward 2D nanomaterials, leading, in turn, to their development of a wide range of applications.


Introduction
Graphene, a single-atom-thick layer of sp2-bonded carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, has been become the linchpin of a variety of

Computational Methods
All calculations were performed with Quantum ESPRESSO 6.4.1 package [57,58] using density functional theory (DFT) [59,60]. Generalized gradient approximation (GGA) was employed using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation function [61]. The ultrasoft pseudopotential was adopted for treating electron-ion interactions [62]. The DFT-D2 method of the Grimme scheme [63] was applied to account for the van der Waals interactions in all computations. The cutoffs of energy and charge density were set to be 50 Ry and 500 Ry, respectively. All structures were fully optimized with respect to the energy convergence threshold of 10 −5 eV and force convergence threshold of 10 −4 eV/Å. Monkhorst-Pack grids of 6 × 6 × 1 and 12 × 12 × 1 k-points were used to sample the first Brillouin zone for geometric optimization and electronic structure calculations, respectively, combined with the Marzari-Vanderbilt smearing technique [64]. A vacuum of 20 Å was settled along the vertical direction of the borophene and the graphene surfaces for all calculations to avoid spurious interactions between the periodic cells in the z-direction. The corresponding space groups of the studied sB and β 12 sheets were Pmmn and P2mm, respectively.
The potential of sB, β 12 , and GN to adsorb BNZ/HFB as electron-rich/electrondeficient aromatic π-systems was comparatively assessed. For adsorption energy calculations, supercells of 9 × 4 × 1, 3 × 4 × 1, and 6 × 5 × 1 were constructed for sB, β 12 , and GN, respectively. The number of atoms in the supercells of sB, β 12 , and GN was 72, 60, and 60, respectively. On the designed 2D sheets, BNZ and HFB were subjected to adsorption process as electron-rich and electron-deficient aromatic π-systems, respectively, within vertical and parallel configurations ( Figure 1). Adsorption energy (E ad ) was computed according to the following equation: where E π−system···2D sheet , E π−system , and E 2D sheet were the energies of complex, adsorbed π-system, and anchoring 2D sheet, respectively. Using Bader charge analysis [65,66], the charge transfer (Q t ) to or from the 2D sheets was assessed as follows: where the Q combined 2D sheet and Q isolated 2D sheet were the charges of the 2D sheet after and before the adsorption process, respectively. Based on Bader charge analysis, the charge density difference (∆ρ) was evaluated according to the following equation: where ρ π−system···2D sheet , ρ π−system , and ρ 2D sheet were the charge of the complex, adsorbed π-system, and anchoring 2D sheet, respectively. The charge density difference maps were visualized using the VESTA [67] package. Furthermore, the electronic band structure, total density of states (TDOSs), and projected density-of-states (PDOSs) calculations were thoroughly studied to understand the electronic properties of the studied 2D sheets.

Geometric Structures
Prior to the adsorption calculations of the aromatic π-systems on the 2D sheets, the structures of the striped sB, β 12 , and GN were constructed and geometrically minimized to obtain the equilibrium geometries. The optimized structures of the 2D sheets are illustrated in Figure 2. According to the optimized structures demonstrated in Figure 2, the equilibrium lattice constants (a × b) of sB and β 12  Because of the buckled structure of the sB with corrugations along the b direction, two types of boron atoms, namely, T and B atoms, were observed, as depicted in Figure 2. The calculated T-T and B-B distances were 1.61 Å. The T-B distance was 1.88 Å, and the buckling height was 0.92 Å. All the measured distances were consistent with the literature [28,32,43]. Accordingly, the sB sheet was found to have four different adsorption sites, termed the top site (T@sB), bottom site (B@sB), and bridge sites (Br1@sB and Br2@sB) ( Figure 2).

Adsorption Energy Calculations
To obtain a better understanding of the adsorption process within the π-system···2D sheet complexes, BNZ and HFB were placed at versatile sites on the surfaces of sB, β 12 , and GN in both vertical and parallel configurations ( Figure 1). Upon the relaxed structures, the adsorption energies were computed according to Equation (1) (see Computational Methods section), and the equilibrium distances were assessed ( Table 1). The obtained relaxed structures for all the studied π-system···2D sheet complexes are depicted in Figure S1. Figure 3 illustrates the relaxed π-systems at the most favorable energetic sites on the studied 2D sheets.
With regard to the adsorption process of the π-system on the surface of the sB sheet in a vertical configuration, the most prominent adsorption energy was detected in the case of the π-system···B@sB complexes, followed by the π-system···Br1@sB, π-system···Br2@sB, and, finally, π-system···T@sB complexes. For instance, the adsorption energies of the BNZ on the surface of the sB sheet at the B@sB, Br1@sB, Br2@sB, and T@sB sites were −5.66, −5.64, −4.40, and −4.35 kcal/mol, respectively. For parallel configuration, the T@sB and Br1@sB sites were found to be the most preferential adsorption sites for the BNZ and HFB, with adsorption energies of −14.93 and −15.76 kcal/mol, respectively.
According to the data registered in Table 1, the adsorption of the BNZ and HFB on the β 12 surface was occurred significantly at the H@β 12 site in the vertical configuration with adsorption energy values of −6.40 and −4.54 kcal/mol, respectively. Turning to the parallel configuration of the π-system···β 12 complexes, the T2@β 12 and H@β 12 sites were found to have significantly negative adsorption energy values in the interactions with BNZ and HFB, respectively.
Similar to the π-system···β 12 interactions, the H@GN site was documented as the most promising site for the adsorption of both BNZ and HFB on the GN surface in the vertical configuration. In comparison, the T@GN site was found to have the largest negative adsorption energies of the π-system···GN complexes in the parallel configuration, followed by the Br@GN and, finally, H@GN sites. For example, the adsorption energies of the BNZ-GN complexes in the parallel configuration were −9.97, −9.89, and −8.78 kcal/mol for the BNZ-T@GN, BNZ···Br@GN, and BNZ···H@GN complexes, respectively. The obtained results were found to be compatible with those of an earlier study, demonstrating that the T@GN site was the most favorable site for the adsorption process of BNZ with an adsorption energy of −5.53 kcal/mol [50]. The slight difference between the adsorption energy values in the present study and the preceding study might be ascribed to the different chosen cutoff energies in the calculations.
Notably, the adsorption process of the aromatic π-systems···sB/β 12 /GN complexes within the parallel configuration was observed to have greater favorability than those in the vertical configuration. For instance, the adsorption energies of the BNZ···B@sB complex were −5.66 and −11.46 kcal/mol in vertical and parallel configurations, respectively. Table 1. Adsorption energies (E ad , kcal/mol) and equilibrium distances (d, Å) of the relaxed structures of BNZ and HFB on the sB, β 12 , and GN sheets in the vertical and parallel configurations at all studied adsorption sites, as well as the charge transfer difference (Q t , e) for the 2D sheets before and after the adsorption process.

2D Sheet
Adsorption Site a

π-System
Benzene (BNZ) Hexafluorobenzene (HFB) a All adsorption sites on the surface of the studied 2D sheets are illustrated in Figure 2. b Q t was estimated by Equation (2) (see Computational Methods section for details). c All the relaxed structures of the π-system···2D sheet complexes are displayed in Figure S1. −0.0357 a All adsorption sites on the surface of the studied 2D sheets are illustrated in Figure 2. b was estimated by Equation (2) (see Computational Methods section for details). c All the relaxed structures of the π-system•••2D sheet complexes are displayed in Figure S1. Side and top views of the relaxed structures of the vertical and parallel configurations of the π-system···2D sheet complexes where π-system = BNZ/HFB and the 2D sheet = sB/β 12 /GN at the most energetically favorable adsorption sites. The π-system-2D sheet equilibrium distances (d) are given in Å.

Charge Transfer Calculations
Bader charge analysis has been documented as a powerful tool to precisely obtain an in-depth theoretical insight into the charge transfer during the adsorption process [65,66]. Utilizing Bader charge analysis, the charge transfer differences (Q t ) of the relaxed π-system···2D sheet complexes at all possible adsorption sites were calculated as illustrated in Equation (2)  the context of Bader charge analysis, the negative values of the charge transfer differences (Q t ) outline the transfer of charge from the π-systems to the 2D sheets, and the positive values mean the opposite.
As can be seen from the data in Table 1, the adsorption of HFB on the sB surface had higher negative values of Q t , compared to BNZ, in the vertical configuration. For example, the Q t values were −0.0275 and −0.0154 e within the adsorption process of the HFB and BNZ, respectively, at the T@sB site in the vertical configuration. Although the adsorption of BNZ in the vertical configuration at the B@sB site exhibited the largest negative adsorption energy value of −5.66 kcal/mol, it had a small Q t value of −0.0136 e. This observation c confirmed that the charge transfer contributed little to the adsorption process within the BNZ···sB complexes in the vertical configuration. On the other hand, the charge transfer in the HFB···B@sB complex in the vertical configuration was shown to play the main dominant role in the interaction by the largest Q t value (i.e., −0.0318 e). Furthermore, a direct correlation between the Q t and the adsorption energy values was observed for the π-system···sB complexes in the parallel configuration. For example, the BNZ···T@sB and HFB-Br1@sB complexes, the most stable complexes in the parallel configuration with adsorption energy values of −14.93 and −15.76 kcal/mol, showed Q t values of 0.0735 and −0.0813 e, respectively.
In general, the charge transfer's contribution to the adsorption process of BNZ and HFB on the β 12 surface, in both vertical and parallel configurations, was signaled by smaller values of Q t compared to the π-system···sB complexes. For instance, the Q t values were −0.0318 and −0.0261 e in the case of the HFB···Br1@sB and ···Br1@β 12 complexes, respectively, in the vertical configuration. Moreover, it was noted that the adsorption of HFB on the β 12 surface resulted from the transfer of a larger amount of the Q t compared to the BNZ analog. For example, the BNZ··· and HFB···H@β 12 complexes in the vertical configuration had Q t values of −0.0199 and −0.0274 e, respectively.
Notably, the Q t showed small values, ranging from −0.0058 e for the BNZ···GN complexes to −0.0124 e for HFB···GN complexes, indicating the small contributions of charge transfer to the adsorption process on the GN surface in the vertical configuration.
Interestingly, in the case of parallel configuration, the adsorption of BNZ on all the studied 2D sheets showed positive Q t values. For example, the Q t values were 0.0735, 0.0436, and 0.0065 e for the BNZ···T@sB, ···T2@β 12 , and ···T@GN, respectively. The latter observation emphasized that the charge was transferred from the 2D sheets to the BNZ. Similar findings of small positive Q t values in the case of the adsorption of BNZ on the GN surface in the parallel configuration were observed in prior theoretical studies [49,50].
To deeply understand the adsorption process, the charge density difference maps for the π-system···2D sheet complexes at the most energetically favorable sites were generated based on Equation (3) in the Computational Methods section (Figure 4). With this in mind, the cyan-and yellow-colored-areas referred to increases and decreases in the charge density around the adsorption systems, respectively.
For the π-system···2D sheet complexes in the vertical configuration, charge accumulation regions were observed around the BNZ and HFB systems and at the interface sites located over the 2D sheets ( Figure 4). According to the latter observation, the charge transfer occurred from the investigated π-systems to the surfaces of the sB, β 12 , and GN sheets, confirmed by the negative sign of the estimated Q t values (Table 1). Evident accumulated charge regions were denoted by more prominent cyan colors in the case of the adsorption of HFB on the investigated 2D sheets compared with BNZ analog. Accordingly, the 2D sheets exhibited greater potential to attract electrons from HFB than from BNZ analog.
For the BNZ···2D sheet complexes in the parallel configuration, the accumulated charge regions were noticed over the 2D sheets, designating the charge transfer from 2D sheets to BNZ. The latter findings were in agreement with the positive Q t values listed in Table 1. By contrast, in the case of the adsorption of HFB on the 2D sheets, the electron depletion regions were observed over the 2D sheets, signifying the transfer of charge from HFB to the 2D sheets. Charge density difference maps of the relaxed structures of the vertical and parallel configurations of the π-system•••2D sheet complexes where π-system = BNZ/HFB and the 2D sheet = sB/β12/GN at the most energetically favorable adsorption sites. Cyan and yellow colors represent the charge accumulation (negative) and depletion (positive), respectively. Green, pink, Gray, and brown balls refer to boron, hydrogen, fluorine, and carbon atoms.

Band Structure Calculations
Electronic band structure analyses were performed to illuminate further the effects of the adsorbed π-systems (i.e., BNZ and HFB) on the electronic properties of the investigated 2D sheets. Using the PBE function, the band structure calculations of the pure 2D sheets were carried out along the high-symmetry points of the Brillouin zone and are depicted in Figure 5. Moreover, the band structures were investigated for the π-system•••2D Charge density difference maps of the relaxed structures of the vertical and parallel configurations of the π-system···2D sheet complexes where π-system = BNZ/HFB and the 2D sheet = sB/β 12 /GN at the most energetically favorable adsorption sites. Cyan and yellow colors represent the charge accumulation (negative) and depletion (positive), respectively. Green, pink, Gray, and brown balls refer to boron, hydrogen, fluorine, and carbon atoms.
In sum, the current Bader charge analysis generally demonstrated that the π-system···sB complexes had the largest charge transfer difference (Q t ) values, followed by the π-system···β 12 and, finally, the π-system···GN complexes.

Band Structure Calculations
Electronic band structure analyses were performed to illuminate further the effects of the adsorbed π-systems (i.e., BNZ and HFB) on the electronic properties of the investigated 2D sheets. Using the PBE function, the band structure calculations of the pure 2D sheets were carried out along the high-symmetry points of the Brillouin zone and are depicted in Figure 5. Moreover, the band structures were investigated for the π-system···2D sheet complexes at the most energetically favorable adsorption sites to determine the effect of the adsorption process on the electronic properties of the 2D sheets ( Figure 6).  As shown in Figure 5, many bands crossing the Fermi level along the Г-Y-S-X-Г path were apparently detected in the case of the pure sB and β 12 sheets. Accordingly, the electrons in the valence band could easily move to the conduction band through these bands. In the case of GN surface, the bands along the Y-S-X-Г-Y direction met at a point along the Fermi level (i.e., Dirac point), where the bandgap value was zero ( Figure 5). Consequently, the findings emphasized that the sB and the β 12 surfaces showed metallic properties, while the GN had semiconductor characters.
For the pure surface of the sB sheet, the bands touched at the Y, Г, and X points at 0.0, −2.0, and 1.6 eV, respectively ( Figure 5). Following the adsorption of the BNZ and HFB on the surface of the sB sheet, it was observed that the bands shifted far away from each other, confirming the prominent effect of the adsorption of the π-systems on the electronic properties of the sB sheet ( Figure 6). Simultaneously, the adsorption of the BNZ on the sB sheet resulted in the appearance of new valence and conduction bands at roughly −1.0/-2.0 eV, and 1.4/1.7 eV, respectively, demonstrating the interference of the BNZ bands with the sB bands. Extra bands were also found in the valence region of −1.5 and −2.0 eV at Г point after the adsorption of HFB on the sB surface in the vertical and parallel configurations.
Similarly, the obtained band structures of the π-system···β 12 complexes showed additional bands after the adsorption of the BNZ in both configurations at around −1.5 and −2.0 eV, which might be attributed to the contribution of the orbitals of BNZ in the adsorption process. In comparison, new conduction and valence bands appeared after the adsorption of the HFB in both configurations at 2.3 and −2.0 eV at Г point, respectively. Conspicuously, the adsorption of both BNZ and HFB had more valence and conduction bands in the parallel configuration than the vertical configuration, revealing the favorability of the parallel configuration over the vertical configuration. The latter results were in line with the adsorption energy results ( Table 1).
The band structure analyses indicated that the adsorption of the electron-rich and electron-deficient π-systems on the GN barely affected the electronic properties of the pure surface and that the Dirac point remained. As shown in Figure 6, the adsorption of BNZ on the surface of the GN in both configurations gave rise to the appearance of a new valence band at −2.0 eV. At the same time, new conduction bands appeared at 1.6 and 2.1 eV for the HFB···H@GN complex in the vertical configuration, exhibiting the HFB and GN surface interaction. Overall, the obtained band structures highlighted the occurrence of interactions between the aromatic π-systems and the GN.

Density of State Calculations
The total and projected density-of-states (TDOS/PDOS) analyses were performed to reveal the nature of the interaction between the electron-rich/deficient π-systems and the sB/β 12 /GN 2D sheets. The TDOS and PDOS plots were generated for the studied 2D sheets before and after the adsorption process (Figures 7 and 8, respectively).  As illustrated in Figure 7, the TDOS peaks at the Fermi level in the case of both pure sB and β 12 surfaces were not zero, highlighting the metallic property of the examined sheets. In addition, the peaks of the pure sB and β 12 surfaces were found to have a high value of TDOS near the Fermi level, ensuring the conductivity of the surfaces.
With regard to the TDOS of the pure GN surface, there was a Dirac point at the Fermi level (Figure 7), which was consistent with that of the band structure affirmations. From the PDOS results illustrated in Figure 7, the p-orbital of the B and C atoms showed the main contribution in the TDOS peaks of the pure sB/β 12 and GN sheets, respectively.
Based on the PDOS peaks of the sB and β 12 surfaces shown in Figure 8, the peaks of the p-orbital of the B atoms exhibited the dominant contribution to the TDOS near the Fermi level. In comparison, the s-orbital of hydrogen atoms made a frail contribution in the adsorption process.
Notably, the H s in the BNZ exhibited a minor contribution in the adsorption process on the surface of the sB sheet, with energy values ranging from −6.0 to −2.5 eV in the vertical configuration and from −6.5 to −3.3 eV in the parallel one. Accordingly, the PDOS findings outlined that the adsorption of the BNZ on the sB surface in the vertical and parallel configurations was dominated by the contribution of the C p in the BNZ. Turning to the HFB···sB complexes in both vertical and parallel configurations, the F p showed the most prevalent contribution to the occurrence of the adsorption process and was found with energy values ranging from −7.0 to −4.5 eV. Remarkably, for the HFB···Br1@sB in the parallel configuration, the adsorption process was dominated by the F p and B p hybridization, which was located at −5.4 eV. Obviously, the adsorption of HFB on the surface of the sB sheet in the parallel configuration showed higher PDOS peaks than in the vertical configuration, which was in agreement with the adsorption energy results (Table 1).
Concerning the β 12 results, the PDOS analyses of the BNZ···H@β 12 and BNZ···T2@β 12 complexes in the vertical and parallel configurations, respectively, showed that the C p in BNZ had the main role in the adsorption process on the β 12 surface. Besides, the H s made a tiny contribution to the adsorption process, with the PDOS peaks appearing at the valence region below the energy value of −3.0 eV. In addition, the C p of the HFB displayed considerable hybridization with the B p in the β 12 sheet, producing a peak in the conduction area at about 3.0 eV. The DOS analyses were compatible with the findings of the adsorption energy and charge transfer calculations (Table 1).
For the GN surface, the adsorption of BNZ at the H@GN and T@GN sites in the vertical and parallel configurations, respectively, originated from the contribution of the C p of the BNZ, which showed prominent peaks at energy values of −2.0 and 3.0 eV. Prominent C p and F p peaks were noted for the adsorption of HFB on the GN surface in both studied configurations, at energy values of −2.5 and 3.0 eV, in the valence and conduction regions, respectively.
Conclusively, the DOS peaks of all the examined π-system···2D sheet complexes shifted towards the Fermi level compared to the pure surfaces, highlighting the enhancement of the electrical properties of the investigated 2D sheets after the adsorption process.

Conclusions
In the current study, the adsorption of electron-rich and electron-deficient π-systems (BNZ and HFB) on borophene and graphene sheets was comparatively investigated using DFT calculations. Adsorption energies, charge transfer analyses, electronic band structures, and DOS calculations were performed for the π-system···2D sheet in the vertical and parallel configurations. The BNZ and HFB adsorption on the sB, β12, and GN surfaces in the parallel configuration demonstrated more favorable amplitude than that in the vertical configuration. The adsorption of BNZ and HFB over the sB and β12 sheets enhanced the electronic properties of their surfaces. On the other hand, the adsorption of BNZ and HFB on the GN sheet exhibited nominal change in the electronic properties of the GN surface. Based on Bader charge analysis, the charge was transferred from BNZ and HFB to the investigated 2D sheets, with the exception of the adsorption of BNZ in the parallel configuration, in which the charge was transferred from the 2D sheets to BNZ. Crucially, the band structure and the density-of-states (DOSs) results confirmed that the adsorption process of the π-system on the surface of the investigated 2D sheets bolstered their electrical properties. The results of this research could provide a base of information for fields relevant to the application of 2D nanomaterials.