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

Abstract

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 (E_ads) values than that within the halogen-oriented analogs. Numerically, E_ads 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 E_HOMO, E_LUMO, and E_gap 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.

1. Introduction

Two-dimensional (2D) nanomaterials have recently been of universal interest owing to their outstanding chemical and physical properties [1,2,3,4]. As a premier developed 2D material, pristine graphene (GN) was regarded as the most intriguing star in the realm of materials science [5,6,7,8,9,10,11]. GN-based materials were denoted with unique features, including a high specific surface area [12], quantum Hall effect [13], high thermal conductivity [14], and ambipolar electric field effect [15]. Such properties shed light on their vast-ranging applications, like energy storage [16,17], drug delivery [18,19,20,21], spintronics [22], and catalysis [23]. Because of their low electronic noise, GN-based materials were also announced as an appealing candidate for adsorbing chemical systems [6,24].

Following the astonishing discovery of GN sheets, considerable research has been directed to develop various 2D materials, including antimonene [25], hexagonal boron nitride (h-BN) [26], bismuthine [27], silicene [28,29], and borophene [30,31]. In the parallel area, borophene, a 2D boron sheet, was announced with extraordinary properties, like electron mobility, anisotropic properties, superconductivity, and its phonon-mediated form [32,33,34]. Borophene was successfully fabricated on a single surface of Ag(111) under ultrahigh-vacuum conditions [30,31]. Different borophene phases were observed at various deposition temperatures using a high-resolution scanning tunneling microscope (STM), such as the striped, β₁₂, and χ₃ phases [31]. The puckered shape and metallic characteristics of the striped phase led to its utility in various potential applications for metal ion storage and electric conduction [35]. Compared with the striped phase, the preferable stability of the β₁₂ and the χ₃ phases, with planar shapes having hexagonal and triangular vacancies, was demonstrated [36,37]. Because of its structure with a hexagonal vacancy, borophene was utilized in adsorbing gas molecules [10,38,39,40].

An upsurge in interest has recently been oriented toward investigating the utility of borophene and GN in the detection of gas molecules, like NO, CO, NO₂, CO₂, CS₂, and NH₃ molecules [40,41,42,43]. Halomethanes are known for being toxic molecules [44,45,46]; however, scant attention has been directed toward exploring novel nanomaterials for adsorbing them. Using density functional theory (DFT), the adsorption of tetrahalomethanes CX₄ (X = F, Cl, and Br) was studied on carbon nanotubes [47] and GN nanosheets [48]. Nevertheless, no comparative study provided a full insight into the adsorption process of the tetrahalomethanes via all their possible oriented configurations on the surface of the borophene and GN nanosheets.

Herein, the adsorption features of tetrahalomethanes (CX₄, where X = F, Cl, and Br) on the β₁₂ borophene (β₁₂) nanosheet were unveiled and compared with those with the utilization of the GN nanosheet as the starting 2D nanomaterial. The CX₄∙∙∙β₁₂/GN complexes were selectively studied within tetrel (XC-X₃)- and halogen (X₃C-X)-oriented configurations (Figure 1) using various density functional theory (DFT) method. Initially, geometry relaxation of the potential binding modes of the two suggested configurations and their corresponding adsorption energies were first carried out. Additionally, to assess the change in the electronic characteristics of the studied 2D nanosheets following the adsorption of the CX₄ molecules, Bader charge, electronic band structure, and density of state (DOS) calculations were conducted. Further, the solvent effect on the adsorption energy of the studied complexes was evaluated. The obtained results would be an informative base for the utilization of the β₁₂ and GN in adsorbing small molecules, such as tetrahalomethanes.

2. Results and Discussion

2.1. 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 lattice 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 lattice 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).

2.2. 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. Adsorption energies (E_ads, 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 (Q_t, e) for the 2D nanosheets before and after the adsorption process.

2D Nanosheets	Adsorption Site a	X = F			X = Cl			X = Br
		Eads (kcal/mol)	d (Å)	Qtb (e)	Eads (kcal/mol)	d (Å)	Qtb (e)	Eads (kcal/mol)	d (Å)	Qtb (e)
Tetrel-oriented configuration
β12	T1	−4.42	3.69	−0.0309	−7.47	4.09	−0.0275	−11.45	4.14	−0.0231
	T2	−4.25	3.72	−0.0289	−7.69	4.06	−0.0230	−11.42	4.13	−0.0080
	T3	−4.14	3.68	−0.0309	−7.22	4.11	−0.0275	−11.07	4.17	−0.0215
	H	−4.39	3.65	−0.0306	−7.21	4.07	−0.0219	−11.15	4.13	−0.0115
	Br1	−4.46	3.67	−0.0313	−7.74	4.05	−0.0283	−12.33	4.11	−0.0263
	Br2	−4.14	3.74	−0.0291	−7.15	4.12	−0.0269	−11.03	4.18	−0.0175
GN	T	−4.66	3.50	−0.0175	−7.32	3.93	−0.0072	−10.03	4.07	0.0036
	Br	−4.36	3.57	−0.0177	−6.82	4.02	−0.0051	−9.49	4.13	0.0023
	H	−4.12	3.63	−0.0168	−6.57	4.06	−0.0025	−9.43	4.13	0.0070
Halogen-oriented configuration
β12	T1	−2.54	3.10	−0.0164	−5.14	3.16	−0.0410	−8.65	3.10	−0.0654
	T2	−2.62	3.12	−0.0149	−4.33	3.26	−0.0254	−6.72	3.21	−0.0291
	T3	−2.63	3.06	−0.0167	−4.97	3.17	−0.0366	--- c	--- c	--- c
	H	−2.71	2.93	−0.0185	−5.58	3.02	−0.0321	−9.00	2.98	−0.0424
	Br1	−2.46	3.11	−0.0165	−5.25	3.13	−0.0413	−8.91	2.98	−0.0697
	Br2	−2.69	3.05	−0.0163	−4.26	3.26	−0.0258	−6.37	3.24	−0.0317
GN	T	−2.46	3.00	−0.0095	−4.22	3.16	−0.0149	−6.00	3.17	−0.0196
	Br	−2.47	2.99	−0.0094	−4.18	3.17	−0.0152	−5.93	3.18	−0.0174
	H	−2.61	2.89	−0.0093	−3.99	3.18	−0.0093	−5.54	3.23	−0.0086

^a All adsorption sites on the investigated 2D nanosheets are depicted in Figure 2. ^b Q_t was calculated based on Equation (3). ^c Desired configuration was not observed after geometry relaxation (see Figure S1).

. Figure S1 illustrates all relaxed complexes. The relaxed CX₄∙∙∙β₁₂/GN complexes at the most energetically preferable adsorption sites are displayed in Figure 3.

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 E_ads values, followed by the ClC-Cl₃∙∙∙β₁₂, then the FC-F₃∙∙∙β₁₂ complexes (Table 1). Numerically, the E_ads 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 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-Br₃∙∙∙Br1@β₁₂ 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., X₃C-X∙∙∙β₁₂) showed the existence of a direct correlation between the adsorption energy and the atomic size of the halogen atom. Apparently, the H@β₁₂ site was the most appropriate adsorption site for adsorbing the X₃C-X molecules in the halogen-oriented configuration. Moreover, the Br₃C-Br∙∙∙H@β₁₂ 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 β₁₂ nanosheet to adsorb the CX₄ 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 CBr₄ at the Br1@β₁₂ site were −12.33 and −8.91 kcal/mol in the tetrel- and halogen-oriented configurations, respectively.

For the adsorption of CX₄ on the GN nanosheet, all complexes showed negative E_ads values, confirming the occurrence of the adsorption process. Similar to the CX₄∙∙∙β₁₂ complexes, the preferentiality of the adsorption process of the CX₄ 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-Cl₃∙∙∙ and Cl₃C-Cl∙∙∙T@GN complexes had E_ads values of −7.32 and −4.22 kcal/mol, respectively (Table 1).

For all CX₄∙∙∙β₁₂/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 CH₄∙∙∙, CF₄∙∙∙, and CCl₄∙∙∙GN complexes with values of −1.61, −3.46, and −8.99 kcal/mol, respectively [52]. While the adsorption of the CH₄ 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 β₁₂ nanosheet showed more affinity to adsorb the CX₄ 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 CF₄∙∙∙ > CCl₄∙∙∙ > CBr₄∙∙∙β₁₂/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-X₃ molecules to the overall interaction.

2.3. 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. The energies of the highest occupied molecular orbitals (E_HOMO, eV), the lowest unoccupied molecular orbitals (E_LUMO, eV), and the energy gap (E_gap, eV) of the CX₄ molecules and the β₁₂/GN nanosheets before and after the adsorption process.

Complex a	EHOMO (eV)	ELUMO (eV)	Egap (eV)
Isolated systems
GN Nanosheet	−2.354	−2.343	0.011
β12 Nanosheet	−2.875	−3.501	−0.626
CF4	−10.333	−0.477	9.855
CCl4	−7.416	−2.680	4.735
CBr4	−6.644	−3.394	3.250
Tetrel-oriented Configuration
FC-F3∙∙∙Br1@β12	−2.734	−3.358	−0.625
ClC-Cl3∙∙∙Br1@β12	−2.602	−3.217	−0.615
BrC-Br3∙∙∙Br1@β12	−2.544	−3.146	−0.602
FC-F3∙∙∙T@GN	−2.202	−2.191	0.0104
ClC-Cl3∙∙∙T@GN	−2.064	−2.054	0.0107
BrC-Br3∙∙∙T@GN	−2.010	−1.999	0.0108
Halogen-oriented Configuration
F3C-F∙∙∙H@β12	−2.737	−3.364	−0.627
Cl3C-Cl∙∙∙H@β12	−2.612	−3.237	−0.626
Br3C-Br∙∙∙H@β12	−2.564	−3.190	−0.626
F3C-F∙∙∙H@GN	−2.200	−2.190	0.0104
Cl3C-Cl∙∙∙T@GN	−2.066	−2.056	0.0104
Br3C-Br∙∙∙T@GN	−2.021	−2.010	0.0105

^a Structures of the most stable relaxed CX₄∙∙∙β₁₂/GN complexes within both configurations are presented in Figure 3.

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-Br₃∙∙∙Br1@β₁₂ complex was −2.544 eV, whereas the pure β₁₂ nanosheet had an E_HOMO value of −2.875 eV (Table 2). Moreover, the E_gap values of all CX₄ molecules, β₁₂, and GN nanosheets were altered, confirming the occurrence of adsorption processes. For example, the pure β₁₂ nanosheet had an E_gap value of −0.626 eV that was changed to −0.602 eV after the adsorption process within the BrC-Br₃∙∙∙Br1@β₁₂ complex (Table 2).

2.4. 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 CX₄ 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 CX₄ molecules towards the β₁₂ and GN nanosheets, and vice versa was true for the positive Q_t values.

Table 1 shows Q_t values with a negative sign for the CX₄∙∙∙β₁₂ complexes, demonstrating the ability of the inspected tetrahalomethanes to donate electrons to the β₁₂ nanosheets within the tetrel- and halogen-oriented configurations. Notably, the Q_t values of the CX₄∙∙∙β₁₂ complexes within the halogen-oriented configuration generally decreased as the adsorption energies decreased (i.e., in the order CBr₄∙∙∙ > CC1₄∙∙∙ > CF₄∙∙∙β₁₂). For instance, the Q_t values of the Br₃C-Br∙∙∙, Cl₃C-Cl∙∙∙, and F₃C-F∙∙∙T1@β₁₂ 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 CF₄∙∙∙, CCl₄∙∙∙, and CBr₄∙∙∙Br1@β₁₂ complexes within the tetrel-oriented configuration were −0.0313, −0.0283, and −0.0263 e, respectively.

The Q_t values of the CX₄∙∙∙GN complexes within the tetrel- and halogen-oriented configurations showed similar trends to the CX₄∙∙∙β₁₂ complexes, except for the CBr₄∙∙∙GN complexes within the former configuration that had positive Q_t values. For the latter complexes, the electron-accepting 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 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 CX₄ molecules had an electron-donating character except for the CBr₄∙∙∙GN complexes within the tetrel-oriented configuration. According to the Q_t values, the amount of charge transferred from the tetrahalomethanes to the β₁₂ 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-F₃∙∙∙ < ClC-Cl₃∙∙∙ < BrC-Br₃∙∙∙Br1@β₁₂ complexes.

Given that the Q_t values of the CX₄∙∙∙β₁₂/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.

2.5. Band Structure Calculations

To ascertain the impact of the adsorption of the CX₄ molecules on the electronic properties of the β₁₂ 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 β₁₂ 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 β₁₂ 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 CX₄∙∙∙β₁₂/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 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 latter 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 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-F₃∙∙∙T@GN complex shifted to −2.60 eV in the ClC-Cl₃∙∙∙T@GN complex, and then to −2.65 eV in the BrC-Br₃∙∙∙T@GN complex (Figure 5).

Summing up, the band structures of the β₁₂ nanosheet demonstrated more new bands after adsorbing the CX₄ molecules than those of the GN nanosheet. The latter affirmation indicated the further desirability of the adsorption process on the β₁₂ 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 CX₄ molecule and the studied 2D nanosheet. Further, the number of the new bands increased as the electronegativity of the halogen atom decreased. Illustratively, the CBr₄∙∙∙β₁₂/GN complexes, which exhibited the highest negative adsorption energy, showed the largest number of new bands among the other complexes (Figure 5).

2.6. 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.

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 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 ${\mathrm{X}}_{P-{\mathrm{C}\mathrm{X}}_4}$ and ${\mathrm{C}}_{P-{\mathrm{C}\mathrm{X}}_4}$, 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.

For example, the contribution of Cl_p to the CCl₄∙∙∙β₁₂ 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 β₁₂ 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 CCl₄ molecule on the β₁₂ 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 CCl₄ molecule on the β₁₂ 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 CX₄ 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 CCl₄∙∙∙Br1@β₁₂ complex within the tetrel-oriented configuration, affirming the ability of the β₁₂ nanosheet to adsorb the CCl₄ molecule. The latter observation was consistent with the E_ads of the CCl₄∙∙∙Br1@β₁₂ complex with a value of −7.74 kcal/mol (Table 1). While in the CCl₄∙∙∙H@β₁₂ complex within the halogen-oriented configuration, a small overlap between the PDOS_(Bp) of the β₁₂ nanosheet and the PDOS_(Clp) of the CCl₄ 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 CX₄ molecules on the β₁₂ 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 β₁₂ nanosheet over the GN analog to adsorb the tetrahalomethanes.

2.7. Solvent Effect Calculations

To speculate the effect of the solvent on the adsorption process within the CX₄∙∙∙β₁₂/GN complexes, the adsorption energy was evaluated in the presence of a water solvent. Afterwards, the solvent effect ($E_{ads}^{solventeffect}$) 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 $E_{ads}^{water}$ and $E_{ads}^{solventeffect}$ values are listed in

Table 3. Adsorption energy in the vacuum medium ($E_{ads}^{vacuum}$, kcal/mol), water medium ($E_{ads}^{water}$, kcal/mol), and the energy of the solvent effect ($E_{ads}^{\mathit{solvent\; effect}}$, kcal/mol) for the relaxed CX₄∙∙∙β₁₂/GN complexes (where X = F, Cl, and Br) at the most preferable adsorption sites within the tetrel (XC-X₃)- and halogen (X₃C-X)-oriented configurations.

System a	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}}^{\mathit{v}\mathit{a}\mathit{c}\mathit{u}\mathit{u}\mathit{m}}$ (kcal/mol)	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}}^{\mathit{w}\mathit{a}\mathit{t}\mathit{e}\mathit{r}}$ (kcal/mol)	${\mathit{E}}_{\mathit{a}\mathit{d}\mathit{s}}^{{\mathit{solvent\; effect}}^{\mathbf{b}}}$ (kcal/mol)
Tetrel-oriented Configuration
FC-F3∙∙∙Br1@β12	−4.46	−6.91	−2.45
ClC-Cl3∙∙∙Br1@β12	−7.74	−11.21	−3.47
BrC-Br3∙∙∙Br1@β12	−12.33	−15.99	−3.66
FC-F3∙∙∙T@GN	−4.66	−7.14	−2.48
ClC-Cl3∙∙∙T@GN	−7.32	−10.99	−3.67
BrC-Br3∙∙∙T@GN	−10.03	−14.09	−4.06
Halogen-oriented Configuration
F3C-F∙∙∙H@β12	−2.71	−4.22	−1.51
ClC-Cl3∙∙∙H@β12	−5.58	−7.26	−1.68
BrC-Br3∙∙∙H@β12	−9.00	−10.60	−1.60
F3C-F∙∙∙H@GN	−2.61	−4.17	−1.56
Cl3C-Cl∙∙∙T@GN	−4.22	−5.98	−1.76
Br3C-Br∙∙∙T@GN	−6.00	−7.72	−1.72

^a The structures of the relaxed complexes are depicted in Figure 3. ^b $E_{ads}^{\mathit{solvent\; effect}}=E_{ads}^{water}-E_{ads}^{vacuum}$.

.

According to the data presented in Table 3, the adsorption energies of the CX₄∙∙∙β₁₂/GN complexes in the water medium showed higher negative values compared with those in a vacuum. For instance, the $E_{ads}^{water}$ and $E_{ads}^{vacuum}$ values of the CBr₄∙∙∙Br1@β₁₂ complex within the tetrel-oriented configuration were −15.99 and −12.33 kcal/mol, respectively (Table 1 and Table 3, respectively). Subsequently, $E_{ads}^{\mathit{solvent\; effect}}$ exhibited negative values, confirming the occurrence of the adsorption process in the water medium. As an illustration, the $E_{ads}^{\mathit{solvent\; effect}}$ value of the CBr₄∙∙∙Br1@β₁₂ 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 $E_{ads}^{\mathit{solvent\; effect}}$ values of the CBr₄∙∙∙Br1@β₁₂ and ∙∙∙H@β₁₂ complexes within the tetrel- and halogen-oriented configurations were −3.66 and −1.60 kcal/mol, respectively.

3. 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 β₁₂ and GN nanosheets.

To model the adsorption of the tetrahalomethanes (CX₄; X = F, Cl, and Br) on β₁₂ and GN nanosheets, 3 × 4 × 1 and 6 × 5 × 1 supercells were constructed for β₁₂ and GN nanosheets, respectively. Adsorption energies (E_ads) of the CX₄∙∙∙β₁₂/GN complexes within tetrel (XC-X₃)- and halogen (X₃C-X)-oriented configurations were assessed as follows:

$$E_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{{\mathrm{C}\mathrm{X}}_4···2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}-\left({E_{{\mathrm{C}\mathrm{X}}_4}+E}_{2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}\right)$$

(1)

where $E_{{\mathrm{C}\mathrm{X}}_4···2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}$, $E_{{\mathrm{C}\mathrm{X}}_4}$, and $E_{2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}$ 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 CX₄ 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 CX₄∙∙∙β₁₂/GN complexes were computed. The energy gap (E_gap) was estimated according to the following equation:

$$E_{\mathrm{g}\mathrm{a}\mathrm{p}}=E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$$

(2)

The charge transfer of the adsorbed CX₄ molecules was determined using the Bader charge method [55,64] based on the following equation:

$$Q_{\mathrm{t}}=Q_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{d} 2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}\mathrm{s}}-Q_{\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} 2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}\mathrm{s}}$$

(3)

where $Q_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{d} 2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}\mathrm{s}}$ and $Q_{\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} 2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}\mathrm{s}}$ 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:

$$∆\rho ={\rho }_{{\mathrm{C}\mathrm{X}}_4···2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}-{\rho }_{{\mathrm{C}\mathrm{X}}_4}-{\rho }_{2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}$$

(4)

where ${\rho }_{{\mathrm{C}\mathrm{X}}_4···2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}$, ${\rho }_{{\mathrm{C}\mathrm{X}}_4}$, and ${\rho }_{2\mathrm{D} \mathrm{n}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{t}}$ 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 β₁₂ and GN nanosheets, band structure and density of state (DOS) calculations were executed. For implicit water solvent calculations, the Environ code [66] of Quantum ESPRESSO was utilized with a dielectric constant of 78.3. The solvent effect on the adsorption energy of the studied complexes ($E_{ads}^{\mathit{solvent\; effect}}$) was computed according to the following equation:

$$E_{ads}^{\mathit{solvent\; effect}}=E_{ads}^{water}-E_{ads}^{vacuum}$$

(5)

where $E_{ads}^{water}$ and $E_{ads}^{vacuum}$ are the adsorption energies of the complex in water and vacuum media, respectively.

4. Conclusions

In the presented work, a DFT study was conducted to comparatively illustrate the adsorption features of tetrahalomethanes (CX₄, where X = F, Cl, and Br) on β₁₂ borophene (β₁₂) 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 CX₄ molecules on the studied 2D nanosheets within tetrel (XC-X₃)- and halogen (X₃C-X)-oriented configurations. From the energetic perspective, the adsorption of the CX₄ model on the β₁₂ and GN nanosheets within the tetrel-oriented configuration was more desirable than that within the halogen-oriented configuration. Further favorability of the Br1@β₁₂ and T@GN adsorption sites were announced toward adsorbing the CX₄ molecules within the tetrel-oriented configuration and showed the most significant E_ads for the CBr₄ 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 β₁₂ and GN nanosheets were changed following the adsorption process. Based on the Bader charge results, the electron-donating characters for all the CX₄ molecules after adsorbing on the β₁₂ and GN nanosheets within tetrel- and halogen-oriented configurations were illustrated, except the CBr₄∙∙∙GN complexes within the former configuration. In the latter complexes, the adsorbed CBr₄ 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 CX₄ 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 β₁₂ and GN nanosheets to adsorb small molecules.