On the Use of Graphene Nanosheets for Drug Delivery: A Case Study of Cisplatin and Some of Its Analogs

Graphene (GN) nanosheets have been widely exploited in biomedical applications as potential nanocarriers for various drugs due to their distinct physical and chemical properties. In this regard, the adsorption behavior of cisplatin (cisPtCl2) and some of its analogs on a GN nanosheet was investigated in perpendicular and parallel configurations by using density functional theory (DFT). According to the findings, the most significant negative adsorption energies (Eads) within the cisPtX2⋯GN complexes (where X = Cl, Br, and I) were observed for the parallel configuration, with values up to –25.67 kcal/mol at the H@GN site. Within the perpendicular configuration of the cisPtX2⋯GN complexes, three orientations were investigated for the adsorption process, namely, X/X, X/NH3, and NH3/NH3. The negative Eads values of the cisPtX2⋯GN complexes increased with the increasing atomic weight of the halogen atom. The Br@GN site showed the largest negative Eads values for the cisPtX2⋯GN complexes in the perpendicular configuration. The Bader charge transfer outcomes highlighted the electron-accepting properties of cisPtI2 within the cisPtI2⋯GN complexes in both configurations. The electron-donating character of the GN nanosheet increased as the electronegativity of the halogen atom increased. The band structure and density of state plots revealed the occurrence of the physical adsorption of the cisPtX2 on the GN nanosheet, which was indicated by the appearance of new bands and peaks. Based on the solvent effect outlines, the negative Eads values generally decreased after the adsorption process in a water medium. The recovery time results were in line with the Eads findings, where the cisPtI2 in the parallel configuration took the longest time to be desorbed from the GN nanosheet with values of 61.6 × 108 ms at 298.15 K. The findings of this study provide better insights into the utilization of GN nanosheets in drug delivery applications.

Metal-based compounds have long been thought to have therapeutic potential because metals exhibit superior properties, such as reactivity toward organic substrates, redox activity, and variable coordination modes [23]. In 1978, Cisplatin (cisPtCl 2 ), a platinummetal-based drug with the molecular formula cis-[PtCl 2 (NH 3 ) 2 ], was approved by the U.S. Food and Drug Administration (FDA) and has since been commonly used as an effective drug against lung, ovarian, and colorectal cancers [24][25][26][27][28][29][30]. The enormous clinical success of the cisPtCl 2 drug has sparked an intensive search for platinum analogs with possibly superior biological and pharmacological properties. Examples of such analogs were prepared by replacing the two chloride atoms of the cisPtCl 2 with different halides, including bromide and iodide atoms [31,32]. Intriguingly, cis-[PtBr 2 (NH 3 ) 2 ] (cisPtBr 2 ) and cis-[PtI 2 (NH 3 ) 2 ] (cisPtI 2 ) exhibited remarkable biological characteristics relative to the cisPtCl 2 drug [31,32]. However, generally, platinum-based chemotherapy has serious side effects caused by its low specificity and non-selectivity, resulting in systemic toxicities that severely limit its efficacy [33,34]. One of the potential remedies for these side effects is utilizing a nanocarrier that can offer a better-guided delivery form that increases the percentage of the drug that reaches the target cancerous cells out of the administered dose. This, in turn, decreases the systemic dose and increases the therapeutic outcomes [35,36]. In this regard, GN-based materials were employed as effective nanocarriers for the cisPtCl 2 drug [37][38][39][40]. More than one theoretical study was conducted with the aim of characterizing the nature of the interactions between drugs, including cisplatin, and non-drug biological adsorbents with GN and GN-oxide surfaces [11,37,38]. However, the potential of GN nanosheets for delivering the cisPtBr 2 and cisPtI 2 analogs has not yet been investigated.
In the current study, the utilization of GN nanosheets as a drug delivery system for the anticancer drug cisPtCl 2 and its analogs was investigated ( Figure 1). The adsorption behavior of the cisPtX 2 (where X = Cl, Br, and I) molecules on a GN nanosheet was systematically investigated and comparatively assessed via various DFT calculations. To better understand the adsorption process of the cisPtX 2 · · · GN complexes, adsorption of the cisPtX 2 on the GN nanosheet was conducted at different adsorption sites in perpendicular and parallel configurations. Geometric optimizations were performed for all complexes, followed by adsorption energy calculations. Based on the relaxed structures, post-analyses, including Bader charge, density of states (DOS), and band structure, were executed for the most favorable cisPtX 2 · · · GN complexes. Furthermore, the solvent effect and recovery time were evaluated for the most favorable configurations. This study provides an understanding of the adsorption energetics, binding relationships, regioselectivity, and electron donor/acceptor sites of the cisPtX 2 molecules and GN nanosheet. This can further support the informative design of GN nanocarriers that can better suit cisPtX 2 drug delivery.

Computational Methods
All computations for the adsorption of cisPtX2 on GN were performed with the DFT method [41,42] as implemented in Quantum ESPRESSO 6.4.1 code [43,44]. The Perdew-Burke-Ernzerhof method within the generalized gradient approximation was applied to describe the exchange-correlation functional of the electronic interactions [45]. To denote the electron-ion interactions, the ultrasoft pseudopotential was utilized [46]. Grimme's DFT-D2 method was adopted to correct the dispersion interaction [47]. The cutoffs of the optimized kinetic energy and the charge density were set to 40 and 400 Ry, respectively. For all calculations, the thresholds for force and energy convergence were chosen at 10 −4 eV/Å and 10 −5 eV, respectively. The first Brillouin zone was sampled depending on Monkhorst-Pack grids as 4 × 4 × 1 and 8 × 8 × 1 k-points for the geometry optimization and the density of states calculations, respectively. Moreover, the Marzari-Vanderbilt smearing method [48] was applied with a Gaussian spreading value of 10 -4 Ry. A vacuum region of 20 Å was generated to separate artificially periodic cells along the z-direction of the GN surface. A 6 × 6 × 1 supercell involving 72 carbon atoms was designed to investigate the adsorption process.
Adsorption of cisPtX2 over the GN nanosheet was investigated in perpendicular and parallel configurations ( Figure 2). For the perpendicular configuration, three different orientations for the cisPtX2, namely, X/X, X/NH3, and NH3/NH3, were considered for the adsorption process on the GN nanosheet. Based on the optimized geometries, the adsorption energy (Eads) was estimated based on the following formula: , and represent the energies of the complex, the adsorbed cisPtX2, and the GN nanosheet, respectively. For a more detailed examination of the adsorption process of cisPtX2 molecules on the GN nanosheet, frontier molecular orbital (FMO) calculations were performed. Based on the FMO analyses, the energies of the highest occupied molecular orbitals (EHOMO) and lowest unoccupied molecular orbitals (ELUMO) were computed for the most favorable relaxed cisPtX2···GN complexes. The energy gap (Egap) was calculated according to the following formula: (2) In addition, Bader charge analysis [49,50] was applied to determine the charge transfer (Qt) from or towards the GN nanosheet after the adsorption process according to the following equation:

Computational Methods
All computations for the adsorption of cisPtX 2 on GN were performed with the DFT method [41,42] as implemented in Quantum ESPRESSO 6.4.1 code [43,44]. The Perdew-Burke-Ernzerhof method within the generalized gradient approximation was applied to describe the exchange-correlation functional of the electronic interactions [45]. To denote the electron-ion interactions, the ultrasoft pseudopotential was utilized [46]. Grimme's DFT-D2 method was adopted to correct the dispersion interaction [47]. The cutoffs of the optimized kinetic energy and the charge density were set to 40 and 400 Ry, respectively. For all calculations, the thresholds for force and energy convergence were chosen at 10 −4 eV/Å and 10 −5 eV, respectively. The first Brillouin zone was sampled depending on Monkhorst-Pack grids as 4 × 4 × 1 and 8 × 8 × 1 k-points for the geometry optimization and the density of states calculations, respectively. Moreover, the Marzari-Vanderbilt smearing method [48] was applied with a Gaussian spreading value of 10 −4 Ry. A vacuum region of 20 Å was generated to separate artificially periodic cells along the z-direction of the GN surface. A 6 × 6 × 1 supercell involving 72 carbon atoms was designed to investigate the adsorption process.
Adsorption of cisPtX 2 over the GN nanosheet was investigated in perpendicular and parallel configurations ( Figure 2). For the perpendicular configuration, three different orientations for the cisPtX 2 , namely, X/X, X/NH 3 , and NH 3 /NH 3 , were considered for the adsorption process on the GN nanosheet. Based on the optimized geometries, the adsorption energy (E ads ) was estimated based on the following formula: where E cisPtX 2 ···GN , E cisPtX 2 , and E GN represent the energies of the complex, the adsorbed cisPtX 2 , and the GN nanosheet, respectively. For a more detailed examination of the adsorption process of cisPtX 2 molecules on the GN nanosheet, frontier molecular orbital (FMO) calculations were performed. Based on the FMO analyses, the energies of the highest occupied molecular orbitals (E HOMO ) and lowest unoccupied molecular orbitals (E LUMO ) were computed for the most favorable relaxed cisPtX 2 · · · GN complexes. The energy gap (E gap ) was calculated according to the following formula: where stands for the attempt frequency with a value of 10 12 s −1 . K stands for the Boltzmann constant. T refers to the temperature, where the values of 295.15, 310.15, and 315.15 K were used for room, human body, and cancer cell temperatures, respectively. The computational approach adopted in this study was developed and successfully implemented in several previous reports [53][54][55][56].  In addition, Bader charge analysis [49,50] was applied to determine the charge transfer (Q t ) from or towards the GN nanosheet after the adsorption process according to the following equation: where Q combinedGN and Q isolatedGN are the charge of the GN nanosheet after and before the adsorption process, respectively. In addition, charge density difference (∆ρ) maps were plotted based on the following formula: Visualization for Electronic and Structural Analysis (VESTA) package was utilized to generate ∆ρ maps [51]. The band structure, total density of states (TDOS), and projected density of states (PDOS) analyses were also conducted. To investigate the effect of the water solvent on the adsorption process, the environ code, which is available for Quantum ESPRESSO, was utilized with the self-consistent charge solvation model by using a dielectric constant of 78.3 [52]. The solvent effect (E solvent e f f ect ads ) on the adsorption process of the investigated complexes was evaluated as follows: E solvent e f f ect ads where E water ads and E vacuum ads are the adsorption energies of the complex in water and vacuum media, respectively. Furthermore, the recovery time (τ) was also computed for the desorption process of the drug from the GN nanosheet based on the following equation: where v −1 stands for the attempt frequency with a value of 10 12 s −1 . K stands for the Boltzmann constant. T refers to the temperature, where the values of 295.15, 310.15, and 315.15 K were used for room, human body, and cancer cell temperatures, respectively. The computational approach adopted in this study was developed and successfully implemented in several previous reports [53][54][55][56].

Geometric Structures
A GN nanosheet was constructed, and all carbon atoms in the supercell were fully relaxed to obtain the equilibrium structure. Based on the relaxed structures, the lattice constant of the GN unit cell was a = 2.47 Å, which was in good agreement with the theoretical and experimental values for bulk graphite [57][58][59][60][61]. The GN nanosheet featured a symmetric carbon-carbon bond with a length of 1.42 Å, which produced three adsorption sites, namely, the top (T), hollow (H), and bridge (Br) sites.

Adsorption Energy Calculations
The adsorption process of the cisPtX 2 was explored at different adsorption sites on the GN nanosheet in perpendicular and parallel configurations ( Figure 2). All of the constructed cisPtX 2 · · · GN complexes (where X = Cl, Br, and I) were fully relaxed, and their optimized structures are depicted in Figure S1. After that, the adsorption energies of the relaxed systems were computed, and their results are listed in Table 1. Based on the obtained adsorption energies, the structures of the most favorable cisPtX 2 · · · GN complexes are displayed in Figure 3. Table 1. Adsorption energy (E ads , kcal/mol) of cisPtX 2 (where X = Cl, Br, and I) on the GN nanosheet at all adsorption sites. The charge transfer (Q t ) of the GN nanosheet before and after the adsorption process is given in e.  Figure S1. b Adsorption sites on the surface of the GN nanosheet (see Figure 1). c Q t was evaluated according to Equation (   As shown in Table 1, all relaxed cisPtX 2 · · · GN complexes showed negative adsorption energy values, demonstrating that cisPtX 2 could be loaded onto the GN nanosheet. For the cisPtX 2 · · · GN complexes, it can be seen that the cisPtI 2 · · · GN complexes in the X/X orientation showed the most significant E ads values, followed by the cisPtBr 2 · · · and then cisPtCl 2 · · · GN complexes. For instance, the E ads values of the cisPtI 2 · · · , cisPtBr 2 · · · , and cisPtCl 2 · · · T@GN were −10.68, −9.19, and −8.13 kcal/mol, respectively. Almost all E ads values of the cisPtX 2 · · · GN complexes increased in the following order: cisPtX 2 · · · H@GN < · · · T@GN < · · · Br@GN. For example, the E ads value of the cisPtI 2 · · · GN complexes were −10.68, −10.69, and −10.83 kcal/mol at H@GN, T@GN, and Br@GN sites, respectively ( Table 1).

Orientation
For the cisPtX 2 · · · GN complexes in the X/NH 3 orientation, the negative E ads values increased as the electronegativity of the halogen atom decreased. In this regard, the cisPtCl 2 · · · GN complexes showed the smallest negative E ads values compared with the cisPtBr 2 · · · and cisPtI 2 · · · GN complexes, with E ads values of −9.89, −10.60, and −11.14 kcal/mol, respectively (Table 1).
In the NH 3 /NH 3 orientation of the cisPtX 2 · · · GN complexes, the Br@GN site showed the most considerable adsorption energies compared with the T@GN and H@GN sites. For instance, the E ads values of the cisPtCl 2 · · · Br@GN, · · · T@GN, and · · · H@GN complexes were −12.73, −12.60, and −12.27 kcal/mol, respectively ( Table 1). The adsorption of the cisPtI 2 on the GN nanosheet at the Br@GN site showed the largest E ads value of −13.36 kcal/mol.
To sum up, the negative E ads values increased with the increase in the atomic weight of the halogen atoms in the following order: cisPtCl 2 · · · < cisPtBr 2 · · · < cisPtI 2 · · · GN complexes. The latter finding agreed with a finding of a previous study that reported the interaction strength decreased with the decrease in the atomic weight of the halogen atom [55]. The parallel configuration of the studied cisPtX 2 molecules on the GN nanosheet had more significant adsorption energy than that in the perpendicular configuration. The Br@GN and H@GN sites were preferential for adsorbing the cisPtX 2 in the perpendicular and parallel configurations, respectively. These results are in agreement with previously reported results for the most favorable conformation for the interaction of cisPtCl 2 with different graphene models, in which the parallel configuration showed a more favorable binding with an average adsorption energy of 20 kcal/mol over different graphene models [37,38].

Frontier Molecular Orbital (FMO) Calculations
The energies of the highest occupied molecular orbitals (E HOMO ), the lowest unoccupied molecular orbitals (E LUMO ), and the energy gap (E gap ) were evaluated to thoroughly reveal the impact of the adsorption process on the electronic characteristics of the investigated systems. The E HOMO , E LUMO , and E gap values before and after the adsorption process are presented in Tables 2 and 3, respectively. To understand the electron transfer regioselectivity of the studied molecules, the distributions of both HOMO and LUMO were generated for the isolated systems and the most favorable relaxed cisPtX 2 · · · GN complexes were determined (Figures S2 and S3).
From the summarized data in Tables 2 and 3, the E HOMO , E LUMO , and E gap values of the studied systems were observed with notable differences before and after the adsorption process. For example, in the parallel configuration, the E HOMO values of the cisPtCl 2 · · · , cisPtBr 2 · · · , and cisPtI 2 · · · H@GN complexes were −2.155, −2.143, and −2.127 eV, respectively, whereas the pure GN nanosheet had an E HOMO value of −2.355 eV (Tables 2 and 3). Further, the E gap values of the cisPtX 2 molecules and GN nanosheet were changed after the adsorption process, demonstrating the occurrence of the adsorption. For instance, in the parallel configuration, the pure GN nanosheet had an E gap value of 0.016 eV that was changed after the adsorption process to 0.026 eV in the case of the cisPtI 2 · · · H@GN complex  (Tables 2 and 3). Notably, the E gap was denoted with small values, which demonstrated the feasibility of transferring the charge within the complex.  Figure S1. b The most favorable relaxed cisPtX 2 · · · GN complexes are depicted in Figure 3.
Looking at Figure S2, it can be seen that the HOMO orbitals of the cisPtX 2 molecules were located on the halogen and platinum atoms, indicating that these atoms acted as electron donor sites in the adsorption process with the GN nanosheet. Furthermore, the LUMO orbitals were observed on the NH 3 group of the cisPtX 2 molecules, indicating the electron-accepting character of this group in the adsorption process. For the relaxed cisPtX 2 · · · GN complexes, the HOMO and LUMO orbitals were located on the carbon atoms of the GN nanosheet, while the LUMO orbitals were observed on the Pt atom, demonstrating its electron-accepting property ( Figure S3).

Charge Transfer Calculations
Bader charge analysis is an effective tool for gaining better insight into charge transfer between the adsorbate and the substrate through adsorption processes [49,62]. Within the context of Bader charge analysis, the charge transfer differences (Q t ) were determined for the relaxed cisPtX 2 · · · GN complexes in the perpendicular and parallel configurations  (Table 1). Notably, the Q t values had negative signs, indicating the charge transfer from the cisPtX 2 to the GN nanosheet. In contrast to the negative Q t values, the positive signs indicated that the charge shifted from the GN nanosheet to the adsorbed cisPtX 2 .
In the NH 3 /NH 3 orientation, the adsorption of the cisPtCl 2 and cisPtBr 2 on the GN nanosheet led to a transfer of the charge from the adsorbate to the substrate, which was indicated by the negative Q t values. In comparison, the cisPtI 2 acted as an electron donor within the cisPtI 2 · · · GN complexes, giving positive Q t values (Table 1). Notable electrondonating properties were observed for cisPtCl 2 and cisPtBr 2 and disappeared for cisPtI 2 within the adsorption process in the NH 3 /NH 3 orientation. For instance, the Q t values of the cisPtCl 2 · · · , cisPtBr 2 · · · , and cisPtI 2 · · · Br@GN were −0.0159, −0.0028, and 0.0250 e, respectively (Table 1).
In the parallel configuration, almost all of the Q t values of the cisPtX 2 · · · GN complexes had positive signs, revealing the electron-donating character of the GN nanosheet. In this regard, the ability of cisPtX 2 to gain the charge from the GN nanosheet increased with the increase in the atomic weight of the halogen atom. For example, the cisPtCl 2 · · · , cisPtBr 2 · · · , and cisPtI 2 · · · H@GN complexes had positive Q t with values of 0.0042, 0.0156, and 0.0312 e, respectively (Table 1).
Following the Bader charge analysis, the charge density difference (∆ρ) maps were generated for the most favorable cisPtX 2 · · · GN complexes to evaluate the distribution of charge ( Figure 4). According to the ∆ρ maps, the amount of the accumulated (i.e., positive) and depleted (i.e., negative) charge agreed with the Q t results (Table 1). For example, in the X/X orientation, adsorption of cisPtX 2 on GN nanosheet showed electron-accepting properties in the perpendicular and parallel configurations, as confirmed by the accumulated charge region (yellow color) below the cisPtX 2 ( Figure 4). In line with the E ads findings, the parallel configuration of the cisPtX 2 · · · GN complexes showed that the largest amount of charge was accumulated in a region distributed over the complexes. However, it can be seen that in the X/NH 3 orientation, the charge-depleted region was observed below the NH 3 part, and the charge-accumulated region was noted below the X part, as shown by the cyan and yellow colors, respectively. The latter observation indicated that the X atoms had the dominant contribution to the adsorption process of cisPtX 2 on the GN nanosheet.
Based on the Bader charge outcomes, the cisPtI 2 behaved as an electron acceptor through the adsorption process on the GN nanosheet in both the perpendicular and parallel configurations. The adsorption of the cisPtBr 2 on the GN nanosheet resulted in gaining the charge from the GN nanosheet in both configurations, except for in the NH 3 /NH 3 orientation in the perpendicular configuration. Furthermore, the electron-accepting character of the GN nanosheet decreased as the electronegativity of the X atom decreased. Pharmaceutics 2023, 15, x FOR PEER REVIEW 10 of 19  Charge density difference (∆ρ) maps of the most favorable cisPtX 2 · · · GN complexes (where X = Cl, Br, and I) in the perpendicular and parallel configurations. Electron accumulation and depletion sites are indicated by yellow-and cyan-colored regions, respectively. Pale brown, silver, pink, gray, green, dark brown, and violet balls refer to carbon, platinum, hydrogen, nitrogen, chloride, bromide, and iodide atoms, respectively.

Band Structure Calculations
In order to ascertain how the adsorbed cisPtX 2 affected the electronic properties of the GN nanosheet, electronic band structure calculations were performed for the GN nanosheet before and after the adsorption process ( Figure 5 and Figure S4a).

Band Structure Calculations
In order to ascertain how the adsorbed cisPtX2 affected the electronic properties of the GN nanosheet, electronic band structure calculations were performed for the GN nanosheet before and after the adsorption process (Figures 5 and S4a). According to the Eads findings, the electronic band structures were plotted for the most favorable cisPtX2···GN complexes in the perpendicular and parallel configurations ( Figure 5). As shown in Figure 5, all of the band structure plots demonstrated that the adsorption of cisPtX2 on the GN nanosheet affected the electronic characteristics of the pure GN surface. According to the E ads findings, the electronic band structures were plotted for the most favorable cisPtX 2 · · · GN complexes in the perpendicular and parallel configurations ( Figure 5). As shown in Figure 5, all of the band structure plots demonstrated that the adsorption of cisPtX 2 on the GN nanosheet affected the electronic characteristics of the pure GN surface.
In the perpendicular configuration of the studied complexes in the X/X orientation, new bands appeared for the cisPtX 2 · · · Br@GN complexes, highlighting the contribution of the cisPtX 2 s bands with those of the pure GN nanosheet. In the cisPtCl 2 · · · Br@GN complex, additional bands appeared at −1.53, −1.70, −1.80, and −2.00 eV in the valence region, while in the conduction region, new bands appeared at 1.75 and 1.35 eV ( Figure 5). The adsorption of the cisPtBr 2 at the Br@GN site resulted in the appearance of new valence bands at −1.20, −1.55, −1.62, and −2.08 eV, while additional bands in the conduction region were observed at 1.75 and 1.23 eV. Obviously, the valence and conduction bands in the cisPtI 2 · · · Br@GN complex were shifted toward the Fermi level, announcing the significant adsorption process of the cisPtI 2 on the GN nanosheet. The latter observation confirmed the significant adsorption of the cisPtI 2 on the GN nanosheet, which was compatible with the E ads findings (Table 1).
New bands were observed in the band structures of the cisPtX 2 · · · GN complexes in the X/NH 3 orientation. For instance, in the cisPtBr 2 · · · Br@GN complex, many bands in the valence region were noted between −0.58 and −2.50 eV. In line with the adsorption energy affirmations, the band structures showed that the cisPtI 2 · · · GN complexes were preferable, as revealed by the bands that shifted toward the Fermi level ( Figure 5).
In addition, the adsorption of the cisPtX 2 on the GN nanosheet in the parallel configuration led to the appearance of new bands in the valence and conduction regions. For example, the band structure of the cisPtI 2 · · · H@GN complex showed new valence bands at −2.25 and −2.30 eV, while new conduction bands appeared at 0.50, 0.75, 0.88, and 1.15 eV.
Summing up, the adsorption of the cisPtX 2 on the GN nanosheet in the perpendicular and parallel configurations affected the band structure of the GN nanosheet. In line with the E ads and Q t findings, the band structure plots revealed the most favorable adsorption process of the cisPtI 2 on the GN nanosheet. In addition, the presence of the Dirac point on the GN nanosheet after the adsorption process indicated the physical adsorption of the cisPtX 2 on the GN nanosheet.

Density of States (DOS) Calculations
To describe the influence of the adsorption of the cisPtX 2 on the electronic characteristics of the GN nanosheet, the TDOS and PDOS were generated for pure and combined GN nanosheets ( Figure S4b). Figure 6 illustrates the TDOS and PDOS analyses for the most favorable cisPtX 2 · · · GN complexes in the perpendicular and parallel configurations.
As depicted in Figure 6, it was observed that the adsorption process mainly originated from the contributions of the X p , C p , N p , and Pt d of the cisPtX 2 with the C p of the GN nanosheet. In contrast, the H s of the cisPtX 2 showed a small effect on the adsorption process. For instance, the PDOS plot of the cisPtCl 2 · · · Br@GN complex in both the perpendicular and parallel configurations demonstrated the contribution of the Cl p to the adsorption process, which appeared in the valence region from −4.50 to −1.00 eV. In addition, the participation of N p and Pt d in the adsorption process of the cisPtCl 2 on the GN nanosheet was detected in the valence region at energies ranging from −7.

Recovery Time
Recovery time (τ) calculations are necessary to comprehend the desorption process of the cisPtX 2 from the GN nanosheet. Therefore, τ was evaluated at three different temperatures. The findings on τ for the most favorable cisPtX 2 · · · GN complexes (where X = Cl, Br, and I) in the perpendicular and parallel configurations are listed in Table 4.  Figure S1.
According to the data in Table 4, τ had a direct correlation with the E ads findings, showing that as the negative E ads value increased, τ increased, and the desorption process became more difficult. For example, the cisPtI 2 · · · H@GN complex in the parallel configuration had the most prominent negative E ads with a value of −25.67 kcal/mol and the longest τ of 61.63 × 10 8 , 11.56 × 10 8 , and 5.97 × 10 8 ms at the room, human body, and cancer cell temperatures, respectively. The τ values showed a clear decrease with increasing temperature; for instance, the τ values of the cisPtCl 2 · · · Br@GN complexes were 12.30 × 10 −4 , 7.15 × 10 −4 , and 5.77 × 10 −4 ms at the room, human body, and cancer cell temperatures, respectively (Table 4). Therefore, the desorption process at the temperature of cancer cells showed the fastest τ.

Solvent Effects
In order to hypothesize about the influence of solvent on the adsorption process of the cisPtX 2 on the GN nanosheet, the adsorption energy was assessed in the presence of a water medium. The solvent effect (E solvent e f f ect ads ) energy was calculated for the most favorable cisPtX 2 · · · GN configurations by subtracting the adsorption energies in the vacuum medium from those in the water solvent. The computed E water ads and E solvent e f f ect ads values are tabulated in Table 5.
According to Table 5, negative E water ads values demonstrated that the GN nanosheet had the potential to adsorb the cisPtX 2 in a water solvent within the perpendicular and parallel configurations. It can be seen that the parallel configuration of the cisPtX 2 · · · H@GN complexes showed the most significant negative E water ads with values of −18.21, −20.02, and −22.40 kcal/mol for cisPtCl 2 · · · , cisPtBr 2 · · · , and cisPtI 2 · · · H@GN, respectively.  Figure S1.
Generally, the obtained results showed that the most favorable cisPtX 2 · · · GN complexes in the water solvent had lower negative E ads values compared to those in the vacuum medium. For instance, the cisPtCl 2 · · · H@GN complex had negative E ads values of −22.76 and −18.21 kcal/mol in the vacuum and water media, respectively. The latter observation revealed the occurrence of physical adsorption between the cisPtX 2 and the GN nanosheet in the water medium.

Conclusions
To gain a better insight into the use of GN nanosheets as nanocarriers for anticancer drugs, the adsorption behavior of cisPtCl 2 and its analogs (cisPtX 2 , where X = Br, and I) on a GN nanosheet in the perpendicular and parallel configurations was investigated. Based on the findings, the largest negative E ads values were observed for the parallel configuration of the cisPtX 2 · · · GN complexes with values of up to −25.67 kcal/mol. In the perpendicular configuration of the cisPtX 2 · · · GN complexes, three possible orientations were observed, namely, X/X, X/NH 3 , and NH 3 /NH 3 . The NH 3 /NH 3 orientation had the greatest negative E ads values compared to the other orientations. For instance, the E ads values of the cisPtCl 2 · · · T@GN complexes in the X/X, X/NH 3 , and NH 3 /NH 3 orientations were −8.13, −9.70, and −12.60 kcal/mol, respectively. Remarkably, the negative E ads values decreased by increasing the electronegativity of the halogen atoms within the cisPtX 2 · · · GN complexes in the following order: cisPtI 2 · · · > cisPtBr 2 · · · > cisPtCl 2 · · · GN. The Br@GN site showed the largest negative E ads values in the perpendicular configuration for the cisPtX 2 · · · GN complexes, while the H@GN was the most favorable site in the parallel configuration. Based on FMO findings, changes in the E HOMO , E LUMO , and E gap values of the GN nanosheet were noticed after the adsorption process. According to the Bader charge outlines, the cisPtI 2 exhibited an electron-accepting character through the adsorption process on the GN nanosheet in both configurations. The appearance of new bands and peaks in the band structure and the DOS plots affirmed the occurrence of the adsorption process of the cisPtX 2 on the GN nanosheet. The solvent effect results demonstrated that the cisPtX 2 could be adsorbed on the GN nanosheet in a water solvent via a physical adsorption process. The cisPtI 2 · · · GN complexes with the largest negative E ads values had the longest recovery time for the desorption process in the parallel configuration of up to 61.63 × 10 8 ms at 298.15 K. The outcomes of this work will contribute to a better understanding of the utilization of GN nanosheets in drug delivery applications for anticancer drugs. Developing a better understanding of the adsorption process of cisplatin, its analogs, and other reported drug molecules on GN surfaces opens the door for more efficiently designed GN-based nanocarriers and provides the possibility of co-adsorption of more than one active drug molecule.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/pharmaceutics15061640/s1, Figure S1: Top and side views of all the relaxed structures for cisPtX 2 · · · GN complexes (where X = Cl, Br, and I) in the perpendicular and parallel configurations at all adsorption sites. The equilibrium distances (d) are presented in Å.; Figure S2: Distributions of the HOMO and LUMO for the GN nanosheet and cisPtX 2 molecules before the adsorption process.; Figure S3: Distributions of the HOMO and LUMO for the most favorable relaxed cisPtX 2 · · · GN complexes in the parallel configuration.; Figure S4: (a) Band structure of the pure GN nanosheet along high-symmetry points of the Brillouin zone; (b) total and projected density of states (TDOS/PDOS) for the pure GN nanosheet. The contribution of the p-orbital of carbon atoms is indicated by C p . The Fermi level is located at zero energy. Data Availability Statement: Data will be made available on request.