DFT investigation on the application of pure and doped X12N12 (X = B and Al) fullerene-like nano-cages toward the adsorption of temozolomide

The sensitivity of pure and doped X12N12 (X = B and Al) fullerene-like nano-cages (FLNs) toward the anti-cancer drug temozolomide (TMZ) is probed herein at DFT/M06-2X-D3/6-311G(d,p) theoretical level in both gas phase and water. A noticeable affinity of the FLNs toward TMZ was observed along with the negative gas-phase adsorption energies −1.37 and −2.09 eV for the most stable configurations of pure B12N12 and Al12N12 pristines, respectively. Considerable charge transfer from TMZ to the FLNs was also revealed via NBO analysis and the Hirshfeld atomic charges, making the dipole moment vector of the molecular complexes to be oriented from the nano-cages to the TMZ moiety. Furthermore, a percentage decrease in the HOMO-LUMO energy gap (ΔEg) of 38.09 and 17.72% was obtained for the B12N12 and Al12N12 nano-cages, respectively. The percentage change in ΔEg was found to be reduced upon doping and solvation of the FLNs. Finally, a recovery time in vacuum ultraviolet light of 1.06 s is found for the complex with pure B12N12, which in addition to the above-mentioned parameters make this boron nitride cage the best sensor for TMZ, among the FLNs considered in the present work.


Introduction
Temozolomide (TMZ) (marketed under the trademarks temodar or temodal) is an oral chemotherapeutic agent approved for the treatment of anaplastic astrocytoma and gliomas (the most common and most malignant primary tumours of the central nervous system). Malignant gliomas diffusive infiltration into adjacent brain parenchyma and resistance to cell death [1]. TMZ is spontaneously converted into the active alkylation metabolite (methyl-triazene-1-yl)-imidazole-4-carboxamide (MTIC) under physiological conditions. The commonest side effects of TMZ include nausea, diarrhea, vomiting, headaches, constipation, taste changes and rashes. The less common side effects are hair loss (including eyebrows and eyelashes), dizziness, shortness of breath, infertility (depending on the combination of medicines and the dose that is given) [2]. TMZ has also been reported to affect CD4 + T cells, leading to clinically significant opportunistic infections like Pneumocystis carinii, Aspergillus pneumoniae, herpes simplex, herpes zoster, hepatitis B virus etc. [1][2][3][4][5]. It is worthy of note that patients suffering from glioma may easily die from infectious complications. Owing to the wide therapeutic scale and effects of TMZ, Mariano and coworkers have reported several analytical methods for its detection [6]. In this regard, nanotechnologies have been of paramount importance in recent decades.
Experimental and theoretical chemistry methods are widely used in probing the sensing ability of nanoparticles (NPs) toward various classes of chemicals. Organic NPs (like lipids and micelles), inorganic NPs (like metal oxide, quantum dots and fullerenes) or a hybrid of these components are the common classes of NPs used for sensing and drug delivery. Several studies have been published on carbonic and non-carbonic nanostructures such as nano-sheets [7][8][9], fullerene-like nano-cages (FLN) [10,11] and nano-tubes [12,13], due to their excellent physical, chemical and surface characteristic properties. Among these NPs, FLNs are recently receiving considerable attention. They have been found to be excellent gas sensors [14][15][16]. One of the most prominent fields of application of the FLNs is their use as drug sensors, as well as carriers for drug delivery. In that regard, the adsorption of anticancer drugs, including thioguanine isomers [11], melphalan [17], Zolinza drug [10], 5-fluorouracil [18], exemestane [19] and Celecoxib [20] at the external surface of FLNs has been reported. The aforementioned works have highlighted the potential of FLNs as a medium for anti-cancer drug delivery.
The main objective of this work was to probe the adsorption of the anti-cancer drug TMZ onto the external surface of pure and doped X 12 N 12 (X = B and Al) using the density functional theory (DFT) computational chemistry method. Interestingly, DFT calculations have been used to study the adsorption of TMZ onto the surface of iron-oxide (Fe 3 O 4 ) nanoparticles via an interaction involving the oxygen and nitrogen atoms of the former, and the Fe 2+ and/or Fe 3+ ion of the latter [21]. Furthermore, Zhu and co-workers have recently shown, via the DFT/B3LYP/6-31G (d) method, that pristine BC 3 NT is a promising drug deliverer for TMZ [8]. Nevertheless, B 12 N 12 and Al 12 N 12 have been proven to be the most stable FLN structures, which have been synthesized by Oku et al. [22] and Liu et al. [23], respectively. These compounds possess unique physico-chemical properties such as high thermal conductivity, chemical stability, wide band gap and oxidation resistance [24]. Owing to the exceptional results obtained for the delivery of many anti-cancer drugs by B 12 N 12 and Al 12 N 12 , the adsorption of TMZ at the surface of these nano-cages is investigated herein in order to propose a new drug delivery system for TMZ. The adsorbent-adsorbate interactions have been extensively described using the quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analysis. The effects of adsorption on the electronic properties (such as molecular orbitals energy and distribution and electronic spectra) of the nano-cages have also been evaluated. The calculations have been performed using DFT methods in gas phase and water. The findings of this research endeavour can be useful for designing an appropriate and novel carrier for the detection, as well as the delivery, of TMZ.

Computational details
All molecular structures considered here have been relaxed at DFT/M06-2X/6-311G(d,p) [25][26][27] level of theory using the Gaussian 09 package [28]. The reliability of the M06-2X hybrid functional for such calculations has long been proven since it accurately estimates structural, energetic and electronic properties [29][30][31]. The Gordon dispersion GD3 correction was applied in order to better describe the non-covalent interactions (NCI) in the molecules studied [32]. Harmonic vibrational frequencies have been calculated at the same computational level after geometry relaxation, and their analysis showed that all structures corresponded to minima on their potential energy surfaces. The adsorption ability of the nano-cages toward TMZ was evaluated through adsorption energies (ΔE Ads ), enthalpies (ΔH ) royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 and free energy changes (ΔG), calculated as shown in equations (2.1)-(2.3). E FLN-TMZ is the total energy of the complex formed between the nano-cage and TMZ, whereas E FLN and E TMZ are the total energies of the FLNs and TMZ, respectively. The energy and distribution of the frontier molecular orbitals of the investigated molecular systems were also studied in a bid to gain more insight into their stability. The NBO analysis at the above-mentioned level of theory has been performed to deepen our understanding of the FLN-TMZ interactions. This was further buttressed via QTAIM and NCI index analyses performed using the multiwfn 3.8 software [33]. The electronic transition spectra were calculated using the TD-DFT method at the M06-2X-D3/6-311G(d, p) theoretical level. Calculations in water medium were performed using the SMD solvation method [34].

Geometric and energetic parameters
The optimized structures of TMZ, B 12 N 12 and Al 12 N 12 are depicted in figure 1, alongside the distribution of the FMOs of TMZ. The geometric parameters obtained herein from the optimized structures of pure B 12 N 12 (B-N bond lengths and angles) and Al 12 N 12 (Al-N bond lengths and angles) are in perfect agreement with those reported in the literature [35][36][37]. The structure obtained from the relaxation of TMZ is displayed in figure 1, along with the interatomic distances in gas phase. In order to locate the sites of TMZ exhibiting the greatest Lewis figure 1S indicates the high nucleophile character of these atoms. The yellow coloured of the MEP map around N 10 of TMZ also shows an electron-rich site. These atoms are, therefore, predicted to be the most prominent to form Lewis-type acid-base interactions with the boron and aluminium atoms of the FLNs. This observation is in good agreement with the findings of Harris [21] who predicted, via frontier molecular orbitals analysis, that these atoms are the most reactive sites of TMZ. Therefore, the ability of the pure FLNs considered in the present work to adsorb TMZ at their external surface has been evaluated by simulating the adsorbent-adsorbate interactions including the foregoing atoms. The relaxed structures of the complexes simulated at the M06-2X-D3/6-311G(d,p) level in the case of B 12 N 12 are depicted in figure 2, whereas those of Al 12 N 12 are presented in electronic supplementary material, figure S1. The energetic parameters (E Ads , ΔH and ΔG) describing the adsorption process are summarized in table 1. In order to facilitate the discussion of the results, the complexes are denoted A, B, C and D corresponding to O 12 , O 16 , N 10 and N 13 respectively. The complexes involving the B 12 N 12 and Al 12 N 12 FLNs are distinguished by the use of the roman numerals I and II, respectively, after the above-mentioned letters (figure 2 and electronic supplementary material, figure 2S).
From the values in table 1, all complexes comprising B 12 N 12 are interestingly found to be stable, since they are characterized by negative values of E Ads . The adsorption energies follow the trend: AI < CI < DI < BI. Accordingly, AI is the most stable of all the complexes studied. Zhu and co-workers studied the adsorption of TMZ on pristine BC 3 NT by linking the former to the adsorbent via its two oxygen atoms [8]. The adsorption energies found at the B3LYP/6-31G(d) level are, respectively, −18.84 kcal mol −1 (−0.8717 eV) when BC 3 NT is linked to O 12 and −16.73 kcal mol −1 (−0.7256 eV) when it is linked to O 16 . Therefore, the B 12 N 12 FLN is a better adsorbent of TMZ than BC 3 NT, since the most stable complex herein has a lower adsorption energy (−1.3697 eV) than that of Zhu et al. [8]. However, in the case of O 16 , our E Ads value (−0.6564 eV) is similar to that of Zhu et al. The gas-phase enthalpy and Gibbs free energy change are also negative, suggesting exergonic and exothermic processes. The values of these thermodynamic parameters are found to follow the same trend as the adsorption energy. Increment in the bond lengths around the adsorption sites of both TMZ and the B 12 N 12 FLN are observed upon adsorption. In the case of AI, the interatomic distance between C 11 and O 12 increases from 1.209 to 1.259 Å, and the B-N bond lengths royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 of the nano-cage are found to increase from 1.483 to 1.562 and 1.597 Å (in the four-membered ring (4-MR) of the nano-cage), as well as from 1.437 to 1.503 Å in the 6-MR. The increment in the C 2 = O 16 bond length in BI is also 0.050 Å (from 1.199 to 1.249 Å). Additionally in BI, the B-N bond lengths of the nano-cage increased from 1.483 to 1.536 or 1.567 Å in the 4-MRs, and from 1.437 to 1.503 Å in the 6-MR. Similar observations were made in the cases of CI and DI. Moreover, the lengths of the B-O/B-N bonds linking the nano-cage (B 12 N 12 ) to TMZ are found to be 1.547, 1.626, 1.627 and 1.683 Å respectively in AI, BI, CI and DI. Consequently, the most stable complex (AI) is characterized by the smallest adsorbent-adsorbate interatomic interaction. Zhu and co-workers obtained B-O 12 and B-O 16 interatomic distances of 1.82 and 1.91 Å, respectively, in their previous work [8]. These values are obviously greater than those obtained from the B 12 N 12 nano-cages in the present work (AI and BI).  royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 are more negative for each of these molecular systems than those of their respective counterparts comprising B 12 N 12 as the adsorbent. However, these parameters are found to increase in the same order as those for the boron-nitride nano-cage. In studying the adsorption of pyrrole on some fullerene-like nano-cages, Rad and Ayub also found that the adsorption energy of the complex involving Al 12 N 12 was more negative than that of B 12 N 12 [38]. A similar observation has been made by other researchers [24,39,40]. The values of the bond lengths around the adsorption sites of AII, BII, CII and DII are provided in electronic supplementary material, figure S1. The Al-O/Al-N interatomic distances within these complexes have the values 1.870, 1.918, 2.009 and 2.066 Å, which are greater than those obtained from the complexes of B 12 N 12 . In this case, the complexes involving O 12 (AII) which is the most stable, also features the lowest adsorbent-adsorbate interatomic interaction. The C 11 =O 12 , N 10 -C 3 and N 10 -C 4 bond lengths of TMZ upon adsorption to the external surface of Al 12 N 12 FLN (AII and CII), are similar to those of AI and CI. However, the C 2 =O 16 interatomic distance in BII (1.241 Å) is shorter than that in BI (1.249 Å). A similar observation is made with regard to the C 11 -N 13 bond length in BL, which is shorter in DII (1.441 Å) than in DI (1.462 Å).

Effects of doping and solvation
Doping is a routinely used method for improving the sensing and adsorption ability of FLNs. In this perspective, Bahrami and co-workers reported the good adsorption ability of Al-doped B 11 N 12 FLN toward amphetamine [41]. Similar results were published for the adsorption of aspirin by Vessally et al. [35]. Moreover, the B 11 GaN 12 nano-cluster was also reported to be a better sensor for CO than pure B 12 N 12 [14]. In the present research endeavour, the ability of Al-doped B 12 N 12 and B-doped Al 12 N 12 to adsorb TMZ is probed. In this analysis, only the two most stable structures obtained with the pure nano-clusters (AI, CI, AII and CII) are considered. The optimized structures of the doped  which interestingly reveals an improvement in the adsorption ability of the doped nano-cages. In addition, the adsorption reactions involving AlB 11 N 12 are more exothermic and more exergonic than those of pure B 12 N 12 . However, unlike the non-doped BN nano-cage, the doping of Al 12 N 12 leads to an increment in the E Ads , ΔH and ΔG values (yielding more positive values). Although exothermic, the gas-phase adsorption of TMZ at the external surface of the B-doped Al 12 N 12 FLN is non-spontaneous under standard conditions. Adsorption at the external surface of the Al-doped B 12 N 12 leads to a greater change in the C 11 =O 12 bond length of TMZ than is the case with adsorption at the surface of pure B 12 N 12 . Indeed, the length of these bonds increase by 0.058 Å (i.e. from 1.209 to 1.267 Å) in AI_Al, which is slightly greater than 0.050 Å in the case of AI. An opposite trend is observed between AII and AII_B, implying that the length of the C 11 =O 12 bond in the first complex (1.260 Å) is greater than that in the second (1.248 Å). Furthermore, the discrepancies in the values of the C 3 -N 10 and C 4 -N 10 bond lengths between the complexes comprising the pure and doped FLN are negligible.

Topological analysis
In theoretical chemistry, the nature and strength of non-covalent interactions are frequently characterized via a set of methods known as topological analysis techniques, of which the quantum theory of atoms in molecules (QTAIM) is the most popular. QTAIM topological analysis is based on the partitioning of a molecular space into a set of interconnected critical points (CPs) [42]. A CP is a space point where the first derivative of the electron density function ρ(r) is null. Therefore, the philosophy of the Bader's QTAIM approach is to define bonds using the electron density. According to that theory, an interaction between two atoms is identified by the presence of a bond path between them. The presence of a bond path or a bond critical point (BCP) between two atoms confirms the existence of a covalent or non-covalent interaction between the atoms. Within the QTAIM framework, covalent and non-covalent interactions can be distinguished as follows [43]: -Shared interactions for which the Laplacian of the electron density ∇²ρ(r) is negative at the BCP (3, −1) are classified as covalent bonds. -Closed shell interactions for which ∇²ρ(r) greater than 0 are ionic or Van der Waals (VdW) interactions.
In the present work, the Bader's QTAIM has been used as implemented in the multiwfn 3.8 package, to characterize FLN-TMZ interactions in all the complexes under investigation. For that purpose, in addition to ρ(r) and ∇²ρ(r), the identified hydrogen bonds (HBs) were also characterized by their energy, approximated as half of the potential energy density v(r) at the BCPs. The sum (denoted h(r)) of the kinetic energy density at the BCP, g(r), and the potential energy density, v(r), is also useful in determining the nature of HBs. Negative values of h(r) are associated with strong HBs, while positive values are associated with both intermediate and weak HBs.
The Bader's topological analysis in this work has been complemented by the visual analysis of noncovalent interactions using the reduced gradient density (RDG) to identify non-covalent interactions (NCIs) [44]. This method uses coloured iso-surfaces to distinguish between different types of NCIs. Strong interactions like conventional HBs are characterized by blue-coloured iso-surfaces, whereas the green-coloured surfaces indicate attractive VDW interactions. Red-coloured iso-surfaces describe repulsive interactions.
The molecular diagrams of AI, BI, CI and DI are displayed in figure 3, along with their respective NCI iso-surfaces. Some topological parameters describing the interactions between the B 12  royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 obtained with pure B 12 N 12 (B-O 12 and B-N 10 ). The reverse is observed when the ρ(r) and E values of Al 12 N 12 and BAl 11 N 12 are compared. However, the values of adsorption energy in the molecular systems involving direct interactions of TMZ with the boron atom were found in the previous section to be lower than those involving direct Al-TMZ interactions (Al 12 N 12 and AlB 11 N 12 ). This is indicative of the fact that the said interactions might not be playing a prominent role in stabilizing the molecular systems obtained via adsorption.

Natural bond orbital analysis
Natural bond orbital (NBO) allows the quantification of interaction of electron based on the Lewis theory. It uses the stabilization energy E (2) , which is estimated based on the second order perturbation theory, to predict the strength of Lewis-type donor-acceptor interactions that contribute to the electron delocalization from bonding (BD) or lone pair orbitals (LP) to anti-bonding orbitals (BD Ã ) [46,47]. Large values of E (2) indicate strong interactions. Several interactions in both the nano-cage and TMZ moieties have been observed from calculations of NBO parameters. In the present work, only the values of the stabilization energy E (2) (greater than 10 kcal mol −1 ) describing the interactions between the FLNs and TMZ are reported (   ) interactions, respectively. Moreover, the N 28 -H … N hydrogen bond previously observed in the molecular structure of AI is also confirmed to greatly contribute to the stabilization of the said complexes. Indeed, an interaction energy of 12.05 kcal mol −1 describing that HB bond is found from the NBO analysis. Interactions within the frameworks of FLN and TMZ are found to be of paramount importance to the stability of the CI and DI complexes, and only one major interaction involving both structures is obtained in CI. Specifically, this interaction involves the delocalization of electron density from the LP of one N-atoms of the FLN (adjacent to the B-atom of the cage linked to TMZ) to the anti-bonding orbital of the B-N 10 bond enabling the interaction between the adsorbent and the adsorbate. Similarly, electron density delocalization from the LP of all three N-atoms neighbouring the B-atom of B 12 N 12 bearing the TMZ structure to σ Ã (B-N 13 ) (leading to the B 12 N 12 -TMZ complex) are observed in DI.
Concerning the complexes of pure Al 12 N 12 , the interactions found in AII are similar to those in AI. The interaction from LP(O 16 ) to σ Ã (Al 33 -N 8 ) (with E (2) = 44.37 kcal mol −1 ) is the main interaction involving both the cage and TMZ. The delocalization from σ(Al 33 -N 8 ) to σ Ã (N 28 -H 31 ) describing the HB with E (2) value of 25.01 kcal mol −1 is observed. In the case of BII, the O-atom of TMZ (O 12 ) that is linked to the FLN was found to delocalize electrons from its LP to the σ Ã (Al-N) of the cage, which stabilizes the complex. A similar observation is made in the case of CII. Finally, no major interaction involving both the nano-cage and TMZ is found in DII.
In the Al-doped complexes, electron transfer from the LP of O 16  The absolute value of the Hirshfeld charges (HCs) of the B and N atoms in pure B 12 N 12 is 0.33 e. The gas-phase HCs on the B and Al atoms linked to TMZ in all molecular complexes considered herein are summarized in electronic supplementary material, table 1S, along with those of the N-atoms adjacent to the B and Al atoms. For the molecular complexes involving the above-mentioned pristine, the HCs of the B-atom linked to TMZ are in the range 0.25-0.27 e, while those of the N-atoms bonded to the said B-atom are between −0.34 and −0.37 e. Therefore, the B and N atoms gain electron upon adsorption of TMZ at the external surface of B 12 N 12 . Moreover, it can be seen from electronic supplementary material, table 1S that the HCs of the O and N atoms of TMZ increase (as the charge becomes less negative) after its adsorption by the pure BN FLN. All these observations account for charge transfer between TMZ and the nano-cage. Similar remarks can be made with pure Al 12 N 12 (though the change in the HCs of atoms is less significant than in the case of pure B 12 N 12 ), as well as the doped FLN under investigation.

Electronic properties
Electronic properties are key parameters in the description of the sensing ability of nano-cage materials. The HOMO and LUMO levels are of paramount importance in evaluating these parameters. The calculated gas and aqueous phases values of HOMO-LUMO gap (E g ) and Fermi level (E F ) of the molecular systems under investigation are summarized in table 4. The distributions of the FMOs of TMZ are also presented in figure 1, while those of AI, AI_Al, AII and AII_Al are presented in figure 4. It can be seen from figure 4 that the HOMO iso-surface distribution of all molecular complexes are nearly the same, and are exclusively centred on the N-atoms of the nano-cages. The LUMO iso-surfaces are similarly distributed but are mainly localized around the TMZ atoms. These findings corroborate the density of states (DOS) of these systems, which are also similar (reasons why only that of AI is presented in figure 5). Therefore, the adsorption of TMZ at the external surface of the pure and doped FLNs considered herein greatly modifies their FMOs, thereby altering their properties. Inspection of table 4 indicates an increment in the HOMO levels, as well as a change in the LUMO levels of all the FLNs upon adsorption of TMZ. This is a very important observation when royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 Table 3. Values of the second-order perturbation energy E (2)  royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 Table 4.  probing the sensing ability of nanostructures via the theoretical chemistry methods. The E g value of TMZ is 6.95 eV as evidenced in table 4. This parameter is, however, known to be very sensitive to the theoretical level. Zhu and co-workers published for TMZ, an E g value of 3.97 eV at the B3LYP/6-31G(d) level of theory [8]. The gas-phase magnitudes of E g obtained herein for B 12 N 12 (9.44 eV) and Al 12 N 12 (6.32 eV) perfectly agree with those obtained by Padash and co-workers at M062X/6-311G(d,p) level of theory [24]. Analysis of the values in table 4 also reveals that adsorption of TMZ at the external surface of pure B 12 N 12 FLN leads to a huge reduction in its E g value. The values of ΔE g (%) (calculated taking the FLNs as references) for the molecular complexes of that nano-cage increase as follows: CI < BI < DI < AI. The reference point for changes in HOMO and LUMO is the adsorbent (nano-cage here) [8,24]. It turns out that AI, which was found to be the most stable of these complexes has the greatest ΔE g (%) value of 38.09%. The magnitude of this value clearly shows that the FLN is very sensitive to TMZ, and can accordingly be efficiently applied as sensor for its detection. This result is consistent with the change in the Fermi levels, for which AI is still the molecular complex exhibiting the greatest change. In the case of pure Al 12 N 12 , the percentages of energy gap change upon adsorption of TMZ at the external surface of pure Al 12 N 12 are significantly lower than those of B 12 N 12 . In that case, the greatest value of ΔE g (%) is 17.72, which is still obtained with AII. Furthermore, the change in the E F values of the Al 12 N 12 FLN is smaller than that of the B 12 N 12 FLN. These observations clearly confirm the fact that pure B 12 N 12 FLN is a better TMZ sensor than Al 12 N 12 .
The dipole moment of a molecular system strongly depends on the magnitude and separation of charges within the system, and is thus important in predicting their chemical reactivity. It is evident in table 4 that adsorption leads to huge increments in the dipole moment of the FLNs. In all cases, complex A is found to have the greatest value of the DM, indicating the strength of the covalent Short recovery period (fast desorption) is a requirement for a suitable sensor. Therefore, too strong chemical interactions are not ideal for sensors, since such adsorption often leads to long recovery times which are not ideal for sensor applications [8]. The recovery time (τ) for complexes indexed as A (the most stable with respect to the different FLNs) was calculated as:

Electronic spectra analysis
The TD-DFT/M06-2X-D3/6-311G(d,p) level of theory has been used to predict the absorption spectra of TMZ alongside its most stable complexes (AI, AII, AI_Al and AII_B) in both gas phase and aqueous environments. The results obtained are summarized in table 6, while the corresponding spectra diagrams are displayed in figure 6. Figure 6a shows three absorption maxima of the electronic spectrum    Table 6. Absorption maxima (λ max ), absorption energy (E), oscillator strength (F) and composition of electronic transfer obtained from the electronic spectra of the studied compounds. of TMZ, the most intense of which appears at 268 nm in gas phase and at 282 nm in water. A red shift of the absorption maxima is evident upon solvation of TMZ. These maxima arise from electronic transitions originating from the HOMO to the LUMO of TMZ, which according to these frontier molecular orbital distributions, are attributable to π → π Ã type transitions. It is clear from figure 6b that in the gas phase, the electronic spectra of AI and AI_Al are similar, the only difference being the slight bathochromic effect caused by the doping of the B 12 N 12 FLN. Indeed, the main absorption bands of these complexes are centred around 271 nm (due to H-5 → L(31%)) and 274 nm (H-7 → L(31%)), respectively, for AI and AI_Al. A strong bathochromic effect can also be observed from figure 6b induced by the solvation of these compounds, but their spectra remain similar in aqueous solution. The increments in the values of λ max are 11 and 15 nm for AI and AI_Al respectively, upon solvation. As concerns the molecular complexes based on Al 12 N 12 nano-cage, doping also leads to a red shift in both study media. An increment of about 15 nm in the value of λ max is observed when passing from AII to AII_B. However, unlike the BN-based complexes studied, a blue shift is observed for the absorption maxima of the Al 12 N 12 -based complexes upon solvation. It should, however, be noticed that the values of excited-state energies as well as the HOMO-LUMO gap of the compounds studied might be improved using range-separated functionals. Indeed, it has been shown that these functionals best describe the mentioned parameters due to their −1.00/R dependence on the exchange potential instead of the −0.50/R dependence of the M06-2X Minnesota functional [48][49][50][51].

Concluding remarks
The adsorption of the anti-cancer drug dubbed TMZ herein at the external surface of pure and doped X 12 N 12 (X = B and Al) using the DFT/M06-2X-D3/6-311G(d,p) theoretical chemistry method was the main concern of the present work. Quantum chemical calculations were carried out in both gas and aqueous phases. The results have revealed that apart from the doped BAl 11 N 12 FLN, all the other investigated nano-cages can spontaneously adsorb TMZ in both study media. Moreover, TMZ was royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211650 found to bind onto the FLNs preferentially through O 12 , via a partially covalent interaction. The complexes involving that O-atom are also found to exhibit the greatest dipole moment values. Charge transfer from TMZ to the respective FLNs was clearly elucidated via NBO and Hirshfeld atomic charge analyses. The analysis of calculated electronic parameters has shown that AI (the most stable molecular complex) witnessed the greatest change in FMOs distribution, E gap and E F . In addition, the release time in vacuum ultraviolet light of AI was found to be only 1.06 s at room temperature. Finally, the best sensor must strongly link the adsorbed molecule (giving rise to negative values of adsorption energy as well as Gibbs free energy), must greatly alter (reduce) the HOMO-LUMO energy gap of the sensor (FLNs herein). The desorption time too must be the smallest possible so that the FLN can be easily regenerated and re-used. So all these parameters are combined to elect the best sensor, the most important being the change in the HOMO-LUMO energy gap as well the desorption time. From the foregoing observations, B 12 N 12 among the FLNs investigated is the most sensitive to TMZ and can be proposed for industrial applications.
Data accessibility. All output files as well as supplementary materials are available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.6m905qg12 [52].
Authors' contributions. B.L.N.W.: data curation, formal analysis, investigation, writing-original draft; A.D.T.F.: conceptualization, data curation, investigation, methodology, software, writing-original draft, writing-review and editing; N.K.N.: methodology, software, writing-review and editing; R.A.N.: conceptualization, methodology, supervision, validation, writing-review and editing; A.W.: conceptualization, project administration, supervision, writing-review and editing. All authors gave final approval for publication and agreed to be held accountable for the work performed therein.