Theoretical Evaluation of the Properties of Nitrogen-Doped C₂₄ Fullerenes and Their Interactions with Two Adamantane-Derived Antivirals

Abstract

The replacement of carbon with a heteroatom within the structure of a fullerene gives the possibility of obtaining compounds with adjustable properties. The influence of aza-substitution on C₂₄ fullerenes was investigated and a comparison of HF and DFT calculations was performed. Various substitution patterns were proposed and the characterization of C₂₂N₂ and C₂₀N₄ structures was performed. Global reactivity descriptors like chemical potential, hardness, HOMO–LUMO gap and singlet–triplet gap were computed. Aromaticity descriptors like delocalization indices and NICS(0) index were employed for the characterization of each six-membered ring of the studied fullerenes. The possible use of aza-fullerenes as drug delivery systems for two adamantane-derived antivirals was evaluated through molecular docking studies. The best results were obtained for the fullerenes with a pronounced hydrophobic character, the favored configuration of the antiviral drugs being the one oriented toward the side consisting of carbon atoms of the fullerenes.

1. Introduction

Since the discovery of fullerenes, several of their applications in the nanomaterials field have emerged. The special interest is caused by the unique physicochemical properties of these compounds. Their low toxicity [1] also plays an important role in the research regarding their use as drug delivery systems and biologic active molecules themselves [2,3].

Heteroatom containing fullerenes—especially nitrogen and boron—are suitable for the design of new nanomaterials with adjustable properties. Different studies have outlined the importance of the number of doping atoms and their nature and position within the fullerene structure [4,5,6,7]. Several recent studies have dealt with the evaluation of the interactions between fullerenes and various drugs or bioactive compounds. Zoua et al. [8] investigated the adsorption of juglone on all-carbon and boron-doped C₂₄ fullerene; according to the results of their DFT study, the stability of the molecular complex juglone–fullerene is significantly improved for the boron-doped structure BC₂₃, compared to C₂₄. Another study [9] depicted the interaction between silicon-doped fullerene and flurbiprofen and salicylic acid drugs. According to the results, Si₂C₅₈ fullerene proved to be a suitable sensor and drug delivery system for both flurbiprofen and salicylic acid. All-carbon hexa-peri-hexabenzocoronene and their derivatives doped with AlN, BN and AlP have been investigated as drug delivery systems for 5-fluorouracil [10]. The study outlined that the best results were obtained for AlN- and AlP-doped hexa-peri-hexabenzocoronene. Karimzadeh et al. [11] reported a theoretical investigation regarding the adsorption mechanism of doxorubicin on pristine and functionalized carbon nanotubes. The single-walled carbon nanotubes functionalized with -COOH groups have given the most stable compounds, outlining the importance of intermolecular hydrogen bonds in choosing or designing delivery systems. Celaya et al. [12] have investigated the adsorption of melphalan on nanocages consisting of 24 atoms: C₂₄, B₁₂N₁₂, B₁₂C₆N₆, B₆C₁₂N₆ and B₆C₆N₁₂. The DFT study showed that the most stable chemisorption state has been obtained through the oxygen atoms of melphalan. Among nanocages, promising results have been obtained for boron nitrides. Perveen et al. [13] have studied the drug loading efficacy of graphitic-carbon nitride for cisplatin. The results showed that the main interactions occur between the hydrogen atoms of cisplatin and the nitrogen atoms of the nanomaterial. Another study [14] delt with the evaluation of the interactions between C₂₄ fullerene and amphetamine, ketamine and mercaptopurine, respectively. The best results for the adsorption studies in gas phase were obtained for amphetamine, followed by ketamine. According to these observations, C₂₄ can be a suitable compound for the removal of the two above-mentioned drugs from the environment. Jana et al. [15] investigated the possibility of using C₂₄ fullerene as a DNA nucleobase biosensor. It was demonstrated that a strong chemical interaction appears in the gas phase between the adenine and C₂₄, suggesting a higher sensing response and a longer recovery time. Various nanocages consisting of 24 atoms, C₂₄, B₁₂N₁₂, BC₂₃ and CB₁₁N₁₂, have been investigated as possible nanocarriers for the antiviral drug favipiravir [16]. According to the results, BC₂₃, B₁₂N₁₂ and CB₁₁N₁₂ nanocages can be utilized as promising drug delivery vehicles for the antiviral drug. DFT and TD-DFT studies have been performed to evaluate the potential use of C₂₄ fullerene and its derivatives as a glucose sensor [17]. Tukadiya et al. [17] showed that the best sensing response among the investigated compounds was obtained for Al₁₂P₁₂.

There are also an increasing number of studies regarding functionalized fullerenes with biologic activity [18]. For example, water-soluble derivatives of C₆₀ (fullerols and malonic acid derivatives) are of particular interest in the field of neuroscience [19]. The brain contains many unsaturated fatty acids and has a limited ability to regenerate tissue damage, thus being an organ sensitive to oxidative damage caused by free radicals. Fullerene derivatives are able to inhibit the chain reactions of lipid peroxidation by neutralizing intermediate peroxyl radicals, preventing the oxidation of fatty acid chains [18]. The antioxidant activity of fullerenes is based on both the existence of the large number of conjugated double bonds and the low energy of the LUMO orbitals that can quickly accept an electron [2,19]. The neutralization mechanism is assumed to be catalytic (they can react with several oxidizing agents without being consumed) [19].

Over the decades, the development of drug delivery systems has been studied to ensure the safe and efficient delivery of a drug to its target tissues, organs and cells. Targeting a drug delivery system to specific organs or cells increases the accumulation of active components delivered to the desired site of action and limits their accumulation in healthy organs, tissues and cells [20,21]. Therefore, the design and functionalization of carbon-based nanomaterials has become a frequently used strategy to achieve certain properties. Carbon-based nanomaterials show chemical stability, good thermal conductivity, good mechanical properties and improved optical properties. Due to these unique properties, functionalized carbon-based nanomaterials are of high interest for applications in the most diverse fields [21,22].

Previous studies of our research team delt with the investigation of the effect of heteroatoms like N and P on the properties and aromaticity of coronene, benzene and C₅₂ fullerenes to obtain new nanomaterials with improved properties [23,24,25]. Various nitrogen- and phosphorus-doped fullerenes derived from C₅₂ have been evaluated as possible drug delivery systems for phthalocyanines, with good results and no significant differences due to the presence of the heteroatoms [26].

The present study aims to investigate the electronic, geometric and magnetic properties, as well as the aromatic character, of fullerenes derived from C₂₄ structure, namely, C₂₂N₂ and C₂₀N₄. The main objective is to obtain information regarding the properties of the aza-compounds that can be further used for the design of new, improved nanomaterials for drug delivery. In this regard, different substitution patterns have been employed in order to establish their impact on the physico-chemical properties. Also, molecular docking studies have been performed to investigate their potential use as nanocarriers for two adamantane-derived drugs, amantadine and rimantadine. Fullerene C₂₄ consists of six four-membered rings and eight six-membered rings. The substitution with two and four nitrogen atoms has led to the following structures, depicted in Figure 1.

The investigated fullerenes may consist of different types of six-membered and four-membered rings, as presented in

Table 1. Number of six- and four-membered cycles containing two nitrogen atoms (A), one nitrogen atom (B and D) and all carbon atoms (C and E).

	A (Cycles)	B (Cycles)	C (Cycles)	D (Cycles)	E (Cycles)
C22N2_1a	1	2	5	2	4
C22N2_1b	-	4	4	2	4
C22N2_2a	-	4	4	2	4
C22N2_2b	-	4	4	2	4
C20N4_3a	4	-	4	4	2
C20N4_3b	2	4	2	4	2
C20N4_3c	-	8	-	4	2
C24	-	-	8	-	6

.

2. Materials and Methods

Geometry optimization of the fullerenes was performed at both the HF/6-311+G and B3LYP/6-311+G level of theory using the Gaussian 09 software [27]. No imaginary frequencies were obtained, proving that the structures are true minima. NICS (Nucleus Independent Chemical Shift) indices, the absolute magnetic shielding computed at the center of each ring, were computed using the GIAO method [28] (HF/6-311G+). Within the GIAO method, implemented in Gaussian 09 [27] for the computation of chemical shifts, each atomic orbital has an exponential term containing the vector potential [28].

The chemical potential (µ), chemical hardness (η) and electrophilicity index (ω) have been computed by means of Equations (1)–(3) [29]:

$$\mu =\frac{E_{HOMO}+E_{LUMO}}{2}$$

(1)

$$\eta =\frac{E_{LUMO}-E_{HOMO}}{2}$$

(2)

$$\omega =\frac{{\mu }^2}{2\eta }$$

(3)

Delocalization indices PDI [30] and FLU [31] were calculated using the Multiwfn_3.3.4 software [32]. Computation of the para-delocalization index (PDI) is based on Equations (4) and (5):

$$\delta \left(A,B\right)=4{\displaystyle \sum _i^{occ}{\displaystyle \sum _j^{occ}{S}_{ij}\left(A\right)}}{S}_{ij}\left(B\right)$$

(4)

$$PDI=\frac{\delta \left(1,4\right)+\delta \left(2,5\right)+\delta \left(3,6\right)}{3}$$

(5)

The aromatic fluctuation index (FLU) [31] represents an indicator of the electronic charge fluctuation between adjacent atoms in a ring:

$$FLU\left(A\to B\right)=\frac{\delta \left(A,B\right)}{{{\displaystyle \sum }}_{B\ne A}\delta \left(A,B\right)}=\frac{\delta \left(A,B\right)}{2\left[N\left(A\right)-\mathsf{\Lambda }\left(A\right)\right]}$$

(6)

where: Λ(A)—atomic localization indices; N(A)—average population of atom A; δ(A,B)—delocalization indices.

Prior to the molecular docking studies, the geometric optimization of amantadine and rimantadine was performed at the same level of theory, using the Gaussian 09 package.

The descriptors of the molecular shape [33]—namely, ovality—Connolly accessible area (CAA), Connolly solvent-excluded volume (CSEV) and the partition coefficient logP have been computed with Chem3D software. Connolly accessible area stands for the surface of the compound that is accessible to a solvent; Connolly solvent-excluded volume is the sum of the van der Waals volume and the interstitial volume (small packing defects among the atoms) [34]. The ovality estimates the degree of deviation from the spheric shape. AutoDock Vina [35] has been employed for the docking simulation. The fullerenes were assigned as receptors and a grid box of 40 × 40 × 40 Å was used, the center of the grid box being considered the center of the fullerenes. The optimized structures of the two antiviral drugs were loaded as ligands and the torsions along the rotatable bonds were assigned. The visualization of the results was also performed by means of AutoDock Vina software [35]. The binding constant K_B has been calculated with the following equation:

$$K_B=e^{\frac{-\mathsf{\Delta }{G}_B}{R·T}}$$

(7)

where ΔG_B is the binding affinity (J·mol⁻¹), R is the gas constant (J·mol⁻¹·K⁻¹) and T is the temperature (298 K).

3. Results and Discussions

3.1. Frontier Molecular Orbital (FMO) Analysis, Energetic Characterization and Local Aromaticity of 24-Membered Fullerenes

3.1.1. FMO Analysis

The frontier molecular orbital (FMO) analysis predicts the reactivity of the compounds by means of the HOMO and LUMO orbitals interactions. The HOMO orbital energy is directly related to the ionization potential and characterizes the susceptibility of the molecule to electrophilic attack. The LUMO energy is directly related to the electron affinity and characterizes the sensitivity of the molecule to nucleophilic attack. The lowest LUMO energies correspond to the best electron acceptors, while the highest HOMO energies are associated with the best electron donor properties.

According to the results depicted in

Table 2. Frontier molecular orbitals energies at the HF/6-311+G (regular) vs. B3LYP/6-311+G (italics) level of theory.

Compound	HOMO (Eh)	LUMO (Eh)
C22N2_1a	−0.261/−0.231	−0.039/−0.148
C22N2_1b	−0.243/−0.219	−0.043/−0.150
C22N2_2a	−0.232/−0.213	−0.047/−0.153
C22N2_2b	−0.231/−0.207	−0.042/−0.148
C20N4_3a	−0.247/−0.217	−0.044/−0.145
C20N4_3b	−0.217/−0.199	−0.049/−0.152
C20N4_3c	−0.222/−0.204	−0.052/−0.151
C24	−0.310/−0.243	−0.017/−0.142

, the HOMO energies are slightly higher when computed with DFT methods.

The most significant differences were recorded for the LUMO energies; according to the results presented in Table 2, the hybrid functional B3LYP predicts highly stabilized LUMO orbitals (observe the larger negative values compared to the one obtained from the HF computations). Also, the DFT method leads to a narrower LUMO energy range (−0.142 to −0.153 a.u.). These results have a great impact on the estimation of the global reactivity descriptors like chemical potential, hardness and electrophilicity.

According to the HF method, the hierarchy of the lowest HOMO and highest LUMO is C₂₄ > 1a > 3a > 1b. For the compounds 3b and 3c, the increase in the HOMO energy is more pronounced than the drop in the LUMO energy, thus leading to narrower HOMO–LUMO gaps.

Meanwhile, the hybrid functional B3LYP employment suggests that HOMO energies increase as C₂₄ > 1a > 1b > 3a and the highest LUMO are found at C₂₄ > 3a > 1a = 2b > 1b.

Both the HF and B3LYP computations showed that among the investigated compounds, fullerene C₂₄ has both the lowest HOMO and the highest LUMO, thus leading to the largest HOMO–LUMO (HL) gap. Although the HOMO–LUMO gap decreases as C₂₄ > 1a > 3a > 1b for both computation methods, significantly lower values have been obtained from the DFT calculation. According to other studies, the amount of HF exchange may overestimate the HOMO–LUMO energy gap [36,37].

Other global reactivity descriptors like chemical hardness, chemical potential and electrophilicity have been computed; the results are presented in

Table 3. Global descriptors of reactivity computed at HF/6-311+G (regular) and B3LYP/6-311+G (italics).

Compound	HL Gap (eV)	Hardness η (eV)	Chemical Potential μ (eV)	Electrophilicity ω (eV)
C22N2_1a	6.04/2.26	3.02/1.13	−4.08/−5.15	2.76/11.73
C22N2_1b	5.44/1.88	2.72/0.94	−3.89/−5.02	2.78/13.40
C22N2_2a	5.03/1.63	2.51/0.82	−3.79/−4.98	2.86/15.12
C22N2_2b	5.14/1.60	2.57/0.80	−3.71/−4.83	2.68/14.58
C20N4_3a	5.52/1.96	2.76/0.98	−3.96/−4.92	2.84/12.35
C20N4_3b	4.57/1.28	2.28/0.64	−3.62/−4.77	2.87/17.78
C20N4_3c	4.62/1.44	2.31/0.72	−3.73/−4.83	3.01/16.20
C24	7.97/2.75	3.98/1.37	−4.45/−5.24	2.49/10.02

.

Chemical hardness (η) is considered a measure of the resistance to electronic transitions. Among the investigated fullerenes, the compounds C₂₄ and 1a are the least polarizable. The structures 3b and 3c, characterized by smaller values of hardness, are expected to be the most polarizable within the series. The above-mentioned observations correspond to both the HF and B3LYP results, with a significant decrease in the chemical hardness of the DFT-computed values because of the lower LUMO energy levels. Also, the DFT results suggest a pronounced electrophilic character of the fullerenes, given the lower chemical hardness and larger chemical potential.

Chemical potential (µ) stands for the charge transfer within a system in the ground state and follows the hierarchy C₂₄ > 1a > 3a > 1b (HF) and C₂₄ > 1a > 1b > 3a (DFT).

The distribution of the frontier molecular orbitals, computed at the HF level of theory, is depicted in Figure 2 and Figure 3 and outlines no significant differences among the fullerenes. The LUMO orbitals appear to be delocalized on the carbon atoms but to a lesser extent on the nitrogen atoms.

The frontier molecular orbitals HOMO are delocalized on the entire structure (Figure 3), with a slight emphasis on the carbon atoms near the nitrogen ones.

Figure 4 and Figure 5 illustrate the graphic distribution of the frontier molecular orbitals computed at the B3LYP/6-311+G level of theory. It can be observed that the similarity of the LUMO distribution of the investigated fullerenes corresponds to the narrow energy range presented in Table 2.

The HOMO orbitals of the fullerenes appear to be mostly localized at the carbon atoms which are found next to the nitrogen ones.

3.1.2. Energetic Characterization: Total Binding Energy and Singlet–Triplet Gap

The substitution of some carbon atoms with isovalent nitrogen within the C₂₄ structure has been first evaluated by means of the relative energy and total binding energy (TBE) per atom. According to the results depicted in

Table 4. Relative and total binding energies of the fullerenes, computed at HF/6-311+G (regular) and B3LYP/6-311+G (italics).

Compound	E Rel (eV)	TBE/Atom (Eh)
C22N2_1a	37.482/33.265	−39.196/−39.458
C22N2_1b	37.509/33.275	−39.195/−39.458
C22N2_2a	37.509/33.281	−39.195/−39.457
C22N2_2b	37.509/33.283	−39.195/−39.457
C20N4_3a	0/0	−40.574/−40.844
C20N4_3b	0.054/0.036	−40.572/−40.842
C20N4_3c	0.027/0.019	−40.573/−40.843
C24	74.800/66.541	−37.824/−38.071

, regardless of the computation method, the most stable ones are the compounds where four carbon atoms have been replaced with nitrogen. Among them, the isomer with the greatest number of A-type cycles (3a) is favored. No significant difference has been obtained for the compounds substituted with two heteroatoms, regardless of the substitution pattern.

The influence of the heteroatom substitution is also reflected on the total energies of the fullerenes. The energy increases with the number of nitrogen atoms, with no significant differences being observed among the compounds doped with the same number of nitrogen atoms.

The singlet–triplet gap has been computed as part of the general characterization of the fullerenes to evaluate all of the possible influences on their ability as delivery systems for the adamantane-derived drugs. Computation of the singlet–triplet ST gap is depicted in

Table 5. Energies of the singlet and triplet states, as well as the ST gap computed at HF/6-311+G (regular) and B3LYP/6-311+G (italics).

Compound	Singlet (Eh)	Triplet (Eh)	ΔEST (eV)
C22N2_1a	−940.700/−946.990	−940.685/−946.779	−0.408/−5.739
C22N2_1b	−940.681/−946.980	−940.673/−946.782	−0.218/−5.385
C22N2_2a	−940.672/−946.974	−940.764/−946.791	2.502/−4.977
C22N2_2b	−940.680/−946.972	−940.709/−946.768	0.788/−5.549
C20N4_3a	−973.780/−980.255	−973.823/−980.053	1.170/−5.494
C20N4_3b	−973.738/−980.219	−973.773/−980.047	0.952/−4.678
C20N4_3c	−973.751/−980.236	−973.888/−980.127	3.726/−2.965
C24	−907.769/−913.714	−907.602/−913.438	−4.542/−7.507

.

According to the HF values, three compounds—1a, 1b and C₂₄—show inverted singlet–triplet gaps. For all of the fullerenes substituted with four nitrogen atoms as well as for the compounds 2a and 2b, the triplet state T1 is lower in energy than the singlet state.

As regards the DFT results, all of the investigated fullerenes show inverted singlet–triplet gap, in agreement with other studies that predict inverted ST gaps for nitrogen- and boron-doped π-conjugated hydrocarbons [38].

3.1.3. Local Aromaticity Evaluation of Nitrogen-Doped Fullerenes

The aromaticity of the compounds refers to a sum of geometric, energetic, magnetic and electronic properties. As a result, it is difficult to propose a universal definition and criterion for estimating the aromaticity. There are various local indices that are employed to evaluate the aromatic character of a single ring within a polycyclic compound. The major drawbacks are the lack of consistency of the results and their dependence on the basis set [39].

The evaluation of the possible aromatic character has been performed by means of local aromaticity indices like NICS, FLU and PDI. The results are presented in

Table 6. Para-delocalization index PDI (only for six-membered rings) computed for the HF-optimized structures (regular) and B3LYP-optimized structures (italics).

	Rings
Compound	A	B	C
C22N2_1a	0.025/0.031	0.025/0.027	0.047/0.051
C22N2_1b	-	0.036/0.038	0.035/0.042
C22N2_2a	-	0.030/0.032	0.043/0.050
C22N2_2b	-	0.027/0.033	0.043/0.045
C20N4_3a	0.017/0.030	-	0.039/0.052
C20N4_3b	0.024/0.028	0.019/0.025	0.041/0.033
C20N4_3c	-	0.028/0.029	-
C24	-	-	0.048/0.051

,

Table 7. Aromatic fluctuation index (FLU) computed for the HF-optimized structures (regular) and B3LYP-optimized structures (italics).

	Rings
Compound	A	B	C	D	E
C22N2_1a	0.063/0.079	0.054/0.072	0.028/0.035	0.087/0.111	0.050/0.080
C22N2_1b	-	0.044/0.056	0.032/0.039	0.079/0.110	0.057/0.078
C22N2_2a	-	0.046/0.058	0.033/0.035	0.088/0.115	0.049/0.084
C22N2_2b	-	0.050/0.054	0.029/0.037	0.077/0.099	0.053/0.082
C20N4_3a	0.071/0.074	-	0.031/0.031	0.074/0.104	0.049/0.070
C20N4_3b	0.056/0.051	0.054/0.052	0.027/0.037	0.070/0.093	0.047/0.062
C20N4_3c	-	0.041/0.052	-	0.046/0.090	0.072/0.063
C24	-	-	0.041/0.039	-	0.079/0.078

and

Table 8. NICS(0) index (ppm) computed for the HF-optimized structures (regular) and B3LYP-optimized structures (italics).

	Rings
Compound	A	B	C
C22N2_1a	22.246/41.508	18.548/36.527	7.972/24.891
C22N2_1b	-	20.504/45.047	18.933/42.597
C22N2_2a	-	75.947/11.023	43.153/4.211
C22N2_2b	-	58.520/9.985	44.415/7.521
C20N4_3a	−15.060/−16.067	-	−9.998/−9.355
C20N4_3b	−12.877/−2.600	−32.293/−20.088	−17.452/−7.142
C20N4_3c	-	−18.981/−4.754	-
C24	-	-	26.763/33.053

. PDI (Para-Delocalization Index) [30] represents the average value of the delocalization indices for all para-related atoms. FLU (Aromatic Fluctuation Index) quantifies the delocalization–fluctuation over all of the adjacent atoms [31]. According to the literature data [39,40], PDI values less than 0.03 suggest antiaromatic character. Our results, performed for both the optimized structures of the fullerenes at HF and B3LYP level of theory, show that all of the a-type and B-type six-membered rings show antiaromatic character. Only the C-type cycles (six-membered all-carbon rings) present PDI values slightly higher than 0.03. The FLU index suggests an antiaromatic character for all types of cycles, larger values than 0.007 [39,40] being obtained for all of the fullerenes. The results presented in Table 6 outline that for the computations performed on the B3LYP/6-311+G-optimized structures, the PDI values of the C- and E-cycles are very close to the ones obtained for the all-carbon C₂₄ fullerene.

The magnetic index NICS, nucleus independent chemical shift, is defined as the negative value of the absolute shielding measured in the center of a given ring [41]. The NICS(0) indices were computed at the center of each six-membered ring. According to the literature data, positive chemical shifts denote antiaromaticity, while the negative ones signify an aromatic character [41]. The major drawback of NICS comprises depending on the size of the investigated system [41,42].

NICS(0) index is defined as the negative value of the absolute shielding computed at the center of a ring. Larger negative values imply a strong aromatic character, while positive ones suggest an antiaromatic character.

Regardless of the general trend (positive vs. negative values), the discrepancies must be outlined regarding the magnitude of the chemical shifts as a function of the chosen computation method. Also, it can be said that the NICS(0) values are also influenced by the σ-contributions. According to the above-mentioned results, the six-membered rings that compose C₂₄ and C₂₂N₂ fullerenes are antiaromatic, while local aromatic behavior has been observed for the C₂₀N₄ cycles.

3.2. Evaluation of the Interactions between Fullerenes and Adamantane-Derived Structures (Amantadine and Rimantadine)

In order to analyze the possibility of using the 24-membered investigated fullerenes as delivery systems, molecular docking studies have been performed for evaluating the nature of the interactions between the receptor (fullerene) and the ligand (drug structure).

Prior to the molecular docking, the evaluation of the steric properties of the fullerenes has been performed. The influence of both the heteroatoms number and their substitution type can be observed in the results presented below. The ovality, Connolly accessible area (CAA) and Connolly solvent-excluded volume (CSEV) have similar values for the fullerenes C₂₂N₂, regardless of the substitution pattern. The results are included in

Table 9. Partition coefficient and steric parameters of the 24-membered fullerenes.

Compound	logP	Ovality	CAA (Å2)	CSEV (Å3)
C22N2_1a	1.166	1.221	228	414
C22N2_1b	0.715	1.221	228	414
C22N2_2a	0.054	1.221	228	414
C22N2_2b	−1.296	1.221	228	414
C20N4_3a	−0.672	1.213	220	408
C20N4_3b	−2.614	1.213	220	408
C20N4_3c	−2.377	1.219	226	414
C24	8.448	-	-	-

. Small changes have been obtained for C₂₀N₄ fullerenes, which are characterized by lower values of ovality, CAA and CSEV. Fullerene 3c has steric properties closer to the C₂₂N₂ compounds. The most significant influence of the number of nitrogen atoms and their position can be observed in the values of the partition coefficient.

The same characterization has been performed for the two antiviral drugs, amantadine and rimantadine, whose structures are shown in Figure 6. Compared with amantadine, rimantadine has a more pronounced hydrophobic character and larger accessible area and solvent-excluded volume; the results are presented in

Table 10. Partition coefficient and steric parameters of the ligands.

Compound	logP	Ovality	CAA (Å2)	CSEV (Å3)
Amantadine	2.236	1.132	336.179	159.145
Rimantadine	3.513	1.162	376.252	192.175

.

The evaluation of the molecular docking results showed that for all of the investigated fullerenes, the only type of interaction is atoms in close contact. It was also noticed that the ligand is oriented towards the fullerenes side consisting of carbon atoms. The ligand–receptor interactions are depicted in Figure 7.

The average value of the binding affinities is depicted in

Table 11. The final Lamarckian genetic algorithm docked state—binding affinities of amantadine and rimantadine with the nanostructures (kcal/mol).

Compound	1a	1b	2a	2b	3a	3b	3c	24
Amantadine	−2.23	−2.22	−2.1	−2.1	−2.0	−1.9	−1.7	−2.2
Rimantadine	−2.65	−2.6	−2.5	−2.44	−2.35	−2.2	−1.91	−2.6

.

For comparison, fullerene C₆₀ has been employed as receptor; in this case, −2.7 kcal/mol and −3.31 kcal/mol have been obtained for amantadine and rimantadine, respectively. The results show that the best results were obtained for rimantadine, a compound with higher hydrophobic character and higher accessible area and solvent-excluded volume (compared to amantadine).

Also, for evaluating the strength of the interactions between fullerenes and the two antiviral drugs, the binding constant has been computed. Larger values suggest stronger interactions; the results are depicted in

Table 12. Calculated binding constant K_B for each fullerene–ligand interaction.

Compound	C22N2_1a	C22N2_1b	C22N2_2a	C22N2_2b	C20N4_3a	C20N4_3b	C20N4_3c	C24
Amantadine	15.705	15.550	13.791	13.791	12.479	11.291	9.245	15.241
Rimantadine	23.904	22.738	20.574	19.376	17.708	15.241	11.405	22.738

. Fullerene C₂₂N₂_1a led to the best results, followed by all-carbon C₂₄ and C₂₂N₂_1b. For both amantadine and rimantadine, lower binding affinities were obtained toward the fullerenes substituted with four nitrogen atoms (3a, 3b and 3c).

The calculated binding constants prove that the best binding affinities were obtained for rimantadine when docked on fullerenes 1a, 1b and C₂₄. Consequently, our future studies will be oriented toward the design of functionalized fullerenes to establish stronger interactions with the receptor, like the hydrogen bonds, with hydrophobic character and increased stability.

4. Discussion

This paper dealt with the characterization of several fullerenes doped with nitrogen atoms, derived from C₂₄ structure. The properties of seven compounds with the general formula C₂₂N₂ and C₂₀N₄ were investigated and compared to the corresponding ones for pristine C₂₄. The results show that the substitution pattern significantly influences the energetic, geometric and magnetic properties of the fullerenes. The computations were performed using the basis set 6-311G+, with both Hartree–Fock and DFT (B3LYP functional) methods being employed.

Analysis of the frontier molecular orbitals can be considered a good indicator of the global reactivity of a compound. One of the descriptors based on these energies is the difference between the HOMO and LUMO energy, which can be tuned by means of dopant atoms or functional groups on the main ring. The present study aimed to investigate the influence of the number and position of the nitrogen atoms on the HOMO–LUMO gap values. The results reveal that larger HOMO–LUMO HL gaps, associated with a lower reactivity and greater stability, were obtained for the fullerenes C₂₄, 1a, 3a and 1b. It has been shown that the values calculated by the HF method are significantly larger than the ones obtained via the DFT method. This difference is a consequence of the LUMO energies calculated at the B3LYP/6-311G+ level of theory. The same hierarchy was obtained for the electronic chemical potential. The energies of the frontier molecular orbitals show that the presence of the nitrogen atoms lowers the energies of HOMO orbitals and increases those of LUMO, compared to the pristine C₂₄.

Also, the singlet–triplet gap was computed as part of the investigation of the general properties of the fullerenes to evaluate all of the possible influences of the nitrogen-doping and to consider them for the design of new nanomaterials. For the DFT computations, the results suggest inverted singlet–triplet gaps for all of the fullerenes.

The local aromatic character of the six-membered cycles A, B and C was evaluated by means of two delocalization indices, PDI and FLU, and one magnetic index, NICS(0). PDI values suggest that all of the six-membered rings containing nitrogen atoms show antiaromatic character. The FLU index suggests an antiaromatic character for all types of cycles, regardless of the presence of the heteroatom. The positive NICS values for the six-membered rings that compose C₂₄ and C₂₂N₂ fullerenes suggest antiaromaticity, while negative NICS(0) values were calculated for the six-membered cycles within C₂₀N₄. Although negative NICS values are a sign of aromaticity, it must be outlined that the latter results are not sustained by the delocalization indices values, which clearly indicate antiaromatic character. The computed negative values of the NICS(0) index may be due to the sigma contributions.

Molecular docking studies were performed for verifying the possible use of nitrogen-doped C₂₄ fullerene as delivery systems for two antiviral drugs with adamantane structure. Prior to those, some steric parameters of the fullerenes were computed. The C₂₂N₂ fullerenes were characterized by similar values of ovality, CAA and CSEV, regardless of the substitution pattern. The increase in the number of nitrogen atoms led to smaller values of ovality, CAA and CSEV for fullerenes C₂₀N₄. The major influence of the number and position of nitrogen atoms was observed on the partition coefficient values.

The calculated binding affinities show that best results were obtained for the hydrophobic fullerenes 1a, 1b and C₂₄. The ligand–receptor interactions were of the type “atoms in close contact”, with the ligand (the adamantane-derived drug) oriented toward the fullerenes side consisting of carbon atoms. According to the results, higher or equal binding affinities (compared to C₂₄) were obtained for the fullerenes 1a and 2b. It can be stated that the best affinities for the adamantane-derived drugs were obtained for the hydrophobic fullerenes, substituted with two nitrogen atoms and with a higher HOMO–LUMO gap. Among the two investigated ligands, better results were obtained for rimantadine, characterized by higher CAA and CSEV values and a more pronounced hydrophobic character than the amantadine.

5. Conclusions

The present paper dealt with the investigation of the properties of 24-membered aza-substituted fullerenes in terms of their energetic properties, global reactivity descriptors and local aromaticity evaluation. The fullerenes were also studied as possible delivery systems of two adamantane-derived drugs, amantadine and rimantadine. The results outline the following:

(i)

The stability of the newly designed aza-fullerenes is influenced both by the number and the position of the heteroatoms, given that better values of the HOMO–LUMO gap, chemical potential and hardness were obtained for two of the C₂₂N₂ fullerenes (1a and 1b) and one of the C₂₀N₄ fullerene (3a);

(ii)

The aromaticity evaluation suggests that the six-membered and four-membered rings of the fullerenes present antiaromatic character;

(iii)

The steric parameters of the fullerenes, calculated prior to the molecular docking study, show little differences among them; the most significant influence of the number and position of the nitrogen atoms is reflected in the logP values;

(iv)

All of the fullerenes presented better binding affinities towards rimantadine than amantadine; among them, the most hydrophobic aza-fullerenes C₂₂N₂ 1a and 1b gave better or equal results compared to pristine C₂₄.