Smart drug delivery: a DFT study of C₂₄ fullerene and doped analogs for pyrazinamide

Abstract

The potential applicability of the C₂₄ nanocage and its boron nitride-doped analogs (C₁₈B₃N₃ and C₁₂B₆N₆) as pyrazinamide (PA) carriers was investigated using density functional theory. Geometry optimization and energy calculations were performed using the B3LYP functional and 6-31G(d) basis set. Besides, dispersion-corrected interaction energies were calculated at CAM (Coulomb attenuated method)-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory. The adsorption energy (E_ads), enthalpy (ΔH), and Gibbs free energy (ΔG) values for C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA structures were calculated. The molecular descriptors such as electrophilicity (ω), chemical potential (μ), chemical hardness (η) and chemical softness (S) of compounds were investigated. Natural bond orbital (NBO) analysis confirms the charge transfer from the drug molecule to nanocarriers upon adsorption. Based on the quantum theory of atoms in molecules (QTAIM), the nature of interactions in the complexes was determined. These findings suggest that C₂₄ and its doped analogs are promising candidates for smart drug delivery systems and PA sensing applications, offering significant potential for advancements in targeted tuberculosis treatment.

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Introduction

Tuberculosis (TB) is a prevalent and often fatal infectious disease caused by various species of mycobacteria, particularly Mycobacterium tuberculosis.¹ TB remains one of the most significant infectious diseases of our time, capable of affecting all organs of the body, especially the lungs. Despite widespread optimism in the 1980s that TB would be controlled by the turn of the century, the World Health Organization (WHO) declared it a global emergency in 1993.^2,3 According to WHO reports, approximately 10 million people were diagnosed with TB in 2017, with the number increasing to about 6.4 million in 2019. Annually, around 1.3 million patients succumb to TB.⁴ The treatment of TB has become increasingly challenging due to the emergence of drug-resistant strains of Mycobacterium tuberculosis. In 2012, there were about 45 000 cases of multidrug-resistant TB (MDR-TB), resulting in an estimated 170 000 deaths. The situation is exacerbated when these strains develop resistance to multiple drugs, undermining the significant advances made in TB control over the past century.⁵ Currently, more than 8 million people worldwide contract TB each year, and approximately one-third of the global population harbors the bacterium asymptomatically. Despite significant efforts to control TB, the emergence of drug resistance remains a critical concern, underscoring the need for rapid and accurate diagnosis to facilitate timely and effective treatment.

One of the four first-line anti-tuberculosis drugs is pyrazinamide (PA), which, in addition to shortening the treatment period from nine to six months, eradicates the organism by destroying the active and inactive forms of bacillus tuberculosis in the acidic environment inside the macrophages.⁶ Like other drugs, PA has important side effects, such as fever, anorexia, liver enlargement, jaundice, and liver failure. Targeted drug delivery is a new way to reduce problems caused by direct drug use and drug resistance.^7–9 Considering the common challenges of using drugs such as PA, the controlled release of the drug has attracted the attention of researchers. Targeted drug delivery and controlled release has advantages such as the possibility of drug delivery in nanometer dimensions, the ability to maintain the drug concentration in a relatively constant amount for a certain time, the ability to adjust the drug release rate depending on the place of drug delivery, and the ability to transfer several drug substances to a specific tissue or organ.^10,11 Nowadays, drug delivery based on nanocarriers is at the center of attention of many companies acting in the pharmaceutical industry since nanomaterials have special properties and potential applications that make them superior to the traditional drug delivery vectors. The use of nanocarriers in medical science helps to increase the availability of the drug at the site of disease, and reduces the dose frequency and adverse side effects.^12–15 As new drugs are developed, significant efforts have been directed toward exploring innovative delivery routes. Targeted delivery systems represent a promising solution to overcome the limitations of conventional methods. To realize this potential, a wide range of nanoparticles have been proposed and extensively studied.^16–20 These nanoparticles must interact well with biological environments and pass through the cell membrane to deliver therapeutic molecules. Fullerenes (C₆₀) are one of the pioneering classes of carbon-based nanoparticles, which have been widely studied for targeted drug delivery applications.²¹ Fullerenes have a unique structure and have suitable properties for interaction with drugs. Although fullerene toxicity is somewhat of a concern, several water-soluble fullerene derivatives have shown acceptable cytotoxicity for drug delivery applications.²² Recently, new fullerene-like compounds and hexagonal boron nitrides have been developed, and their potential applications as advanced delivery systems have been investigated.^23–27 Studies provide a detailed drug interaction mechanism with boron nitride fullerenes (BNF) and reveal that the BNF can be a smart drug delivery vehicle for the drugs.^23,28–30 In this study, the interaction of the pyrazinamide drug with C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ nanocages was investigated using density functional theory (DFT) calculations. To achieve this, we employed a range of analytical tools, including adsorption energy (E_ads), thermochemical parameters (ΔH and ΔG), frontier molecular orbitals, ionization energy, electrophilicity, chemical hardness, softness, electronegativity, natural bond orbitals (NBO), and atoms in molecules (AIM), as well as NMR, IR, and UV-Vis spectroscopy. These comprehensive analyses provide a detailed understanding of the interaction mechanisms and potential applications of these nanocages in drug delivery and sensing systems.

Computational details

All of the calculations were performed using the Gaussian 09 package.³¹ In the first stage, geometry optimization and energy calculations were carried out using the B3LYP^32,33 functional and 6-31G(d)³⁴ basis set. Besides, dispersion-corrected adsorption energies employing CAM-B3LYP³⁵ and M06-2X³⁶ functionals with the 6-31G(d,p)³⁴ basis set were calculated. The counterpoise procedure (CP)³⁷ was used to correct for basis set superposition error (BSSE) in the calculation of the adsorption energies. To obtain the thermal and Gibbs free energies and ensure that the optimized structures are true local minima on the potential energy surface (not saddle points or transition states), the vibrational frequency calculations were performed at all computational levels. All reported structures were identified as true minima on the PES. The adsorption energy (E_ads) of the obtained structures of the interaction between pristine and doped C₂₄ with PA at T = 298 K and P = 1 atm is given by the following equation:

E_ads = E_complex − (E_nanocage + E_PA) (1)

Natural bond orbital analysis provides a chemical viewpoint of van der Waals interactions using a donor–acceptor type interpretation of molecular orbitals.³⁸ Therefore, we used NBO analyses to calculate the charge distribution over the atoms of interacting species and to estimate the stabilization energies (E⁽²⁾) of bond–antibond interactions. The energy difference between the highest occupied (HOMO) and the lowest unoccupied molecular orbital (LUMO), known as E_g, for a system is given as:

E_g = E_LUMO − E_HOMO (2)

The electronic sensitivity of the pristine and doped C₂₄ nanocage toward PA is calculated as follows:

Quantum molecular descriptors (also known as the conceptual density functional theory (CDFT) parameters), including the electronegativity (χ), global hardness (η), electrophilicity index (ω), ionization potential (I), electron affinity (A), and electronic chemical potential (μ), were calculated with the help of HOMO and LUMO values. The electrophilicity index (ω) measures the stability of a compound in the presence of an additional electronic charge from the environment. In a charge transfer process, higher values of ω indicate the higher electrophilic power of the structure.^39,40

μ = −χ = −(E_HOMO + E_LUMO)/2 (4)

η = (E_LUMO − E_HOMO)/2 (5)

ω = μ²/2η (6)

The ionization energy (I) and electron affinity (A) can be expressed as −E_HOMO and −E_LUMO, respectively. Chemical shielding (CS) calculations were performed using the gauge-including atomic orbital (GIAO) method.⁴¹ The chemical shift isotropy (σ_iso) and anisotropy (Δσ) parameters were calculated applying principal components (σ₁₁ ≤ σ₂₂ ≤ σ₃₃) of the chemical shift tensor, as follows:

σ_iso (ppm) = (σ₁₁ + σ₂₂ + σ₃₃)/3 (7)

Δσ (ppm) = σ₃₃ − (σ₁₁ + σ₂₂)/2 (8)

The NBO and AIM analysis was carried out at the M06-2X/6-31G(d) level of theory.^38,42

Results and discussion

Optimized geometry of the adsorbents

The fully optimized geometry, highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and molecular electrostatic potential (MEP) maps of the adsorbent nanocages (C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆) are shown in Fig. 1. The optimized structures of these nanocages are characterized by two hexagons joined by twelve pentagons with D6, C3, and C3 point groups for C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆, respectively. The C–C bond length within the hexagons of C₂₄ is about 1.42 Å; however, the value of the C–C bond length is in the range of 1.36 Å to 1.53 Å in pentagons. The average value of the C–C bond length is calculated to be about 1.44 Å, which is in agreement with the reported values in the literature.^43,44 The C₁₈B₃N₃ is derived by substituting the carbon atoms of a hexagon of C₂₄ with boron and nitrogen atoms as one in between. Thus, C₁₈B₃N₃ includes a B₃N₃ ring, six pentagons with C₃BN formula, six pentagons with C₅ formula, and a C₆ ring. The average length of C–C, B–C, N–C, and B–N bonds is about 1.47, 1.57, 1.46, and 1.48 Å, respectively. In the structure of C₁₂B₆N₆, five distinct types of rings are present: a B₃N₃ ring, six pentagons with B₂N₂C formula, three C₄N pentagons, three C₄B pentagons, and a C₆ ring. Here, the C–C, B–C, N–C, and B–N average bond lengths are about 1.47 Å, 1.54 Å, 1.41 Å, and 1.50 Å, respectively.

Fig. 1 (a) Optimized geometries, (b) HOMOs, (c) LUMOs, and (d) MEP plots for C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ nanocages at the M06-2X/6-31G(d,p) level of theory.

The molecular electrostatic potential (MEP) plot is a valuable tool for determining the electron density distribution over the atoms of a molecule and predicting its most reactive sites. It is widely known that the chemical and physical properties of a molecule are associated with its electrostatic potential. Therefore, the MEP plot can be utilized to characterize electrophilic and nucleophilic sites within an electrostatic interaction.⁴⁵ In a MEP contour, the surfaces are defined based on electron density and represented by an RGB color model, in which red regions are more negative than −0.010 a.u., yellow shows the regions with electron density between 0 and −0.010 a.u., green regions are between 0.010 and 0.0 a.u., and blue color represents regions more positive than 0.010 a.u. Fig. 2 reveals that O13, N8, and N10 atoms are the most negatively charged centers of the PA molecule. Additionally, the oxygen atom is more prone to contribute to the nucleophilic attack. The most positive atoms are C12 (0.68 |e|), H9 (0.45 |e|), H16 (0.43 |e|), H11 (0.41 |e|), and H15 (0.42 |e|), respectively, as shown by NBO analysis, which is in agreement with the MEP plot of the PA molecule.

Fig. 2 (a) Optimized geometry, (b) MEP, (c) HOMO, and (d) LUMO profiles of PA at the M06-2X/6-31G(d,p) level of theory.

The frequency calculations were performed at the M06-2X/6-31G(d,p) level of theory. The vibrational frequency modes of C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ appear in a positive range of 343–1630 cm⁻¹, 345–1603 cm⁻¹, and 282–1473 cm⁻¹, respectively, indicating that the optimized geometries are true local minima on the potential energy surface. Frontier molecular orbitals (HOMO and LUMO) of a molecule play a vital role in determining its reactivity. HOMO and LUMO energy levels are usually considered as the electron-donating and electron-accepting abilities of an organic molecule. A higher E_HOMO value indicates that the molecule can donate electrons, while a lower E_LUMO implies the molecule's willingness to accept electrons. Considering eqn (2), it can be concluded that molecules with a low HOMO–LUMO energy gap are more polarizable and have high chemical reactivity and low kinetic stability.⁴⁶ The HOMO levels of C₂₄ are distributed over the C–C bonds throughout the nanocage except some C–C bonds in pentagons, whereas the LUMO levels are located on the C–C bonds of 5-membered rings. In the case of C₁₈B₃N₃ and C₁₂B₆N₆, the HOMO levels are mainly located on the N atoms and C–C bonds of pentagons, while the LUMO levels are situated on the B atoms and C–C bonds. The HOMO–LUMO energy gaps of C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ are about 3.92, 4.24, and 4.86 eV, respectively, indicating that these nanocages are semiconductors. In the following sections, we will discuss the role of frontier molecular orbitals in the electronic properties of molecules.

Adsorption of PA on the C₂₄ nanocage

Aimed at identifying the most stable C₂₄-PA configuration, we considered all probable orientations of the PA molecule on the surface of C₂₄ using the MEP plots of adsorbent and adsorbate molecules. All initial configurations were optimized employing the B3LYP/6-31G(d), CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory. The adsorption energies (E_ads) for different configurations have been summarized in Table 1. More precisely it should be said that in the initial structures of C₂₄-PA, the drug molecule approached the 5- and 6-membered rings of C₂₄ through (a) N8–H9, (b) N10–H11, (c) C12–O13, and (d) NH₂ group. The last configuration was the structure where PA is adsorbed in parallel on top of C₂₄. After careful optimization and performing vibrational frequency calculations, it was found that the drug molecule adopts a parallel orientation towards C₂₄. From Table 1, adsorption energies depend on both the method and basis set. Also, the energy difference between the configurations is significant in different methods. The amount of adsorption energy at the B3LYP/6-31G(d), CAM-B3LYP/6-31G(d,p), and M06-2X/6-31G(d,p) levels is −13.88 kJ mol⁻¹, −25.72 kJ mol⁻¹, and −125.58 kJ mol⁻¹, respectively. The minimum interaction distance between PA and C₂₄ in the mentioned theoretical levels is 2.85 Å, 2.81 Å, and 2.82 Å, respectively (Fig. 3).

Table 1 Adsorption energies (E_ads), enthalpy changes (ΔH), and Gibbs free energy changes (ΔG) calculated for C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA complexes at different levels of theory

Method	Eads (kJ mol^−1)	E^bsseads (kJ mol^−1)	ΔH (kJ mol^−1)	ΔG (kJ mol^−1)
B3LYP/6-31G(d)
C24-PA	−13.88	−1.34	−9.86	27.48
C18B3N3-PA	−25.72	−5.75	−22.16	21.98
C12B6N6-PA	−125.58	−98.05	−120.99	−70.88
CAM-B3LYP/6-31G(d,p)
C24-PA	−14.81	−8.34	−9.57	−35.40
C18B3N3-PA	−124.73	−97.78	−119.43	−68.50
C12B6N6-PA	−138.55	−124.21	−309.76	−83.07
M06-2X/6-31G(d,p)
C24-PA	−45.95	−29.98	−40.08	−3.62
C18B3N3-PA	−163.63	−56.62	−155.81	−95.25
C12B6N6-PA	−156.48	−137.69	−150.71	−99.17

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Fig. 3 (a) Optimized geometry, (b) MEP, (c) HOMO, and (d) LUMO profiles of C₂₄-PA at the M06-2X/6-31G(d,p) level of theory.

The values of enthalpy (ΔH) and Gibbs free energy changes (ΔG) of the C₂₄-PA complex are negative (with the exception of the B3LYP/6-31G(d) level), indicating that an exothermic and spontaneous reaction has occurred.

The changes in bond length and bond angles of the drug molecule, upon interaction with C₂₄ at the M06-2X/6-31G(d,p) level of theory are illustrated in Tables 2 and S1,† respectively. The length of the C1–C2, C4–N8, C1–N8, N8–H9, and C12–O13 bonds increases while the length of other bonds decreases upon complexation. The results show that the interaction between the drug molecule and C₁₂B₆N₆ has no significant effect on the bond lengths of the PA molecule. The most obvious change in the bond angles of the PA molecule is related to the C12–N14–H16 angle, which ranges from 114.5° to 119.1°. Table 3 summarizes the quantum chemistry reactivity parameters of the nonionic surfactants, including E_HOMO, E_LUMO, and their associated energy gap (E_g), ionization potential (I), electron affinity (A), electronegativity (χ), electronic chemical potential (μ), chemical hardness (η), electrophilicity index (ω), and dipole moments (in Debye). Frontier molecular orbital (FMO) analysis implies that the E_HOMO and E_LUMO of C₂₄ become more stable by about 1.15 and 0.29 eV, respectively, upon complex formation (Fig. 4). Therefore, the E_g value decreases by 21.9%; thus, the electronic properties of C₂₄ change considerably in the presence of PA molecules. The reduction of parameters ω, χ, A, and I is in agreement with the reduction of E_g. It is also observed that with the decrease of the E_g value, the softness and chemical hardness have increased and decreased, respectively, which indicates the tendency of the nanocarrier to interact with PA. The decrease in electrophilicity by 0.42 eV after interaction with the PA molecule confirms the charge transfer from the drug to the nanocarrier. The dipole moment of the C₂₄-PA complex is significantly higher than that of its components. Therefore, the solubility of the C₂₄-PA complex is expected to be higher than the solubility of C₂₄ and PA.

Table 2 Changes in the length of bonds of the PA molecule in interaction with C₂₄ at the M06-2X/6-31G(d,p) level of theory

Bond	Bond length (Å)		Δr
	After interaction	Before interaction
C1–C2	1.343	1.341	0.002
C3–C4	1.331	1.333	−0.002
C2–H5	1.083	1.085	−0.002
C3–H6	1.081	1.082	−0.001
C4–H7	1.082	1.083	−0.001
C4–N8	1.418	1.403	0.015
N8–H9	1.017	1.011	0.006
C1–N8	1.425	1.407	0.018
C2–N10	1.400	1.413	−0.013
C3–N10	1.423	1.434	−0.011
N10–H11	1.011	1.016	−0.005
C1–C12	1.481	1.486	−0.005
C12–O13	1.223	1.221	0.002
C12–N14	1.367	1.369	−0.002
N14–H15	1.009	1.009	0.000
N14–H16	1.007	1.007	0.000

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Table 3 Frontier molecular orbital energies (E_HOMO and E_LUMO) and their associated energy gaps (E_g) as well as CDFT parameters for the investigated structures at the M06-2X/6-31G(d,p) level of theory

Structure	EHOMO (eV)	ELUMO (eV)	Eg (eV)	EF (eV)	I (eV)	A (eV)	χ (eV)	η (eV)	μ (eV)	S (1/eV)	ω (eV)	μ (Debye)
PA	−5.68	0.31	5.99	0.15	5.68	−0.31	2.69	3.00	−2.69	0.17	1.20	2.73
C24	−6.92	−3.00	3.92	−1.50	6.92	3.00	4.96	1.96	−4.96	0.25	6.27	0.00
C24-PA	−5.77	−2.70	3.06	−1.35	5.77	2.70	4.24	1.53	−4.24	0.33	5.86	3.79
C18B3N3	−7.04	−2.80	4.24	−1.40	7.04	2.80	4.92	2.12	−4.92	0.24	5.70	1.10
C18B3N3-PA	−5.84	−1.65	4.19	−0.83	5.84	1.65	3.75	2.10	−3.75	0.24	3.35	11.46
C12B6N6	−7.14	−2.27	4.87	−1.14	7.14	2.27	4.70	2.43	−4.70	0.21	4.55	2.10
C12B6N6-PA	−6.00	−1.38	4.62	−0.69	6.00	1.38	3.69	2.31	−3.69	0.22	2.95	14.48

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Fig. 4 DOS plots of (a) C₂₄-PA and (b) C₂₄.

The mechanism of action of a chemical sensor is directly related to the change in its resistance due to charge exchange with the chemical agent. It is known that the E_g is a dependable indicator to determine the sensitivity of a sensor towards a molecule. The electrical conductivity of a molecule decreases with increasing E_g.^47,48 The population of conduction electrons of a nanostructure increases significantly upon the decrease of E_g and vice versa. Changing the population of conducting electrons after the adsorption process causes the generation of an electrical signal.⁴⁹ The work function (Φ) is another electronic parameter that is affected by the adsorption process and is defined as the minimum amount of energy (i.e., thermodynamic work) required to remove an electron from a solid to a point in the vacuum immediately outside the solid surface (i.e., the Fermi level) and is defined as follows:

Φ = V_el(+∞) − E_F (9)

where E_F is the energy of the Fermi level and V_el(+∞) is the electron electrostatic potential energy far from the solid surface. The value of V_el(+∞) is estimated to be zero, and therefore, we can write eqn (9) as Φ = −E_F. The energy of the Fermi level is given as:

E_F = E_HOMO + (E_LUMO − E_HOMO)/2 (10)

The Φ-type sensors apply a Kelvin oscillator instrument to calculate the values of Φ before and after adsorption.^32,50 In these sensors, the adsorption of a molecule changes the gate voltage and produces an electrical signal that leads to chemical agent detection.⁵¹ The value of Φ is changed by about −0.147 eV going from C₂₄ to C₂₄-PA; therefore, C₂₄ can be used as a Φ-type sensor for PA detection.

To understand the donor–acceptor (bond–antibond) interactions between the drug molecule and the nanocages, NBO analysis has been performed at the M06-2X/6-31G(d,p) level of theory. In this analysis, all possible interactions between filled (donors) Lewis-type NBOs and empty (acceptors) non-Lewis NBOs are examined. Then, their energetic relevance is evaluated by second order perturbation theory. These interactions are called delocalization corrections to the zeroth-order natural Lewis structure because they result in a donation of electrons from the localized NBOs of the idealized Lewis structure into the empty non-Lewis orbitals. The stabilization energy (E⁽²⁾) associated with delocalization i → j is defined as:

where q_i is the donor orbital occupancy, ε_i and ε_j are diagonal elements (orbital energies), and F(i,j) is the off-diagonal NBO Fock matrix element. This equation states a direct relationship between the off-diagonal NBO Fock matrix element and the orbital overlap. The greater values of E⁽²⁾ indicate stronger interactions. The NBO analysis results showed that the highest values of stabilization energies E⁽²⁾ of the C₂₄ nanocarrier are: BD*(2) C12–C13 → BD*(2) C18–C19; E⁽²⁾ = 30.29 kcal mol⁻¹, BD*(2) C10–C11 → BD*(2) C2–C16; E⁽²⁾ = 30.36 kcal mol⁻¹, BD*(2) C21–C22 → BD*(2) C18–C19; E⁽²⁾ = 22.63 kcal mol⁻¹, BD*(2) C9–C24 → BD*(2) C6–C7; E⁽²⁾ = 30.47 kcal mol⁻¹, and BD*(2) C21–C22 → BD*(2) C15–C17; E⁽²⁾ = 30.36 kcal mol⁻¹. Additionally, the most important stabilization energies related to the interaction of C₂₄ and PA are BD (1) C3–C4 → RY*(3) C26; E⁽²⁾ = 0.48 kcal mol⁻¹ and BD(2) C3–C4 → BD*(2)C26–C27; E⁽²⁾ = 3.19 kcal mol⁻¹. The changes in the atomic charges of the PA molecule due to the interaction with C₂₄ are shown in Table S2† and confirm a charge transfer of 0.07 |e| from the drug to the nanocarrier. A closer look into the atomic charges shows that the partial charge of C1, C2, C3, and N10 atoms has decreased by about 0.016, 0.018, 0.012, and 0.033 |e| after the adsorption process. However, no noticeable change is observed in the charge of other atoms. The calculated partial atomic charges using the NBO technique are in good agreement with the MEP plots. Comparing the MEP plots of C₂₄ and PA molecules with that of the C₂₄-PA complex shows that the interaction between the drug molecule and the nanocarrier causes the transfer of electron density from PA to the nanocage. The contours in Fig. S1† show the atoms involved in electron resonance in C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA complexes. As seen, most of the atoms in the structure of the complexes contribute to the resonance interactions.

Adsorption of PA on the C₁₈B₃N₃ nanocage

To improve the interaction between the C₂₄ and PA drug molecule, we adopted the doping technique so that six carbon atoms were replaced by three boron and three nitrogen atoms to form the C₁₈B₃N₃ nanocage. The most stable complex between C₁₈B₃N₃ and the PA drug molecule was obtained by adopting a method similar to that used for C₂₄-PA. The drug molecule approached the 5- and 6-membered rings of C₁₈B₃N₃, B, and N heteroatoms through (a) N8–H9, (b) N10–H11, (c) C12–O13, and (d) NH₂ group. Adsorption of PA on the surface of the C₁₈B₃N₃ nanocage is an exothermic process. The adsorption energies of PA on the C₁₈B₃N₃ at the mentioned levels of theory are reported in Table 1. The nearest interaction distance between PA and C₁₈B₃N₃ is 1.5 Å, in which the drug molecule has adopted a parallel orientation towards C₁₈B₃N₃ (Fig. 5). It seems that the weak π–π interactions are also effective in stabilizing the C₁₈B₃N₃ complex. The values of ΔH and ΔG of the C₁₈B₃N₃-PA complex at T = 298 K and P = 1 atm are shown in Table 1, which are more negative than the corresponding values of C₂₄-PA.

Fig. 5 (a) Optimized geometry, (b) MEP, (c) HOMO, and (d) LUMO profiles of C₁₈B₃N₃-PA at the M06-2X/6-31G(d,p) level of theory.

Tables 4 and S3† show the structural parameters (bond lengths and bond angles) of the drug molecule before and after interaction with the C₁₈B₃N₃ nanostructure. The interaction between the drug molecule and C₁₈B₃N₃ does not have a significant effect on the length of bond of the PA molecule and is similar to the structure of C₂₄PA. In any case, these changes are very small and can be ignored. The greatest decrease in the bond angle due to PA adsorption on the C₁₈B₃N₃ surface is related to the C4–N8–H9 angle, which decreased by 8.8°, while C12–N14–H15 and C1–C12–N14 bond angles show increases of 3.8° and 2.6°, respectively. Frontier molecular orbital (FMO) analysis reveals that E_HOMO of C₁₈B₃N₃ changes from −7.04 eV to −5.84 eV after adsorption of PA; also, E_LUMO stabilizes by approximately 1.14 eV (Fig. 5). Therefore, the E_g value decreases by 1.2%; thus, the electronic properties of C₁₈B₃N₃ are sensitive to the presence of PA molecules. Here again the reductions in parameters ω, χ, A, and I are in agreement with the reduction in E_g (Fig. 6).

Table 4 Change in the length of bonds of the PA molecule upon interaction with C₁₈B₃N₃ PA at the M06-2X/6-31G(d,p) level of theory

Bond	Bond length (Å)		Δr
	After interaction	Before interaction
C1–C2	1.352	1.341	0.012
C3–C4	1.331	1.333	−0.002
C2–H5	1.084	1.085	−0.001
C3–H6	1.080	1.082	−0.002
C4–H7	1.082	1.083	−0.001
C4–N8	1.423	1.403	0.02
N8–H9	1.019	1.011	0.008
C1–N8	1.427	1.407	0.020
C2–N10	1.375	1.413	−0.038
C3–N10	1.427	1.434	−0.0.007
N10–H11	1.011	1.016	−0.005
C1–C12	1.450	1.486	−0.036
C12–O13	1.284	1.221	0.063
C12–N14	1.324	1.369	−0.045
N14–H15	1.008	1.007	0.001
N14–H16	1.011	1.009	0.002

---

Fig. 6 DOS plots of (a) C₁₈B₃N₃-PA and (b) C₁₈B₃N₃.

The decrease in electrophilicity upon adsorption of PA is calculated to be approximately 0.159 eV, showing that charge transfers from the drug molecule to C₁₈B₃N₃. Table S4† represents the partial atomic charges of the PA molecule before and after interaction with C₁₈B₃N₃. The charge of C1, C4, N8, and O13 atoms increased by approximately 0.048, 0.012, 0.001, and 0.022 |e|, respectively. The comparison of the total atomic charges of PA and C₁₈B₃N₃ shows that due to the formation of a complex between PA and C₁₈B₃N₃, 0.398 |e| of charge is transferred from the drug to the nanocarrier.

The NBO analysis results showed that the highest values of stabilization energies E⁽²⁾ of the C₁₈B₃N₃ nanocarrier are BD*(2) C33–C34 → BD*(2) C23–C24; E⁽²⁾ = 49.82 kcal mol⁻¹, BD*(2) C29–C30 → BD*(2) C31–C32; E⁽²⁾ = 50.27 kcal mol⁻¹, BD*(2) C27–C28 → BD*(2) C25–C26; E⁽²⁾ = 49.69 kcal mol⁻¹, BD(2) C33–C34 → LP*(1) B21; E⁽²⁾ = 45.12 kcal mol⁻¹, and BD(2) C25–C26 → LP*(1) B21; E⁽²⁾ = 44.91 kcal mol⁻¹. The antibonding orbitals of boron atoms are the most important non-Lewis acceptors. The greatest values of stabilization energy in the C₁₈B₃N₃-PA complex are related to transitions within the C₁₈B₃N₃ molecule: BD*(2) C33–C34 → BD*(2) C23–C24; E⁽²⁾ = 34.89 kcal mol⁻¹, BD*(2) C29–C30 → BD*(2) C31–C32; E⁽²⁾ = 42.29 kcal mol⁻¹, BD*(2) C27–C28 → BD*(2) C25–C26; E⁽²⁾ = 37.10 kcal mol⁻¹, and BD*(2) C37–C36 → BD*(2) C23–C24; E⁽²⁾ = 57.13 kcal mol⁻¹. The most important stabilization energies related to the interaction between C₁₈B₃N₃ and PA are BD(2) C25–C26 → LP*(1) B21; E⁽²⁾ = 46.33 kcal mol⁻¹ and BD(1) C25–C26 → LP*(1) B21; E⁽²⁾ = 3.43 kcal mol⁻¹, which indicates charge transfer from the drug molecule to C₁₈B₃N₃.

Adsorption of PA on the C₁₂B₆N₆ nanocage

In the next step, 12 carbon atoms of C₂₄ were replaced by six boron atoms and six nitrogen atoms to obtain the C₁₂B₆N₆ structure. In the most stable C₁₂B₆N₆-PA complex, the oxygen atom of the drug molecule has established a bond with one of the boron atoms of the nanostructure with a length of 1.523 Å, which leads to an adsorption energy of −125.58 kJ mol⁻¹, −138.55 kJ mol⁻¹, and −156.48 kJ mol⁻¹ at the B3LYP/6-31G(d), CAM-B3LYP/6-31G(d,p), and M06-2X/6-31G(d,p) levels of theory, respectively (Fig. 7 and Table 1).

Fig. 7 (a) Optimized geometry, (b) MEP, (c) HOMO, and (d) LUMO profiles of C₁₂B₆N₆-PA at the M06-2X/6-31G(d,p) level pf theory.

Table 5 shows that despite the relatively strong interaction between the drug molecule and C₁₂B₆N₆, the geometrical parameters of PA did not change significantly. However, the bond length changes are more evident in the areas involved in the interaction with the nanostructure. For example, after forming the C₁₂B₆N₆-PA complex, the C–O bond length of PA has increased by approximately 0.057 Å. The process of bond length changes in C₁₂B₆N₆-PA is similar to that in the C₁₈B₃N₃-PA and C₂₄-PA complexes. Additionally, the lengths of C1–C12 and C1–N8 bonds increased, which can be attributed to resonance effects. The highest bond angle increase due to PA adsorption on the C₁₂B₆N₆ surface is related to C1–C12–N14, C2–N10–H11, and C12–N14–H16 angles, which increased by 4.7°, 2.5° and 2.4°, respectively. The C1–C12–O13 bond angle decreased from 120.1° to 115.4° (Table S5†).

Table 5 Change in the length of bonds of the PA molecule upon interaction with C₁₂B₆N₆ at the M06-2X/6-31G(d,p) level of theory

Bond	Bond length (Å)		Δr
	After interaction	Before interaction
C1–C2	1.350	1.341	0.009
C3–C4	1.329	1.333	−0.004
C2–H5	1.084	1.085	−0.001
C3–H6	1.080	1.082	−0.002
C4–H7	1.081	1.083	−0.002
C4–N8	1.416	1.403	0.013
N8–H9	1.014	1.011	0.003
C1–N8	1.425	1.407	0.018
C2–N10	1.375	1.413	−0.038
C3–N10	1.433	1.434	−0.001
N10–H11	1.009	1.016	−0.007
C1–C12	1.450	1.486	−0.036
C12–O13	1.278	1.221	0.057
C12–N14	1.326	1.369	−0.043
N14–H15	1.006	1.007	−0.001
N14–H16	1.024	1.009	0.015

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According to Table 3, the E_g of C₁₂B₆N₆ has decreased by 0.24 eV after interaction with the drug molecule, which indicates the high reactivity of the nanocarrier (Fig. 8). The significant decrease of E_g shows that the electronic properties of C₁₂B₆N₆ are very sensitive to the presence of drug molecules in the environment, and therefore, C₁₂B₆N₆ can be used as a PA sensor. The reduction in parameters ω, χ, A, and I is in agreement with the reduction in E_g. It is also observed that with the decrease in the E_g value, the softness and chemical hardness have increased and decreased, respectively, which indicates the tendency of the nanocarrier to interact with the PA molecule. A considerable decrease in the electrophilicity parameter by 1.60 eV confirms the charge transfer from the drug to the nanocarrier.

Fig. 8 DOS plots of (a) C₁₂B₆N₆-PA and (b) C₁₂B₆N₆.

Table S6† shows that the partial charge of PA atoms is affected by the presence of the C₁₂B₆N₆ nanocarrier in the environment. Therefore, the charges of the C1, C3, N8, and O13 atoms increased by 0.029, 0.001, 0.009, and 0.020 |e|. On the other hand, the charges of the C2, N14 and N10 atoms have become more positive by 0.078, 0.067, and 0.053 |e| respectively. Additionally, NBO calculations show that due to the formation of a complex between PA and C₁₂B₆N₆, a charge amount of 0.324 |e| is transferred from the drug to the nanocarrier. The dipole moment is an important parameter for understanding the symmetry of the complex; the higher the dipole moment, the higher the interaction between the adsorbate and adsorbent molecules.⁵² The significant increase in the dipole moment of C₁₂B₆N₆ indicates that the solubility of C₁₂B₆N₆-PA increases upon the adsorption process.

Examining the stabilization energies E⁽²⁾ shows that the most important electron transfers of the drug molecule are: LP(1) N14 → BD*(2) C12–O13; E⁽²⁾ = 56.14 kcal mol⁻¹, LP(1) N10 → BD*(2) C1–C2; E⁽²⁾ = 34.28 kcal mol⁻¹, LP(1) N8 → BD*(2) C1–C2; E⁽²⁾ = 33.13 kcal mol⁻¹, LP(2) O13 → BD*(1) C12–N14; E⁽²⁾ = 29.41 kcal mol⁻¹, and BD(2) C1–C2 → BD*(2) C12–O13; E⁽²⁾ = 19.41 kcal mol⁻¹. The most important donors are free electron pairs of nitrogen and oxygen that fill the C1–C2 and C12–O13 antibonding orbitals. Additionally, the greatest stabilization energy E⁽²⁾ values of the nanocarrier are: LP(1) N25 → LP*(1) B17; E⁽²⁾ = 24.73 kcal mol⁻¹, LP(1) N29 → LP*(1) B19; E⁽²⁾ = 24.75 kcal mol⁻¹, BD(2) N17–B19 → LP*(1) B19; E⁽²⁾ = 62.33 kcal mol⁻¹, BD(2) N17–B19 → LP*(1) B121; E⁽²⁾ = 63.09 kcal mol⁻¹, and BD(2) N33–B21 → LP*(1) B19; E⁽²⁾ = 62.86 kcal mol⁻¹. As seen, non-Lewis acceptors are antibonding orbitals of boron atoms. Regarding the donor–acceptor transitions in the C₁₂B₆N₆-PA complex, it should be said that the largest amounts of stabilization energy are related to transitions within the C₁₂B₆N₆ molecule which are: BD*(2) C24–N25 → LP*(1) B23; E⁽²⁾ = 99.29 kcal mol⁻¹, LP(1) C2 → LP*(1) C4; E⁽²⁾ = 90.21 kcal mol⁻¹, LP(1) C26 → BD*(2) C24–N25; E⁽²⁾ = 74.59 kcal mol⁻¹, BD(2) N27–B18 → LP*(1) B17; E⁽²⁾ = 70.14 kcal mol⁻¹, and BD*(2) C12–N14 → BD*(2) C1–C2; E⁽²⁾ = 69.22 kcal mol⁻¹. The most important stabilization energies related to the interaction between C₁₂B₆N₆ and PA are: BD(2) B17–N18 → BD*(1) B17–O13; E⁽²⁾ = 13.34 kcal mol⁻¹, LP(2) O13 → BD*(1) B17–N25; E⁽²⁾ = 6.22 kcal mol⁻¹, and BD(2) C12–N14 → BD*(1) B17–O; E⁽²⁾ = 1.35 kcal mol⁻¹, which is in agreement with the increase of the C12–O13 bond and also bond formation between the PA oxygen and the boron atom of C₁₂B₆N₆. As can be seen, the replacement of carbon atoms with boron and nitrogen atoms increased the stabilization energies.

Atoms in molecule analysis

Bader's quantum theory of atoms in molecules (QTAIM)⁵³ was utilized to explore electron density and bonding characteristics of the investigated systems. This theory states that upon chemical bond formation between two atoms a bond critical point (BCP) appears between them. The characteristics of BCPs are of great relevance in determining the electron density (ρ_C) and its corresponding Laplacian (∇²ρ_C), and therefore, designating the nature of interactions at a molecular level. ∇²ρ_C is the second derivative of a scalar function and provides information about the tendency of electron density to concentrate or deplete. The total electronic energy density at the BCP (H_C) elucidates the energetic properties of BCPs and it is the sum of the local kinetic energy density (G_C) and local potential energy density (V_C) at the BCP.

H_C = G_C + V_C (12)

On the other hand, the virial theorem states a relation between the Laplacian of the electron density at BCP and its other characteristics.

(1/4)∇²ρ_C = 2G_C + V_C (13)

A negative value of the Laplacian indicates the concentration of the electron density among the nuclei of interacting atoms, and one may assume a shared interaction such as covalent bonds and lone pairs. A positive Laplacian electron density value at corresponding BCP shows the depletion of electron density as in ionic, van der Waals, and hydrogen bond interactions. Fig. 9 illustrates the molecular graph of C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA complexes obtained from AIM calculations. The graphs were obtained at the M06-2X/6-31G(d,p) level of theory. Large circles correspond to attractors and small red and yellow circles are bond and ring critical points, respectively. However, sometimes ∇²ρ_C > 0 but the total electronic energy density, H_C, is negative and such a situation is attributed to the partially covalent interaction. Fig. 9 shows that the adsorption of the PA molecule on the surface of the C₂₄ nanocage led to the appearance of two critical points between the drug and the nanostructure. The electron density properties calculated for the C₂₄-PA complex reveal that for the O13_PA⋯C19 interaction ∇²ρ_C > 0 and H_C > 0; hence, this interaction belongs to the category of electrostatic interactions. The C4_PA⋯C20 interaction has more electron density (0.006 a.u.), and the values of ∇²ρ_C (0.019 a.u.) and H_C (0.001 a.u.) are positive. Therefore, this bond is also the result of an electrostatic interaction (Table 6).

Fig. 9 Molecular graphs for C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA complexes at the M06-2X/6-31G(d,p) level of theory (large circles correspond to attractors, while small red and yellow circles are bond and ring critical points, respectively).

Table 6 Topological parameters (all in atomic units) for the optimized structures analyzed here at the M06-2X/6-31G(d,p) level of theory

Complex	Interaction site	ρC	∇^2ρC	GC	VC	HC	Type of interaction
C24-PA	O13(PA)⋯C19	0.010	0.031	0.007	−0.006	0.001	Electrostatic
	C4(PA)⋯C20	0.006	0.019	0.004	−0.003	0.001
C18B3N3-PA	O(PA)⋯B17	0.117	0.512	0.194	−0.259	−0.065	Partly covalent
C12B6N6-PA	O13(PA)⋯B17	0.126	−0.138	0.209	−0.280	−0.071	Covalent
	H(PA)⋯N18	0.033	0.089	0.023	−0.024	−0.001	Partly covalent

---

AIM calculations showed that only one critical point has appeared between O13 of the PA molecule and B17 of the C₁₈B₃N₃ nanostructure, for which the values of ρ_C, ∇²ρ_C and H_C are 0.117, 0.512, and −0.065 a.u. respectively. Therefore, the O_PA⋯B17 interaction is partially covalent. The electron density properties calculated for the C₁₂B₆N₆-PA complex show that the O13_PA⋯B17 bond possesses a significant charge density (0.126 a.u.). Moreover, the values of ∇²ρ_C (−0.138 a.u.) and H_C (−0.071 a.u.) are negative. Therefore, as we mentioned before, the O13_PA⋯B17 bond is a covalent interaction. AIM calculations show that the H_PA⋯N18 interaction has lower values of ρ_C and ∇²ρ_C > 0; however, this interaction is categorized as a partly covalent interaction because ∇²ρ_C > 0 and H_C < 0.

NMR and IR spectra

The changes in charge density around the nuclei involved in the adsorption process can be very efficient in verifying the nature of host–guest interactions because the magnitude of these variations reveals the contribution of each nucleus to the interaction.⁵⁴ Therefore, we performed NMR chemical shift calculations using the GIAO method to investigate the nature of interactions involved in the adsorption of PA on the surface of C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆. The chemical shift (CS) principal components (σ_ii), CS isotropy (σ_iso), and CS anisotropy values of ¹³C, ¹⁵N, ¹⁷O, and ¹H for the surfactant molecules calculated at the M06-2X/6-31G(d,p) level of theory are shown in Tables S7 to S13.† The isotropy (σ_iso) parameter shows the average value of the CS tensor, while the anisotropy (Δσ) parameter specifies the orientations of the CS tensor at the atomic site. The calculated chemical shift tensors for ¹³C, ¹⁵N, ¹⁷O, and ¹H nuclei are sensitive to complex formation at the active site. The values of σ_iso and Δσ parameters of the C12, O13, and N14 atoms of the drug molecule increase significantly due to the adsorption on C₁₂B₆N₆. After complex formation, the values of σ_iso and Δσ of the N8 and N10 atoms in the PA molecule decrease and increase, respectively. The value of σ_iso for C1 to C4 atoms in the drug molecule increases, while the Δσ value for these atoms decreases. The changes in the σ_iso and Δσ values of the PA atoms in C₁₈B₃N₃-PA and C₂₄-PA complexes also follow the same trend. The values of σ_iso and Δσ parameters of the C10, C11, C12, B13, B14, and B15 atoms of the C₁₂B₆N₆ nanocage increase due to complex formation, while the values of σ_iso and Δσ of the C1, C5, C8, N18, B19, B20, N22, N23, and N24 atoms have decreased. In general, the results obtained from NMR spectra are in agreement with the previous results. Fig. S2 to S7† show the IR spectra of the compounds investigated in this study. Fig. S6† shows that a new peak appears in the region of 3300 cm⁻¹ after C₁₂B₆N₆-PA complex formation, which indicates the interaction between the functional groups of the host and guest molecules. Although the interaction of the drug molecule with C₁₈B₃N₃ and C₂₄ nanocarriers also leads to changes in the IR spectrum of the nanocages, due to the orientation of the interacting molecules, the intensity and the location of the peaks are different.

UV-Vis spectra

The interaction between light and matter has always been of interest and is used to investigate the electronic properties of molecules precisely. The UV-Vis spectrum of the PA molecule (Fig. S9†) shows that the highest peak corresponds to the wavelength of 228 nm with f = 0.099. The higher the value of f, the higher the transition peak. The highest peak for the C₁₂B₆N₆ molecule appears at 327 nm with f = 0.002 and for C₁₂B₆N₆-PA at 496 nm with f = 0.069. In general, as shown in Tables S15–S20 and Fig. S9–S14,† adsorption of PA on the surface of nanocarriers, the wavelengths of the C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆, and thus, the highest peaks are shifted to higher values. Therefore, a redshift occurs after the adsorption process.

Conclusions

In this study, we investigated the potential of the pristine C₂₄ nanocage and its doped boron nitride analogs (C₁₈B₃N₃ and C₁₂B₆N₆) as carriers for the pyrazinamide (PA) drug using density functional theory (DFT). All calculations including geometry optimization, vibrational frequencies, QTAIM, NBO, NMR, and IR were carried out using the B3LYP/6-31G(d), CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory. To calculation of the dispersion energy, the modified CAM-B3LYP and M06-2X methods were used. The results show that the adsorption energies calculated by B3LYP, CAM-B3LYP, and M06-2X methods are different. The M06-2X values are greater than those calculated by B3LYP and CAM-B3LYP methods. The adsorption energy (E_ads), enthalpy (ΔH), and Gibbs free energy (ΔG) of C₂₄-PA, C₁₈B₃N₃-PA, and C₁₂B₆N₆-PA complexes were calculated using the B3LYP/6-31G(d), CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory. The results show that the interaction of the drug with the nanocages is exothermic and a spontaneous reaction has occurred at all theoretical levels (with the exception of the B3LYP/6-31G(d) level for C₂₄-PA and C₁₈B₃N₃). The results show that doping has increased the conductivity of nanocages. On the other hand, the interaction of PA with nanocages leads to a reduction in the energy gap of complexes. The E_g values of C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ at the M06-2X/6-31G(d,p) level decrease by approximately 21%, 1.2%, and 5%, respectively, upon complexation. Furthermore, the decrease of E_g in complexes suggests that nanocages can be utilized for sensing PA molecules. Despite the relatively strong interactions between the drug molecule and nanocages, the geometrical parameters of PA did not change significantly. The changes in the atomic charges of the PA molecule due to the interaction with C₂₄, C₁₈B₃N₃, and C₁₂B₆N₆ confirm a charge transfer of 0.07, 0.327, and 0.398 |e| from the drug to the nanocage, respectively. Based on the NBO results, the replacement of carbon atoms with boron and nitrogen atoms increased the stabilization energies (E⁽²⁾). AIM calculations revealed that the observed interactions between the nanocage and PA drug in C₁₂B₆N₆-PA and C₁₈B₃N₃-PA nanocages are stronger than those with the C₂₄-PA nanocage. The results show that all three types of nanocages can be used as drug delivery systems for PA molecules.

Ethics approval and consent to participate

This study did not involve human subjects, animal experimentation, or other activities necessitating ethical review.

Consent for publication

The authors of this manuscript confirm that all authors have reviewed and approved the final version of the manuscript for submission to the journal of Nanoscale Advances.

Data availability

The datasets generated during the current study are available upon request from the corresponding author. Additionally, some of the data and materials supporting this article have been included in the main text and ESI.†

Author contributions

F. Naderi: conceived and designed the study, reviewing, editing of the manuscript, conceptualization, supervision; A. Moumivand: writing, software; O. Moradi: validation, visualization, methodology; B. Makiabadi: editing of the manuscript.

Conflicts of interest

All authors declare that they have no competing interests.

Acknowledgements

No funding was received to assist with the preparation of this manuscript.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4na00560k

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