DFT insights into heteroatom-doped C₆₀ nanocages as potential drug carriers for lorazepam

Abstract

Efficient delivery of lorazepam remains challenging due to its poor aqueous solubility, limited bioavailability, and delayed onset of action. In this work, a density functional theory (DFT) study was conducted to investigate the adsorption behavior of lorazepam on pristine C₆₀, SiC₅₉, and GeC₅₉ nanostructures as potential drug delivery systems. Various adsorption configurations were optimized to identify the most stable binding modes and interaction mechanisms. The calculated adsorption energies indicate that C₆₀ exhibits relatively weaker interactions compared to doped systems, while silicon and germanium doping significantly enhance the adsorption strength. In particular, the SiC₅₉ system shows the highest stability, with adsorption energies reaching approximately −6.1 eV, indicating strong binding suitable for drug loading applications. GeC₅₉ also demonstrates enhanced adsorption compared to C₆₀, although weaker than Si doping. Several analytical tools were employed, including reduced density gradient (RDG–NCI) analysis, partial density of states (PDOS), natural bond orbital (NBO) analysis, infrared (IR) spectroscopy, work function (φ), and HOMO–LUMO gap, which confirm significant electronic interaction and charge transfer between the drug and nanocarrier. Solvent effects further reveal that adsorption remains energetically favorable in aqueous environments. Importantly, protonation studies under acidic conditions demonstrate a significant weakening of the interaction, confirming the feasibility of a pH-responsive drug release mechanism. Overall, these findings highlight doped C₆₀ nanocages, especially SiC₅₉, as promising candidates for efficient and controlled lorazepam delivery.

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1. Introduction

Efficient drug delivery remains one of the most significant challenges in achieving optimal therapeutic efficacy for treating various diseases and viral infections. Despite significant advances in pharmacology and formulation development, conventional drug administration routes continue to face major biopharmaceutical limitations, including poor aqueous solubility, limited permeability across biological membranes, and low bioavailability. These drawbacks often result in reduced therapeutic efficacy and unpredictable pharmacokinetics.¹ Moreover, systemic distribution of drugs without targeting mechanisms can lead to nonspecific accumulation in healthy tissues and undesirable side effects, particularly in treatments requiring high drug concentrations for efficacy.^2–4

To overcome these limitations, nanotechnology has emerged as a promising strategy for developing advanced drug delivery systems (DDSs) capable of improving drug solubility, stability, and targeted delivery while minimizing systemic toxicity.^5,6

Among clinically important therapeutic agents, lorazepam, a benzodiazepine derivative, is widely used for its anxiolytic and sedative properties but suffers from several delivery related limitations. These include its low aqueous solubility (∼0.08 mg mL⁻¹),⁷ poor chemical stability,⁸ and delayed onset of action following oral administration.^9–11 Such limitations can lead to suboptimal therapeutic outcomes and increase the risk of overdose due to delayed pharmacological response. Consequently, developing alternative delivery strategies for lorazepam is essential to enhance its clinical performance.

In this context, adsorption of lorazepam onto suitable nanocarriers represents a promising strategy to improve its solubility, stability, and delivery efficiency. Carbon-based nanostructures, such as fullerenes, carbon nanotubes, and graphene, have attracted considerable attention as potential drug carriers due to their unique physicochemical properties, including high surface area, tunable electronic characteristics, and favorable biocompatibility.^12–14 These properties facilitate strong interactions with drug molecules, enabling improved drug loading, stability, and controlled release behavior.

Among carbon nanomaterials, fullerene C₆₀ has emerged as a particularly attractive nanocarrier owing to its spherical geometry, high symmetry, and electron-accepting ability.¹⁵ The π-conjugated cage-like structure of C₆₀, composed of 60 carbon atoms, provides an extensive surface area that promotes efficient interaction with therapeutic molecules, primarily through chemisorptive mechanisms.^16,17 Previous theoretical and experimental studies have demonstrated that fullerenes can form stable complexes with a wide range of drugs, leading to enhanced pharmacokinetic properties and prolonged circulation times.¹⁶

To gain molecular level insight into these interactions, DFT has been widely employed as a reliable computational approach for studying drug–nanocarrier systems. DFT enables detailed analysis of adsorption energies, charge transfer, electronic structure modifications, and interaction mechanisms, offering valuable information for the rational design of nanocarrier-based DDSs.^18–20

Furthermore, the adsorption performance and electronic properties of fullerene surfaces can be significantly enhanced through heteroatom doping. Incorporation of dopant atoms such as silicon (Si) and germanium (Ge) introduces localized electronic density variations, creates new active adsorption sites, and improves charge transfer between the drug molecule and the nanocarrier.^21–23

Silicon doping has been reported to enhance the thermal and mechanical stability of C₆₀ while increasing the number of active binding sites and modifying the band gap, thereby improving sensitivity to photoreactions and molecular interactions.^24–32 Similarly, germanium doping, owing to its larger atomic radius and higher polarizability, further enhances surface reactivity and adsorption stability, making it particularly advantageous for drug delivery applications involving lorazepam.^33–35 In addition to elemental doping, various surface modification and functionalization strategies have been explored to improve the delivery efficiency and controlled release behavior of fullerene-based carriers. For instance, PEG-functionalized iron-encapsulated C₆₀ (Fe@C₆₀:PEG) has shown enhanced stability and dipole moment, leading to improved adsorption energetics for anticancer drugs such as carboplatin.³⁶ Alkali metal decoration (Li, Na, K) of C₆₀ has also been demonstrated to generate multiple active sites capable of carrying several drug molecules, such as 5-fluorouracil, while maintaining reversible adsorption suitable for controlled release under physiological conditions.³⁷ Additionally, transition metal-doped fullerenes (e.g., Cr, Fe, Ni) have exhibited enhanced adsorption and charge transfer interactions with antiviral drugs, suggesting improved delivery performance in aqueous biological environments.³⁸ Experimental studies further support the potential of fullerene-based DDSs. Complexes of C₆₀ with anticancer drugs, such as doxorubicin, have demonstrated enhanced cytotoxicity and improved antitumor efficacy in vivo compared to the free drug, highlighting the ability of fullerene carriers to improve drug accumulation at target sites and modulate biological responses.³⁹ Moreover, C₆₀ nanocomplexes have been shown to influence immune cell activity and oxidative stress pathways, indicating potential synergistic therapeutic effects beyond conventional drug transport.⁴⁰

Based on these findings, the present study employs DFT to systematically investigate and compare the adsorption behavior of lorazepam on pristine fullerene C₆₀, silicon-doped fullerene, and germanium-doped fullerene. Multiple adsorption configurations, from configuration (1) to configuration (5), were optimized and analyzed. Electronic structure properties were examined through partial density of states (PDOS) and HOMO–LUMO analysis to elucidate the charge transfer mechanisms and adsorption stability.^15,41 Vibrational properties were explored using IR spectroscopy to identify characteristic frequency shifts and distinguish between physisorption and chemisorption interactions.⁴² Additionally, RDG–NCI and NBO analyses, along with thermodynamic parameters (ΔG, ΔH, and ΔS), were evaluated to obtain comprehensive insight into the interaction mechanisms and feasibility of these systems.^33,43–46 The work function and solvent effects in aqueous environments were also assessed to evaluate the practical applicability of these nanocarriers in biological systems. Furthermore, to assess the potential for controlled drug release, the effect of protonation under acidic conditions (pH < 7) on the interaction strength was also investigated for config. (1) of SiC₅₉, demonstrating that the drug–nanocarrier complexes maintain strong and stable interactions without any loss of adsorption efficiency.

2. Computational methods

DFT calculations were used to investigate the adsorption behavior of lorazepam onto both pristine and metal-doped fullerene surfaces in gaseous and aqueous phases. These calculations allowed for the prediction of adsorption mechanisms through the determination of molecular descriptors and adsorption energies, specifically by evaluating the binding energy between the lorazepam drug and fullerene. Geometry optimizations and electronic characteristics for all the studied complexes and different binding orientations were performed using the Gaussian 16 software on both pristine fullerene and metal-doped fullerene,^47,48 where the system was modeled as a finite molecular cluster.^49,50 Fullerene C₆₀ is a spherical molecule composed of sixty carbon atoms arranged in a hollow cage structure resembling a soccer ball. Its geometry consists of twelve pentagonal and twenty hexagonal carbon rings that are interconnected, giving the molecule a highly symmetrical shape. Because the carbon atoms are distributed in all three spatial directions, C₆₀ is classified as a three-dimensional (3D) form of carbon. This distinguishes it from materials like graphene, which is two-dimensional since its atoms lie on a single plane, and from carbon nanotubes, which are one-dimensional. The closed, cage-like structure of fullerene provides it with a definite volume in space, making it one of the most fascinating 3D allotropes of carbon, alongside diamond.

The B3LYP functional with Grimme's dispersion correction (B3LYP-D3) was employed in this study, as it is one of the most extensively used and well-validated functionals in the literature for investigating molecular adsorption on carbon-based nanostructures,^43,51 offering a reliable balance between accuracy and computational efficiency. As a methodological validation, selected complexes were re-optimized using the 6-31+G(d) basis set and with the ωB97XD functional to validate the reliability of the chosen level of theory, revealing that the adsorption orientations and interaction sites remain unchanged, with no significant structural rearrangement; the detailed comparison is provided in the supplementary information (SI, Fig. S8 in pages 8–9). This combination has been successfully employed to represent various chemical systems.^52–56 The standard 6-31G(d) basis set was applied to ensure a suitable balance between computational cost and accuracy, and has been widely used for fullerene–drug interaction studies.^57–59 DFT enabled the identification of potential adsorption sites and the characterization of drug–surface interactions, including chemisorptive bonding.⁶⁰ In this study, all geometries were re-optimized in the solvent environment, by accounting for solvent effects, and the integral equation formalism polarizable continuum model (IEFPCM) was employed, simulating water as the solvent.^61–64 Water was considered as a basic approximation to represent solvent effects; however, it is acknowledged that real physiological environments contain various ions, biomolecules, and other competing species that may influence the interactions. This approach allowed us to evaluate the influence of the aqueous environment on the adsorption behavior and electronic properties of the lorazepam drug on pristine and doped fullerene surfaces. Frequency calculations confirmed that all optimized structures correspond to true minima on the potential energy surface, with no imaginary frequencies detected. Partial density of states (PDOS) calculations were carried out for the optimized lorazepam–fullerene complexes in the vacuum phase to analyze the orbital contributions of the drug and the surface to the interfacial electronic structure. In contrast, total density of states (DOS) calculations were performed for the solvated systems to assess solvent-induced modifications in the overall electronic structure. The molecular structures and the electronic properties, including the highest occupied molecular orbits (HOMO) and lowest unoccupied molecular orbits (LUMO) have been analyzed and visualized utilizing GaussView 6.0. To explore intermolecular interactions, visual molecular dynamics (VMD),⁶⁵ Gnuplot,⁶⁶ and natural bond orbital (NBO) analysis were performed on the obtained C₆₀–lorazepam drug complexes, employing the same level of theory and basis set,⁶⁷ and Multiwfn software⁶⁸ was employed for generating RDG plots and NCI iso-surfaces. DOS, PDOS and IR spectra were analyzed utilizing GaussSum software.⁶⁹ The binding energy (E_bind) is defined as the following:

E_bind = E_{C60\lorazepam drug} − (E_{lorazepam drug} + E_C60) (1)

Here, E_{lorazepam drug} represents the energy of the lorazepam drug, E_C60 is the energy of the fullerene, and E_{C60\lorazepam drug} is the energy of the fullerene after interacting with drug molecules to form the corresponding complexes with different orientations, where the negative adsorption energies indicate that the complexation process is exothermic.

The HOMO–LUMO energy gap (E_gap) is estimated by the difference between the HOMO’ energy (E_H) and LUMO energy (E_L),⁷⁰ which is expressed as follows:

E_gap = E_L − E_H (2)

where a large E_gap signifies chemically hard molecules that interact weakly with other systems; in contrast, a moderate E_gap enhances reactivity by facilitating favorable HOMO–LUMO interactions in chemical processes.

E_F = (E_LUMO + E_HOMO)/2 (3)

where E_LUMO and E_HOMO represent the energies of the LUMO and HOMO, respectively.

To evaluate solvent effects, the integral equation formalism polarizable continuum model (IEFPCM)⁷¹ has been employed using H₂O as a solvent phase. The solvation energy (E_sol) was obtained according to the following equation;⁷²

E_sol = E_water − E_gas (4)

where E_water and E_gas represent the total energies of the complexes in the aqueous and gas phases, respectively. To verify the reliability and stability of the optimized structures, thermodynamic parameters such as Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) were computed.

3. Results and discussion

Initially, five different adsorption configurations were examined for the interaction of the lorazepam molecule with pristine–C₆₀ surfaces. Among these models, the two most stable configurations (1) and (5) were selected, which are shown in Fig. 1. This investigation has been further expanded using several analytical tools, such as RDG-NCI analysis, PDOS, IR spectroscopy, NBO analysis and HOMO–LUMO gap analysis, to gain a comprehensive understanding of the molecular interactions and behavior.

Fig. 1 The optimized geometries of lorazepam adsorbed on C₆₀ fullerenes of different orientations (1) to (5) are represented as (a)–(e) with their binding energy, respectively.

In this study, the two most stable adsorption configurations, (1) and (5), were selected based on their highest binding energy values. These two complexes were further modified by doping the C₆₀ surface with Si and Ge atoms. The details of the doped systems and their comparative analysis will be discussed in the following sections.

3.1. Molecular insights into lorazepam drug adsorption on C₆₀

The adsorption behavior of lorazepam on the C₆₀ fullerene surface was examined through geometric optimization, electron density analysis, vibrational assessment, and electronic structure calculations. Among the explored orientations, configurations (1) and (5) were identified as the most stable, exhibiting adsorption energies of −4.70 eV and −4.67 eV, respectively. The close energetic values suggest strong physisorption with partial charge transfer character rather than purely chemisorptive interaction. In both cases, however, configuration (1) is slightly more thermodynamically favorable, suggesting marginally stronger binding.

Geometric analysis reveals that lorazepam adsorbs parallel to the curved π-surface of C₆₀ in both configurations as shown in Fig. 2, enabling maximum contact between the aromatic rings of the drug and the fullerene surface. The equilibrium adsorption distances fall within the range of 3.2–3.4 Å for configuration (1) and 3.5 Å for configuration (5). Despite these moderate interaction distances, the large magnitude of the adsorption energies indicates enhanced interaction strength compared to typical physisorption systems. The shorter interaction distance observed in configuration (1) directly explains its slightly more negative adsorption energy, indicating a stronger drug–C₆₀ interaction.

Fig. 2 The optimized models for most stable complexes: (a) configuration (1) and (b) configuration (5) of the lorazepam drug onto pristine C₆₀, respectively, and their HOMO and LUMO orbital.

In addition to π–π interactions, the orientation of the heteroatoms plays a crucial role in stabilizing the complexes. The oxygen and nitrogen atoms of lorazepam are favorably oriented toward electron deficient regions of the C₆₀ surface, promoting significant electronic interaction and charge redistribution. Moreover, the chlorine substituent contributes sterically to the adsorption stability. In configuration (1), the Cl atom is oriented away from the fullerene surface, minimizing steric repulsion and allowing closer approach of the aromatic framework, whereas in configuration (5), the slightly increased adsorption distance of 3.5 Å reflects reduced surface contact.

In Fig. 3e and f, the RDG-NCI analysis further supports the presence of strong interaction. Localized charge redistribution is observed at the adsorption interface, indicating polarization and partial charge transfer between lorazepam and the fullerene surface, consistent with chemisorption.

Fig. 3 The IR spectra (a) and (b), and partial density of states (PDOS) spectra (c) and (d). The RDG (left) and NCI (right) are shown in (e) and (f) under vacuum for the most stable configurations (1, 5) of lorazepam adsorbed on C₆₀, respectively.

This interpretation is fully supported by frontier molecular orbital (FMO) analysis, as shown in Fig. 2. The HOMO is mainly localized on the lorazepam molecule, while the LUMO is predominantly distributed over the C₆₀ surface, with noticeable spatial interaction between them. Such HOMO–LUMO interaction is consistent with chemisorption and suggests electronic coupling between the drug and the surface. The HOMO and LUMO for the remaining configurations (2, 3, and 4) under vacuum are illustrated in Fig. S1.

In Fig. 3c and d, partial density of states (PDOS) analysis provides additional insight into the electronic interaction strength. Configuration (1) exhibits a higher density of occupied states near the valence region and more pronounced virtual states close to the Fermi level compared to configuration (5). This enhanced electronic contribution correlates well with the shorter adsorption distance and more negative adsorption energy, reinforcing the superior stability of configuration (1), and supporting its partial chemisorption character.

Vibrational analysis confirms the structural stability of both complexes, as no imaginary frequencies are detected in their IR spectra, as shown in Fig. 3a and b. Notably, configuration (1) shows slightly stronger vibrational perturbations in the fingerprint region, reflecting stronger intermolecular interactions and a more constrained adsorption geometry, in agreement with its reduced equilibrium distance and enhanced electronic coupling. The corresponding analyses for the remaining configurations (2, 3, and 4) are provided in Fig. S2, including RDG, NCI, PDOS, and IR spectra, and their HOMO–LUMO are shown in Fig. S1.

Overall, the combined geometric, vibrational, and electronic analyses clearly demonstrate that configurations (1) and (5) represent the most stable adsorption modes of lorazepam on pristine C₆₀. The energetic magnitude, −4.70 eV and −4.67 eV, confirms strong physisorption with partial charge transfer. The relatively high adsorption energies indicate enhanced interaction strength compared to typical physisorption systems, while the marginal energetic advantage of configuration (1) arises from its shorter adsorption distance from 3.2 to 3.4 Å, optimal molecular orientation, and stronger electronic interaction with the fullerene surface. These results provide a clear molecular level understanding of lorazepam adsorption on C₆₀ and establish a solid foundation for the subsequent investigation of heteroatom-doped fullerene systems aimed at further enhancing adsorption performance.

3.2. Modulated lorazepam adsorption over SiC₅₉

This study investigates the adsorption behavior of lorazepam on SiC₅₉ through two distinct adsorption configurations, denoted as configuration (1) and configuration (5). The results clearly demonstrate that silicon doping plays a crucial role in creating an active adsorption site on the fullerene surface, significantly enhancing the interaction between the drug molecule and C₆₀ compared to the pristine structure.

In Fig. 4a, lorazepam approaches the silicon atom at a short distance of approximately 1.8 Å, indicating a strong interaction characteristic of chemisorption. This structural proximity is reflected in a high adsorption energy of −6.1 eV under vacuum, confirming the formation of a highly stable complex suitable for drug loading applications, because of strong orbital overlap between the drug molecule and the SiC₅₉ surface. In contrast, configuration (5), which is shown in Fig. 4b, exhibits a larger adsorption distance of about 4.2 Å, corresponding to a weaker chemisorptive interaction compared to configuration (1), with an adsorption energy of −4.7 eV under vacuum. Although less intense than configuration (1), this value still confirms chemisorption, highlighting the effectiveness of silicon doping in strengthening adsorption even at less favorable orientations.

Fig. 4 The optimized models of the lorazepam drug adsorbed onto SiC₅₉ for (a) configuration (1), and (b) configuration (5), respectively with their HOMO and LUMO orbitals.

HOMO–LUMO analysis (Fig. 4) reveals that silicon doping induces a significant redistribution of electron density within the system, indicating effective charge transfer between the two components.

Based on the short interaction distance of approximately 1.8 Å, the high adsorption energy of −6.1 eV, and the significant NBO stabilization energy of 92.28 kcal mol⁻¹, the interaction in SiC₅₉ is classified as chemisorption. Four converging criteria define this classification: adsorption energies exceeding −3 eV, interaction distances below 2.5 Å, NBO stabilization energies exceeding 20 kcal mol⁻¹, and significant PDOS orbital overlap near the Fermi level.

3.3. Enhanced lorazepam adsorption on GeC₅₉

The optimized geometries, electronic structures, vibrational spectra, and partial density of states analyses further confirm the strong interaction between lorazepam and the GeC₅₉ surface for both adsorption configurations (1) and (5). As shown in the optimized structures, lorazepam approaches the Ge active site with short interaction distances of about 2 Å for configuration (1) and 2.6 Å for configuration (5), indicating chemisorption behavior, although weaker than the Si-doped systems.

This is supported by the highly negative adsorption energies, where configuration (1) exhibits an adsorption energy of −5.84 eV, while configuration (5) shows a slightly more negative value of −5.85 eV, confirming the energetic stability of both complexes with a marginal preference for configuration (5).

Fig. 5 illustrates the HOMO–LUMO distributions, revealing a pronounced redistribution of the frontier molecular orbitals upon adsorption. The HOMO is mainly localized on the lorazepam molecule with partial contribution from the Ge atom, whereas the LUMO is predominantly delocalized over the GeC₅₉ nanocage. This orbital overlap facilitates charge transfer from the drug molecule toward the doped fullerene surface, enhancing the adsorption strength.

Fig. 5 The optimized models of the lorazepam drug adsorbed onto GeC₅₉ (a) and (b) and their HOMO and LUMO with various orientations: (a) configuration (1), and (b) configuration (5).

The adsorption behavior of lorazepam on doped fullerene surfaces is further clarified through vibrational and electronic structure analyses, as presented in Fig. 6. The IR spectra shown in Fig. 6(a) and (d) exhibit noticeable shifts in both the positions and intensities of several vibrational bands after adsorption, particularly those associated with the active functional groups of lorazepam. These changes indicate the direct involvement of these groups in the adsorption process and reflect the structural perturbations induced by interaction with the doped C₆₀ surfaces.

Fig. 6 The IR spectra (a)–(d), as well as the partial density of states (PDOS) spectra (e)–(h) of the lorazepam drug adsorbed onto SiC₅₉ and GeC₅₉ of two configurations (1 and 5), respectively.

The corresponding partial density of states (PDOS) spectra depicted in Fig. 6(e) and (h) reveal significant modifications in the electronic structure upon adsorption. An increased density of electronic states near the Fermi level, along with enhanced overlap between the molecular orbitals of lorazepam and the electronic states of the substrate, is observed for both the SiC₅₉ and GeC₅₉ systems. This behavior indicates enhanced electronic coupling and a reduction in the effective energy gap, suggesting improved electronic conductivity following adsorption.

A comparative analysis shows that the SiC₅₉ system exhibits slightly stronger electronic interaction with lorazepam than the GeC₅₉ counterpart, consistent with the more pronounced orbital overlap and higher stability observed for SiC₅₉. Nevertheless, both dopants significantly enhance the adsorption capability of pristine C₆₀. Similarly, for GeC₅₉, the short interaction distances of 2.0 to 2.6 Å and NBO stabilization energies of 22.5 kcal mol⁻¹ confirm the chemisorption nature of the interaction, although it remains slightly weaker than that observed for the SiC₅₉ system.

The relatively high adsorption energies observed for the doped systems can be attributed to strong donor–acceptor interactions between the heteroatom dopant and the functional groups of lorazepam. The presence of silicon or germanium introduces highly active adsorption sites on the fullerene surface and enhances charge transfer between the drug molecule and the nanocage, leading to stronger binding compared with pristine C₆₀ and explaining the increased adsorption stability observed for the doped systems.

3.4. Exploring non-covalent interactions: insights from reduced density gradient analysis

To elucidate the adsorption mechanism, we performed non-covalent interaction (NCI) analysis and reduced density gradient (RDG) mapping for the lorazepam drug adsorbed on pristine C₆₀, SiC₅₉, and GeC₅₉ under vacuum conditions. These visual tools clearly differentiate weak interactions – including hydrogen bonding, van der Waals forces (vdW), and steric repulsions – providing critical insights into the stability and nature of the drug–surface interactions.^71,73 The RDG is derived from the electron density (ρ) and its gradient, as defined by eqn (5):

Analysis of RDG versus sign(λ₂)ρ plots enables identification of interaction types:

Negative sign(λ₂)ρ values (green-blue regions) correspond to attractive forces (e.g., hydrogen bonding, π–π interactions). Positive values (red regions) indicate steric repulsion and when ρ approaches zero, the interactions are characteristic of van der Waals forces.

In (Fig. 7a and b), the RDG versus sign(λ₂)ρ plots and corresponding NCI iso-surfaces for the SiC₅₉–lorazepam configurations are presented. The RDG plots show pronounced spikes in the negative sign(λ₂)ρ region, indicating the presence of significant attractive interactions, associated with strong adsorption. These interactions are further confirmed by the green and blue regions in the NCI iso-surfaces, which are localized around the Si dopant and the nearby functional groups of lorazepam. This behavior suggests that Si doping creates an effective active site, enhancing charge redistribution and strengthening adsorption through electrostatic and donor–acceptor interactions and partial covalent character.

Fig. 7 RDG (left) and NCI (right) analyses under vacuum for lorazepam adsorption on (a) and (b) SiC₅₉ and (c) and (d) GeC₅₉ surfaces for configurations (1) and (5).

In contrast, Fig. 7c and d illustrate the GeC₅₉–lorazepam complexes. Although attractive interactions are still observed, the intensity of the negative sign(λ₂)ρ spikes is relatively weaker compared to the Si-doped case. The NCI iso-surfaces are dominated by green regions with fewer blue areas, indicating comparatively weaker attractive interactions than in the Si system, yet still consistent with chemisorption. This implies that Ge doping is less effective than Si doping in activating the fullerene surface toward strong adsorption.

Overall, the comparison demonstrates that SiC₅₉ exhibits stronger and more localized attractive interactions than GeC₅₉, which explains the higher adsorption stability observed for the Si-doped configurations.

3.5. Global indices parameters

We calculated global reactivity descriptors, including electron affinity (E_A), ionization potential (IP), electrophilicity index (ω), chemical potential (μ_ch), chemical hardness (η), and softness (χ) to assess the electronic reactivity and stability of the system. These global indices provide essential insights into the nature of molecular interactions and reactivity of the lorazepam drug on the C₆₀ surface. Their respective expressions are given below:^68,74

Electron affinity (E_A), which indicates a molecule's ability to accept electrons (LUMO energy):

E_A = −E_L (6)

The ionization potential (IP), which provides a molecule's ability to donate electrons (HOMO energy):

IP = −E_H (7)

The electrophilicity index (ω), which reflects the molecule's tendency to accept electrons to form bonds with nucleophilic molecules:

Additionally, the HOMO and LUMO orbitals, along with the molecular electrostatic potential (MESP), are sometimes used to enhance the prediction of the adsorption mechanism.^75–80

Chemical potential (μ_ch):

Chemical hardness (η):

Softness (χ):

3.6. Work function

The adsorption of lorazepam affects the work function (φ) of the nanocarrier, reflecting changes in electronic properties. The work function is defined as:⁷²

φ = V_∞ − E_F (12)

where V_∞ and E_F are electrostatic potential energy far from the material surface and Fermi energy, respectively. From the above equation, if V_∞ = 0, this implies φ = −E_F. The variation in φ upon adsorption indicates redistribution of electronic density, confirming strong interaction between lorazepam and the nanocarrier surface.

These descriptors, especially under vacuum (as shown in Table 1), are widely used to predict molecular reactivity, and complement experimental adsorption studies.^75,81–86 The stability of molecular orientations plays a crucial role in adsorption behavior, as certain configurations may exhibit stability in the doped state but lack it in the non-doped state. This difference in stability significantly influences adsorption energy, leading to remarkable differences in adsorption performance. Although the interactions are strong and stable under vacuum, the adsorption remains stable and energetically favorable in aqueous environments.

Table 1 HOMO and LUMO energies (E_HOMO and E_LUMO), HOMO–LUMO gap (E_G), difference in E_g (ΔE_g), ionization potential (IP), electron affinity (EA), chemical hardness (η), softness (χ), chemical potential (μ_ch), electrophilicity index (ω), Fermi level (E_F), binding energies (E_bind), and work function for systems of lorazepam–C₅₉, lorazepam–SiC₅₉, and lorazepam–GeC₅₉ with different orientations under vacuum

System	HOMO (eV)	LUMO (eV)	EG (eV)	ΔEg (eV)	IP (eV)	EA (eV)	η (eV)	χ (eV)^−1	μch (eV)	ω (eV)	EF (eV)	Ebind (eV)	Work function (φ)
Config. 1	−5.75	−3.02	−2.731	−0.03	5.75	3.02	1.37	0.73	−4.38	7.03	−4.38	−4.70	4.38
Config. 2	−5.98	−3.24	−2.73	−0.03	5.98	3.24	1.37	0.73	−4.61	7.78	−4.61	−4.66	4.61
Config. 3	−5.89	−3.16	−2.73	−2.73	5.89	3.16	1.37	0.73	−4.53	7.51	−4.53	−4.63	4.53
Config. 4	−5.89	−3.16	−2.74	−0.03	5.89	3.16	1.37	0.73	−4.53	7.48	−4.53	−4.62	4.53
Config. 5	−5.98	−3.24	−2.74	−0.03	5.98	3.24	1.37	0.73	−4.61	7.76	−4.61	−4.67	4.61
SiC59
Config. 1	−4.72	−2.85	−1.88	−0.29	4.72	2.85	0.94	1.07	−3.78	7.63	−3.78	−6.08	3.78
Config. 5	−5.83	−3.66	−2.17	0.002	5.83	3.66	1.09	0.92	−4.74	10.36	−4.74	−4.71	4.74
GeC59
Config. 1	−4.56	−2.81	−1.76	−0.36	4.56	2.81	0.88	1.14	−3.68	7.72	−3.68	−5.84	3.68
Config. 5	−5.28	−3.30	−1.98	−0.14	5.28	3.30	0.99	1.01	−4.29	9.31	−4.29	−5.85	4.29

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3.7. Thermodynamic analysis

The thermodynamic parameters of the optimized complexes were determined through harmonic frequency analysis under standard conditions (298.15 K, 1 atm). Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) values for all five orientationally distinct complexes under vacuum and in a solvent are summarized in Table 2. The relative stability of the inclusion complexes was assessed by comparing the Gibbs free energy of each complex to the combined Gibbs free energies of its adsorbent and adsorbate. Negative ΔG values confirm spontaneous complex formation at 25 °C, and to drive spontaneous complexation and improve efficiency, strategic doping (e.g., with Si or Ge) is proposed.

Table 2 The calculated thermodynamic parameters, enthalpy (ΔH), Gibbs free energy (ΔG), and entropy (ΔS), of the studied complexes lorazepam–C₆₀, lorazepam–SiC₅₉, and lorazepam–GeC₅₉ with different orientations under vacuum and in a solvent

System	ΔH (eV)	ΔG (eV)	ΔS (eV)
Vacuum
C60
Config. 1	−4.62	−4.16	−0.0015
Config. 2	−4.58	−4.11	−0.0016
Config. 3	−4.55	−4.07	−0.0016
Config. 4	−4.55	−4.05	−0.0016
Config. 5	−4.59	−4.10	−0.0016
SiC59
Config. 1	−5.96	−5.47	−0.0016
Config. 5	−4.64	−4.16	−0.0016
GeC59
Config. 1	−5.76	−5.17	−0.0019
Config. 5	−5.31	−4.80	−0.0017
Solvent
C60
Config. 1	−4.52	−4.04	−0.0016
Config. 2	−4.55	−4.07	−0.0016
Config. 3	−4.52	−4.03	−0.0016
Config. 4	−4.51	−4.03	−0.0016
Config. 5	−4.55	−4.07	−0.0016
SiC59
Config. 1	−6.12	−5.53	−0.0019
Config. 5	−4.88	−4.33	−0.0018
GeC59
Config. 1	−5.98	−5.38	−0.00197
Config. 5	−5.48	−4.88	−0.00196

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The negative values of both enthalpy (ΔH) and entropy (ΔS) suggest an enthalpy-driven inclusion process. Meanwhile, the negative ΔS reflects restricted mobility of the encapsulated guest molecule due to the constrained cavity of the host framework.

ΔG = G_com − (G_host + G_guest) (13)

ΔH = H_com − (H_host + H_guest) (14)

ΔS = S_com − (S_host + S_guest) (15)

3.8. Solvent effect

To assess the adsorption behavior of pristine C₆₀, SiC₅₉, and GeC₅₉ in an aqueous environment, the binding energies (E_bind) of the lorazepam–surface complexes were systematically investigated in water. All geometries of the lorazepam–C₆₀, lorazepam–SiC₅₉, and lorazepam–GeC₅₉ complexes were fully re-optimized using the IEFPCM implicit solvation model combined with the hybrid B3LYP functional and the 6-31G(d) basis set, including empirical dispersion corrections (B3LYP-D3, Grimme's GD3) to accurately account for long-range van der Waals interactions. The inclusion of solvent and dispersion effects resulted in noticeable modifications to the optimized geometrical parameters, reflecting solvent-induced rearrangements that enhance intermolecular interactions at the drug–surface interface. In addition, global reactivity indices were calculated in the solvent phase (Table S1) to provide further insight into the electronic properties of the investigated systems. Importantly, the Gibbs free energy of adsorption (ΔG) in water, reported in Table 2, provides a more realistic measure of stability under physiological conditions than electronic adsorption energies alone. The negative ΔG values ranging from −4.04 to −5.53 eV confirm that complex formation remains spontaneous and stable in aqueous environments, with SiC₅₉ showing the highest stability at −5.53 eV for configuration (1).

For pristine C₆₀, the aqueous environment alters the relative stability of the adsorption configurations, rendering configuration (5) the most favorable with an adsorption energy of −4.64 eV. Although solvation slightly weakens the adsorption strength compared to the vacuum phase, the interaction remains sufficiently strong, indicating that lorazepam adsorption on pristine C₆₀ is stable under realistic solvent conditions.

In the case of SiC₅₉, solvation exerts a more pronounced effect on both geometry and energetics. Configuration (1) becomes the most thermodynamically stable structure in water, exhibiting a significantly enhanced adsorption energy of −6.23 eV. This improvement highlights the crucial role of solvent polarization and dispersion interactions in improving the adsorption efficiency of the Si-doped system by stabilizing favorable adsorption orientations and strengthening dipole–dipole and charge-transfer interactions. The synergistic effect of silicon doping, solvent effects, and dispersion contributions leads to superior interaction efficiency compared to pristine C₆₀ and the corresponding vacuum-phase results.

Similarly, for GeC₅₉, configuration (1) emerges as the most stable adsorption mode in the aqueous environment, with an adsorption energy of −6.07 eV. This stabilization can be attributed to improved dipolar alignment, and favorable electrostatic contributions between lorazepam and the Ge-doped surface, accompanied by subtle solvent-induced geometric rearrangements.

The solvation energy (E_sol) values listed in Table S1 are negative for all studied systems, indicating that solvation is a thermodynamically favorable process and enhances the stability of the complexes in the solvent. Among all systems, for lorazepam–GeC₅₉, configuration (1) exhibits the most negative solvation energy, making it the most stable system and suggesting the strongest interaction with the solvent.

Overall, while the general stability trends observed under vacuum are largely preserved, solvation in water induces noticeable changes in both geometry and thermodynamic preference among the adsorption configurations. Importantly, the solvent and dispersion effects do not drastically diminish the overall adsorption strength; instead, they enhance the adsorption efficiency, particularly in the SiC₅₉ system, by promoting more favorable interaction mechanisms. The optimized configurations and analysis in aqueous environments (Fig. S3–S7) for pristine C₆₀, SiC₅₉, and GeC₅₉ further confirm that water primarily modulates the relative energetic ordering of the adsorption modes while maintaining strong and stable drug–surface interactions across different environments.

3.9. The natural bond orbital (NBO) charge analysis

Natural bond orbital (NBO) analysis was carried out to gain deeper insight into the nature of intermolecular interactions and charge-transfer mechanisms between the lorazepam molecule and pristine as well as doped C₆₀ surfaces. The interaction parameters, including the second-order perturbation stabilization energy (E⁽²⁾), the energy difference between donor and acceptor orbitals (E_(j) − E_(i)), and the Fock matrix element (F_(i,j)), were analyzed to evaluate the strength and character of donor–acceptor interactions. The second-order stabilization energy (E⁽²⁾), estimated from the Fock matrix, quantifies the delocalization energy associated with donor (i) to acceptor (j) orbital interactions and is calculated using the following expression:

In the above equation, q_i presents the occupancy of the donor orbital, E_(j) and E_(i) are the diagonal elements corresponding to the acceptor and donor orbitals, respectively, and F_(i,j) denotes the off-diagonal NBO Fock matrix element. The second-order perturbation stabilization energy (E⁽²⁾) is directly proportional to the intensity of the donor–acceptor interaction. A stronger donor–acceptor interaction leads to a larger E⁽²⁾ value, thereby increasing the overall stability of the C₆₀–drug complexes. For the pristine C₆₀ system, the obtained E⁽²⁾ values are relatively small, ranging from 0.07 to 0.93 kcal mol⁻¹. These weak stabilization energies mainly originate from π → π* and n → π* interactions between the lorazepam molecule and the fullerene surface, indicating limited charge transfer. Such low E⁽²⁾ values suggest that the adsorption process on pristine C₆₀ involves comparatively weaker donor–acceptor interactions relative to the doped systems, yet still consistent with partial chemisorption, as supported by the calculated adsorption energy. In contrast, a remarkable enhancement in donor–acceptor interactions is observed upon silicon doping. In the SiC₅₉ system, an exceptionally strong interaction is detected for the LP (2) O → LP* (1) Si transition, with a stabilization energy of 92.89 kcal mol⁻¹ and a high F_(i,j) value of 0.226 a.u. This strong interaction indicates significant charge transfer from the lone pair of the oxygen atom in lorazepam to the vacant orbitals of the silicon dopant, reflecting the formation of a partially covalent bond. The presence of silicon introduces an electron-deficient active site on the C₆₀ surface, thereby dramatically enhancing the adsorption strength and promoting chemisorption behavior.

Similarly, the GeC₅₉ system exhibits stronger donor–acceptor interactions compared to the pristine system, although weaker than those observed for the silicon-doped structure. The LP (2) O → BD* (1) O–Ge interaction shows a stabilization energy of 22.51 kcal mol⁻¹, while the BD (2) C–C → LP* (1) Ge transition contributes 13.99 kcal mol⁻¹. These values confirm effective charge transfer between lorazepam and the Ge-doped surface, suggesting a moderate chemisorption interaction. The relatively lower E² values compared to SiC₅₉ can be attributed to the reduced electron-accepting ability of germanium relative to silicon.

Overall, the NBO results clearly demonstrate that heteroatom doping significantly enhances charge transfer and intermolecular interactions, thereby improving the adsorption stability of lorazepam on the C₆₀ surface. The strength of donor–acceptor interactions follows the order SiC₅₉ > GeC₅₉ > C₆₀, which is in excellent agreement with the calculated adsorption energies and electronic structure analyses. These findings support the potential application of doped C₆₀ systems as efficient nanocarriers for lorazepam delivery. These parameters for each model of the complexes are summarized in Table 3.

Table 3 The results of the donor and acceptor NBOs, as well as the second-order perturbation stabilization energies (E⁽²⁾, kcal mol⁻¹), corresponding to the charge transfer of C₆₀, SiC₅₉, and GeC₅₉ with lorazepam drug molecules under vacuum

System	Donor NBO (i)	Acceptor NBO (j)	E^(2) (kcal mol^−1)	E(j) − E(i) (a.u.)	F(i,j) (a.u.)
Config. 1	LP (1) N 88	BD* (2) C 27–C 36	0.50	0.40	0.013
Config. 2	LP (1) O 86	BD* (2) C 13–C 14	0.10	0.61	0.008
Config. 3	LP (1) O 86	BD* (2) C 53–C 56	0.07	0.61	0.007
Config. 4	BD (2) C 29–C 37	BD* (2) C 67–C 68	0.26	0.27	0.008
Config. 5	BD (2) C 62–N 88	BD* (2) C 47–C 48	0.44	0.36	0.012
SiC59
Config. 1	LP (2) O 84	LP* (1) Si 91	92.89	0.65	0.226
Config.5	BD (2) C 47–Si 90	BD* (1) C 62–H 91	0.37	0.66	0.016
GeC59
Config. 1	LP (2) O 84	BD* (1) O 84–Ge 91	22.51	0.71	0.119
Config. 5	BD (2) C 66–C 67	LP* (1) Ge 90	13.99	0.33	0.064

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4. Protonation-driven drug release under acidic conditions

The relatively high adsorption energies obtained for the doped systems indicate strong drug–carrier interactions, which are advantageous for drug loading. Despite this strong binding, these interactions can be significantly weakened under realistic environmental conditions, such as solvent effects, pH or temperature, enabling controlled drug release.

To investigate the possibility of lorazepam drug release behavior from the nanocarrier, a dual protonation model was applied to simulate the impact of acidic tumor microenvironment (pH < 7). Among the investigated systems, Config.1 of SiC₅₉ was selected for the release invistigation due to its highest adsorption stability compared with the other studied configurations. Protonation was introduced at two key interaction sites: the ketone oxygen atom of the drug molecule and the dopant atom of the fullerene surface. The optimized structure shows a noticeable geometrical change upon protonation, where the equilibrium distance between the drug and the nanocarrier increases from 1.8 Å in the neutral system to 4.98 Å in the protonated system. This increase suggests considerable weakening in the interaction between the two components compared to the neutral state.

These results are supported by previous theoretical studies on similar nanocarrier systems, where protonation was shown to significantly reduce adsorption energy and promote drug desorption from carbon-based nanostructures.⁸⁷ In doped fullerene systems, protonation has been reported to induce strong weakening of drug–surface interactions, leading to partial or nearly complete separation of the drug molecule from the carrier.⁸⁸ Furthermore, studies on nitrogen-containing carbon frameworks demonstrated that acidic conditions lead to a substantial decrease in adsorption strength, indicating enhanced release behavior.⁸⁹ Other investigations revealed that protonation shifts the interaction regime from strong adsorption to weaker noncovalent interactions accompanied by an increase in drug–surface distance.⁹⁰ Additionally, it has been shown that protonation under acidic environments results in both reduced adsorption energy and increased separation distance, confirming a general trend of facilitated drug release⁹¹ (Fig. 8).

Fig. 8 The optimized structures for the bound drug–C₅₆Si and the released drug where the coordination bond has been fully cleaved.

Overall, the obtained results demonstrate that protonation under acidic conditions, known for the tumor microenvironment, weakens the interaction between the drug and the nanocarrier, supporting a pH-responsive release mechanism within the framework of density functional theory calculations.

5. Comparison of adsorption energy (E_bind) and adsorption distance (d) of the lorazepam drug adsorbed on pristine C₆₀, SiC₅₉ and GeC₅₉ with previously reported materials

The results of the present study clearly demonstrate stronger adsorption interactions, as reflected by the more negative binding energy values, particularly for the Si and Ge systems reaching −6.08 eV and −5.85 eV, respectively. These values are consistent with recent reports on high-performance drug delivery systems, including nitride-derived fullerenes with an adsorption energy of −6.521 eV for felodipine delivery, Stone–Wales defective graphene nanoribbons showing −6.027 eV for fluorouracil, and Nb₂C MXene quantum dots exhibiting −6.775 eV for fluorouracil adsorption. While earlier studies report weak to moderate adsorption on pristine and other modified fullerene structures, the doped systems investigated here exhibit significantly enhanced binding energies reaching approximately −6 eV, indicating a substantial enhancement in chemisorption strength. In addition, the shorter adsorption distances calculated in this work of 1.8 to 2.0 Å for the doped systems compared to most literature values further support the formation of stronger interfacial interactions.

Overall, this comparison highlights that silicon and germanium doping provides a more effective strategy for improving the adsorption performance of C₆₀ than other previously reported modifications, and that the binding energies obtained are within the range reported for other promising drug delivery platforms, emphasizing the superior stability and adsorption capability of the systems studied in this work (Table 4). It should also be noted that the calculated adsorption energies are relatively high, reflecting very strong interactions between the drug and the nanocarrier surface. Although these values are obtained under the present computational conditions, effective interactions may be reduced under different environmental conditions, such as solvent effects, pH or temperature, thereby allowing reversible binding or drug release. In fact, the tumor microenvironment is known to be acidic, which can lead to protonation of the chemical system and facilitate drug release, as reported in previous studies.^87–91

Table 4 Comparison of binding energies (E_bind (eV)) and adsorption distances (d, Å) for the studied C₆₀, SiC₅₉, and GeC₅₉ systems in different configurations, along with previously reported values from the literature

System	Ebind (eV)	d (Å)	Ref.
C60
Config. 1	−4.70	3.4	This work
Config. 5	−4.67	3.5	This work
SiC59
Config. 1	−6.08	1.8	This work
Config. 5	−4.71	4.2	This work
GeC59
Config. 1	−5.84	2	This work
Config. 5	−5.85	2.6	This work
AS
C60	−0.29	3.01	92
BC59	−1.04	1.58	92
NC59	−0.41	3.11	92
BNC58	−0.96	1.57	92
MAT
C60	1.474	—	93
GaC59	−1.263	—	93
AP
C20 (II-isomer)	−5.61 × 10^4	1.620	94
Met
C59Si–C	−1.65	1.934	95
C59Si–N	−0.90	1.850	95
C60–C	0.055	1.580	95
MF
C60	0.0187	4.27	96
SiC59	−1.61	1.79	96
PEG/C60
H	−0.95	—	97
G	−0.83	—	97
Nb2C-s-Flu	−6.775	2.053	98
Nb2C-e-Flu	−3.576	2.132	98
GaNF	−6.521	—	99
FU/AGNRs-SW	−6.027	—	100
TP/AGNRs-SW	−5.917	—	100
HU/AGNRs-SW	−7.534	—	100
NU/AGNRs-SW	−8.972	—	100

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6. Conclusion

A density functional theory (DFT) study was carried out to evaluate pristine and doped C₆₀ nanocages as potential drug carriers for lorazepam. The results show that pristine C₆₀ exhibits relatively weak adsorption compared with the doped systems. Doping with silicon or germanium significantly enhances the interaction strength by creating active adsorption sites and promoting charge transfer between the drug molecule and the fullerene surface. Among the studied systems, SiC₅₉ demonstrates the strongest adsorption with an adsorption energy of approximately −6.1 eV and shorter interaction distances, indicating the formation of a highly stable drug–carrier complex. GeC₅₉ also improves the adsorption behavior compared with pristine C₆₀, although its interaction remains weaker than that of SiC₅₉.

Electronic structure analyses, including HOMO–LUMO, PDOS, and NBO charge transfer confirm strong electronic interactions between lorazepam and the doped nanocages. Thermodynamic calculations further indicate that the adsorption process is energetically favorable and remains stable under aqueous conditions. Overall, the results suggest that doped C₆₀ nanocages, especially SiC₅₉, are promising candidates for lorazepam delivery. Additionally, protonation under acidic conditions reduces the adsorption strength, suggesting a feasible pH-responsive drug release mechanism.

Author contributions

Mariam M. Seliem: computational analysis, investigation, data curation, visualization, formal analysis, methodology, writing – original draft. Mohamed M. Aboelnga: supervision, validation, conceptualization, project administration, computational analysis, investigation, visualization, data analysis, software, resources, writing – review & editing. Elsayed El-bayoumy: supervision, validation, conceptualization, writing – review & editing, Mohsen El-Tahawy: supervision, validation, conceptualization, computational analysis, investigation, visualization, data analysis, software, resources, writing – review & editing.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d6ma00154h.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Footnote

† These authors contributed equally to this work.

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