A computational dive into tuning nitrosourea adsorption on T-graphene nanosheets

Abstract

This study examines the adsorption of a nitrosourea (NU) drug molecule onto pristine and doped T-graphene (TG) nanosheets, specifically those doped with boron (BTG) and aluminum (AlTG), utilizing density functional theory (DFT) at the M06-2X/6-31 + G(d,p) level of theory. We investigated the geometric, electronic, and energetic properties of the resulting complexes, focusing on adsorption energies, HOMO–LUMO gaps (E_g), molecular electrostatic potential (MEP), natural bond orbital (NBO) analysis, and quantum theory of atoms in molecules (QTAIM). Our findings indicate that aluminum doping significantly enhances the adsorption of NU onto the TG nanosheet, exhibiting strong chemisorption as evidenced by a high adsorption energy (E_ads) of − 41.46 kcal mol⁻¹ and substantial charge transfer. However, this high adsorption energy results in a very lengthy desorption time of 2.3 × 10¹⁸ s. In contrast, boron doping increases the E_ads to a more manageable level (− 14.91 kcal mol⁻¹), leading to a recovery time of 8.3 × 10⁻² s, which is advantageous from a drug delivery perspective. Frontier molecular orbitals analysis revealed that the most prominent E_g change upon adsorption of NU occurs in the case of BTG with a 10.46% reduction. While the variations of E_g for TG-NU and AlTG-NU are − 1.31% and 5.20%, respectively. NBO analysis confirmed substantial donor–acceptor interactions in the AlTG-NU complex, while QTAIM indicated the presence of partially covalent interactions. Pristine TG and BTG exhibited weaker interactions with NU; however, the bonding nature remained partially covalent in both cases. The calculated recovery times further suggest that BTG provides a more favorable drug release profile compared to TG and AlTG. This study highlights the potential of boron-doped TG as an effective nanocarrier for drug delivery, underscoring the essential role of doping in tailoring the electronic and adsorption properties of graphene-based materials.

Introduction

Nitrosoureas (NUs) are a class of alkylating agents that have gained significant attention in oncology due to their potent anticancer properties. These compounds function by cross-linking DNA, thereby inhibiting DNA replication and transcription, which ultimately leads to cell death. Their high lipid solubility allows them to cross the blood–brain barrier, making them particularly effective in treating central nervous system (CNS) malignancies¹. These compounds are synthesized through the nitrosation of urea derivatives, resulting in the formation of a nitroso group (–NO) attached to a urea backbone. This chemical structure is critical for their alkylating activity, which involves transferring alkyl groups to DNA, RNA, and proteins, leading to cellular damage and apoptosis². The NUs are unique among alkylating agents due to their ability to exert oral and parenteral therapeutic effects. Their lipophilic nature facilitates penetration into the CNS, making them highly effective against intracerebral tumors and experimental meningeal leukemias. Additionally, NUs have demonstrated a broad spectrum of activity against various transplantable and spontaneous tumors in preclinical models, including gliomas, ependymoblastomas, and astrocytomas in mice and hamsters³. In modern clinical practice, NUs such as CCNU and BCNU are commonly used as second-line chemotherapies. They are frequently included as the standard arm in randomized phase II trials evaluating novel therapeutic agents. Despite their efficacy, attempts to enhance therapeutic outcomes through NU-based polychemotherapy regimens have largely been unsuccessful, with single-agent NU therapy remaining the preferred approach. Despite their therapeutic benefits, NUs are associated with significant side effects. Their alkylating activity is not selective for cancer cells, leading to toxicity in normal tissues. Common adverse effects include myelosuppression, which can result in leukopenia and thrombocytopenia, as well as gastrointestinal disturbances such as nausea and vomiting. Prolonged use of NUs has also been linked to pulmonary fibrosis and renal toxicity^4–6. The integration of nanocarriers, such as graphene and other carbon-based nanostructures, into NU delivery systems represents a promising strategy to mitigate the unwanted side effects of these potent anticancer agents. By enhancing targeted delivery, controlled release, and drug stability, nanocarriers can improve the therapeutic index of NUs, making them safer and more effective for cancer treatment. As research in this field continues to advance, the development of nanocarrier-based NU formulations has the potential to revolutionize cancer therapy and improve patient outcomes.

Among graphene-like nanomaterials, T-graphene (TG) stands out due to its distinctive triangular lattice configuration, offering remarkable advantages over traditional graphene. The structural curvature and built-in strain in TG modify its electronic properties and increase its chemical reactivity, making it a highly promising material for drug delivery systems. This heightened reactivity facilitates stronger binding with pharmaceutical compounds, improving drug-loading efficiency, precision in targeted delivery, and tunable release kinetics of therapeutic agents⁷. TG’s unique structural and electronic properties make it an ideal candidate for drug delivery systems. Its high surface area and porosity allow for efficient drug loading, while its modified electronic properties enhance interactions with drug molecules. The curvature and strain in TG’s lattice structure create active sites that can bind drug molecules more effectively, ensuring stable encapsulation and protection of the therapeutic payload. Additionally, TG’s biocompatibility and ability to functionalize its surface make it suitable for biomedical applications.

Beyond graphene and its derivatives, a wide array of other two-dimensional (2D) nanomaterials have emerged as promising candidates for drug delivery systems due to their unique structural and electronic properties. For instance, graphitic carbon nitride (g-C₃N₄) nanosheets have garnered significant attention, with studies exploring their potential for drug adsorption and delivery. Research by Ilyas et al.⁸ investigated the adsorption of curcumin on g-C₃N₄, reporting adsorption energies of − 0.25 eV (approximately − 5.77 kcal mol⁻¹) in the gas phase and − 0.09 eV (approximately − 2.08 kcal mol⁻¹) in the aqueous phase, with weak N–H bonds anchoring the drug. Similarly, they explored graphitic carbon nitride (GRP) as a nanocarrier for Hesperetin, reporting an exothermic adsorption energy of − 0.18 eV (approximately − 4.15 kcal mol⁻¹), suggesting increased stability⁹. Furthermore, borophene, a monolayer boron material, has also shown intriguing properties for biomedical applications. A study by Ahmad Khan et al.¹⁰ explored the interaction of resveratrol with nano-borophene, indicating a weak force of attraction through noncovalent interactions, which is beneficial for drug offloading. While a specific adsorption energy value was not provided, the description of weak force of attraction suggests a physisorption regime, similar to or weaker than the lowest adsorption energies found for g-C₃N₄ systems. These findings collectively underscore the diverse potential of 2D nanomaterials as drug carriers and emphasize the importance of material selection and modification in optimizing drug delivery efficiency.

The drug delivery efficiency of nanomaterials can be significantly improved through strategic modifications such as doping, surface decoration, and chemical functionalization^11–15. Among these approaches, doping serves as a powerful tool to fine-tune the electronic and chemical characteristics of host materials, optimizing their performance in pharmaceutical applications. This process involves incorporating foreign atoms (dopants) with distinct valence electron configurations into the base material’s lattice structure. The presence of dopants introduces additional charge carriers -electrons or holes- modifying the host material’s electrical properties. Furthermore, these impurities generate new energy states within the bandgap, promoting charge mobility and influencing conductivity. From a drug delivery perspective, doping enhances surface reactivity by creating localized active sites with preferential binding affinity for specific drug molecules. This results in improved drug-loading efficiency and stronger adsorption. The electronegativity contrast between dopant and host atoms facilitates charge redistribution, further strengthening interactions with therapeutic compounds. By carefully selecting dopant species, researchers can customize material properties to achieve selective drug binding while minimizing off-target interactions, enhancing delivery precision. Moreover, the chemical nature of dopants plays a crucial role in determining compatibility with specific drugs, allowing for the rational design of doped nanomaterials tailored to particular therapeutic agents^16–19. In this study, we employ density functional theory (DFT) to investigate the structural, electronic, and binding properties of pristine and doped TG as a nanocarrier for NU. This work aims to elucidate the mechanisms by which Al or B doping affects the interaction between TG and NU molecules and evaluate the potential of these nanosheets as targeted drug delivery systems.

Computational methodology

The numerical simulations in this study were performed using density functional theory (DFT) calculations carried out with Gaussian 09²⁰. Initial molecular structures were visualized using GaussView 5.0²¹, while frontier molecular orbitals, MEP plots, and AIM analysis figures were visualized and analyzed using Multiwfn²² and VMD 1.9.3 (Visual Molecular Dynamics)²³ software packages. We used the M06-2X meta-hybrid functional paired with the 6-31 + G(d,p) basis set for all quantum chemical computations²⁴. The M06-2X approach was selected for its well-documented reliability in predicting various molecular properties, particularly its proficiency in handling non-covalent bonding phenomena—a crucial requirement for adsorption modeling. This functional demonstrates exceptional performance in characterizing the interfacial interactions between NU molecules and TG nanostructures. The 6-31 + G(d,p) basis set was chosen because it offers an excellent compromise between computational demand and result reliability²⁵. Its diffuse functions are especially valuable for accurately representing the electronic distribution of negatively charged species that might arise during NU adsorption, while the polarization functions enable precise characterization of the electronic configuration and bonding features of both the nanosheets and dopant atoms. Although more extensive basis sets might provide slightly better accuracy, the selected basis set maintains adequate precision without excessive computational overhead. To ensure the accuracy of the interaction energies, Basis Set Superposition Error (BSSE) was corrected using the counterpoise method. To confirm that all optimized structures truly represented energy minima instead of transition states, we performed vibrational frequency analyses. These calculations provided zero-point energy adjustments as well as thermodynamic quantities, specifically the variations in enthalpy (ΔH) and Gibbs free energy (ΔG), under standard temperature and pressure conditions (298.15 K, 1 atm). The enthalpy change associated with the adsorption process was determined through the following relation:

1

where , , and represent the sum of electronic and thermal enthalpies of the (B, Al)TG:NU complex, pristine or doped TG nanosheets, and the NU molecule, respectively. Natural bond orbital (NBO) analysis was conducted to investigate charge distribution and electron transfer processes during adsorption^26–28. Using second-order perturbation theory within the NBO framework, donor–acceptor interactions were quantified, providing insights into the stability of the system. In addition to the NBO analysis, we also conducted Quantum Theory of Atoms in Molecules (QTAIM) calculations to further investigate the electronic structure and bonding characteristics of our systems. QTAIM, based on the work of Richard Bader, provides a rigorous framework for analyzing electron density and identifying bonding interactions within molecules²⁹. By examining the topology of the electron density, we can identify bond critical points (BCPs), which are points of minimum electron density along the bond path between two atoms. The properties of these BCPs, such as the electron density (ρ) and its Laplacian (), provide valuable information about the nature and strength of the bonding interactions. The QTAIM analysis complements the NBO analysis by providing a real-space perspective on bonding interactions. While NBO focuses on orbital interactions and charge transfer, QTAIM examines the electron density distribution and topology, offering a complementary view of the chemical bonding. Together, these two methods provide a comprehensive understanding of the electronic structure and bonding in our systems. The electronic characteristics of the studied systems were investigated through the evaluation of frontier molecular orbitals. Specifically, we examined the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) distributions and their corresponding energy levels. The HOMO–LUMO energy gap (E_g) was computed as a fundamental indicator of chemical reactivity, using the relationship:

2

The Conceptual Density Functional Theory (CDFT), originally developed by Robert Parr, provides a robust theoretical foundation for understanding and predicting the reactivity of chemical systems. This framework encompasses a variety of concepts and quantities, many of which are instrumental in identifying favorable reactive sites, characterizing reactivity, and comparing reactivity across different chemical species³⁰. All CDFT-related quantities were computed using the Multiwfn software²². To calculate the CDFT quantities, the electronic energy (E) and electron density of the system in its N, N + 1, and N − 1 electron states are required. Here, N represents the number of electrons in the chemical system at its most stable (ground) state. The geometry optimized for the N-electron state was used as the basis for all subsequent calculations. The following global reactivity indices were computed to characterize the chemical reactivity of the systems under study: first vertical ionization potential (I₁), first vertical electron affinity (A), Mulliken electronegativity (χ), chemical potential (µ), hardness (η), softness (S)³¹, electrophilicity index (ω)³², and nucleophilicity index (N_Nu)³³.

3

4

5

6

7

This quantity is also equivalent to the fundamental energy gap³⁴.

8

9

10

here Nu denotes the nucleophile, and TCE (tetracyanoethylene) is used as a reference system due to its exceptionally low HOMO energy among organic molecules. These indices collectively provide a comprehensive understanding of the reactivity and electronic properties of the studied chemical systems.

Results and discussion

Electronic and geometrical aspects of (B, Al)TG-drug interaction

The TG nanosheet features a unique structure made up of interconnected tetragonal and octagonal rings^35–37. The pristine TG, measuring 18 Å × 18 Å, consists of 100 carbon atoms, with the edge carbon atoms capped by 20 hydrogens. The average C–C bond length is approximately 1.40 Å, while the bond angles for the tetragonal and octagonal rings are about 90° and 135°, respectively. Al and B, as dopants, introduce new active sites on the surface of TG. These sites exhibit increased affinity for NU molecules for the following reasons: Al and B have a lower electronegativity than carbon, creating a charge imbalance that enhances the interaction between the doped TG and NU molecules. This charge transfer facilitates stronger binding of NUs to the nanocarrier. Dopants act as a Lewis acid, which can form coordination bonds with the electron-rich functional groups (e.g., nitroso and carbonyl groups) present in NUs. This interaction ensures stable encapsulation of the drug molecules, preventing premature release. The introduction of Al and B into TG’s lattice structure modifies its electronic properties and increases its surface reactivity. This modification leads to increased surface area and enhanced drug adsorption^38,39. Previous studies have shown that doping graphene and other carbon-based materials with Al and B significantly enhances their electronic and catalytic properties^12,40. These findings establish a robust basis for investigating the potential of B- and Al-doped TG as an advantageous material. Given that the TG structure contains only one type of carbon atom, common to two octagonals and a tetragonal ring, we have a single option for replacing a carbon atom with a dopant atom. All pristine and doped TG nanosheets were geometrically optimized, followed by vibrational frequency calculations to identify the true local minima on the potential energy surface (Fig. 1).

Fig. 1.

The optimized geometry of pristine and doped TG nanosheets calculated using the M06-2X functional and 6-31 + G(d,p) basis set.

The frontier molecular orbitals of TG, as well as its boron and aluminum-doped counterparts, were investigated to assign their reactivity. As depicted in Fig. 2, the HOMO of pristine TG (a) exhibits a delocalized distribution across the conjugated framework, indicative of efficient electron mobility. However, upon doping with boron (b) or aluminum (c), the HOMO becomes localized around the dopant atom, suggesting enhanced electron density at these sites and potential implications for reactivity. Similarly, the LUMO of pristine TG (d) is delocalized, but doping with boron (e) or aluminum (f) induces localization around the dopant atom. This localization of both HOMO and LUMO upon doping suggests that these sites may become preferential centers for electron transfer and chemical reactions. Furthermore, the alteration of the HOMO–LUMO gap due to doping can be expected to influence the conductivity and optical properties of the material. These findings highlight the significant impact of doping on the electronic structure of TG, offering potential avenues for tailoring its properties for various applications such as catalysis, sensing, and electronic devices.

Fig. 2.

The spatial distribution of HOMO and LUMO in pristine and doped TG nanosheets. Letters (a), (b), and (c) represent the HOMO of TG, BTG, and AlTG, respectively, while (d), (e), and (f) show the LUMO of these structures.

The frontier orbital analysis revealed that pristine TG exhibits a HOMO energy level of − 5.37 eV and a LUMO energy at − 2.81 eV, yielding a band gap (E_g) of 2.56 eV. According to solid-state physics principles, materials can be categorized by their band gap characteristics:

1. Insulators (E_g > 4 eV): The substantial energy separation between valence and conduction bands prevents significant electron mobility at standard conditions.

2. Semiconductors (0.1 eV < E_g < 4 eV): These materials demonstrate intermediate band gaps that permit controlled electron excitation through thermal or photonic energy input.

3. Conductors (E_g ≈ 0 eV): The minimal energy barrier allows spontaneous electron flow, resulting in high conductivity.

Our calculations clearly identify pristine TG as a semiconductor material. Boron doping induces notable electronic modifications, specifically stabilizing the LUMO energy by 0.28 eV while maintaining the HOMO level. This electronic restructuring consequently reduces the overall band gap of the doped system. Given that the HOMO–LUMO energy gap is indicative of molecular reactivity, it can be inferred that BTG exhibits enhanced reactivity compared to pristine TG. Conversely, aluminum doping leads to a stabilization of the HOMO energy by approximately 0.14 eV and a destabilization of the LUMO energy by approximately 0.12 eV. Consequently, the E_g of AlTG increases by 0.26 eV. This suggests that the electrical properties of AlTG may exhibit reduced sensitivity to the presence of target molecules compared to pristine TG. Based on the calculated energy gaps, both B-doped and Al-doped TG nanosheets are classified as semiconductors. The molecular electrostatic potential (MEP) map at a point in space is defined as the electrostatic potential created by the nuclei and electrons of a molecule. It is a powerful computational tool employed to visualize the spatial distribution of electrostatic potential around a molecule. This visualization identifies electrophilic and nucleophilic regions, crucial for understanding molecular reactivity and intermolecular interactions. Consequently, the MEP map provides a visual representation of the potential energy experienced by a positive test charge at any given point around the molecule. This representation is typically displayed as a color-coded surface mapped onto the molecule’s electron density. Regions of varying electrostatic potential are commonly depicted using a color gradient. In this context, red regions indicate areas of positive electrostatic potential, signifying electron-deficient regions and potential electrophilic sites. Blue regions represent areas of negative electrostatic potential, indicating electron-rich regions and potential nucleophilic sites. Green or yellow regions represent areas of near-neutral electrostatic potential. By plotting the MEPs of two interacting species, a qualitative assessment of the most probable interaction sites can be obtained. This allows researchers to predict and understand the nature of intermolecular interactions⁴¹. As illustrated in Fig. 3, the charge distribution of the TG surface is significantly altered upon doping with boron and aluminum atoms. Specifically, these dopants induce the formation of electrophilic sites on the TG surface. This increase in positive electrostatic potential enhances the probability of favorable interactions with nucleophilic centers present on the NU molecule.

Fig. 3.

The MEP plot of TG, BTG, and AlTG nanosheets. Red and blue regions indicate areas of positive and negative electrostatic potential, respectively. Green or yellow regions represent areas of near-neutral electrostatic potential.

With the help of MEP plots, we investigated all possible orientations of the NU molecule as it approached the nanosheets, both horizontally and vertically, from its oxygen and hydrogen ends. The adsorption energies and thermochemical parameters (ΔH and ΔG) calculated for each optimized nanosheet-drug complex indicated that the most energetically favorable configuration for the TG- and BTG-NU complexes is one where the drug molecule is adsorbed horizontally on the surface of the nanosheets (Fig. 4). The E_ads value for the pristine TG-NU interaction is approximately − 7.02 kcal mol⁻¹, with ΔH and ΔG calculated to be − 8.90 kcal mol⁻¹ and 4.87 kcal mol⁻¹, respectively, indicating that the ΔG value is not conducive to a spontaneous reaction. In contrast, for the B-doped configuration, the E_ads, ΔH, and ΔG values are − 14.91, − 13.59, and − 4.06 kcal mol⁻¹, respectively (Table 1). In contrast to TG and BTG, the adsorption of NU on the AlTG surface results in a configuration where NU interacts with the aluminum atom through the oxygen atom of its carbonyl group. This interaction is characterized by strong chemisorption, as evidenced by the calculated values of E_ads (− 41.46 kcal mol⁻¹), ΔH (− 43.46 kcal mol⁻¹), and ΔG (− 32.25 kcal mol⁻¹). These thermodynamic parameters indicate a highly stable and energetically favorable adsorption process.

Fig. 4.

The optimized structure of TG-NU, BTG-NU, and AlTG-NU was calculated using the M06-2X functional and 6-31 + G(d,p) basis set. Carbon and hydrogen atoms are represented as dark and light grey spheres. Nitrogen, boron, and aluminum are blue, purple, and pink spheres, respectively.

Table 1.

Adsorption energies (E_ads), BSSE corrections, and BSSE-corrected E_ads, enthalpy changes (ΔH), Gibbs free energies (ΔG) (all in kcal mol⁻¹), and changes in HOMO–LUMO energy gap (∆E_g (%)) resulting from NU adsorption on the surface of TG nanosheets.

Complex	E ads	E BSSE	Corrected Eads	∆H	∆G	∆Eg (%)
TG-NU	− 10.97	3.95	− 7.02	− 8.90	4.87	− 1.31
BTG-NU	− 19.72	4.81	− 14.91	− 13.59	− 4.06	− 10.46
AlTG-NU	− 45.90	4.44	− 41.46	− 43.46	− 32.25	5.20

Al and B, as dopants, introduce new active sites on the surface of TG. These sites exhibit increased affinity for NU molecules for the following reasons: Al and B have a lower electronegativity than carbon, creating a charge imbalance that enhances the interaction between the doped TG and NU molecules. This charge transfer facilitates stronger binding of NUs to the nanocarrier. Dopants act as a Lewis acid, which can form coordination bonds with the electron-rich functional groups (e.g., nitroso and carbonyl groups) present in NUs. This interaction ensures stable encapsulation of the drug molecules, preventing premature release. The introduction of Al and B into TG’s lattice structure modifies its electronic properties and increases its surface reactivity. This modification leads to increased surface area and enhanced drug adsorption^38,39.

Previous studies have shown that doping graphene and other carbon-based materials with Al and B significantly enhances their electronic and catalytic properties^12,40. These findings establish a robust basis for investigating the potential of B- and Al-doped TG as an advantageous material.

Table 2 summarizes the electronic properties and conceptual density functional theory (CDFT) indices for isolated nanosheets and nanosheet-drug systems. Significant changes in electronegativity (χ) and chemical hardness (η) are observed upon complexation with NU. Specifically, BTG-NU and AlTG-NU exhibit a reduction in electronegativity, while the chemical hardness of BTG decreases, indicating an enhanced charge transfer capability and reactivity. The chemical potential (μ), which is directly related to electronegativity, follows a similar trend, further corroborating the enhanced charge transfer in doped systems upon NU complexation. The dipole moment, a critical parameter for assessing polarity and intermolecular interactions, is notably higher in AlTG-NU (6.33) compared to BTG-NU (3.46) and TG-NU (2.17). This suggests that AlTG-NU has a greater capacity for electrostatic interactions with NU. This observation aligns with the high adsorption energy calculated for AlTG-NU. Nucleophilicity (Nu) values increase in both BTG-NU and AlTG-NU relative to their pristine counterparts, indicating an enhanced electron-donating ability upon NU complexation. This trend supports the hypothesis that NU interacts with the nanostructure, altering its electronic properties. In contrast, the change in nucleophilicity is less pronounced in TG-NU, suggesting a weaker interaction between pristine TG and NU. In summary, the CDFT analysis demonstrates that BTG shows promising characteristics, including a reduction in E_g, electronegativity, and chemical hardness. These findings underscore the potential of boron-doped TG as an effective nanocarrier for nitrosourea, highlighting its suitability for drug delivery applications.

Table 2.

Electronic properties and conceptual density functional theory (CDFT) indices of isolated and complexed pristine and doped TG systems.

Structure	E HOMO	E LUMO	E g	χ	η	I	A	µ	S	ω	Nu	Dipole moment
TG	–5.37	–2.81	2.56	3.95	3.50	5.70	2.19	–3.95	0.29	2.22	3.75	0.00
TG-NU	–5.41	–2.88	2.52	3.98	3.14	5.55	2.41	–3.98	0.32	2.52	3.71	2.17
BTG	–5.37	–3.09	2.28	4.31	2.71	5.66	2.95	–4.31	0.37	3.42	3.75	0.29
BTG-NU	–5.31	–3.26	2.04	4.13	2.61	5.44	2.83	–4.13	0.38	3.27	3.81	3.46
AlTG	–5.51	–2.69	2.82	3.85	6.47	7.09	0.61	–3.85	0.15	1.15	3.61	1.28
AlTG-NU	–5.38	–2.41	2.97	3.80	6.51	7.05	0.54	–3.80	0.15	1.11	3.78	6.33

The interaction dynamics between nanostructures and drug entities serve as a pivotal indicator of the conditions governing drug release. It is essential to note that a weak physical adsorption energy does not inherently guarantee the timely and spatially precise release of drug molecules. Conversely, excessive chemisorption, characterized by a strong binding of the drug to the nanocarrier’s surface, may result in prolonged release times that hinder therapeutic effectiveness. To address these challenges, evaluating an effective recovery time, which can be derived through transition state theory within the framework of DFT calculations, is critical for establishing the reliability of a drug delivery system. The equation governing this relationship is articulated as:

11

In this equation, k represents the gas constant (1.99 × 10⁻³ kcal mol⁻¹ K⁻¹), while ν₀ symbolizes the attempt frequency⁴². At ambient temperatures, the desorption durations for the drug molecule (NU) from various nanosheet substrates-namely pristine TG, BTG, and AlTG-demonstrate significant variation: approximately 1.4 × 10⁻⁷ s, 8.3 × 10⁻² s, and 2.3 × 10¹⁸ s, respectively. These findings indicate that the BTG nanosheet exhibits a considerably more favorable recovery time compared to its pristine TG and AlTG counterparts, underscoring its potential as a more effective drug delivery vehicle. Such distinctions are instrumental in optimizing drug release profiles and enhancing therapeutic outcomes in clinical applications. Frontier molecular orbital analysis was conducted to examine the energy levels and spatial distributions of the HOMO and LUMO, as presented in Table 2. It is observed that the HOMO and LUMO energies of TG-NU are approximately 0.04 eV and 0.07 eV more stable than those of isolated TG, resulting in a reduction of the E_g value by about 0.04 eV. In the case of BTG-NU, the changes in HOMO and LUMO energies do not align; specifically, the HOMO energy level of BTG destabilizes by approximately 0.06 eV following its interaction with NU, whereas the LUMO level stabilizes significantly, by an amount of 0.17 eV. Consequently, this system experiences a reduction of 10.46%.

In contrast, the situation for AlTG is markedly different, with both the HOMO and LUMO becoming less stable after the adsorption process, decreasing by 0.13 eV and 0.28 eV, respectively. However, this results in a 5.20% increase in the E_g value compared to the isolated AlTG. The spatial distribution of the HOMO and LUMO across the nanosheet-drug complexes is illustrated in Fig. 5. Figure 6, illustrating the total density of states (TDOS) and partial density of states (PDOS), provides crucial insights into the specific contributions of each interacting fragment (the nanosheet and the NU molecule) to the overall electronic structure of the complex. In all complexes, the PDOS plots show relatively minimal overlap between the electronic states of the nanosheet (orange) and the NU molecule (green) around the HOMO and LUMO regions. While there is some interaction, the peaks mostly retain their individual characteristics, with no significant broadening or shifting.

Fig. 5.

The spatial distribution of HOMO and LUMO in pristine and doped TG nanosheets complexed with the drug molecule. Letters (a), (b), and (c) represent the HOMO of TG-NU, BTG-NU, and AlTG-NU, respectively, while (d), (e), and (f) show the LUMO of these structures.

Fig. 6.

Total density of states (TDOS) and partial density of states (PDOS) plots for the (a) TG-NU, (b) BTG-NU, and (c) AlTG-NU complexes. The blue line represents the TDOS, while the orange and green lines indicate the PDOS contributions from the TG nanosheet and NU, respectively.

In contrast, the situation for AlTG is significantly different, as both the HOMO and LUMO exhibit decreased stability following the adsorption process, with reductions of 0.13 eV and 0.28 eV, respectively. Nevertheless, this leads to a 5.20% increase in the Eg value compared to isolated AlTG. The spatial distribution of the HOMO and LUMO across the nanosheet-drug complexes is depicted in Fig. 5. Additionally, Fig. 6 illustrates the total density of states (TDOS) and partial density of states (PDOS), offering critical insights into the specific contributions of each interacting fragment—the nanosheet and the NU molecule—to the overall electronic structure of the complex. In all complexes, the PDOS plots indicate relatively minimal overlap between the electronic states of the nanosheet (orange) and the NU molecule (green) in the regions of the HOMO and LUMO. While some interaction is observed, the peaks largely maintain their characteristics, showing no significant broadening or shifting. These findings are in agreement with the spatial distribution of HOMO and LUMO shown in Fig. 5.

Natural bond orbital analysis methodology

Natural Bond Orbital (NBO) analysis is a valuable tool for understanding intermolecular interactions, offering a localized and chemically intuitive description of bonding. A key aspect of this analysis is the application of second-order perturbation theory, which calculates stabilization energies, denoted as E(2), quantifying the energetic impact of electron delocalization between donor and acceptor NBOs. A high E(2) value indicates a strong interaction, reflecting substantial charge transfer and stabilization. By examining these E(2) values, researchers can identify and quantify specific orbital interactions, such as lone pair to antibonding orbital interactions, which are critical for understanding phenomena like hydrogen bonding, halogen bonding, and other non-covalent forces. Consequently, E(2) values provide a direct measure of the strength and nature of interactions, allowing for detailed interpretation of how one species influences the electronic structure and stability of another. The electronic interactions in our systems were characterized employing second-order perturbation theory to evaluate the Fock matrix in the NBO basis. This approach quantitatively assesses stabilization energies arising from electron delocalization and charge transfer phenomena between molecular orbitals. The Fock matrix serves as the fundamental operator in these calculations, containing essential information about orbital energies and their mutual overlap. Within this framework, the second-order stabilization energy E(2) represents the energetic consequence of interactions between electron-donating (occupied) and electron-accepting (virtual) NBOs. These calculations reveal critical details about:

• Chemical bonding patterns

• Hyperconjugative effects

• Other electronic delocalization phenomena

Our analysis of the TG-drug complexes (Table 3) showed minimal charge transfer stabilization between pristine TG and the pharmaceutical compound. The bidirectional donor–acceptor interactions demonstrated similarly low E(2) values, indicating weak electronic coupling in the undoped system. This suggests a minimal contribution of orbital interactions to the overall complex stability. Furthermore, boron doping (BTG) did not induce a substantial enhancement in E(2) values compared to pristine TG, indicating that charge transfer is not a dominant factor in the stabilization of the BTG-NU complex. Conversely, aluminum doping (AlTG) resulted in a significant increase in donor–acceptor interactions, particularly for transitions from the drug molecule to the AlTG nanosheet. Notably, prominent donor–acceptor transitions, such as LP(2) O121 → LP*(2) Al120 (E(2) = 43 kcal mol⁻¹) and LP(1) O121 → LP*(2) Al120 (E(2) = 10.3 kcal mol⁻¹), were identified, suggesting a substantial charge transfer from the drug molecule to the AlTG sheet. This highlights the critical role of aluminum doping in modulating the electronic interactions and enhancing the charge transfer characteristics of the TG-drug complex.

Table 3.

Selected donor → acceptor interaction energies (kcal mol⁻¹) calculated using the second-order perturbation theory.

from sheet to Drug			from Drug to sheet
Donor	Acceptor	E(2)	Donor	Acceptor	E(2)
TG-NU
π C16–C84	σ* N124–H129	1.05	π O122–N125	RY*(3) C85	0.43
π* C38–C62	π* O121–C126	0.60	σ N123–N125	RY*(3) C17	0.31
π C17–C85	σ* O122–N125	0.56	σ N123–C126	RY*(3) C62	0.27
π C38–C62	π* O121–C126	0.45	LP(1) N123	π* C17–C85	0.19
π C30–C52	σ* N124–H128	0.37	σ* O122–N125	π* C27–C49	0.19
σ C6–C62	RY* (6) C126	0.31	σ* O122–N125	π* C17–C85	0.14
π* C6–C76	π* O121–C126	0.29	σ O122–N125	π* C17–C85	0.12
BTG-NU
π C17-C84	σ* N124–H129	0.57	LP (1) N123	LP*(1) B120	1.77
LP(1) C38	π* O121–C126	0.48	σ O122–N125	LP*(1) C75	0.25
LP*(1) C75	σ* O122–N125	0.35	σ N123–H127	LP*(1) B120	0.22
LP*(1) B120	π* O121–C126	0.29	LP(1) O122	LP*(1) C75	0.15
π* C26–C48	π* O121–C126	0.13	π O122–N125	RY*(3) C75	0.12
σ C38–C71	RY*(6) C126	0.12	σ N123–C126	RY*(3) B120	0.11
π C27–C49	σ* N124–H129	0.09	σ N123–C126	LP*(1) B120	0.10
AlTG-NU
σ C17–Al120	σ* N124–H128	1.24	LP(2) O121	LP*(2) Al120	43.00
LP(1) C84	σ* N124–H128	0.99	LP(1) O121	LP*(2) Al120	10.30
LP*(2) Al120	σ* O121–C126	0.96	σ O121–C126	LP*(2) Al120	5.73
LP*(1) C17	σ* N124–H128	0.41	LP(2) O121	σ* C17–Al120	5.24
CR(2) Al120	σ* O121–C126	0.38	LP(3) O121	LP*(1) Al120	4.79
π C27–C49	σ* N124–H128	0.35	LP(2) O121	LP*(1) Al120	3.69
σ*C17–Al120	σ* N124–H128	0.29	CR(1) O121	LP*(2) Al120	3.42

Atoms in molecules analysis methodology

To elucidate the electron density distribution and bonding characteristics within the (B-, Al-)TG-NU complexes, we performed a Quantum Theory of Atoms in Molecules (QTAIM) analysis, following Bader’s methodology²⁹. This approach posits that the formation of a chemical bond is evidenced by the presence of a bond critical point (BCP) between interacting atoms. The properties of these BCPs, specifically the electron density (ρ_C) and its Laplacian , provide critical insights into the nature of interatomic interactions. The Laplacian, representing the second derivative of the electron density, reveals the tendency for electron density to either accumulate or deplete. Furthermore, the total electronic energy density at the BCP (H_C), which is the sum of the local kinetic energy density (G_C) and the local potential energy density (V_C), quantifies the energetic characteristics of these interactions:

12

According to the Virial theorem, the Laplacian of the electron density at the BCP is intrinsically linked to its associated properties. A negative Laplacian value indicates electron density concentration, indicative of shared interactions such as covalent bonds and lone pairs. Conversely, a positive Laplacian value signifies electron density depletion, characteristic of non-covalent interactions like ionic, van der Waals, and hydrogen bonds. However, instances where and suggest partially covalent interactions that are not fully covalent bonds, which would imply irreversible binding, but rather interactions with a degree of shared electron density that is less rigid. QTAIM calculations were performed using the AIM2000 software package at the M06-2X/6-31 + G(d,p) level of theory⁴³.

The analysis for TG-NU and BTG-NU complexes showed positive Laplacian values and negative total electronic energy densities at the BCPs, which, although relatively small, suggest partially covalent interactions. For AlTG-NU, the magnitudes of and were significantly higher, indicating stronger interactions. The compatibility with effective drug release, particularly for BTG, can be justified by considering the calculated recovery times. Despite the presence of partially covalent interactions, the BTG nanosheet exhibits a significantly more favorable recovery time of 8.3 × 10⁻² s. This is in stark contrast to AlTG, which, due to its strong chemisorption and higher magnitude of partially covalent interactions, has a very lengthy desorption time of 2.3 × 10¹⁸ s. Pristine TG also shows partially covalent interactions but has an even faster desorption time of 1.4 × 10⁻⁷ s. Therefore, while partially covalent interactions are present, their strength varies depending on the doping. In the case of BTG, these interactions are not so strong as to hinder effective drug release, as evidenced by its manageable recovery time. The “partially covalent” nature in BTG-NU implies a degree of interaction that is more robust than pure physisorption (Table 4) but avoids the irreversible binding characteristic of full covalent bonds (Fig. 7).

Table 4.

Topological parameters (all in atomic units) for the optimized (B-, Al-)TG-NU complex.

Complex	Site	ρ C	∇2ρC	K C	V C	H C
TG-NU	H129…C84	0.0088	0.0291	− 0.0011	− 0.0096	− 0.0107
	N123…C62	0.0092	0.0273	− 0.0006	− 0.0081	− 0.0087
	C126…C6	0.0079	0.0298	− 0.0014	− 0.0103	− 0.0117
	O123…C85	0.0075	0.0261	− 0.0008	− 0.0082	− 0.0091
	H128…C30	0.0064	0.0222	− 0.0011	− 0.0077	− 0.0087
BTG-NU	O122…C75	0.0100	0.0338	− 0.0009	− 0.0103	− 0.0112
	N123…B120	0.0095	0.0249	− 0.0002	− 0.0067	− 0.0069
	C126…C38	0.0079	0.0282	− 0.0013	− 0.0097	− 0.0111
	H129…C84	0.0084	0.0267	− 0.0010	− 0.0087	− 0.0097
	N124…C3	0.0072	0.0231	− 0.0009	− 0.0075	− 0.0084
AlTG-NU	Al120…O121	0.0595	0.4379	− 0.0088	− 0.1272	− 0.1360
	H128…C84	0.0155	0.0467	− 0.0008	− 0.0133	− 0.0141

Fig. 7.

Molecular graph of nanosheet-NU complexes. The graphs were obtained at the M06-2X/6-31 + G(d,p). Large circles correspond to attractors and small red and yellow circles are bond and ring critical points, respectively.

Electron localization function (ELF) analysis

The electron localization function (ELF), initially introduced by Becke and Edgecombe⁴⁴, is a versatile quantum chemical tool that provides a real-space visualization of electron localization within molecules and materials. It serves as a powerful descriptor for characterizing chemical bonding, lone pairs, and core electron regions. Unlike electron density alone, which can be high in both bonding and non-bonding regions, ELF maps the probability of finding an electron pair in a given spatial region, effectively identifying areas where electrons are spatially confined. The ELF values typically range from 0 to 1, where specific ranges correspond to distinct electron localization characteristics:

• ELF values close to 1 (red/yellow regions in typical visualizations) indicate strong electron localization, characteristic of core electron regions, covalent bonds, and lone pairs. High values imply a high probability of finding an electron pair in that specific region.

• ELF values around 0.5 (green regions) represent electron distributions similar to a homogeneous electron gas, often found in delocalized systems or regions where electron density is shared more broadly.

• ELF values close to 0 (blue regions) signify very low electron localization, typically found in inter-basin regions between atoms or where electron density is depleted.

By analyzing the ELF topological features, such as basins of attraction and their centroids, one can gain intuitive insights into the nature of chemical bonds (e.g., shared-electron interactions versus lone pairs), the degree of electron delocalization, and the strength of intermolecular interactions. This makes ELF an invaluable complement to other analyses, such as the quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analysis, as it offers a direct visual representation of electron pairing and localization. In the ELF plot for the pristine TG-NU complex (Fig. 8a), the electron localization in the interaction region between the NU molecule and the T-graphene nanosheet appears relatively less intense compared to the doped systems. While there are regions of intermediate localization (greenish areas) indicating some electron sharing, the absence of highly concentrated (yellow/red) basins directly bridging the NU molecule to the TG surface suggests a weaker overall interaction. This visual observation is consistent with the lower adsorption energy for TG-NU (− 7.02 kcal mol⁻¹) and its faster desorption time (1.4 × 10⁻⁷ s), indicating a predominant physisorption character, albeit with a subtle “partially covalent” component as identified by QTAIM. The electron density is less perturbed, signifying weaker orbital overlap and charge transfer. The ELF plot for the BTG-NU complex (Fig. 8b) shows a noticeable increase in electron localization in the interaction region between the boron atom and the NU molecule. While perhaps not as intensely localized as in the AlTG-NU complex, there are more defined regions of higher ELF values (more pronounced green/yellow areas) connecting the interacting atoms. This visually confirms a stronger, more pronounced interaction compared to pristine TG. This aligns excellently with our findings of an increased and more manageable adsorption energy (− 14.91 kcal mol⁻¹) for BTG-NU. The observed electron localization supports the “partially covalent” nature of the interaction and the improved electron-donating ability suggested by CDFT analysis, leading to a favorable recovery time (8.3 × 10⁻² s) for drug delivery. The ELF plot for the AlTG-NU complex (Fig. 8c) vividly illustrates the strongest interaction among the three systems. There is a clear and highly concentrated basin of electron localization (intense yellow/red regions) directly between the aluminum atom and the oxygen atom of the nitrosourea molecule (from its carbonyl group). This strong localization indicates a significant sharing of electron density, characteristic of a robust chemical bond, consistent with our finding of strong chemisorption. This visual evidence perfectly corroborates the very high adsorption energy (− 41.46 kcal mol⁻¹) and the substantial charge transfer from the drug to the AlTG nanosheet, as identified by NBO analysis. The prominent ELF basin strongly supports the conclusion that the AlTG-NU interaction is indeed a strong partially covalent one, explaining the exceedingly long desorption time (2.3 × 10¹⁸ s) that renders it unsuitable for drug release. In conclusion, the ELF analysis provides compelling visual evidence that directly aligns with and reinforces the quantitative results from the DFT calculations. It differentiates the nature and strength of the interactions: from weaker, predominantly physisorptive interactions in TG-NU, to a balanced partially covalent interaction in BTG-NU ideal for drug delivery, and finally to a strong chemisorptive bond in AlTG-NU. This visual corroboration significantly strengthens the mechanistic understanding of the doping effects on NU adsorption properties.

Fig. 8.

Electron localization function (ELF) plots for the (a) TG-NU, (b) BTG-NU, and (c) AlTG-NU complexes. High ELF values (yellow/red) indicate strong electron localization (e.g., covalent bonds, lone pairs), while lower values (green/blue) suggest delocalized electrons or depleted regions. The plots visually demonstrate the varying degrees of electron sharing and interaction strength between the NU molecule and the pristine and doped TG nanosheets.

Conclusion

This study employed density functional theory (DFT) to meticulously investigate the adsorption behavior of a nitrosourea (NU) drug molecule on pristine, boron-doped, and aluminum-doped T-graphene nanosheets (TG, BTG, and AlTG, respectively). Our comprehensive analysis, encompassing geometric, electronic, and energetic properties, including adsorption energies, HOMO–LUMO gaps, molecular electrostatic potential (MEP), natural bond orbital (NBO) analysis, and quantum theory of atoms in molecules (QTAIM), provides crucial insights into the potential of these materials as drug delivery systems. Our findings reveal distinct interaction profiles governed by the type of doping. Aluminum doping significantly enhanced the adsorption of NU onto the TG nanosheet, leading to strong chemisorption with a notably high adsorption energy of − 41.46 kcal mol⁻¹ and substantial charge transfer. While this indicates robust binding, the calculated desorption time of 2.3 × 10¹⁸ s renders AlTG impractical for efficient drug release in therapeutic applications. In contrast, boron doping presented a more favorable scenario. The adsorption energy for BTG-NU (− 14.91 kcal mol⁻¹) was significantly increased compared to pristine TG, yet it resulted in a remarkably manageable recovery time of 8.3 × 10⁻² s. This balance is highly advantageous for drug delivery, ensuring sufficient drug loading while permitting timely release. Furthermore, the most prominent HOMO–LUMO gap reduction (10.46%) was observed in BTG upon NU adsorption, indicative of enhanced reactivity. Both NBO and QTAIM analyses corroborated these findings, confirming substantial donor–acceptor interactions in AlTG-NU and characterizing the partially covalent nature of interactions in all complexes, with BTG exhibiting strengths that are robust yet conducive to release. In essence, this computational investigation highlights the critical role of strategic doping in fine-tuning the electronic and adsorption properties of T-graphene. While Al-doping leads to overly strong, irreversible binding, B-doping optimizes the interaction, achieving a desirable balance between effective drug loading and efficient drug release. Our results unequivocally demonstrate the promising potential of boron-doped T-graphene as an effective nanocarrier for nitrosourea, laying a strong foundation for the rational design and development of next-generation graphene-based drug delivery systems with tailored therapeutic outcomes.

Author contributions

M.D.: Conceptualization, Investigation, Methodology, Software, Writing—original draft; A.K.: Investigation, Software, Visualization, Writing—original draft; P.K.: Formal analysis, Investigation, Writing—original draft; M.M.: Data curation, Investigation, Writing—original draft; R.K.: Data curation, Visualization, Writing—original draft; S.A.-H.: Visualization, Writing—original draft; D.S.J.: Data curation, Review and editing; A.G.: Validation, Review and editing; G.R.: Supervision, Validation, Review and editing.

Data and code availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.