A DFT insight into the potential of cycloparaphenylenes as efficient sensors for detecting Paracetamol

Interaction energies and NBO analysis

The interactions between the PCT drug and the [n]MCPP nanorings are explored to identify the energy minima and stable structures for the encapsulation of the drug into the cavity of the nanorings. The optimized structures of the PCT drug and [n]MCPP nanorings are shown in Fig. 2, while their optimized complex structures are depicted in 3. The interaction energies are reported in Table 1. All studied complexes (PCT@⁶MCPP, PCT@⁸MCPP, and PCT@¹⁰MCPP) exhibit negative interaction energy values, revealing that all the complexes are stable and maintain relatively uniform structural shapes.

To assess the spontaneity and whether the encapsulation process is exothermic or endothermic, the thermodynamic parameters, including Gibbs energy changes (ΔG), enthalpy changs (ΔH), and entropy changes (ΔS) were calculated and reported in Table S1. The negative values of ΔG and ΔH for all complexes indicate that the adsorption process is spontaneous and exothermic, respectively, in both gas phase and water. The observed decrease in ΔG compared to ΔH can be attributed to significant entropic effects. All complexes show negative values for ΔS, indicating that atomic movement is restricted due to the presence of the PCT drug and the new intermolecular interactions formed. This entropy reduction underscores the importance of enthalpy contributions in driving the encapsulation mechanism.

The degree of interaction is influenced by the interaction energies of the complexes. Interaction energies below 1 eV indicate weak interactions (physical interactions), whereas energies exceeding 1 eV suggest strong chemical interactions⁵⁵. Estimates of interaction energy presented in Table 1indicate that the PCT drug undergoes physical interactions with the [n]MCPP nanorings. The interaction energies for the nanorings, in increasing order, are as follows¹⁰:MCPP (−0.89eV) >⁸MCPP (−0.78eV) >⁶MCPP (−0.09eV) in the gas phase, indicating that¹⁰MCPP has the strongest interaction, while⁶MCPP has the weakest. Additionally, it is evident that the binding energy values ​​for all structures analyzed in an aqueous environment are lower than those observed in the gas phase.

The charge transfer (Q_NBO) values ​​are computed following the encapsulation of the PCT drug within the [n]MCPP nanorings. The positive charges indicate a deficiency of electronic density on the PCT, as shown in Table 1. This positive sign on the PCT reflects the transfer of charges from the PCT to the nanorings. In the aqueous phase, the role of solvation becomes significant. The presence of water molecules can stabilize the charged states of both the [n]MCPP nanorings and PCT, potentially enhancing the charge transfer processes.

Optimized structure of (a) PCT, (b)⁶MCPP, (c)⁸MCPP, and (d)¹⁰MCPP generated by VESTA 3.5.8.

Figure 3. Optimized structure of (a) PCT@⁶MCPP, (b) PCT@⁸MCPP, and (c) PCT@¹⁰MCPP complexes generated by VESTA 3.5.8.

The NBO analysis serves as an effective method for gaining insights into the characteristics of intermolecular interactions⁵⁶. The stability of the molecular system results from donor-acceptor interactions, which arises from the transfer of electron density between bonding and non-bonding orbitals. In this context, we consider the stabilization energy resulting from the interactions between the donor and acceptor. This energy can be determined by utilizing the Fork Matrix values ​​of the second-order perturbation energy (E²), as denoted by the following equation:

where q_i represents the occupancy of the donor orbital, Ei and Ej are the diagonal elements, and F_ij denotes the off-diagonal element of the NBO Fock matrix.

A higher E² value indicates stronger and more effective electron transfer from the donor to the acceptor, resulting in greater overall conjugation of the entire system. According to the results presented in Table 2, the PCT@¹⁰MCPP complex exhibits the highest stabilization energy (32.23 kcal/mol) compared to all other complexes. This notable stabilization energy arises from the LP O117 to σ* C48-H108 transition occurring in the PCT@¹⁰MCPP complex. The second highest stabilization energy, measured at 25.22 kcal/mol, is observed in the PCT@⁸MCPP complex, which is attributed to the LP O95 to σ* C43\(\:-\)H87 transition. The stabilization energy of the PCT@⁶MCPP complex is the lowest (17.27 kcal/mol), also due to the transition of LP O73 to σ* C22\(\:-\)C23. The results indicate that encapsulating PCT into nonrings with different porosities results in varying stabilization energies. Increased porosity typically leads to an expanded surface area, which facilitates interaction between the PCT and the nanorings. A greater surface area can provide more sites for charge transfer and binding, potentially enhancing the overall stabilization energy. Additionally, a more porous structure could improve the movement of the drug molecule within the nanoring. This increased mobility may promote better packing and interaction with the nanoring, resulting in enhanced stabilization.

Molecular orbital and global reactivity indices

Molecular orbital analysis is conducted to gain insights into the sensitivity, electron distribution, and reactivity of the nanoring in detecting the PCT drug molecule. A key focus of this investigation is the energy gap (E_g) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which is typically determined by calculating the energy difference between these two molecular orbitals. A small change in the E_g values ​​leads to an exponential variation in electrical conductivity. As a result, lower E_g values ​​can be associated with increased sensitivity, reactivity, and electrical conductivity. The percentage fluctuations of the energy gap following the interaction between the nanorings and the drug can be calculated using the following equation:

where E_g(complex) and E_g(nanoring) represent the energy gaps of the complex and nanoring, respectively. The Fermi level energy (E_FL) is determined by taking the midpoint between the HOMO energy (E_H) and the LUMO energy (E_L) calculated using the following equation:

The depiction of molecular orbitals is given in Fig. 4. This figure clearly demonstrates that the HOMO and LUMO are extensively distributed across all the atoms of the drug molecule prior to encapsulation. Following the interaction with the nanoring, the HOMO becomes predominantly localized on the drug, while the LUMO shifts to the nanoring. This movement of the orbitals indicates that electrons are delocalized within the complexes, signifying charge transfer between the nanorings and the PCT drug.

Visualization of molecular orbitals (HOMO and LUMO) for [n]MCPP nanorings and their complexes with PCT generated by Avogadro 1.2.0.

The various electronic parameters, including E_H, E_L, E_g, %ΔE_g, and E_FL, are presented in Table 3. According to the results, the (E_g) for the⁶MCPP⁸, MCPP, and¹⁰MCPP nanorings are 1.92 eV, 2.02 eV, and 2.06 eV, respectively. This means that increasing the porosity of carbon nanorings leads to an increase in the band gap. As porosity increases, the overall structure of the carbon nanorings may become more disordered due to the presence of more pores and vacancies. This disorder can lead to the localization of electronic states, which may affect the conduction band and valence band characteristics. Furthermore, our calculated band gap energies for [n] MCPP nanorings in water media are lower (0.7–0.8 eV) than those reported in previous study by Kono et al.³⁸. This difference is attributed to the inclusion of water as a solvent in our calculations. Water has a high dielectric constant (78.40), which reduces the Coulombic interactions between charged species. This screening effect can lead to a reduction in the energy required to promote an electron from the valence band to the conduction band, effectively lowering the band gap.

After drug encapsulation, the E_g for all [n]MCPP nanorings decreases. The most significant reduction in the E_goccurs in the PCT@⁶MCPP complex, with a change of approximately − 44.79% (0.86 eV). The corresponding changes in the other complexes are − 32.89% and − 19.90% for PCT@⁸MCPP and PCT@¹⁰MCPP, respectively. A more significant reduction in the energy gap of the⁶MCPP nanoring upon interaction with PCT indicates enhanced electrical conductivity and charge transfer, ultimately leading to increased sensing performance for the detection of the PCT drug.

Another key factor influencing the electronic properties of a material is the Fermi level. The Fermi level indicates the highest energy state occupied by electrons in a system; thus, a decrease in the Fermi level promotes electron transfer. The calculated data indicates that the Fermi level decreases as the energy gap narrows. The lowering of the Fermi level suggests that electron transfer between the valence band and conduction band is facilitated.

Global reactivity descriptors, including chemical potential, chemical hardness, and electrophilicity, are evaluated to understand how the PCT drug influences the selectivity and chemical reactivity of the nanorings. The results are summarized in Table 3. The hardness significantly diminishes when PCT interacts with [n]MCPP nanorings, indicating that the newly formed complexes exhibit increased reactivity. All complexes show thermodynamic stability, as their chemical potential values become negative following the encapsulation of the PCT drug within the nanorings. The electrophilicity values provide insight into a molecule’s ability to receive electrons. According to the data presented in Table 3, the electrophilicities of all complexes increase compared to those of the isolated nanorings. Therefore, the global reactivity analysis indicates that the [n]MCPP nanorings exhibit high sensitivity and reactivity towards the PCT drug.

DOS analysis

The analysis of Density of States (DOS) graphs is used to assess the distribution of energy orbitals and the arrangement of electrons⁵⁷. The outcomes from DOS graphs can be utilized to evaluate the energy distribution of orbitals and the distribution of electrons. Following the molecular orbital investigations in the previous section, the interaction mechanism between the [n]MCPP nanorings and the PCT drug can be further validated through the analysis of DOS plots for all studied complexes. The total density of states (TDOS) and partial density of states (PDOS) plots for the studied systems are provided in Fig. 5. The results clearly indicate that, following the interaction between the nanorings and the drug, the energy gaps of all the complexes decrease. The significant variations in the PDOS peaks after the encapsulation of the PCT drug are predominantly related to the PCT@⁶MCPP complex. This is due to a greater decrease in the energy gap and improved overlap of the orbitals of PCT with the⁶MCPP nanoring. The narrow energy gap of the PCT@⁶MCPP complex results in increased electrical conductivity and alters the fluorescence emission across all designed complexes, aiding in the detection of the PCT drug.

Graphical visualization of DOS spectra for (a)⁶MCPP, (b)⁸MCPP, (c)¹⁰MCPP, (d) PCT@⁶MCPP, (e) PCT@⁸MCPP, and (f) PCT@¹⁰MCPP.

UV-Vis spectra

The photo-sensing characteristics of materials can be assessed through variations in their absorption properties⁵⁸. To investigate the UV-Vis spectra of the MCPP nanorings and their drug complexes, time-dependent density functional theory (TD-DFT) calculations were conducted. Table 4 presents the values for maximum absorption (λ_max), oscillator strength (f_o), and excitation energy (E_exc). The UV-Vis spectra of all studied systems are shown in Fig. 6. The⁶MCPP⁸, MCPP, and¹⁰MCPP nanorings show maximum absorbance at 330.58, 360.50, and 382.70 nm, respectively. The results clearly indicate that transitions (red-shifts) occur at λ_maxfor all PCT@[n]MCPP complexes, with the PCT@⁶MCPP complex exhibiting a red-shift at a higher absorption wavelength. Therefore, the greater extent of red-shift observed after PCT drug loading suggests that⁶MCPP nanorings may serve as a selective and sensitive sensor for PCT drug, potentially enabling monitoring in biomedical applications. Additionally, the oscillator strength and excitation energy play a crucial role in accurately evaluating the interaction characteristics in conjunction with the absorption maximum. Upon the interaction of PCT with the MCPP nanorings, the oscillator strengths diminish, while the excitation energies increase due to an enhanced overlap of the wave functions between the drug and the nanorings. From this study, it can be concluded that the photo-sensing characteristics of all complexes change after encapsulation with the PCT drug.

Graphical representation of UV-Vis spectra for [n]MCPP nanorings and their complexes with PCT.

QTAIM analysis

The QTAIM Bader’s theory⁵⁹ is used to examine the nature of the bonds and the interactions between the PCT drug and the surfaces of the MCPP nanorings. This analysis assesses several topological parameters at bond critical points (BCPs), including the electron density (ρ(r)), the Laplacian of the electron density (∇²ρ(r)), the kinetic energy density (G(r)), the potential energy density (V(r)), and the total energy density (H(r)). The results are represented as topological graphs in Fig. 7, while Table S2lists the topological parameters obtained through this analysis. The strength of the analyzed interactions can be inferred from their electron density ρ(r) values; higher values indicate stronger covalent interactions (ρ(r) > 0.1 a.u.), while lower values suggest weaker non-covalent interactions (ρ(r) < 0.1 a.u.). All ρ(r) values are less than 0.1 a.u., indicating weak non-covalent interactions. A negative value for the ∇²ρ(r) indicates the presence of electron charge between interacting atomic nuclei, which is typically associated with covalent interactions. Conversely, when ∇²ρ(r) is positive, it suggests a reduced electron charge between the atoms, characteristic of interactions governed by van der Waals forces. The positive ∇²ρ(r) for all interactions reveals the presence of van der Waals forces. When ∇²ρ(r) and H(r) are both greater than zero, it indicates the presence of closed-shell (non-covalent) interactions. Conversely, if ∇²ρ(r) is less than zero and H(r) is negative, this suggests the occurrence of covalent bonding. A scenario where H(r) is negative and ∇²ρ is positive indicates a significantly polar covalent interaction⁶⁰. Table S2 indicates that closed-shell interactions predominantly occur between the PCT drug and MCPP nanorings for all bond pathways. The type of interaction can be confirmed by the ratio –G(r)/V(r). Interactions are classified as covalent if this ratio falls between 1 and 0.5, while interactions are considered partially covalent when the ratio is between 0.5 and 1. If the ratio exceeds 1, the interaction is identified as completely non-covalent. According to the results, the ratio –G(r) to V(r) for all intermolecular interactions is greater than 1, confirming the presence of non-covalent interactions.

Quantum theory of atoms in molecules (QTAIM) molecular graph of (a) PCT@⁶MCPP, (b) PCT@⁸MCPP, and c) PCT@¹⁰MCPP complexes generated by Multiwfn 3.7. The BCPs are shown with orange dots.

NCI analysis

The analysis of non-covalent interactions was conducted to explore the attractive or repulsive interactions between PCT drug and nanorings. This interaction can be further investigated through the use of the 2D RDG graph and 3D iso-surface as displayed in Fig. 8 (right side). The graph features three colors: blue, red, and green, which denote strong hydrogen bonding, repulsive interactions, and weak van der Waals interactions, respectively. In RDG scatter plots, the interactions are represented by colors, where values of λ2(r)ρ(r) \(\:>\:\)0 indicate hydrogen bonding interactions. Conversely, λ2(r)ρ(r) \(\:>\:\)0 signifies strong repulsive or steric forces, while λ2(r)ρ(r) ≈ 0 reflects the relatively weak van der Waals interactions. The 3D iso-surface plots represent hydrogen bonding in blue, weak van der Waals interactions in green, and repulsive forces in red. The gradient from blue to red effectively confirms the various types of interactions. The 3D iso-surface plots in Fig. 8 (left side) illustrate that there are extensive green regions between the PCT drug and nanorings, suggesting the presence of weak van der Waals interactions. Additionally, the green spikes observed in the 2D plots of all these complexes further support the presence of weak van der Waals interactions between the two components. Additionally, intense repulsive interactions, primarily occurring within the interior of benzene rings due to steric effects, are highlighted by the red area.

Non-covalent interactions (NCI) for all complexes, including reduced density gradients (RDG) graphs (right side) and 3D isosurface maps (left side) generated by VMD 1.9 and Multiwfn 3.7.

EDD analysis

EDD analysis is used to visually represent the charge transfer between the PCT drug and nanorings. This analysis involves calculating the difference between the two fragments. In EDD analysis, the resulting isosurfaces are composed of two colors: blue and red. The blue isosurfaces indicate areas of increased electronic density, while the red isosurfaces represent regions of electronic density depletion. The presence of both red and blue isosurfaces signifies the transfer of charges between the nanocapsule and the drug molecules. Figure 9 illustrates the EDD isosurfaces for the PCT@[n]MCPP complexes. According to the results, blue isosurfaces predominantly appear on the carbon and hydrogen atoms of the nanorings, indicating areas of high electronic density. In contrast, the red isosurfaces mainly appear on the oxygen atoms of the PCT drug, signifying regions of electronic density depletion. Therefore, the electron density EDD isosurfaces suggest that charge is transferred from the PCT drug to the nanorings.

Electron density difference (EDD) isosurface of (a) PCT@⁶MCPP, (b) PCT@⁸MCPP, and c) PCT@¹⁰MCPP complexes generated by Avogadro 1.2.0.

Solvent effect and dipole moment

To assess the impact of the solvent on the PCT@[n]MCPP complexes, we evaluated the solvation energy and dipole moment (DM) of the complexes in aqueous media. The findings are presented in Table 5. The negative values of the solvation energy of the complexes indicate their stability and solubility in water. The calculated solvation energy values for the nanorings are − 0.01, − 0.02, and − 0.02 eV for⁶MCPP⁸, MCPP, and¹⁰MCPP, respectively. Upon interaction with the PCT drug, the solvation energies for the complexes of PCT@⁶MCPP, PCT@⁸MCPP, and PCT@¹⁰MCPP change to − 0.02, − 0.03, and − 0.03 eV, respectively. This increase in the negativity of the solvation energies after the interaction with the PCT drug indicates that the complexes exhibit greater stability in aqueous media. In practical terms, this improved stability shows better performance in real environmental sensing applications. In aqueous environments such as natural water bodies or biological fluids, the ability of the [n]MCPP nanorings to remain stable while interacting with PCT drug is crucial. Moreover, the favorable solvation energy implies that the [n]MCPP nanorings are less likely to aggregate or degrade, which could otherwise interfere with the selectivity of the sensing process.

The dipole moment plays an important role in understanding the interactions between a nanostructure and a drug. It also helps clarify the asymmetrical charge distribution and reactivity within a system. A higher dipole moment suggests greater reactivity and increased solubility in polar solvents. The dipole moments of the [n]MCPP nanorings and their complexes with the PCT drug are listed in Table 5. The [n]MCPP nanorings are nonpolar due to their high symmetry. After the interaction of the PCT drug with the nanosheets, the dipole moment increases, with the most significant increase (2.43 Debye) observed for the PCT@⁶MCPP complex. Therefore, PCT@⁶MCPP demonstrates greater reactivity and solubility in water.

Work function (Φ)

The work function (Φ) plays a vital role in the development of an effective drug detection device. It represents the minimum energy needed to liberate a bound electron from its Fermi energy level within a solid and move it to a vacuum state. It is defined as the difference between the Fermi level energy (E_FL) and the vacuum level energy (V_vac(∞)). The term V_vac(∞) refers to the electrostatic potential energy of an electron when it is far removed from a material, where its potential energy approaches zero. Consequently, the work function can be defined as the negative of the Fermi level energy. Furthermore, the following equation is used to calculate the percentage change in work function (%ΔΦ).

Table 6 presents the values of the work function along with their corresponding percentage changes. The graphical representation of work function values is depicted in Fig. 10. The work function value for the nanorings increases after interaction with the PCT drug. The highest change in work function occurs in the PCT@⁶MCPP complex, with a value of 0.84 eV. The rise in work function values is attributed to the low energy gap values of the complexes.

Comparison of Work functions between [n] MCPP nanorings and their Complexes with PCT.

Sensor response factor

The sensor response is a crucial factor that determines the sensitivity and detection range for the PCT drug in the examined complexes. The following equation is utilized to calculate the sensor response factor (R)⁶².

where σ_complex and σ_nanocage are the electrical conductivities of complex and nanoring respectively, which can be calculated using the following equation:

In this equation, A is Richardson constant (6 × 10⁵ A m⁻²), T represents temperature (298 K) and K_B is Boltzmann constant (8.318 × 10⁻³ kJ mol⁻¹ K⁻¹). According to the Eq. (11), the low energy gaps observed in the PCT@[n]MCPP complexes promote higher electrical conductivities. The calculated sensitivity values are presented in Table 6. The data indicate that all complexes exhibit positive sensitivity values, suggesting that the PCT drug is detected effectively by the nanorings.

Recovery time (τ)

Calculating recovery time is essential for determining the efficacy of nanostructures as molecular sensors⁶³. A short recovery time may prevent the sensor from adequately interacting with the drug. To optimize sensor performance, achieving an ideal recovery response period for drug detection is essential. Based on transition state theory⁶⁴, the recovery time (τ) for the PCT drug from the nanorings can be estimated using the following equation:

where υ₀ represents the attempt frequency (10¹² s⁻¹). The recovery times recorded for the PCT@⁶MCPP, PCT@⁸MCPP, and PCT@¹⁰MCPP complexes are 1.52 × 10⁻¹¹, 0.31, and 1.47 s, respectively, as shown in Table 6. It suggests that the PCT@[n]MCPP complexes benefit from a short recovery time, particularly for the PCT@⁶MCPP complex.

Scalability for water treatment

The promising interaction energies and outstanding electronic properties observed in the PCT@[n]MCPP complexes suggest that [n]MCPP nanorings could be adapted for use in water treatment systems. By immobilizing the MCPP nanorings in filtration membranes or incorporating them into advanced oxidation processes, it may be possible to create a responsive filtration system capable of selectively capturing paracetamol and potentially other pharmaceuticals and personal care products (PPCPs) from contaminated water sources. The highly rapid recovery time of 1.52 × 10⁻¹¹s for PCT@⁶MCPP indicates that the⁶MCPP nanorings could facilitate quick release cycles, allowing for continuous operation in a dynamic water treatment environment and thereby enhancing the sustainability of the system.