Exohedral Adsorption of N-(4-Methoxybenzylidene) Isonicotinohydrazone Molecule onto X<sub>12</sub>N<sub>12</sub> Nanocages (where X=B and Al) and the Effect on Its NLO Properties by DFT and TD-DFT

Tsapi, Charly Tedjeuguim; Tasheh, Stanley Numbonui; Nkungli, Nyiang Kennet; Fouegue, Aymard Didier Tamafo; Alongamo, Caryne Isabelle Lekeufack; Ghogomu, Julius Numbonui

doi:https://doi.org/10.1155/2023/5287422

Journal of Chemistry

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Research Article | Open Access

Volume 2023 | Article ID 5287422 | https://doi.org/10.1155/2023/5287422

Exohedral Adsorption of N-(4-Methoxybenzylidene) Isonicotinohydrazone Molecule onto X₁₂N₁₂ Nanocages (where X=B and Al) and the Effect on Its NLO Properties by DFT and TD-DFT

Charly Tedjeuguim Tsapi,¹Stanley Numbonui Tasheh,²Nyiang Kennet Nkungli,²Aymard Didier Tamafo Fouegue,³Caryne Isabelle Lekeufack Alongamo,¹and Julius Numbonui Ghogomu^1,2

Academic Editor: Franck Rabilloud

Received23 Jan 2023

Revised13 Apr 2023

Accepted19 Apr 2023

Published02 May 2023

Abstract

This study reports the nonlinear optical (NLO) properties of the exohedral adsorption of N-(4-methoxybenzylidene) isonicotinohydrazone (INH) onto B₁₂N₁₂ and Al₁₂N₁₂ nanocages. All ground state computations were performed using the density functional theory (DFT) method at the B3LYP-D3/6-311G(d,p) level of theory in the gaseous phase. Excited state computations were achieved via the time-dependent density functional theory (TD-DFT) at the CAM-B3LYP/6-311G(d,p) level of theory. Molecular electrostatic potential (MEP) analysis of INH reveals the presence of three preferential interaction sites: the O-atom of carbonyl (site 1), the N-atom of pyridine (site 2), and the N-atom of the azomethine group (site 3). The highest interaction energy values for the adsorption of INH onto the B₁₂N₁₂ and Al₁₂N₁₂ were −43.560 and −52.724 kcal·mol⁻¹, respectively, indicating a chemisorption process. The computed Gibbs free energy change (ΔG_ad) and adsorption enthalpy change (ΔH_ad) values for all complexes studied are negative, indicating that the adsorption process is spontaneous and exothermic. Quantum theory of atoms in molecules (QTAIM) analysis reveals that the adsorbate-adsorbent interactions are partially covalent, which agrees with the reduced density gradient (RDG) analysis. Exohedral adsorption on the nanocages reduces the band gap, which ranges between 2.851 eV and 6.748 eV, according to density of state (DOS) diagrams. Furthermore, the first and second hyperpolarizabilities (β_tot and γ_tot) were also determined. The outcomes show that adsorption improves these values over INH, and the complexes could be useful materials in optoelectronics and the development of more responsive NLO devices.

1. Introduction

In recent years, the search for nonlinear optical (NLO) materials for applications in the field of modern laser technology, photonics, optical transmission, switching, sensing and computing, electronics and optoelectronics, and telecommunication is on a constant upsurge [1–3]. Theoretical and experimental studies reveal that boron nitride (BN) and aluminum nitride (AlN) nanocages are excellent adsorbents and are generally used in optoelectronics [4–8]. B₁₂N₁₂ and Al₁₂N₁₂ appear to be the most interesting nanocages because of their structural stabilities, high thermal conductivities, and their capacities to be adsorbed at the sites of the analytes [9–12]. The NLO properties of B₁₂N₁₂ and Al₁₂N₁₂ have been studied theoretically by Shakerzadeh et al. and their results show that dopants increase the hyperpolarizability values of B₁₂N₁₂ and Al₁₂N₁₂ [8]. Organic materials with push-pull (D-π-A) structures exhibiting NLO properties are characterized by a strong intramolecular charge transfer (ICT) and exist only in noncentrosymmetrical materials [13, 14]. Hydrazone compounds have been studied as organic nonlinear optical materials [15]. Namitha et al. showed that benzaldehyde, 2-hydroxy,-[2-hydroxyphenyl)methylene]hydrazone has fascinating NLO properties with second-order responses approximately 4 times greater than that of urea [16]. The adsorption of compounds by B₁₂N₁₂ nanocages such as cyanogen [12], trinitroanisole [17], cysteine [6], melphalan [5], glyphosate herbicide [18], superhalogen (AlF₄) [19], and urea [20] has been investigated. In the same vein, several compounds such as hydrogen peroxide [21], 5-fluorouracil [22], acetylene and ethylene molecules [23], hydrogen [7], and sulfanilamide [24] have been adsorbed on Al₁₂N₁₂. The NLO properties of cyanogen fluoride complexes on the surface of boron nitride nanocage have also been investigated, and the results reveal that the 3H⁺ functionalized B₁₂N₁₂ in the presence of cyanogen fluoride is optically active [2]. Similarly, the NLO properties of B₁₂N₁₂ doped with super halogen have been investigated, and the findings reveal its suitability for NLO applications [19]. Accordingly, it may be possible to improve the NLO response of organic compounds by adsorbing them onto nanocages. The development of materials with high hyperpolarizability and good chemical and thermal stabilities in optoelectronics is still a challenging task nowadays. The adsorption of organic compounds onto B₁₂N₁₂ and Al₁₂N₁₂ nanocages is of great interest in optoelectronics for the design of more efficient NLO devices [19].

Kudrat-E-Zahan et al. [25] demonstrated the antimicrobial properties of N-(4-methoxybenzylidene) isonicotinohydrazone (INH) (see Figure 1).

Tedjeuguim et al. [26] reported the NLO properties of INH and some derivatives and the NLO properties of some of its transition metal complexes [27]. Results from these studies reveal that INH, its derivatives and the transition metal complexes studied, are potent NLO materials that could serve in producing optoelectronic devices. Even though some studies exist on the NLO properties of INH, there is no theoretical evaluation of the adsorption of INH on the B₁₂N₁₂ and Al₁₂N₁₂ nanocages and the effects of this adsorption on its NLO properties. INH presents a delocalized π-electron system with several possible electron-rich sites; its adsorption at the external surface of these nanocages is feasible and could enhance its NLO properties. In a bid to shed light on the statement of the problem, this study was designed to investigate the adsorption of INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages and to assess the effect of (the adsorbed cages) these cages on its NLO optical properties using the DFT method. To achieve this, geometric, electronic, and thermodynamic parameters as well as analyses of UV spectra, quantum theory of atoms in molecules (QTAIM), and noncovalent interaction (NCI) have been performed and discussed herein. Furthermore, the reactive site selectivity of the investigated compounds was visualized using molecular electrostatic potential (MEP) maps while NLO susceptibilities were studied by determining the dipole moment (μ), isotropic first hyperpolarizability (β), and the isotropic second hyperpolarizability (γ) of the studied compounds. The findings of this study could be very insightful in optoelectronics and the development of more responsive NLO devices.

2. Computational Details

The adsorption of INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages was studied using the density functional theory (DFT) method. The Gaussian 09, revision D.01 program [28] was employed for all quantum calculations. GaussView 6.0.16 visualization software [29] was employed for the preparation of input structures and visualization of the optimized geometries as well as molecular orbitals. Geometry optimizations and frequency computations were achieved by employing the B3LYP functional [30] extended with an empirical dispersion term (D3) [31] and associated with the Pople style 6-311G(d,p) standard basis set [32]. The Gauss Sum 2.2.5 software [33] was used to produce density of states (DOS) diagrams. Quantum theory of atoms in molecules (QTAIM) and noncovalent interaction (NCI) analyses were used to characterize the type of interactions in the investigated compounds using Multiwfn 3.3.7 software [34]. Absorption spectra were simulated with the time-dependent density functional theory (TD-DFT) method at the CAM-B3LYP/6-311G(d,p) level [30]. All calculations were performed under standard conditions (298.15 K and 1 atm). The adsorption energy (E_ad), enthalpy change (ΔH_ad), entropy change (ΔS_ad), and Gibbs free energy change (ΔG_ad) of the mentioned systems were evaluated through the following equation:where E, G, H, and S represent the total electronic energy (sum of electronic and ZPE), Gibbs free energy, the enthalpy, and the entropy of each compound, respectively, while nanocage represents either B₁₂N₁₂ or Al₁₂N₁₂.

Frontier molecular orbital-based parameters such as band gap (), chemical potential (µ), chemical hardness (η), chemical softness (σ), electrophilicity (ω), and the maximum transferred charge (ΔN_max) were calculated via the following equation [5]:where and represent the energy of the lowest unoccupied molecular orbital and the energy of the highest occupied molecular orbital, respectively [5, 17].

The nonlinear optical parameters such as the dipole moment (μ), polarizability (isotropic and anisotropic ), isotropic first hyperpolarizability (β), and isotropic second hyperpolarizability (γ) values were computed at the x, y, and z components using the following equations [35–38].wherewith known (4) becomes:where , , , , , , , , and are the tensor components for second-order nonlinear responses (first hyperpolarizability).where , , , , , and are the tensor components for third-order nonlinear responses (second hyperpolarizability). In this study, the first hyperpolarizability (β) of the molecular systems under investigation was compared to that of urea at the same level of theory, which is a prototype material used for second-order NLO responses [39]. In the same vein, the second hyperpolarizability (γ) of our compounds were compared to that of paranitroaniline (PNA) at the same level of theory, which is one of the reference materials utilized for third-order NLO responses of the conventional D-π-A (donor-pi-acceptor) [39].

3. Results and Discussion

3.1. Optimized Structures and Thermodynamic Parameters

To find the most stable configurations (Conf) of the adsorbed INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages, several possible adsorption structures were evaluated. The molecular electrostatic potential (MEP) map of INH shows three preferential electron-rich sites (see Figure 1): the O-atom of the carbonyl (site 1), N-atom of pyridine (site 2), and N-atom of the azomethine group (site 3). The labels, Conf1, Conf2, and Conf3, are used to ease the discussion of results. In these configurations, Lewis-type acid-base interactions are of paramount importance, where INH acts as the electron donor (Lewis base) and the nanocages as the electron acceptor (Lewis acid). It is worth noting that no imaginary frequencies were discovered after geometry optimization and frequency computations, showing that the geometries are minima on their potential energy surfaces. The optimized Cartesian coordinates of the studied compounds are provided in Tables S1–S8 of the accompanying supplementary file (SF). The optimized structures alongside the interatomic distances between INH and the pure nanocages are presented in Figure 2.

Figure 2 shows that the C=O, C=N, and C-N bond lengths after optimization of INH are 1.210, 1.283, and 1.334 Å, respectively. These distances are found to increase to 1.251, 1.296, and 1.345 Å, respectively, upon adsorption on B₁₂N₁₂ fullerene-like nanocage (leading to Conf1, Conf2, and Conf3 complexes, respectively). Moreover, there is an increase in the B-N bond length for the free B₁₂N₁₂ nanocage from 1.485 to 1.565 Å (for Conf1), 1.485 to 1.514 Å (for Conf2), and 1.485 to 1.580 Å (for Conf3). Similarly, Figure 2 shows that the Al-N bond lengths for pure Al₁₂N₁₂ fullerene are 1.789 Å. Upon interaction of INH with the Al₁₂N₁₂ nanocage, these values are increased to 1.810 Å (for Conf1), 1.820 Å (for Conf2), and 1.811 Å (for Conf3). This increase indicates a strong adsorption process, and this observation is similar to that obtained in [20], for a similar study. According to Dagdag et al. [40], adsorbate-adsorbent bond lengths ranging from 1–3.5 Å suggest chemisorption, while those longer than 3.5 Å reflect physisorption. In the present study, these distances are 1.592, 1.622, and 1.617 Å for Conf1, Conf2, and Conf3 of the B₁₂N₁₂ nanocage, respectively. In the same light, those for Conf1, Conf2, and Conf3 of the Al₁₂N₁₂ nanocage are 1.892, 2.002, and 2.006 Å, respectively. Based on these findings, the adsorbate-adsorbent interactions of the molecules under consideration are chemical in nature.

To understand the thermodynamic process of INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages, adsorption energy (E_ad), enthalpy changes (ΔH_ad), entropy variations (ΔS_ad), and Gibbs free energy variations (ΔG_ad) were evaluated and are listed in Table 1.

The findings indicate that the adsorption energies (E_ads) of the studied compounds are energetically favourable and follow the order: B₁₂N₁₂Conf3 < B₁₂N₁₂Conf2 < B₁₂N₁₂Conf1, for the B₁₂N₁₂ complexes. This implies that B₁₂N₁₂Conf3 is the most stable configuration of the B₁₂N₁₂ complexes since it has the lowest adsorption energy (i.e., −43.560 kcal·mol⁻¹). Likewise, the findings show that all Al₁₂N₁₂ complexes are energetically favourable and follow the sequence: Al₁₂N₁₂Conf3 < Al₁₂N₁₂Conf1 < Al₁₂N₁₂Conf2. This result is due to the fact that Al₁₂N₁₂Conf3 has the most stable configuration with the lowest adsorption energy, E_ads (i.e., −52.724 kcal·mol⁻¹). The E_ad values of all complexes are in the range −52.724 to −31.757 kcal·mol⁻¹, confirming that INH is chemisorbed at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages. This finding is similar to another [41] that indicates a chemisorption mechanism using similar materials. This result also indicates that Al₁₂N₁₂Conf3 has the most stable configuration as compared to B₁₂N₁₂Conf3. It is worth mentioning that the E_ads sequence is the same as that of the Gibbs free energy. The ΔG_ads values fall within the range −28.954 to −8.030 kcal·mol⁻¹. These negative values suggest that the formation of the investigated complexes is spontaneous and thermodynamically stable. In the same vein, the ∆H values follow the same sequence as ∆G_ads with values ranging from −42.155 to −21.226 kcal·mol⁻¹, implying that the adsorption process is exothermic. The values of the entropy change (ΔS_ad) are all negative, implying that the adsorbate (INH) formed an aggregate with the adsorbents (B₁₂N₁₂ and Al₁₂N₁₂).

3.2. Electronic Properties, Density of State (DOS), and Molecular Electrostatic Potential (MEP)

The DFT and TD-DFT methodologies were used to explore the frontier molecular orbitals. For this study, the computed parameters using the DFT method outperforms those from the TD-DFT method (see Table S13). As a result, the outcomes of the DFT approach, which are presented in Table 2, were used in the discussion that follows.

Literature holds that molecules with very low energy gaps require low energy to transfer an electron from the ground state to the excited state, while those with very large band gaps require a lot of energy [17]. The findings reveal that the HOMO values are shifted from −7.855 eV (for pure B₁₂N₁₂) to −6.888(−6.415 eV), for the B₁₂N₁₂ complexes, while the LUMO values are shifted from −1.107 eV (for pure B₁₂N₁₂) to −3.093(−2.787 eV), for the B₁₂N₁₂ complexes. A similar pattern can be seen for pure Al₁₂N₁₂ and its complexes. These data points imply that the HOMOs are destabilized while the LUMOs are stabilized, resulting in a decrease in the energy gap (Eg) values of INH as it is adsorbed on the external surfaces of B₁₂N₁₂ and Al₁₂N₁₂ nanocages. This finding is consistent with the outcomes of Mohammadi et al. [42]. In addition, the results show that all configurations of B₁₂N₁₂ and Al₁₂N₁₂ complexes (Conf1-Conf3) are better conductors than INH and pure nanocages. Indeed, the semiconductor properties of B₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf1 compounds are better, with E_g values of 3.322, 3.008, and 2.851 eV, respectively. Lower values of the materials enhance polarizability and hyperpolarizability of NLO responses [43]. Soft molecules have a low chemical hardness value (η) and are therefore the most energy reactive [17]. The global hardness of all studied compounds is in the range 1.4253.374 eV. Among these compounds, Al₁₂N₁₂Conf1 has a very low hardness value and is therefore the most reactive. Materials with high and positive electrophilicity index (ω) and charge transfer parameter (ΔN_max) values have a greater tendency to absorb an electron. However, if a molecule has a low amount of these indices, it may act as an electron donor [5]. The ΔN_max and ω values for all studied systems are in the range 1.328–3.008 eV and 2.975–6.832 eV, respectively. Hence, the positive ΔN_max values show that there is electron transfer between INH and the nanocages. The high ΔN_max value of Al₁₂N₁₂Conf1 (3.008 eV) suggests that this compound has a greater tendency to absorb an electron as compared to the others. Moreover, it can be seen from Table 2 that Al₁₂N₁₂ complexes have better charge transfer characteristics when compared with B₁₂N₁₂ complexes. The distribution of the frontier molecular orbitals of the studied compounds are depicted in Figure 3.

The total density of states (DOS) of INH, pure B₁₂N₁₂, and Al₁₂N₁₂ nanocages and their complexes was determined from the HOMO and LUMO outputs, employing the Gauss Sum software [33], and the results are illustrated in Figure 4.

The DOS diagrams of pure B₁₂N₁₂ and Al₁₂N₁₂ nanocages change after adsorbate-adsorbent interactions. In a similar manner, the adsorption of INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages induces a variation in the HOMO and LUMO orbitals as compared to those of the pure nanocages. This change in orbitals leads to the reduction of the HOMO-LUMO energy difference and increases the conductivity of materials.

MEP plot is an important tool to predict the reactive sites for electrophilic and nucleophilic attack. Positive and negative electrostatic potential regions in the MEP plots are represented by the blue and red, respectively [6]. The red and blue colours in the MEP surfaces are indicative of electron-rich and electron-deficient sites in a molecule, respectively, while the green colour shows neutral electrostatic potential [43]. The MEP plots of the investigated compounds were computed and the results are shown in Figure 5.

Figure 5 shows a red colour on the peripheral side of the oxygen atom of the carbonyl, and a yellow colour on the nitrogen of pyridine and the nitrogen of the azomethine groups in INH. These are the most likely sites for electrophilic attack. It can also be inferred from this figure that the electron density is localized on the O-atom of carbonyl, N-atom of pyridine, and N-atom of the azomethine group. Thus, INH can approach the B₁₂N₁₂ and Al₁₂N₁₂ nanocages by the O-atom of the carbonyl group, N-atom of the pyridine group, and N-atom of the azomethine group. In contrast, the blue colour is predominant on the proton of the azomethine and methoxide groups and reflects the sites for nucleophilic attacks.

For the case of the pure nanocages, the B and Al atoms show electrophilic character (blue), while the N atom shows nucleophilic character (red). B₁₂N₁₂Conf1 and Al₁₂N₁₂Conf1 show that red is localized on the N atom of the pyridine group, implying that it is susceptible to electrophilic attack, while the rest of the molecule in blue represents the site for nucleophilic attacks. In the same light, B₁₂N₁₂Conf2 and Al₁₂N₁₂Conf2 show that the red is mainly on the O-atom of the carbonyl group, indicative of nucleophilic character, while the rest of molecules in blue are electron deficient. B₁₂N₁₂Conf3 and Al₁₂N₁₂Conf3 show that red is localized on the O-atom of the carbonyl group, N-atom of the pyridine group, implying nucleophilic character, while the rest of molecules in blue represent the sites for nucleophilic attack.

3.3. Quantum Theory of Atoms in Molecules (QTAIM) Analysis

To understand the nature of interactions between INH and the B₁₂N₁₂ or Al₁₂N₁₂ nanocages, QTAIM parameters [44] at the bond critical point (BCP) between INH and the nanocages were calculated. The total electronic densities (ρ(r)), Laplacian of electron densities (∇²ρ(r)), the total electronic energy (H(r)), the potential energy (V(r)), and the kinetic energy (G(r)) at the bond critical points (BCP) were determined for all the systems to apprehend the nature of interactions [45]. According to Cremer et al., a bond can be described as noncovalent (electrostatic) when H(r) values are positive, while negative values indicate partially covalent interactions [46]. The −G(r)/V(r) ratio was used to determine the strength of the interaction between INH and the nanocage as elsewhere [22]. According to QTAIM theory, high values of ρ(r) (generally higher than 0.1 a.u), ∇²ρ(r) < 0 a.u, and −G(r)/V(r) < 1 a.u are generally associated with covalent bonds [47]. Low values of ρ(r) (generally less than 0.1 a.u), ∇²ρ(r) > 0 a.u, and 0.5 < -G(r)/V(r) < 1 a.u characterize intermediate type interactions such as partially covalent bonds and coordination bonds [48, 49]. Low values of ρ(r) (generally less than 0.1 a.u), ∇²ρ(r) > 0 a.u, and −G(r)/V(r) > 1 a.u are associated with the noncovalent bonds interactions like ionic and van der Waals [50]. Table 3 shows the QTAIM parameters of the adsorbate-adsorbent bonds of the studied compounds.

The results indicate that the calculated H(r) values of the adsorbate-adsorbent bonds of B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3 are all negative, while their ∇²ρ(r) values are all positive. This indicates partially covalent interactions. Meanwhile, the H(r) and ∇²ρ(r) values of Al₁₂N₁₂Conf1 bonds are positive, implying weak interactions between the adsorbate-adsorbent bond. The results also show that the −G(r)/V(r) values of the adsorbate-adsorbent bonds are 0.741, 0.635, 0.578, 0.987, and 0.975 a.u for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3, respectively. These values are associated with partially covalent interactions, since they are between 0.5 and 1 a.u. However, the −G(r)/V(r) value of Al₁₂N₁₂Conf1 bond is 1.079 a.u, implying a noncovalent nature of bonds between the adsorbate and the adsorbent. The molecular graphs showing the bond critical point (BCP) of interaction between INH and the nanocages are depicted in Figure 6.

3.4. Noncovalent Interaction (NCI)

The noncovalent interaction method is used to understand the weak interactions between the INH and nanocages. The reduced density gradient (RDG) method is a very powerful way to analyse weak interactions and can be seen as an extension of QTAIM theory for visual research [34]. The noncovalent interaction index is based on the RDG, which depends on the electron density ρ(r) and its first derivative ∇ρ(r) [51].

Different types of interactions are determined based on sign(λ₂)ρ(r), which is the product between the sign of the hessian matrix (λ₂) and the electron density ρ(r). Plots of RDG and signλ₂(r)ρ(r) are used to identify specific areas of the noncovalent interaction. The points that are located in the sign(λ₂)ρ < 0 (blue), sign(λ₂)ρ ≈ 0 (red), and sign(λ₂)ρ > 0 (green) represent the attractive interaction (H-bonding), the van der Waals interaction and repulsion interaction, respectively [51]. The reduced density gradient plots of interaction between INH and the nanocages are depicted in Figure 7.

The RDG distribution for all the systems shows that many points are observed in the sign(λ₂)ρ < 0 (blue) region compared to the other regions. This reveals that the interactions between INH and the nanocages (B₁₂N₁₂ and Al₁₂N₁₂) are attractive.

3.5. UV Spectral Analysis via TD-DFT

The absorption energies, oscillator strengths, wavelengths of absorption, and orbital coefficients of INH and their complexes on the surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages are summarized in Table 4.

The results show that the oscillator strengths for pure B₁₂N₁₂ and Al₁₂N₁₂ are zero and change upon the adsorption of INH. Complexation enhances the oscillator strength of pure nanocages (B₁₂N₁₂ and Al₁₂N₁₂) and the values 0.35, 0.29, 0.61, 0.31, 0.28, and 0.61 are obtained for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3, respectively. The excitation energies (E_abs) are 6.30 and 4.03 eV for pure B₁₂N₁₂ and Al₁₂N₁₂, respectively. Meanwhile the values are 4.43, 4.21, 4.17, 4.20, 4.33, and 4.20 eV for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3, respectively. These results suggest that smaller E_abs values for complexes lead to higher values of oscillator strength and can enhance NLO response. The absorption peaks are at 279, 294, 296, 294, 286, and 294 nm for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3, respectively. The B₁₂N₁₂Conf1 show lower λ_abs values and show more transparency than others. The UV spectra of the INH and the various configurations are presented in Figure 8 in gas phase.

3.6. Nonlinear Optical Properties

According to Khalid et al. [52–55], the NLO feature is associated with calculated values that explain structural and electronic properties. Table 5 exhibits the dipole moments, polarizabilities, as well as the first and second hyperpolarizabilities of the compounds explored. The supplementary file (Tables S9–S12) contains detailed information on their main contributing tensors. The nonlinear values were converted into electrostatic units (esu) using the conversion factor 1 atomic unit (a.u.) = 0.15 × 10^–24 esu for polarizability (α_tot), 1 a.u = 8.6393 × 10^–33 esu for total first hyperpolarizability (β_tot), and 1 a.u = 0.50367 × 10^–39 esu for total second hyperpolarizability (γ_tot) [37].

The dipole moment relates directly to the solubility of the investigated compounds. A compound with higher dipole moment will have higher solubility in polar solvents such as water [5]. The results show that the dipole moments of pure B₁₂N₁₂ and Al₁₂N₁₂ are zero, suggesting they are insoluble in water. The change in dipole moment during adsorption shows a charge transfer between adsorbate-adsorbents and enhancement of NLO responses. The dipole moment tensor along the x-axis (μ_x) contributes the most to total values, while those along the y and z-axes contribute the least (see Table S9 in the SF). From Table 5, the dipole moment of the compounds increases in the order INH < Al₁₂N₁₂Conf3 < Al₁₂N₁₂Conf2 < B₁₂N₁₂Conf3 < Al₁₂N₁₂Conf1 < B₁₂N₁₂Conf2 < B₁₂N₁₂Conf1. This shows that B₁₂N₁₂Conf1 will have a stronger solubility in polar solvents.

Table 5 also depicts that the isotropic polarizabilities () of pure B₁₂N₁₂ and Al₁₂N₁₂ are 22.514 × 10^–24 and 43.173 × 10^–24 esu, respectively. These values increase on doping the nanocages with INH, giving the values 53.978, 53.610, 53.977, 73.574, 74.167, and 75.268 × 10^–24 esu for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf1, respectively. Similarly, the anisotropic polarizabilities () of the complexes increase when contrasted with pure nanocages. These findings indicate that increasing polarizability can improve NLO responses. The average polarizability tensor values along the x-axis (α_xx) are the primary contributors among all the remaining tensor components, as can be seen in Table S10 of the SF.

According to Table 5, the pure B₁₂N₁₂ and Al₁₂N₁₂ nanocages have no second-order NLO responses, which is consistent with their first hyperpolarizabilities. The adsorption of INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages increases the first hyperpolarizability values significantly. The hyperpolarizability values are 14.230, 20.019, 13.105, 17.475, 16.508, and 19.493 × 10^–30 esu for B₁₂N₁₂Conf1, B₁₂N₁₂Conf2, B₁₂N₁₂Conf3, Al₁₂N₁₂Conf1, Al₁₂N₁₂Conf2, and Al₁₂N₁₂Conf3, respectively. The presence of charge transfer between the nanocages and INH increases the first hyperpolarizability value after complexation. As a result, adsorption plays an important role in increasing the first hyperpolarizability of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages. The first hyperpolarizabilities of the compounds examined show that the main contribution tensor component is along the z-axis (see Table S11 in the SF). The first hyperpolarizability of urea (β_tot = 0.777 × 10^–30 esu) was computed at the same level of theory as that of the molecules studied and compared. The predicted first hyperpolarizability of the studied complexes is much greater than that of urea. Based on the ongoing, B₁₂N₁₂Conf2 has the highest first hyperpolarizability value and is approximately 26 times higher than urea. It is therefore considered as the best candidate for second-order NLO responses.

According to the data in Table 5, the second hyperpolarizability (γ_tot) for pure B₁₂N₁₂ and Al₁₂N₁₂ nanocages are 6.17 and 67.84 × 10^–36 esu, respectively. Upon adsorption, these values change and increase in the order: B₁₂N₁₂Conf3 < B₁₂N₁₂Conf1 < B₁₂N₁₂Conf2 < Al₁₂N₁₂Conf3 < Al₁₂N₁₂Conf1 < Al₁₂N₁₂Conf2. The γ_tot value for PNA (7.615 × 10^–36 esu), reference molecule for second hyperpolarizability, was computed at the same level of theory as that of the studied molecules. Based on these results, Al₁₂N₁₂Conf2 has the highest second hyperpolarizability value (205.23 × 10^–36 esu) and is approximately 27 times higher than paranitroaniline. Al₁₂N₁₂Conf2 is consequently the most potential candidate for third-order NLO responses. The x-axis is found to have the dominant tensors for the total values of the molecules under study (see γ_xxxx values in Table S12 of the SF).

4. Conclusion

In this work, DFT and TD-DFT calculations were used to investigate the adsorption of INH at the external surface of B₁₂N₁₂ and Al₁₂N₁₂ nanocages, as well as the overall effect on their nonlinear optical properties. Molecular electrostatic potential (MEP) analyses of the adsorbate reveal three preferential interaction sites: the O-atom of the carbonyl (site1), the N-atom of pyridine (site2), and the N-atom of azomethine (site3) group, all of which are electron-rich regions. The geometrical parameters indicate bond lengths between the INH molecule and nanocages (B₁₂N₁₂ and Al₁₂N₁₂) in the range 1.592 to 2.006 Å. The energy gap of the INH-nanocage complexes are reduced as compared to those of the adsorbate and adsorbents, and therefore the conductivities of the systems are increased. The adsorption energy (E_ad) values and enthalpy changes (ΔH_ad) of the complexes show that the chemisorption of the INH at the external surface of the B₁₂N₁₂ and Al₁₂N₁₂ nanocages is an exothermic process. The Al₁₂N₁₂Conf3 is found to be the most stable configuration because it has the E_ads (−52.724 kcal·mol⁻¹). The negative values of Gibbs free energy changes (ΔG_ad) and entropy variations (ΔS_ad) reveal that the adsorption is spontaneous and the adsorbate (INH) aggregates with the adsorbents (B₁₂N₁₂ and Al₁₂N₁₂). The RDG and QTAIM analyses indicate the adsorbate and adsorbents have partially covalent interactions. The predicted first hyperpolarizability and second hyperpolarizability values for all complexes are much greater than those of urea and paranitroaniline, respectively. These complexes could be useful materials in optoelectronics and the development of more responsive NLO devices.

Data Availability

The data used to support the findings of the study are included within the manuscript and supplementary file.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors thank the Cameroonian Ministry of Higher Education through the research modernization grants to lecturers of higher and tertiary education for their support.

Supplementary Materials

The supplementary material contains tables as a part of this work. Tables S1–S8 give the optimized geometrical coordinates, Tables S9–S12 give the nonlinear tensors, and Table S13 gives the frontier molecular parameters using DFT and TD-DFT methods of the studied compounds. (Supplementary Materials)

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