High incorporation of magnetite nanoparticles inside tetraaza macrocyclic Schiff base cavity: spectroscopic characterization and modeling by DFT calculation

This work presents a simple synthesis of tetraaza macrocyclic Schiff base ligand (C40H28N4), its complex [(C40H28N4)@Fe(II)], and a novel complex of magnetite Fe3O4NPs incorporated inside tetraaza macrocyclic cavity [(C40H28N4)@Fe3O4NPs] by the co-precipitation method in order to obtain well-dispersed nanoparticles, controlled size and prevent the aggregation of Fe3O4 NPs due to strong dipole–dipole magnetic attractions and interactions between particles. The characterization and structural identification were carried out by X-ray spectroscopy as well by 1H NMR, 13C and DEPT 135 NMR spectroscopy, FT-IR, UV–visible, EDX, TGA, and finally by VSM using both experimental and theoretical methods. XRD measurements indicate that the presence of Schiff's bases does not modify the crystal structure of the nanoparticles (11.05 nm). All the NMR spectra suggested the success of the synthesis of all structures with high purity. FTIR was used to illuminate the presence of Fe3O4NPs in tetrahedral and octahedral sites as well as their coordination with imine (C = N) of tetraaza macrocyclic. The UV–visible spectra and frontier molecular orbitals (FMOs) of the title compounds were calculated at TD-DFT/CAM-B3LYP-D3/6–311 G (d, p) level of theory. The corresponding calculated result yield shows a good agreement with the experimental data. The morphological characterization of the nanoparticles was carried out by SEM, which revealed that the shape of the NPs was generally spherical. The SEM images also show that the nanoparticles prepared by in situ with co-precipitation method were able to form stable complexes. Thermal characterization by TGA shows that there are 64% of the magnetite nanoparticles formed in situ, which corresponds to a grafting density of 25 mmol.g−1. The VSM analysis displays a similar magnetic hysteresis loop shape compared to free Fe3O4 NPs, which confirmed a ferromagnetic character due to the significant decrease in saturated magnetization.


Introduction
Macrocyclic Schiff bases and their metal complexes have constituted a field of research in continuous development thanks to their appreciable role based on features of cavity size, rigidity, homo-or hetero-type donor atoms as well as tendency to establish transition metal complexes discovered through macrocyclic ligands [1][2][3][4][5]. Macrocyclic ligands are good candidates with different donor heteroatom(s) in order to arrange molecular topologies of aza (N), sulpha (S), oxo (O), and phospha (P) centers of the cavity [1,2]. These aforementioned are unveiling scope in coordination and bioinorganic chemistry including anticancer, contrasting agents, metal intoxication treatment and magnetic resonance imaging [3][4][5]. The synthesis of macrocyclic ligands Schiff bases tetradentates and their transition metal complexes have been widely studied due to their attractive chemical properties and biological activities [2,[6][7][8] and the presence of amino groups similar to the natural biological structure like hemoglobin and chlorophyll [9,10]. In fact, macrocyclic Schiff bases are particularly important in macrocyclic chemistry because of their flexible synthesis, their selectivity, and even their ability to stabilize many metals in various oxidation states [11][12][13][14][15]. However, a huge number of tetraaza macrocyclic (N 4 ) metal complexes show interesting biological activities such as antifungal [16,17], antibacterial [18][19][20], antimicrobial [21][22][23][24], and anticancer [10,25,26] effects.
On the other hand, the synthesis of magnetic nanomaterials especially magnetite nanoparticles (Fe 3 O 4 NPs) has been attracted due its biocompatibility that show an important role in nanoscience and nanotechnology [27][28][29]. Indeed, magnetite is one of the most abundant ferromagnetic minerals on earth. So, magnetite nanoparticles (Fe 3 O 4 NPs) have been intensively studied due to their interesting chemical and magnetic properties such as size, shape, hydrophobicity, surface functionality, and super magnetic character [30][31][32]. These properties offer the high potential of applications in photocatalyst [33][34][35][36][37][38], biomedical and bioengineering fields such as magnetic resonance imaging (MRI) contrast enhancement agent [30,39], cell separation [40], and drug delivery [29,[41][42][43]. Actually, magnetic iron oxide (Fe 3 O 4 ), which has an inverse spinel structure, forms face-centered cubic with oxygen and in the interstitial octahedral sites and tetrahedral sites is occupied by iron that is present under Fe 2+ and Fe 3+ oxidation states [27,44]. Several methods have been reported in the literature on the synthesis of oxide nanomaterials such as hydrothermal synthesis [45][46][47], sol-gel [48,49], and co-precipitation. Compared to other methods, co-precipitation is the most convenient way to synthesize the magnetic iron oxide nanoparticles because of its lower reaction temperature, easy operation, high nanocrystal purity, and eco-friendly procedure [50,51].
However, the co-precipitation method usually shows the difficulty to control nanoparticle size and distribution size due to the strong dipole-dipole interactions, which lead to the formation of Fe 3 O 4 NPs aggregated, and the disappearence of magnetic properties [18,52].
To conserve these magnetic properties of NPs, Chaabane et al. [18] succeeded in synthesizing magnetite Fe 3 O 4 NPs incorporated in the tetraaza macrocyclic Schiff base cavity. Therefore, the NPs were successfully dispersed and their size was controlled by keeping magnetic properties, which have shown a very interesting biological activity.
The aim of this work was the synthesis of a tetraaza macrocycle Schiff base ligand more stable and more conjugated through the condensation of benzil and o-phenylenediamine followed by the complexation of iron (II) with the ligand as intermediate. Then, the in situ growth of the Fe 3 O 4 NPs inside the tetraaza macrocyclic was produced by a novel co-precipitation technique that gives nanoparticles of magnetite with uniform size and good dispersed over the tetraaza macrocycle, which have a very interesting property. All these products were studied experimentally as well as theoretically by many physicochemical techniques like XRD, NMR, FT-IR, UV-visible. Furthermore, in this paper, SEM, EDX, TGA, and VSM have been employed to characterize and evaluate the incorporation of magnetite NPs onto tetraaza macrocycle.

Characterizations
1 H NMR (300 MHz) and 13 C (75 MHz) spectra were measured by Burker 300 spectrometer in DMSO-d 6 . The infrared spectra FTIR were recorded in the range of 4000-400 cm −1 using a PerkinElmer spectrum in KBr disks. The UV-VIS absorption spectra were measured by spectrophotometer UV-visible SPECORD/200 plus. The field emission scanning electron microscope (SEM) and the energy-dispersive X-ray (EDX) were taken by SEM, FEI Quanta 250 FEG, Eindhoven, Netherlands. Powder X-ray diffraction (XRD) was carried out using a Bruker D8 Advance diffractometer with monochromatic CuKα source operated at 40 kV and 40 mA. Patterns were collected in steps of 0.02°(2θ) over the angular range 1-10.0°(2θ), with an acquisition time of 25 s per step. Additionally, XRD patterns were recorded over a wider angular range, 10-80°(2θ) to determine the presence of segregated crystalline phases. TGA curves were recorded with a Setaram Setsys 16/18 thermobalance under an N 2 atmosphere flowing at 25 mL per min (heating rate of 5 °C/min). The magnetic properties were measured using a superconducting quantum design (MPMS, SQUIR-VSM).

Quantum chemical calculation
The optimized structural parameters of synthesized compounds have been performed at DFT/B3LYP [53] with the empirical dispersion correction D3 of Grimme et al. [54] methods with 6-311G (d, p) basis sets using the Gaussian 09 program [55]. B3LYP-D3/6-311G (d, p) was found to provide a good compromise between accuracy and computation time for structure optimizations. Also, we have found that B3LYP-D3 gives the lowest gap energy and is the closest to the experimental results when compared to the other functional ones. Moreover, 6-311G (d, p) was commonly used in the literature [56,57] where it indicates an efficient and robust basis for III-V semiconductor computations [58]. The 1 H and 13 C NMR calculations utilized the Gauge-Independent Atomic Orbital (GIAO) [59] method. In all cases, 1 H and 13 C NMR for the test molecules were corrected with chemical shift δ (ppm) relative to computed values for tetramethylsilane (TMS), simulated at the same level [60].
Vibrational frequencies have been carried out with the same method as geometry optimization in the gas phase. It has been confirmed that these structures correspond to the characteristics of the local minimum by the absence of an imaginary mode. The simulated harmonic vibrational wavenumbers were scaled down uniformly by a factor of 0.967 for B3LYP-D3/6-311G(d, p) level of theory, which accounts for systematic errors caused by basis set incompleteness, vibrational anharmonicity, and neglect of electron correlation [61].

3
The electronic absorption spectra for optimized molecule calculated at the time-dependent density functional theory (TD-DFT) with CAM-B3LYP-D3/6-311G (d, p) level of theory [62,63] are used to compute energies oscillator and the absorption wavelengths in DMSO solvent. The visualizations were performed by the graphical interfaces GaussView [64].
Moreover, by using the energies of the highest occupied molecular orbital (HOMO) (E HOMO ) and the lowest unoccupied molecular orbital (LUMO) (E LUMO ) for a molecule, electronic gap energy (Eg) , chemical potential ( μ ), global hardness ( η ) and global softness (σ) can be calculated as follows [65]: E g ≈ E LUMO -E HOMO (Electronic gap energy), μ = − E HOMO + E LUMO ∕2(chemical potential), η = E LUMO − E HOMO ∕2 (Global hardness) and = 1∕ (global softness). The chemical potential (µ) characterizes the escaping tendency of electrons from a stable system. The chemical hardness (η) measures the resistance of a molecule to charge transfer. The global softness (σ) is the capacitance of the molecule to acquire charge. The ligand (1) was prepared by dissolving benzil (1 g, 4.76 mmol) in 10 ml of ethanol in the presence of few drops of concentrated sulfuric acid (H 2 SO 4 ) in a 250 mL roundbottom flask. Thus, o-phenylenediamine (0.52 g, 4.76 mmol) was added slowly and was mixed with constant stirring. This mixture was refluxed at 78 °C for 24 h. On cooling, gray crystals' precipitate was formed, which was filtered, washed with cold EtOH, and dried under vacuum over anhydrous MgCl 2 . The whole reaction is shown in Scheme 1.

Synthesis of the Fe (II) complex
Fe (II) complex (2) was prepared by condensation method because the yield of the complex was low as soon as the metal (II) was added with ligand (C 40 H 28 N 4 ). A hot stirring ethanolic solution (20 ml) of o-phenylendiamine (2 mmol) was slowly added to bivalent metal salt Fe(SO 4 )0.7H 2 O (2 mmol). The reaction mixture was heated at 78 °C under argon atmosphere for 30 min. Then, benzil (2 mmol) was added to the refluxing mixture, and refluxing was continued for 24 h as depicted in Scheme 1. Finally, the solid product precipitate was filtered and washed with ethanol and dried under vacuum.

Synthesis of [(C 40 H 28 N 4 )@Fe 3 O 4 NPs]
The preparation of free nanoparticles by the co-precipitation method was widely mentioned in the literature thanks to their different applications. On the other hand, the germination of magnetite nanoparticles in situ on the metal ion complexed in the macrocycle (3) is the novelty of our work. 1.5 g of [(C 40 H 28 N 4 )@Fe(II)] complex is introduced into 250 mL flask previously synthesized in 200 ml of an ethanol/water mixture (ratio 2:1) with severely stirring at 70 °C.
Then, 3 g of FeCl 3 .6H 2 O was added as a source of Fe 3+ ions to the solution. The mixture was reacted for 30 min with constant stirring. After, 20 ml of NH 4 OH (8 M) was injected dropwise into the solution until pH raised to about 10 and stirring continuously for 1 h. The color of the solution was changed from orange to dark brown and then became black denoting the formation of Fe 3 O 4 NPs inside the tetraaza macrocyclic Schiff base ligand. Finally, the solid product was filtered, washed with ethanol and water to remove impurities, and dried under vacuum at 60 °C to remove the excess water. The reaction process is represented in Scheme 1.

XRD
The presence of sharp peaks in the spectrum of the ligand (Fig. 1a) exhibits the crystalline nature of the product. The crystallinity and the intensity of peaks slightly decrease by adding the metal center (Fig. 1b) and the nanoparticles (Fig. 1c) to the ligand [66,67].
In addition, the XRD spectrum of [(C 40 H 28 N 4 )@ Fe 3 O 4 NPs] (Fig. 1c) reveals that the in situ growth of the Fe 3 O 4 magnetite nanoparticles in the tetraaza cavity did not cause a noticeable change in the crystallographic properties of the ligand, which confirms its great stability under the effect of the hyperconjugation. To calculate the size of the nanoparticles developed in situ, we use the FWHM of the most intense peak (311) according to the following Debye-Scherrer equation [70]: where D is the average size of the crystallite, λ is the wavelength of CuK α radiation (λ = 0.154 nm), k is the grain shape factor, considering that the particles are spherical in shape and k takes the value 0.89 (0.9). β is the broadening of diffraction line measured at half maximum in intensity and calculated through this equation β 2 = β 2 observed -β 2 standard (β observed = 0.5731: The value of the experimental spectrum and β standard = 0.5729:The value taken from a reference spectrum [71]) and θ is the Bragg angle of the peak (311). The calculation of D from this equation gives an average size of the Fe 3 O 4 nanoparticles complexed in the tetraaza cavity of the macrocycle around 11,05 nm [72]. This very important result confirms our success in the germination of magnetite nanoparticles in the cavity of a macrocycle from complexed metal ions. Furthermore, the molecular geometries of (a), (b) and (c), presented in Fig. 2, were optimized at B3LYP-D3/6-311 G (d, p) levels. Geometric parameters of these compounds such as the bond lengths (Å) and bond angles (°) are shown in Table 2. They were simulated with the assumption that the solvent used for crystallization is ethanol. In crystallography, the title compounds study has C1 type symmetry. The molecular structure of the ligand (a) (C 40 H 28 N 4 ) exhibits nonplanar distortions of the macrocyclic tetraaza

NMR spectrum analysis
To confirm the structure of the synthesized products (a) ligand (C 40 Table 3. In fact, the synthesized macrocyclic ligand admits a double symmetry as shown schematically in Fig. 3a. This symmetry is clearly seen in the 1 H NMR spectra by the presence only of a quarter of the protons in the structure [73]. In addition, we noticed that our ligand is a macrocycle more or less flat and having a π-σ-type hyperconjugation. This behavior creates a large cycle current generated by the magnetic field of the device, i.e., the movement of electrons π induces a large magnetic anisotropy whose axis is perpendicular to the macrocycle plane that primarily affects the chemical shift of protons and carbons [74] (Fig. 3b). The protons inside this cone are strongly shielded, which is not the case in our macrocycle The H-NMR data for ligand (C 40 H 28 N 4 ) ( Table 3 and Fig. 4a) do not show any signal corresponding to the primary amino protons. This suggests that the proposed Schiff base macrocyclic has been formed. It mainly shows signals Table 2 Selected bond distances (Å) and angles (°) in the molecular structures of (a), (b) and (c)   5 as shown in theoretical spectra at 7.85 ppm. All of the aromatic protons of monosubstituted benzene resonate as a massive δH (20H, 7.3-7.5 ppm) and are theoretically shown between 7.45 and 7.90. Therefore, the integration curves are almost in agreement with the number of protons in the structure, which of course confirms the structure of the ligand synthesized. The 13 C NMR spectrum of the Schiff base tetradentate (Fig. 4b) mainly presented 11 characteristic signals, the main signal of which is observed towards δC (153.05 ppm), corresponds to the azomethine functions (C = N), which by an inductive attracting effect will be the most shielded and subsequently confirmed by theoretical spectra appeared at 164.96 ppm, while the rest of the signals are assigned based on anisotropic effects and even by the theoretical data.
On the 13 C NMR DEPT 135 spectra (Fig. 4c), we see the disappearance of the peaks relating to the quaternary carbons C 1 , C 7 , and C 8 , which confirms the structure proposed for our tetraaza macrocyclic ligand.
By comparing the 1 H, 13 C NMR spectra (Fig. 5b) of the iron complex to that of the free ligand (Fig. 4a), a slight variation in chemical shifts was observed, which proves that the complexation of the metal ion has taken place. On the other hand, the multiplicity of peaks has almost disappeared. Indeed, in the spectrum, we find either broad singlets or broad doublets. It is assumed that this broadening of the peaks is caused by the strong field of Fe(II) in its coordination sphere. Indeed, the Fe(II) ion has a low spin, so its behavior is paramagnetic [75,76]. Hence, the resolution of the 1 H NMR spectrum is slightly reduced. The 13 C NMR spectra are also marked by a change in peak resolution caused by the same phenomenon. The number of peaks in the spectrum confirms the number of carbon atoms in the molecular structure taking into consideration the applied symmetry.
To visualize the phenomenon of paramagnetism, we record the 1 H NMR spectrum of the complex [(C 40 H 28 N 4 )@ Fe 3 O 4 NPs] (Fig. 6), which is a magnetic material possessing magnetization in the presence of a magnetic field (stronger magnetic field). We can therefore see the absence of all signals from aromatic protons. This is also explained by the greater decrease in spectrum resolution. Slight differences between experimental and theoretical values are essentially due to the model used to be taken into account of solvent effect on the molecule. Table 3  carbon of structures. We notice a perfect agreement between the results obtained experimentally and the theoretically and bibliographical data.

IR spectrum analysis
The preliminary identification of the Schiff bases macrocyclic ligand and their complexes have been done by the FTIR. The computed harmonic vibrational wavenumbers were calculated at B3LYP-D3/6-311G (d, p) using scaling factors 0.967, which accounts for systematic errors caused by basis set incompleteness, neglect of electron correlation, and vibrational anharmonicity [77]. The comparative simulated and observed vibrational wavenumbers in the gas phase are gathered in Table 4. The calculated IR spectrum with the experimental FTIR spectra of all products synthesized (a), Fig. 7. We can identify the different vibrations, after calculating the localized modes [78,79] using the graphical interfaces GaussView [64].

(b) and (c) is shown in
Regarding the IR spectrum of the ligand (C 40 H 28 N 4 ), no signals in the range 3200-3390 cm −1 related to an amino group ν(NH 2 ) or near 1716 cm −1 corresponding to the keto group were observed. This indicates the total formation of condensation of the amino groups with keto groups and then an apparition of macrocyclic Schiff's base. The spectrum (a) (Fig. 7) shows the appearance of a weak absorption band in the 3013-3070 cm −1 range corresponding to CH arom ; the computed value of this band is observed in the range of 3064-3104. The appearance of the novel band at 1636 cm −1 is attributable to the characteristic stretching frequencies of the imine linkage υ(C = N), and this confirms a good agreement with the theoretical result, which appears       NPs] to (a), there is a slight shift in the frequency of the absorption band (C = N) as well as shown in theoretical spectra (Table 4), which indicate that the nitrogen atom of the imine group is coordinated to the iron. This bathochromic shift can be explained by the increased delocalization of electrons through the newly coordinated metal center.
A new peak in 427 cm −1 appears in the spectra of [(C 40 H 28 N 4 )@Fe(II)] complex (b) and the magnetized complex (c) attributed to the ν (Fe-N) vibration corresponding, respectively, to 430 cm −1 and 420 cm −1 in the theoretical spectra. However, the vibration band ν(Fe-O) appears at 479 cm −1 attributable to 448 cm −1 theoretically. It is a week and broadband, which confirms the formation of Fe 3 O 4 NPs in situ of the macrocycle. The comparison of the vibrational frequencies calculated at 6-311 G (d, p) basis set gives reasonable deviations from the experimental values. IR spectra showed finally the success of creating a bond between N-Fe and another between Fe-O, which confirms the in situ germination of Fe 3 O 4 NPs in the Schiff base macrocycle.

Absorption properties
The electronic spectrum of the Schiff base ligand (a), complexes (b), and (c) was recorded in DMSO theoretically as well as experimentally. The calculated absorption spectra were done by the TD-DFT method at CAM-B3LYP-D3/6-311G (d, p) level of basis set. These spectra are shown in Fig. 8, and their wavelengths (λ Exp and λ Cal (nm)), oscillator strength (f) and (%) contribution from each transition are given in Table 5 As shown in Fig. 8, all the compounds (a), (b) and (c) exhibit only one broadband ranging from 311 to 390 nm for the experimental spectra and from 361 to 346 nm for the theoretical spectra attributed to the n-π* transitions of the C = N and C = C bands.
By comparing the spectra of the [(C 40 H 28 N 4 )@Fe(II)] and [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] complexes with that of the free ligand, we observe practically the same shape with a slight shift of λ max observed at (344 and 339 nm) and at (355 and 346 nm) for the experimental and theoretical spectra, respectively, due to the complexation and polarization of the (C = N) bond by the metal-ligand interaction. The absence of bands relating to ligand-metal charge transfer phenomena (LMCT) and the d-d transition is probably due to the low solubility of the complexes in the solvent DMSO [80,81].

Frontier molecular orbital analysis
The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are named frontier molecular orbitals (FMOs), and they are a very important parameter for quantum chemistry [82]. The FMOs energy, the electronic chemical potential (µ), the chemical hardness (η), the global softness (σ) and the dipole moment (µ D ) for (a) ligand, (b) [(C 40 H 28 N 4 )@Fe(II)] and (c) [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] are given in Table 6. The computations were done by the CAM-B3LYP-D3/6-311G (d, p) level. These values serve to exemplify the kinetic stability of the molecule and the chemical reactivity [83]. It should be indicated that the change in bandgap brings about variations in conductivity. The relationship between conductivity and energy bandgap (E g ) can be estimated using the following equation [84]: Here, σ is the electric conductivity and K B denotes the Boltzmann constant. It is conspicuous that a small decrease in the bandgap results in a significantly higher electrical conductivity.
(2) ∝ − exp −Eg∕K B T As shown in Table 6, the hard molecule, with a large gap, corresponds to molecule (a) (3.167 eV), where their electron density changed more hardly than a soft molecule [84]. The small HOMO-LUMO energy gap corresponds to compound (b) (1.484 eV), which means small excitation energies. Thus, the HOMO-LUMO gaps decrease by about 1.683 and 1.368 eV for (b) and (c), respectively. The low value of the energy gap of these two molecules, especially for (b), is due to electron-withdrawing groups that enter into conjugation.
Furthermore, the electronic chemical potential and the chemical hardness were slightly reduced under the complexation with the metallic center Fe and the Fe 3 O 4 . The global softness of (a) increases from 0.631 eV −1 to 1.348 and 1.111 eV −1 for (b) and (c), respectively. Based on these quantum chemical parameters, we are able to estimate the geometry of molecules and to provide not only the electronic parameters but also to extract information about the reactivity and selectivity of the compounds. Consequently, we can notice that the complexation of ligand (a) with the metallic center Fe and then with the Fe 3 O 4 affects the stability and the reactivity of this molecule, where (b) and (c) present low chemical stability and they have high reactivity than (a), respectively. It also implies that after the addition of the metallic center Fe in the tetraaza macrocyclic cavity of the ligand, the molecule (b) become more conductive, more polarizable, and softer (with lower molecular stability and high reactivity in chemical reactions) because  it needs small energy to excitation compared to (a) and (c), respectively, and it is thermodynamically favorable for an electron transfer to occur. Moreover, the frontier molecular orbitals of (a), (b) and (c) in DMSO solvent are shown in Fig. 9. The HOMO represents the ability to donate an electron and the LUMO as electron acceptor represents the ability to obtain an electron. The positive and negative phases are given in red and green, respectively [84,85]. It can be seen from this figure that the HOMO of molecule (a) is localized mainly on the tetraaza macrocyclic ligand and on the 1,2-substituted benzene, while the LUMO is localized extensively over the whole molecule. It is also clear from figure that the two compounds (b) and (c) give similar HOMO orbital, which is localized on the 1,2-substituted benzene and on the tetraaza macrocyclic cavity with a large electronic density on Fe-N bond for the molecule (b) further, the electron density is located around the Fe 3 O 4 for the molecule (c). We can observe that there is an electron density transfer between the tetraaza macrocyclic ligand and the metallic center Fe (for (b)) and Fe 3 O 4 Fig. 9 Calculated frontier molecular orbitals of a, b and c in DMSO solvent with CAM-B3LYP-D3 method (for (c)). For the LUMO orbital of these molecules, there is no significant change for the delocalization of HOMO. The qualitative picture proves a flow of electron density (intramolecular charge transfer) from the electron-donor groups by way of the π-electron bridge to the electron acceptor groups.

Scanning electron microscopic SEM and EDX analysis
The scanning electron microscope (SEM) was recorded to observe the morphology of products synthesized. As shown in Fig. 10a, the images of the macrocyclic (C 40 H 28 N 4 ) taken at different resolutions showed a crystal morphology in the form of column crystal.
The SEM micrograph of the complex (Fig. 10b) displayed also the formation of crystals whose metal is clearly attached within the tetraaza macrocycle cavity.
Chemical co-precipitation was widely applied to prepare high-quality iron oxide nanoparticles, but it is very difficult to obtain uniform iron oxide nanoparticles in an aqueous solution [18,86]. The shape, size, and surface morphology of magnetite NPs have been studied previously [30,87]. Nevertheless, the synthesis of uniform NPs of the same size remains a bit difficult, and this is one of the objectives of our work.
As shown in Fig. 10c, it was possible to form dispersed nanoparticles with regular spherical shape by the method of germination that encapsulated in the tetraaza cavity of the macrocyclic ligand. This encapsulation allowed the dispersion of the nanoparticles on the surface of the material by reducing the dipole-dipole magnetic interactions. The diameter of the nanoparticles was determined from the SEM image (Fig. 10c); their average size was approximately between 11 nm and 50 nm; this result is in perfect agreement with the result found by DRX.
The EDX analysis revealed atomic content of samples synthesized, which confirmed the presence of all constituent atoms: carbon (C), nitrogen (N) in the ligand (C 40 H 28 N 4 ) in Fig. 11a. In addition to these elements, iron complex contained iron (Fe) in Fig. 11b, while in the case of magnetite (Fe 3 O 4 ) NPs incorporated in the macrocyclic confirmed the presence of carbon (C), nitrogen (N), iron (Fe) and oxygen (O) in Fig. 11c.
Finally, the presence of (Fe) and (O) indicates the success of the incorporation of magnetite nanoparticles inside the macrocycle [88].  Table 8 presents the value of average size of magnetite nanoparticles found in this work by XRD and SEM pictures by comparing with the literature. According to these references, the synthesis of nanoparticles encapsulated inside tetraaza macrocycle with sizes between 11 and 50 nm is well controlled.  These results confirm furthermore that the Fe 3 O 4 NPs have been successfully encapsulated in the macrocyclic tetraaza concavity and that the Fe 3 O 4 weight content is about 64% and the density is about 25 mmol.g −1 .

Magnetic properties measurement
Some nanoparticles have been characterized not only by their size distribution, shape, and surface chemistry, but also, they are clearly known by their magnetic properties [91,92]. Obviously, the iron element (Fe) has a strong magnetic moment due to the four unpaired electrons in its 3d orbitals. So, when crystals such as magnetite (Fe 3 O 4 ) are formed from iron cations, different magnetic states can occur, and this will be revealed by measuring magnetic properties. Vibrating sample magnetometry (VSM) has been used to study the magnetic properties of [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] by measuring the magnetic hysteresis at 300 K temperature and the thermomagnetic curve depending on temperature between 120 and 300 K. Figure 13a presents the magnetic hysteresis loop analysis based on the relationship between magnetization (M) versus magnetic field (H) that shows a similar shape compared to free Fe 3 O 4 NPs by returning to the literature [93,94]. So the ferromagnetic character of [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] was proved, and the magnetite Fe 3 O 4 was successfully incorporated inside the macrocycle due to the significant decrease of the saturated magnetization (M s ) from (57.33 emu/g) [52] of magnetite to 35 emu/g, suggesting that the tetraaza macrocyclic ligand reduced the magnetic response to an applied magnetic field. In addition, this decrement can be explained either by the change of structure and/or by the surface anisotropy upon coating [95].
The coercivity (H C ) and remnant magnetization (M r ) and squareness (S r = M r /M s ) were calculated and are listed in Table 9. Hence, the remnant magnetization was found to be 22.4 emu/g, whereas the coercive field (H C ) attained 0.11 T. The very small variation of remanence ratio value S r of Fe 3 O 4 NPs coated can be ascribed to interparticle and intraparticle interactions [96].
The zero-field cold (ZFC) and the field cooling (FC) measurements were taken on the [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] to better understand the magnetic properties (Fig. 13b).
In the FC measurement case, each particle magnetization direction is sheltered, while the ZFC net magnetization is zero. In addition, a random distortion characterizes the resulted magnetic spins. Furthermore, the ZFC typically decreased in the case of nanoparticles. In contrast, FC   Fig. 13 a Magnetization curves measured at 300 K for the [(C 40 H 28 N 4 )@Fe 3 O 4 NPs]; b zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves for [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] (applied field = 9 × 10 −3 T and temperature range = 100-300 K increased along with the temperature decrease. In fact, heating the sample induced the ZFC magnetization, which consequently increase and approach the ZFC value to a blocking temperature. The aforementioned temperature characterized the domain's orientation. The homogenous particle size is characterized by an abrupt charge distribution. In the ZFC curve, the maximum value occurred above 302 K (Fig. 13b). The high blocking temperature qualifies a large particle size as well as the particle's magnetic interaction.

Conclusion
To sum up, we have successfully synthesized a tetraaza macrocyclic ligand and its corresponding iron (II) complex. Besides, Fe 3 O 4 NPs were fabricated inside the tetraaza macrocyclic ligand by the co-precipitation method. All the synthesized compounds were characterized by physicochemical techniques like XRD, NMR, FT-IR, UV-visible, SEM, EDX, TGA, and VSM. To identify exactly the structures developed, we used 1 H NMR and 13 C NMR spectroscopy that confirmed the structure of the ligand and its metal complex. FTIR spectroscopy essentially showed the characteristic bands of all functions present in the macrocyclic ligand and the effect of complexation on the band of the C = N function. Then, UV-VIS spectroscopy allowed us to determine the characteristic π-π* absorption band of the ligand attributed to the bonds (C = N) and (C = C). The energy gap of (a), (b) and (c) was 3.167, 1.484 and 1.799 eV, respectively, which indicates that the (b) compound was the most conductive (with high reactivity in chemical reactions and lower molecular stability) and belongs to soft material. All these properties of the mentioned compound were compared to the calculated spectra using the B3LYP-D3 and CAM-B3LYP-D3 /6-311 G (d, p) method, where the theoretical studies showed good agreement with experimental results. Thermogravimetric analysis showed that magnetite nanoparticles weight density was about 25 mmol/g. We were also able to identify some crystallographic properties of the magnetite complex [(C 40 H 28 N 4 )@Fe 3 O 4 NPs] by the X-ray powder diffraction (DRX) method and determine the average size of the magnetite nanoparticles, which is approximately 11.05 nm. This last contribution affirmed a good dispersion and encapsulation of the nanoparticles of magnetite inside the tetraaza macrocycle. This valuable product will be used in the future either by a catalytic application or by a biological application.