Exploring nonlinear and linear optical properties of N, N’-bis(salicylidene)-o-phenylenediamine (salophen) through Z-scan technique and TD-DFT computational analysis

This investigation delves into the comprehensive analysis of the linear and nonlinear optical characteristics exhibited by N, N’-bis(salicylidene)-o-phenylenediamine (salophen) using a combination of Z-scan methodology and quantum chemistry calculations. The Z-scan technique facilitated meticulous computations of the third-order susceptibility, nonlinear absorption coefficient, and nonlinear refractive index of the specimen. Specifically, in the solvent DMSO, the assessed values for the nonlinear refractive index, nonlinear absorption coefficient, and third-order susceptibility were determined to be 0.035 × 10–10 cm2 W −1 , −0.024 × 10–5 cm W −1 , and 0.596 × 10–5 esu, respectively. Furthermore, quantum mechanical analyses were employed to meticulously calculate the molecular hyperpolarizabilities (β and γ), dipole moment (μ), and dipole polarizability (α) of salophen. This thorough exploration highlighted a notable congruence between the outcomes derived from experimental observations and those obtained through quantum mechanical simulations. The collective findings from both theoretical computations and experimental assessments distinctly showcase the robust nonlinear potential inherent in salophen. These insights suggest its promising suitability and potential as a viable candidate for applications in optical devices. The alignment between theoretical predictions and experimental results underlines the reliability and potential practicality of salophen in the realm of optical technology, emphasizing its significance as a potential material for advancing optical device functionalities.


Introduction
The extensive applications of materials in optical storage, limiters, and switches have prompted a myriad of studies on their nonlinear optical (NLO) properties [1].With minerals displaying weak linear optical characteristics, researchers have delved into investigating the nonlinear optical features of organic materials [2].Organic materials, structured as (D-π-A), have a molecular arrangement significantly influencing their polarizability.The π bonds within these materials allow electrons to freely move along the molecule's length, enhancing their polarizability [3,4].Additionally, the connection between electron-donating and electronaccepting groups through an intermediary segment impacts absorption wavelength and energy gap, further contributing to the rapid nonlinear response observed in these materials.This unique trait has led to their widespread utilization in photonics and optical devices [5].
Among these materials, Schiff bases, characterized by a structure represented as R 2 C = N-R, incorporating aromatic rings and imine groups, stand out as promising candidates for exploring NLO properties [6].Their structural diversity, solubility in common solvents, and accessible preparation methods have garnered considerable attention, leading to contemporary research on their NLO characteristics [7].The NLO features exhibited by Schiff bases have driven their integration into the construction of optical devices [8][9][10].
When subjected to intense light, primarily from lasers, materials undergo alterations in their optical properties, sparking extensive research in NLO properties following the discovery of lasers by Maiman in 1960 [11].Various techniques, such as the four-wave mixing method, Marburg displacement measurement, and the Z-Scan technique introduced by Sheikh Bahai and colleagues in 1989, facilitate the calculation of refractive index and nonlinear absorption coefficients [12][13][14][15].
The nonlinear parameters calculated by the Z-scanning technique include the refractive index, n 2 the nonlinear absorption coefficient β, and the acceptance value of order χ (3) were designed and proposed.In this technique, the laser light is focused by a lens and the material moves in the path of the focused Gaussian beam.With this movement, the transmissivity value received by the detector is changed.Examining the transmission spectrum the detector receives, the value and sign of the material's nonlinear coefficients can be calculated.The basis of this technique is the phase change of the Gaussian beam wavefront TEM 00 due to passing through the non-linear medium.
Various factors cause nonlinear refractive index in materials.Factors include electron polarization, thermal effects, molecular orientation, and saturated atomic absorption [1].
In materials with a structure in the form of (D-π-A), charge transfer greatly contributes to hyperpolarization.The charge transfer contribution is affected by the difference in the dipole moment αΔμ between the ground and excited states, the oscillator strength, and finally the transmission wavelength λ max [16].There is also a harmony between the nonlinear properties of an environment and its transparency.This means that an increase in the nonlinear absorption coefficient β brings a red shift in the absorption spectrum.The origin of which is the length of the conjugated system or the acceptor-donor substitution is stronger, for this reason, the absorption spectrum has been investigated in this work.
For theoretical examinations of materials affected by disturbance, the Ab initio method based on Density Functional Theory (DFT) is employed [17].This research delves into the linear and nonlinear optical properties of a specific material.Initially, UV spectra energy gap analysis was conducted, followed by the determination of nonlinear absorption and refraction coefficients utilizing the Z-Scan method.Furthermore, Gaussian software was utilized to calculate the polarizability tensor of Schiff bases and consequently their polarizability.
This research contains organic synthesis and optical characterization of salophen.The z-scan technique was exploited to determine the magnitude and the sign of nonlinear refractive index n 2 , nonlinear absorption coefficient β, and the third-order nonlinear electric susceptibility (χ(3)).Moreover, quantum mechanical calculations were exploited to determine the electric dipole moment (μ), dipole polarizability (α), first and second hyperpolarizability (β, γ), and the anisotropy of the polarizability (Δα).The alignment between theoretical predictions and experimental results underlines the reliability and potential practicality of salophen in the realm of optical technology, emphasizing its significance as a potential material for advancing optical device functionalities.

Material and method
The substances employed in this research were mainly sourced from companies based in Germany, including Merck and Sigma Aldrich, whereas the solvents were specifically acquired from Merck.Assessment of melting points was performed using an electrothermal melting point apparatus.Acquisition of linear absorption spectra was carried out using the Shimadzu 1700 UV-vis spectrometer.We used an Nd: YAG laser second harmonic radiation (5 ns, 532 nm laser at a frequency of 10 Hz) in our studies.The entirety of the computations performed within this research utilized the Gaussian 09 program package as the primary software, supplemented by the Gauss view 05 molecular drawing tool [29].Geometry optimizations and frequency analysis have been performed by Density Functional Theory (DFT) using the Becke 3-Lee-Yang-Parr (B3LYP) level, employing the 6-311 G++(dp) basis set in the gaseous phase.This approach proves particularly effective for organic molecules, especially those exhibiting closed-layer structures.Frequency calculation was done to ensure that were obtained stationary minima of salophen.Furthermore, for calculations involving excited states, we employed a methodology reliant on both B3LYP and the CAM-B3LYP/6-311++G(d, p) setup.This specific configuration is renowned for its accuracy in computing both linear and nonlinear optical responses, offering an excellent balance between computational efficiency and precision [30,31].

Synthesis of salophen components
Salophen synthesis followed the method described in the literature, as outlined by Vinicius [32].A solution composed of 0.02 mol of o-phenylenediamine (2.16 g) in 15 ml of methanol was combined with a solution containing 0.04 mol of salicylaldehyde (4.88 g) in 15 ml of methanol.The resulting mixture underwent stirring for approximately 4-5 h using a magnetic stirrer.An orange precipitate formed, which was subsequently filtered and washed with cold methanol.In addition, for further purification, the compound underwent recrystallization (figure 1).The identity of the product was confirmed using various techniques including melting point determination, IR spectroscopy, and 1H NMR analysis (melting point = 210-215 °C). The

HOMO-LUMO orbital analysis
Molecular excitation energies, oscillator strengths (f), and molecular orbital contribution to each excitation state were calculated using time-dependent density functional theory (TD-DFT) in singlet and triplet excitation modes.The TD-DFT was performed in the gaseous phase.The process uses the 6-311 G++(dp) basis set, which is ideal for organic molecules, especially closed-layer ones.Salophen has three tautomerism structures, and we have obtained the optimized structures for each of them.Based on DFT, the structure of salophen in figure 1 was found to be the most stable.
The essential determinants of a molecule's electronic characteristics, including its hardness (η), softness (S), ionization potential (IP), electronegativity (χ), and electron affinity (EA), are significantly influenced by the frontier molecular orbitals specifically, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).Extracting these properties from the energies of HOMO and LUMO is a viable approach.
The energy of the highest occupied molecular orbital (HOMO) reflects a molecule's capacity to donate electrons, directly tied to its ionization potential (IP).Conversely, the energy of the lowest unoccupied molecular orbital (LUMO) signifies its capacity to receive electrons, associated with the electron affinity (EA).Global characteristics like hardness and softness significantly influence both molecular stability and reactivity.As per Koopmans' theorem, an important deduction can be made (32).Table 1 presents a collection of information regarding the HOMO and LUMO energies, band gap energy, electron affinity (EA), and hardness.A reduced band gap energy indicates the soft nature and increased polarizability of the salophen molecule, defining it as a semiconductor with heightened polarizability.
Figure 2 illustrates the molecular orbitals engaged in salophen's primary transitions.
The HOMO possesses a discernible spin density spread throughout the entire molecule, while the HOMO-1 predominantly localizes within the two phenolic rings, and the HOMO-2 is primarily distributed across the C=N bond and the central phenyl ring.Conversely, the electron cloud of the LUMO is predominantly situated on the C=N bond and the two phenolic rings.The electron cloud of LUMO+1 is also found on the C=N bond and the two phenolic rings.Consequently, any movement of electrons from the ground state to the excited state facilitates a transfer of electron density, causing a shift in the magnetic moment.
An estimation of the light-harvesting efficiency (LHE) from the oscillator strength (f) can be conducted using the following equation (33).
The computations present potential transfers as outlined in tables 2 and 3.In table 2, the most prominent absorptions of salophen occur at 344 nm (with f = 0.2356) and 326 nm (with f = 0.0231).These lengthier wavelengths signify electron shifts from HOMO to LUMO and LUMO+1, whereas shorter wavelengths (317 nm) correspond to transitions from HOMO-2 and HOMO-1 to LUMO.However, findings from the CAM-B3LYP method reveal the compound's most significant absorptions at 330 nm (with f = 0.2639), 313 nm  (with f = 0.1935), and 271 nm (with f = 0.1183).The primary low-energy excitations (ICT band) predominantly involve the transition from HOMO to LUMO.

One photon absorption
The presence of an uneven distribution of molecular charge is depicted through the dipole moment.The orientation of this vector within the molecule relies on the locations of positive and negative charge centers.As illustrated in table 4, the dipole moment holds a value above zero, indicating the molecule's dipolar nature.Intramolecular charge transfer (ICT) is observed in dipolar systems when photons with appropriate energy are absorbed by molecules.Total dipole moment, isotropic polarizability (α) is calculated using the polarization components as follows [33].
The linear average polarizability The first hyperpolarizability (α) is represented by two factors, namely βvec and βtot.
and βvec is the vector component of the first hyperpolarizability represented by: n addition, the direction of charge transfer in molecules can be determined by the ratio of βvec and βtotal using the following equations [35]: Dipole moment, the first, second and third hyperpolarizabilities, and in-plane non-linearity anisotropy (β) of salophen are presented in table 4. Salophen can be used as potential NLO material of the significant value of μβ 0 .

Natural bonding orbital analysis
Natural bond orbital (NBO) analysis provides an efficient method for the investigation of charge delocalization within the molecule.NBO analysis has been performed on salophen in order to explain ICT in the molecule associated with hyperpolarizing abilities.NBO calculations were performed using the NBO 3.1 program in the Gaussian 09 package by TDDFT/B3LYP method.In this analysis, the perturbation energies of donor-acceptor interactions for donor and acceptor NOBs were calculated using the second-order perturbation method as presented in the following equation: Where, Ci is the orbital occupancy, εi and εj are diagonal elements, and Fi, j is the Fock matrix element.The perturbation energies of donor-acceptor interactions have been tabulated in table 5.
The strong intramolecular hyperconjugation interaction was due to the overlap between the π and π * orbitals in aromatic rings, which has caused the stability of the molecule by intramolecular charge transfer.Furthermore, there was the electron-donating from the lone pair of phenolic oxygens and C=N to the corresponding aromatic ring.Another hyperconjugation interaction is due to the intramolecular hydrogen bonds (LP N 10→ σ * H 40 -O 39 , LP N 34→ σ * H 38 -O 37 ).Both nitrogens N 10 and N 34 work as a donors via H 40 and H 38 to form a pseudo-six-membered ring.In nonprotic solvents, double proton transfer in the complex of two salophen molecules occurs.Besides, some strong intermolecular interactions obtained with stable energy are listed in table 5.The natural population analysis of salophen showed the Lewis structure at 97.112% and the non-Lewis structure at 2.674%.

UV-V absorption and fluorescence spectroscopy
Experimental and calculational UV-Vis absorption spectra of salophen are shown in figures 3 and 4. UV-vis spectra show absorption peaks at 334 nm, and 381 nm, which are attributed to π → π * transition in enol and keto forms of salophen, respectively.The low-intensity n → π * transition was completely overloaded by the intensive π → π * transitions.It is evident from the spectra that salophen shows a wide transparency in the visible region that enables it for the second harmonic generation required for all NLO material.
The band gap energy of salophen has been determined using the Tauc relation which is given by [32]: The amount of energy gaps of salophen in DMSO was Eg = 2.85 eV.Moreover, the fluorescence spectra of salophen are shown in figure 5.The maximum emission wavelengths of the sample occurred in the DMSO solvent at 440, 458, and 537 nm.
The larger the wavelength of the emission the maximum absorption wavelength is the result of re-combining part of the electron-hole in a non-radiant way through thermal radiation.Excited-state intramolecular proton transfer (ESIPT) leads to a significant Stokes-shifted emission.The difference between the maximum absorption wavelength and the maximum emission wavelength indicates the stokes shift in the sample equal to 4410 cm −1 [36].

Nonlinear refractive index
When matter is exposed to the electric field, the electric charges move in matter and the electron cloud is perturbed.This perturbation leads to an induced electric dipole in the matter and it would be polarized.Nonlinear parameters which are calculated by the z-scan technique include refractive index n 2 nonlinear absorption coefficient β and X(3) susceptibility values.In this technique, the laser beam is focused by a lens, and the material is replaced in a focused Gaussian beam path.Through this replacement, the transmittance which is received by the detector is changed.It is possible to measure the value of the nonlinear coefficient of material by investigating the transmittance range received by a detector.Various factors may cause nonlinear refractive index in materials, such as electronic polarization, thermal effects, molecular orientation, and saturation atomic absorption.
The Z-scan technique is applied via both open and closed-aperture methods.The open aperture method is used to measure the nonlinear absorption coefficient and the closed aperture method is used to measure the nonlinear refractive index.In general, the refractive index in the nonlinear medium is as follows [37].
where n2 is the nonlinear refractive index of the medium.Transmittance variation between peak and valley is used to measure nonlinear refractive index.Where ΔT p−v is the difference between the normalized peak and valley transmittance.S is the aperture linear transmittance and can be calculated by using the equation: r a is the radius of the aperture and ωa is the radius of the beam at the aperture.where I 0 is the peak intensity at the focal point as follows: Figure 6 shows the observed normalized transmittance versus sample position concerning the focal point of the closed aperture in the Z-scan of the sample.Moreover, the appearance order of the peak valley revealed the salophen had a negative nonlinear refractive index and acts as a concave lens.These results indicate that the nonlinearity, in this case, was of thermal origin.Since the sample has a high negative nonlinear refractive index, it may be a suitable candidate to be used in optical limiter devices.

Nonlinear absorption coefficient
Figure 7 shows the normalized transmittance of open aperture Z-scan of the sample.As can be seen, the peak shape of this figure shows the absorption saturation behavior of the sample.
The nonlinear absorption coefficient of the Salophen can be easily calculated from this curve, using the following equations [28,34].Where: Where Z 0 is rayleigh length I0 is the peak intensity at the focal point, T is the total transmittance, β is the nonlinear absorption (NLA) coefficient, and Leff is the effective length of the system that can be related to α, by the following equation: The nonlinear absorption coefficient of salophen is listed in table 6.  3.7.Third order susceptibility χ(3) In the Z-Scan technique, the first nonlinear absorption coefficient and nonlinear refractive index of matter are measured.Also, the real, imaginary, and absolute amounts of χ(3), can be estimated by the following equations [34,35].
The values of the third-order nonlinear susceptibility and other optical parameters obtained for salophen are tabulated in table 6.
As can be seen in table 6, salophen exhibited large third-order susceptibilities with a magnitude of the order of 10-5 esu.

Conclusion
In this work, we have stated the linear and nonlinear optical properties analysis of salophen.Time-dependent density functional theory (TDDFT) has been used to study the nonlinear optical properties of salophen.The results have shown the large intramolecular charge transfer character (ICT) in salophen molecules.Also, the total first molecular hyperpolarizability and dipole moment of the salophen molecule were found to be 126.26a.u., and 1.78 a.u, respectively.Besides, hyperconjugative interactions and charge delocalization have been investigated using NBO analysis.The strongest electron transfer was from a lone pair of nitrogen atoms (LPN) to the anti-bonding acceptor (OH phenolic) orbitals.
The experimental results obtained from the Z-scan for the nonlinear refractive index, nonlinear absorption coefficient, and third-order susceptibility were determined to be 0.035 × 10-10 cm 2 W −1 , −0.024 × 10-5 cm W −1 , and 0.596 × 10 −5 esu, respectively.The results showed that the NLO responses obtained from the Z-scan experiment of salophen could be described by reverse saturation effects and thermally induced refractive index change respectively.In this molecule, two-photon absorption has been increased by the donor-π-donor (D-π-D) architecture.In addition, the nonlinear properties of the sample are due to the saturated atomic absorption mechanism and this sample behaves like a divergent lens.The experimental and theoretical conclude that salophen seems to be a promising candidate for future optical devices.

Figure 3 .
Figure 3. Experimental UV-V is the absorption spectra of salophen in DMSO.

Figure 4 .
Figure 4. Computational UV-V is the absorption spectra of salophen in the gaseous phase.

Figure 7 .
Figure 7. Open aperture Z-Scan data for the salophen solution.

Table 2 .
Excitation energies (E ex ), oscillator strengths (f), light harvesting efficiencies (LHE), and the main molecular orbitals involved in the selected electronic transitions of salophen at TDDFT-B3LYP/6-311 G(d, p) level in the gaseous phase.

Table 5 .
Second-order perturbation theory analysis of the Fock matrix in NBO basis in salophen.