# Theoretical Investigation of the Nonlinear Optical and Charge Transport Properties of N-(4-Methoxybenzylidene) Isonicotinohydrazone and Some of Its Derivatives: A DFT and TD-DFT Study

Authors: Charly Tsapi Tedjeuguim; Stanley Numbonui Tasheh; Ghogomu Julius Numbonui
Journal: Advances in Materials Science and Engineering
 (2023)

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## Abstract

Here, we report the findings from a study on the charge transport and nonlinear optical (NLO) properties of N-(4-methoxybenzylidene) isonicotinohydrazone (INH) and some of its derivatives named INH1-INH15. The density functional theory (DFT) approach was used for ground state computations at the B3LYP-D/6-311G (d,p) level of theory, while the time-dependent density functional theory (TD-DFT) was carried out at the CAM-B3LYP/6-311G (d,p) level. The results show that the energy gaps of all the studied compounds range from 3.933 to 4.645 eV. INH3 and INH4 have the lowest electron and hole reorganization energies (i.e., 0.409 and 0.634 eV, respectively) and can thus be classified as moderate electron and hole-carrying materials for organic light-emitting diode (OLED) applications. TD-DFT computations demonstrate that an extension of the conjugation (in INH2 and INH3) increases the oscillator strength, improving the NLO response. According to the NLO data, INH2 and INH3 have higher static isotropic polarizabilities (38.509 and 37.986 × 10−24 esu, respectively) and second hyperpolarizabilities (54.440 and 57.598 × 10−36 esu, respectively), while INH4 and INH13 have higher first hyperpolarizability values (11.944 and 10.939 × 10−30 esu, respectively). The results reveal that INH derivatives with different groups are viable alternatives for OLED and NLO applications.


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## Body

## 1. Introduction

Low molecular weight organic compounds have recently become popular in the optoelectronic industry due to their potential applications in organic light-emitting diodes (OLEDs) [1, 2], organic solar cells (OSCs) [3], organic field effect transistors (OFETs) [4], and nonlinear optics (NGOs) [5–7]. NLO and OLED technologies have received a lot of attention due to their applications in optical and flat-panel displays [8]. Owing to its potential applications in modern computers, optical data storage, communications, laser technology, and photonics, NLO materials have attracted the curiosity of many researchers [9]. Organic compounds containing π-delocalized electrons and push-pull mechanisms have attracted the attention of NLO investigators. Prototypical compounds having NLO features, such as urea and para-nitroaniline (PNA) have such properties [10]. Organic NLO materials are more frequent than their inorganic counterparts due to their affordable fee, low toxicity, ease of solution processability, greater electro-optic coefficients, and flexibility [9, 11, 12]. Despite this, the key challenge in optoelectronic engineering continues to be the development of organic materials with high thermal stability and NLO responsiveness. Designing small novel materials with desirable characteristics will be of interest in optoelectronic engineering.OLED technology has gained considerable attention as a result of its significance in the development of flat panel displays and lighting, such as those found in smartphones, computers, smartwatches, and televisions [13–15]. Transparency, low thickness, outstanding contrast, good flexibility, viewing angles, lower energy consumption, and faster response time distinguish OLEDs from traditional liquid crystal devices (LCDs) that use a backlighting system [16].Tris (8-hydroxyquinoline) aluminum complex (Alq3) is the prototype molecule for the electron transport layer (ETL) in OLEDs [17], while N,N′-diphenyl-N,N′-bis(3-methylphenyl)-1,1′-diphenyl-4,4′-diamine [13] is that for the hole transport layer (HTL). Organic materials do not achieve the same charge carrier mobility as inorganic semiconductors, limiting device efficiency [14, 18]. Developing novel conjugated materials with high mobility and stability is a significant problem in the production of OLED devices.Owing to their exceptional thermal, optical, and chemical stability, hydrazone compounds have received a great deal of research interest in the past years in the sectors of NLO and OLED technologies [19, 20].Hentai and collaborators [21] reported that ((1Z)-(4-(dimethylamino) phenyl) methylene) 4-nitrobenzylcarboxyhydrazone monohydrate has a very interesting NLO response. Similarly, Yao and coworkers [22] demonstrated that a class of hydrazone-based photochromic compounds has extremely high hyperpolarizability and can be employed in optoelectronics. Moraes and collaborators [17] discovered that N,N-diisonicotinoyl-2-hydroxy-5-methylisophthalaldehyde hydrazone has intriguing charge transport characteristics. Also, Quirino and colleagues demonstrated that 1-(3-methylphenyl)-1,2,3,4-tetrahydroquinoline-6-carboxaldehyde-1,1′-diphenylhydrazone has excellent hole transport properties and can be employed in optoelectronics [18]. In the same light, Boukabcha and collaborators showed that (Z)-N′-(2, 4-dinitrobenzylidene)-2-quinolinen-8-yloxy) acetohydrazide has a good NLO response and can be employed in optoelectronics [23].Confronted with microbial resistance-related problems, Kudrat-E-Zahan and coworkers [24] synthesized N-(4-methoxybenzylidene) isonicotinohydrazone (INH) (see Figure 1).Figure 1
Structural representation of N-(4-methoxybenzylidene) isonicotinohydrazone (INH) and its studied derivatives.The structural features of this compound with electron delocalization capabilities warrant it to have enhanced NLO responses and charge transport properties. Tedjeuguim and coworkers [25] studied the optoelectronic properties of INH, 2,2′-bipyridine, and their Fe2+, Ni2+, Cu2+, Pd2+, and Pt2+ complexes. Unfortunately, there exists no computational studies of the NLO and charge transport properties of INH and its studied derivatives (see Figure 1).Based on the foregoing, the primary goal of this study is to examine the NLO and charge transport properties of the above-mentioned INH derivatives. To achieve this aim, electronic parameters, UV-spectral analysis, reorganization energiesλelectron/hole, mobility μelectron/hole, static dipole moment (μ), static polarizability (isotropic α and anisotropic ∆α, static isotropic first hyperpolarizability (β), and static isotropic second hyperpolarizability (γ) of the studied compounds were computed via the DFT method and are discussed.


## 2. Computational Details

This study was computed using the Gaussian 09, Revision D.01 program [26]. The GaussView 6.0.16 program was used to visualize and build the investigated compounds [27]. Geometry optimizations and frequency calculations were performed using Becke’s three Lee-Yang-Parr (B3LYP) functional [28] augmented with an empirical dispersion term [29] and associated with the Pople style 6-311G (d,p) basis set [30]. B3LYP was used because it is suitable for predicting the optoelectronic properties of low molecular weight organic molecules [31]. The excited singlet state structures were computed using the TD-DFT/CAM-B3LYP/6-311G (d,p) method, which has proven to be effective in determining the charge transfer transition energies of low molecular weight organic molecules [32].Experimental results of INH (IR and UV spectra) were reported by Kudrat-E-Zahan and coworkers [24]. IR analysis shows that INH displays characteristic bands at 1658.84 and 1598.69 cm−1 assigned to ѵ(C=O) and ѵ(C=N) vibrations, respectively. Theoretically, the ѵ(C=O) and ѵ(C=N) bonds of INH vibrate at 1711.40 and 1600.77 cm−1, respectively. The calculated frequencies were scaled by a factor of 0.99 per the B3LYP-D/6-311G (d,p) level of theory and show good agreement with the experimental results. UV analysis shows that the computed λabs value of INH is 268.39 nm and also shows good agreement with the experimental value (283 nm) [24]. In this work, the electronic properties, nonlinear optical and charge transport properties of the studied compounds were calculated at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.According to Koopman’s theorem [33], frontier molecular orbital parameters such as band gap (ΔEg), chemical potential (µ), chemical hardness (η), chemical softness (S), electrophilicity (ω), and the maximum transferred charge (ΔNmax) were evaluated according to equations (1)–(6), respectively,(1)ΔEg=ELUMO−EHOMO,(2)μ=ELUMO+EHOMO2,(3)η=ELUMO−EHOMO2,(4)S=12η,(5)ω=μ22η,(6)∆Nmax=−μη.The charge transport properties of organic materials can be studied using many parameters such as the reorganization energyλelectron/hole, charge transfer integral telectron/hole, mobility μelectron/hole, charge transport rate kelectron/hole, adiabatic ionization potential IPa, and adiabatic electron affinity EAa. The charge transport rate is one of the key parameters governing the performance of organic electronic devices [34]. It has been extensively used to describe the charge transfer mechanism in many organic materials at room temperature and presents a good agreement with experiment [35]. The charge transport rate can be obtained through Marcus’s theory [36] and is calculated according to (7)as follows:(7)kelectron/hole=4π2h14πKBTλelectron/holetelectron/hole2exp−λelectron/hole4KBT,where λelectron/hole is the reorganization energy of the electron or the hole, telectron/hole is the integral charge transfer of the electron or the hole, kB is the Boltzmann constant (1.380 × 10−23 JK−1), h is Planck’s constant (6.626 × 10−34 Js), and T is the temperature (298.15 K). High temperatures are known to limit Marcus’s theory [37].Reorganization energy is partitioned into internal and external reorganization energies [8]. The internal reorganization energy refers to the energy change of the system caused by the structural relaxation after the gain or loss of electrons, while the external reorganization energy describes the change in electronic polarization of the surrounding compounds [38, 39]. The external reorganization energy contribution is usually neglected owing to the fact that their energies are much smaller than those of their internal counterparts [39, 40]. Reorganization energy is the parameter that affects the charge transport rate (K) of materials. Lower electron (λelectron) and hole (λhole) reorganization energies are beneficial for higher electron and hole transport rates, respectively [41]. The reorganization energy of electrons and holes was calculated using the following equations:(8)λelectron=E0−−E−−+E−0−E00,λhole=E0+−E+++E+0−E00,where E0+E0− indicates the energy of the cation (anion) calculated from the optimized geometry of the neutral compound, E++E−− represents the energy of the cation (anion) computed from the optimized structure of the cationic and anionic forms of the compound, respectively; E+0E−0 is the energy of neutral molecules calculated based on the optimized structures of the cationic and anionic states of the molecule, respectively, while E00 is the energy of the neutral compound computed from the optimized structure of the neutral compound.Another controlling factor to assess the charge transport of compounds is the charge transfer integral (t) [42]. It is directly related to frontier molecular orbitals (highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy) in the dimer configuration [43]. Charge transfer integral t is evaluated using Koopman’s theorem (KT) according to the following equations:(9)telectron=12ELUMO+1−ELUMO,thole=12EHOMO−EHOMO−1.Charge mobility is another parameter that affects the performance of OLED materials. High charge carrier mobility is enhanced by high charge transfer integral and low reorganization energies. The charge mobility is given by Einstein’s equation [43] as follows:(10)µelectron/hole=ed2Kelectron/hole2KBT,where Kelectron/hole is the charge transport rate for the hole or electron, KB is the Boltzmann constant, d is the intermolecular distance between two monomers, e is the electronic charge, and T is the temperature at 298.15 K.Ionization potentials (IPs) and electron affinities (EAs) describe the charge transport properties of OLED materials [5]. A smaller IP and greater EA value lead to the effective hole and electron injection ability [44]. The adiabatic ionization potential (IPa), vertical ionization potential (IPv), adiabatic electron affinity (EAa), and vertical electron affinity (EAV) in this work were calculated as follows:(11)IPa=E++−E00,IPv=E0+−E00,EAa=E00−E−−,EAV=E00−E0−.Stability is a beneficial parameter for the charge transport of organic materials [39]. Good OLED devices are those with larger chemical stabilities. The absolute hardness (η) was calculated to estimate the stability of the organic materials using the following equation [38]:(12)η=IPa−EAa2.To assess the possibility of INH and its derivatives as potential NLO materials, the static dipole moment (μ), static isotropic α and anisotropic ∆α polarizability, static isotropic first hyperpolarizability (β), and static isotropic second hyperpolarizability (γ) were calculated. Values were computed at x, y, and z components using the following equations [45, 46]:(13)µ=μx2+μy2+μz2,α=13αxx+αyy+αzz,∆α=12αxx−αyy2+αyy−αzz2+αzz−αxx2+6αxy2+αxz2+αyz2,βtotal=βx2+βy2+βz21/2,where(14)βx=βxxx+βxyy+βxzz,βy=βyyy+βxxy+βyzz,βz=βzzz+βxxz+βyyz,with βx,βy,andβz known, equation (13) becomes the following equation:(15)βtotal=βxxx+βxyy+βxzz2+βyyy+βxxy+βyzz2+βzzz+βxxz+βyyz21/2,where βxxx, βxyy, βxzz, βyyy, βxxy, βyzz, βzzz, βxxz, and βyyz are the tensor components for the first hyperpolarizability.(16)γ=15γxxxx+γyyyy+γzzzz+2γxxyy+γxxzz+γyyzz,where γxxxx, γyyyy, γzzzz, γxxyy, γxxzz, and γyyzz are the fourth-order tensor components of the second hyperpolarizability. A compound with a large dipole moment and hyperpolarizability value is predicted to be a potential candidate for NLO response [46].


## 3. Results and Discussion

### 3.1. Frontier Molecular Orbital Analysis

Frontier molecular orbitals were calculated from DFT-based optimized structures using the equations specified in the computational details section. Table1 presents the electronic parameters of N-(4-methoxybenzylidene) isonicotinohydrazone and its derivatives.Table 1
Electronic parameters of N-(4-methoxybenzylidene) isonicotinohydrazone and its derivatives calculated at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundsEHaELa∆EgaμaηaЅbωa∆NmaxINH−6.341−1.9184.423−4.1292.2110.2263.8541.867INH1−6.226−1.9024.324−4.0642.1620.2313.8191.879INH2−6.500−1.9914.509−4.2452.2540.2213.9961.883INH3−6.358−2.0224.336−4.1902.1680.2304.0481.932INH4−6.256−1.9864.270−4.1212.1350.2343.9771.930INH5−6.456−2.0454.411−4.2502.2050.2264.0941.927INH6−6.817−2.1764.641−4.4962.3200.2154.3551.937INH7−6.812−2.1674.645−4.4892.3220.2154.3381.933INH8−6.852−2.9193.933−4.8851.9660.2546.0672.484INH9−6.640−2.3784.262−4.5092.1310.2344.7702.115INH10−6.589−2.1154.474−4.3522.2370.2234.2331.945INH11−6.334−1.9664.368−4.1502.1840.2283.9421.900INH12−6.239−1.9234.316−4.0812.1580.2318.8581.891INH13−5.830−1.8224.008−3.8262.0040.2493.6521.909INH14−6.755−2.2304.525−4.4922.2620.2204.4591.985INH15−6.071−1.9294.142−4.0002.0710.2413.8621.931EH ⟶ HOMO energy, EL ⟶ LUMO energy, ∆Eg⟶, µ ⟶ chemical potential, η ⟶ chemical hardness, ω ⟶ electrophilicity index, ΔNmax ⟶ the maximum transferred charge, aunits in eV, and bunits in eV−1.The results show that functionalization of a donor at the terminal of N-(4-methoxybenzylidene) isonicotinohydrazone induces a reduction in the energy gap of INH (see INH1, INH4, INH11, INH12, INH13, and INH15). Similarly, functionalization with an acceptor only raises the band gap in the other cases and decreases it in INH8. Thus, compounds with small band gaps are softer, more reactive, and can show excellent NLO response [47]. The band gaps of all the studied compounds are in the range of 3.933 to 4.645 eV. This reduction in the energy gap of the designed derivatives compared to the synthesized (N-(4-methoxybenzylidene) isonicotinohydrazone) compound is attributed to the introduction of suitable donor and acceptor substituents. Hardness is the ability to resist charge transfer within its environment. The hardness values of all the investigated compounds range from 1.966 to 2.322 eV. Among these compounds, INH8 has the lowest hardness value (1.966 eV) and is therefore the most reactive. Organic materials with high and positive ω and ∆Nmax values have a greater affinity to absorb an electron. However, if a compound has a low amount of these indices, it may be characterized as an electron donor [48]. The maximum transferred charge (ΔNmax) and electrophilicity index (ω) values for all investigated compounds are positive and are in the range of 1.867 to 2.484 eV and 3.652 to 8.858 eV, respectively. The highest ΔNmax value of INH8 (2.484 eV) suggests that this compound has a greater tendency to absorb an electron. Based on the ongoing, INH8 is the most reactive compound and has the highest tendency to absorb an electron.Figure2 shows the HOMO and LUMO distributions of all the investigated compounds.Figure 2
Representation of the HOMOs and LUMOs of the studied compounds as calculated at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.The results show that the HOMOs are distributed on the –OCH3 group and the benzene ring of all the studied compounds. The LUMOs, on their part, are located on the pyridine ring of all the studied compounds except INH2, INH3, INH8, and INH9.


### 3.2. Molecular Electrostatic Potential (MEP) Map

The molecular electrostatic potential (MEP) map is a crucial parameter for describing the electrophilic and nucleophilic centres of a system [49]. On the colour-coded surfaces, the blue region shows the area of low electron density (i.e., the regions of positive potential), while the red region indicates the area of high electron density (i.e., regions of negative potential) [50–52]. Displayed in Figure 3 are the MEP plots of the compounds under investigation.Figure 3
Molecular electrostatic potential plots of the compounds under investigation, calculated at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.These findings show that the red electron-rich sites are centred on the oxygen atom of the carbonyl, the nitrogen atom of the pyridine ring, and the nitrogen atom of the azomethine group in all the studied compounds. In contrast, the blue electron-deficient sites are predominantly on the protons of the azomethine and methoxyl groups (except for INH2, INH3, INH7, and INH15).


### 3.3. Reorganization Energies

Presented in Table2 are important parameters needed to understand the charge transport nature and charge injection.Table 2
Reorganization energies, adiabatic electron affinity, vertical electron affinity, vertical ionization potential, adiabatic ionization potential, and hardness of the studied compounds all in eV, computed at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundsIPaEAaIPVEAVηλelectronλholeINH7.5100.6537.9180.4083.4280.4800.918INH17.4280.6537.8090.4083.7020.4890.859INH27.4560.8707.8910.6253.2930.4400.963INH37.4830.9257.7550.6803.2790.4090.707INH47.5100.7617.7820.5173.3740.4940.634INH57.6190.8708.0270.7073.3740.5780.890INH67.7280.9798.3540.7073.3740.4881.197INH77.7281.0060.2860.7073.3610.4881.181INH87.9181.5788.3541.1973.1690.7030.992INH97.7281.1150.3000.0323.3060.4150.955INH107.6461.0887.8640.7343.2780.5791.007INH117.2920.7617.8640.4893.2650.4950.995INH127.8640.6807.8090.4083.5920.5110.802INH137.1290.5717.4560.2993.2790.5840.845INH147.8641.1978.2720.8163.3330.5630.908INH157.2650.7407.5920.4733.2620.4910.644Note. λelectron/hole: reorganization energies, EAa: adiabatic electron affinity, EAV: vertical electron affinity, IPV: vertical ionization potential, IPa: adiabatic ionization potential, and η: hardness.Small reorganization (λelectron/hole) energy values indicate better charge transport rates and mobility, which give rise to good charge transport properties for the materials [39]. Results from Table 2 show that the increasing trend in the λelectron values is as follows: INH3 < INH9 < INH2 < INH < INH6 = INH5 < INH1 < INH15 < INH4 < INH11 < INH12 < INH14 < INH5 < INH12 < INH13 < INH8. This implies that INH3 (0.409 eV) possesses the best electron transport properties, while INH8 (0.703 eV) has the least. Moreover, the increasing trend in λhole values is as follows: INH4 < INH15 < INH3 < INH12 < INH13 < INH1 < INH5 < INH14 < INH < INH9 < INH2 < INH8 < INH11 < INH10 < INH7 < INH6. This suggests that INH4 (0.634 eV) possesses the best hole transport properties, while INH6 (1.197 eV) has the least. The results also show that the λelectron values are relatively smaller than those of the λhole values. This illustrates the potential of the studied compounds as n-type materials for organic light-emitting devices.A smaller IPa value means easier hole injection ability for the OLED materials, while a larger EAa value facilitates electron injection [8, 53]. Table 2 shows that INH13 (7.129 eV) has the lowest IPa value, while INH8 (1.578 eV) has the highest EAa value. The results also indicate that INH1 is the most stable compound under investigation, with the highest η value (3.702 eV). Good charge transporters for high-performance OLED devices are those with high thermal and chemical stabilities. Thus, the stability of our compounds follows the order: INH8 < INH15 < INH11 < INH10 < INH13 = INH3 < INH2 < INH9 < INH14 < INH7 < INH6 = INH5 = INH4 < INH < INH12 < INH1. Based on the above analyses, the functionalization of N-(4-methoxybenzylidene) isonicotinohydrazone using donor and acceptor groups enhances the performance of the materials in some cases.


### 3.4. Charge Transfer Integrals, Charge Transport Rate, and Mobility of the Studied Compounds

Presented in Table3 are the charge transfer integrals, charge transport rate, and mobility values of the studied compounds. These values were computed using the intermolecular distance of 4.0 Å between the two monomers.Table 3
The charge transfer integrals, charge transport rates, and mobilities of the molecules studied compounds, computed at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundstelectronatholeakelectronbkholebµelectroncµholecINH0.3360.3442.566 × 10132.752 × 10117.982 × 10−18.561 × 10−3INH10.1280.1593.381 × 10121.078 × 10111.051 × 10−13.353 × 10−3INH20.1170.5124.795 × 10123.843 × 10111.491 × 10−11.195 × 10−2INH30.0480.3131.131 × 10122.019 × 10123.518 × 10−26.281 × 10−2INH40.2020.0197.980 × 10121.597 × 10102.482 × 10−14.968 × 10−4INH50.1150.2521.056 × 10121.969 × 10113.285 × 10−26.125 × 10−3INH60.0230.1211.103 × 10111.979 × 1093.431 × 10−36.156 × 10−5INH70.1010.0632.128 × 10126.311 × 1086.620 × 10−21.963 × 10−5INH80.3460.4412.573 × 10123.178 × 10118.004 × 10−29.886 × 10−3INH90.2120.4322.067 × 10132.970 × 10116.430 × 10−19.239 × 10−3INH100.0460.0281.673 × 10117.329 × 1085.204 × 10−32.280 × 10−5INH110.1050.1572.133 × 10122.604 × 10106.635 × 10−28.100 × 10−4INH120.3410.0261.895 × 10135.195 × 1095.895 × 10−11.616 × 10−4INH130.1100.1489.073 × 10111.079 × 10112.822 × 10−23.356 × 10−3INH140.0120.0921.348 × 10102.181 × 10104.193 × 10−46.785 × 10−4INH150.0900.5381.636 × 10121.153 × 10135.089 × 10−23.586 × 10−1Note. telectron/thole ⟶ charge transfer integral of the electron or hole, kelectron/khole ⟶ charge transport rate of the electron or hole, µelectron/µhole ⟶ mobility of the electron or hole, ain eV, bin s−1, and cin cm2V−1s−1.Large charge transfer integral values improve the mobility and conductivity of OLED materials [16]. The findings in Table 3 show that the telectron ranges from 0.012 to 0.346 eV, while the thole varies from 0.019 to 0.538 eV. INH is found to have the highest electron transport rate with a value of 2.566 × 1013 s−1. This leads to an increase in the mobility of electron transport with a value of 7.982 × 10−1 cm2V−1s−1 and can be used for OLED-based applications. The results in the table also show that the electron mobility values of the different compounds follow the trend: INH > INH9 > INH12 > INH4 > INH2 > INH1 > INH8 > INH11 > INH7 > INH15 > INH5 > INH3 > INH13 > INH10 > INH6 > INH14.The results also indicate that INH15 has the highest hole transport rate (1.153 × 1013 s−1) as compared to the others. The increase in this value also leads to an increase in the hole transport mobility with a value of 3.586 × 10−1 cm2V−1s−1 and can be used in OLED technology. Moreover, the hole mobility values of the different compounds decrease as follows: INH15 > INH3 > INH2 > INH8 > INH9 > INH > INH5 > INH13 > INH1 > INH11 > INH14 > NH4 > INH12 > INH6 > INH10 > INH7. In the present work, the electron transfer integral and charge mobility of the studied compounds are generally higher than their hole transfer integral and charge mobility. So, it can be said that the series of N-(4-methoxybenzylidene) isonicotinohydrazone derivatives are good candidates for electron transfer material and charge mobility in OLED technology.


### 3.5. UV Spectral Analyses via TD-DFT

The UV absorption spectra of the studied compounds were evaluated. The first 10 excited states were calculated at the CAM-B3LYP/6-311G (d, p) level of theory. The calculated absorption wavelength (λabs), excitation energy (Eabs), oscillator strength, and orbital coefficients are summarized in Table 4. It is worth mentioning that only the oscillator strengths of the most intense bands are presented.Table 4
Excitation energies, wavelengths, oscillator strengths, molecular orbitals, and dominant electronic transitions of the studied compounds obtained at the CAM-B3LYP/6-311G (d,p) level of theory in the gaseous phase.
CompoundsExcited stateMO + coefficientEabsλabsƒINHS0 ⟶ S2H ⟶ L (48%)4.610268.390.370INH1S0 ⟶ S5H ⟶ L (50%)4.531273.640.270INH2S0 ⟶ S5H⟶L + 1 (42%)5.178239.420.520INH3S0 ⟶ S4H − 1 ⟶ L (49%)4.769259.950.432INH4S0 ⟶ S10H − 1 ⟶ L + 1 (32%)5.592221.720.329INH5S0 ⟶ S2H ⟶ L (39%)4.597269.700.276INH6S0 ⟶ S2H ⟶ L (58%)4.683264.720.410INH7S0 ⟶ S2H ⟶ L (58%)4.692264.200.411INH8S0 ⟶ S5H ⟶ L + (57%)4.663265.870.478INH9S0 ⟶ S4H ⟶ L + 1 (53%)4.701263.700.445INH10S0 ⟶ S3H ⟶ L + 1 (46%)4.705263.470.426INH11S0 ⟶ S9H − 1 ⟶ L(38%)5.738216.060.329INH12S0 ⟶ S1H − 1 ⟶ L (40%)5.709217.150.354INH13S0 ⟶ S9H − 1⟶L (32%)5.506225.140.298INH14S0 ⟶ S3H ⟶ L + 1 (43%)4.685264.610.445INH15S0 ⟶ S5H ⟶ L + 2 (38%)5.103242.960.344Note.Eabs: excitation energies (in eV), λabs: wavelengths (in nm), ƒ: oscillator strengths, MO: molecular orbital coefficients, H: HOMO, and L: LUMO.The result shows that the oscillator strengths range from 0.270 to 0.520. The most intense absorption band was recorded for compound INH2 with an oscillator strength of 0.520. The findings also show that the oscillator strength increases upon the extension of the conjugation system (see INH2 and INH3). The wavelengths of the investigated compounds are found to range from 216.06 to 273.64 nm. Generally, the functionalization of INH is found to reduce the wavelengths of the studied compounds except for INH1 and INH5. The computedλabs value of N-(4-methoxybenzylidene) isonicotinohydrazone is 268.39 nm and shows good agreement with the experimental value of 283 nm [24].The absorption energies are in the range of 4.531 to 5.738 eV. Functionalization of INH is observed to enhance the energy of the studied compounds except for INH1 and INH5. The shorter wavelengths and higher energies show that the investigated compounds are attributed toπ−π∗ transitions. Lower transition energies accompanied by higher oscillator strength will lead to a greater charge transfer, which consecutively results in robust NLO response (second hyperpolarizability) properties [47]. The recorded UV-Vis absorption spectra of the studied compounds are presented in the supplementary information (SI) file. The peaks at longer wavelength regions (lower energy) are associated with intramolecular charge transfer (ICT), whereas π−π∗ transitions appear in the shorter wavelength regions (higher energy) [54].


### 3.6. Nonlinear Optical Properties

Organic molecules are gaining importance in nonlinear optics as they exhibit good NLO activities because of extendableπ-conjugation and the ease of functionalization of a donor and an acceptor at the terminals of a conjugated molecular system [55]. The NLO properties such as static dipole moment (μ), static isotropic α and anisotropic ∆α polarizability, static isotropic first hyperpolarizability (β), and static isotropic second hyperpolarizability (γ) of the studied compounds are reported in Tables 5–8, respectively. The above-mentioned tensor components were recorded in atomic units (a.u) and converted into electrostatic units (esu) using the conversion factors: 1 a.u. = 0.15 × 10−24 esu for polarizability (αstatic), 1 a.u = 8.6393 × 10−33 esu for first hyperpolarizability (βstatic), and 1 a.u = 0.50367 × 10−39 esu for second hyperpolarizability (γstactic) [56].Table 5
The static electric dipole moment (μ) of the studied compounds, calculated at ω = 0 at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Speciesμxμyμzμstatic (a.u)μstatic (debye)INH1.6110.364−2.2922.8257.181INH11.027−0.225−2.4562.6726.792INH21.692−0.085−1.9792.6056.623INH31.531−0.076−2.1132.6116.636INH40.0000.0002.6782.6786.807INH51.0820.169−2.0222.3005.847INH60.2680.153−1.6431.6724.250INH70.0000.0001.6921.6924.302INH80.572−1.015−1.4251.8414.680INH90.0000.0002.7372.7376.957INH101.605−0.160−1.5012.2035.601INH111.4420.973−1.7162.4446.212INH120.759−0.521−2.8202.9667.540INH131.624−0.198−2.6513.1157.919INH140.180−0.615−1.6791.7974.569INH151.5150.772−2.0782.6856.825Table 6
Static average polarizabilities of the studied compounds, calculated atω = 0 at the B3LYP-D/6-311G (d, p) level of theory in the gaseous phase.
Speciesαxxαxyαyyαxzαyzαzzα (a.u)α × 10−24 esu∆α (a.u)∆α × 10−24 esuINH233.2478.5703104.8420−45.12915.1361232.0130190.03428.161152.80222.643INH1246.24513.452119.00−41.57919.576243.558202.93430.071150.78422.343INH2325.52843.596171.007−59.578−13.183283.082259.87238.509189.71428.112INH3315.0874.780170.133−58.606−9.602283.879256.36637.989186.80927.682INH4237.661−34.605128.49138.609−24.876266.467210.87331.248160.66723.808INH5234.4879.672104.145−45.27213.797233.287190.64028.249154.38522.877INH6244.88020.954117.990−41.3784.469235.346199.40529.548146.61521.726INH7236.591−22.178125.60945.01657.842255.322205.84130.502149.95422.220INH8254.82616.177121.556−49.10214.430243.722206.70130.630158.26323.452INH9253.230−37.503128.74327.027−31.849233.080205.01830.380151.15822.399INH10254.29819.375127.220−5.23414.372246.456209.32531.018158.67923.513INH11254.87622.234124.974−40.0485.154240.648206.83330.649146.98121.780INH12233.60711.929110.391−38.91719.621235.560193.18628.627146.80721.755INH13243.88917.250115.908−42.24317.463240.765200.18729.664152.15222.546INH14257.87823.986121.423−54.0169.002242.381207.22830.708165.73524.559INH15281.33023.955138.409−47.4873.358255.100224.94633.333160.89123.842α: isotropic polarizability and ∆α: anisotropic polarizability.Table 7
Static first hyperpolarizability of the studied compounds, calculated atω = 0, at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Compoundsβxβyβzβstatic (a.u)βstatic × 10−30 esuINH−683.005187.200785.0311057.269.130INH1−849.40072.728808.7721175.10910.152INH2−631.867−112.204465.456792.7766.849INH3−846.022−360.898625.35361112.2359.608INH4−850.633411.624−1009.2421382.59911.944INH5−780.19694.948885.1911183.75810.226INH6−586.19725.427289.774654.4025.653INH7−563.781−19.462−236.9632611.8655.286INH8−183.556241.853353.656466.1094.026INH9−411.432−6.167−425.3754591.8265.112INH10−372.997229.686539.475694.9216.003INH11−794.90179.312689.9781055.5699.119INH12−901.872−59.775763.1841182.96010.219INH13−1102.43−125.64983.3091266.21510.939INH14−507.054116.024611.955803.1526.938INH15−847.898−112.808648.6821073.5199.274Table 8
The static second hyperpolarizability (γstatic) of the studied compounds, calculated at ω = 0 at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Speciesγxxxxγyyyyγzzzzγxxyyγxxzzγyyzzγtotal × 10−36 esuINH183239.003854.1387083.702659.5046066.802246.7437.88INH1183722.005950.4590823.404796.2043941.603680.7238.82INH2234874.0020546.5086508.8024211.1063646.4011396.1054.44INH3243315.0025353.4084023.1032513.3064149.1012887.0057.60INH4136059.0010159.80129249.009483.529483.527402.9733.06INH5177961.003555.9595850.102575.2546702.201990.7238.27INH6156375.004737.6080935.104340.6336334.502471.1933.08INH7128524.004901.92107463.004630.4841328.604305.5134.39INH818477.207640.4581610.209315.2552669.305795.2624.51INH9184301.008092.3963934.3013711.8034270.209242.1637.35INH10188585.007622.2782806.507664.5750002.104358.2640.60INH11181608.007284.2793479.205546.2741470.202300.6738.38INH12167395.004662.7587287.703681.2438448.403206.7035.26INH13188566.005535.7694775.705051.4843980.603312.2139.65INH14183228.004196.4589054.404992.8549023.702460.9239.23INH15206706.008567.1585354.209826.6345110.503917.8942.14The molecular dipole moment is the basic property of a molecule, which is used to investigate intermolecular interactions. The higher the dipole moment, the stronger the intermolecular interactions and hence larger hyperpolarizabilities [55]. According to the results in Table 5, the computed dipole moment values of the investigated molecules range from 4.250 to 7.919 Debye. We note that INH13 and INH12 are characterized by the highest value of the total dipole moment; which are 7.919 and 7.541 Debye, respectively. These compounds, therefore, present good NLO responses.Polarizability gives information on the distribution of electrons in the molecule and plays a fundamental role in determining the structure and orientation of a system [56]. The static isotropic α and anisotropic ∆α polarizabilities of all the designed compounds are presented in Table 6.Table6 shows that the amplitudes of α and (∆α) of the N-(4-methoxybenzylidene) isonicotinohydrazone derivatives increase due to the presence of donor and acceptor substituents and the degree of π-conjugation in the system. Moreover, the static isotropic α polarizability values of the studied compounds increase as follows: INH < INH5 < INH12 < INH8 < INH13 < INH1 < INH9 < INH7 < INH11 < INH14 < INH10 < INH9 < INH4 < INH15 < INH3 < INH2. Among all the designed compounds, INH2 has the best isotropic polarizability value while INH has the least. The anisotropic ∆α values follows the order: INH6 < INH12 < INH11 < INH7 < INH1 < INH9 < INH13 < INH < INH5 < INH8 < INH10 < INH4 < INH15 < INH14 < INH3 < INH2. Among all the designed compounds, INH2 also shows the best anisotropic polarizability value. Moreover, the great difference between the isotropic and anisotropic polarizability values of all the compounds shows that polarizability significantly depends on the direction of the applied electric field [47].The first hyperpolarizabilities (second-order response) of the studied compounds are presented in Table7.In Table7, the nonzero value of βstatic shows that the investigated compounds possess first static hyperpolarizability. The first hyperpolarizability of urea (a prototype NLO molecule) was computed at the same level of theory (βstatic = 0.77 × 10−30 esu). The predicted first hyperpolarizability of the studied compounds is much greater than that of urea and has NLO behaviours. Table 7 also presents the calculated values of the components of the first hyperpolarizability and the following order for βstatic has been obtained: INH8 < INH9 < INH7 < INH6 < INH10 < INH2 < INH14 < INH11 < INH < INH15 < INH3 < INH1 < INH12 < INH5 < INH13 < INH4, indicating that INH5 and INH13 possess the highest NLO responses.Presented in Table8 are the second hyperpolarizabilities (third-order response) of the studied compounds.The second hyperpolarizability of para-nitroaniline (reference molecule for the second hyperpolarizability) was computed at the same level of theory (γstatic = 7.615 × 10−36 esu) and compared to those of the studied compounds. The results show that all the studied compounds have second hyperpolarizability values much greater than that of PNA, implying they have good NLO responses. From Table 8, the second hyperpolarizability (γstatic) increases as follows: INH8 < INH4 < INH6 < INH7 < INH12 < INH9 < INH < INH5 < INH11 < INH1 < INH14 < INH13 < INH10 < INH15 < INH2 < INH3. The results also show that the size of the pi-conjugated bridge has a significant effect on the third-NLO response. Among all the designed compounds, INH2 and INH3 possess the best second hyperpolarizability values (i.e., 54.44 × 10−36 and 57.60 × 10−36 esu, respectively.


## 3.1. Frontier Molecular Orbital Analysis

Frontier molecular orbitals were calculated from DFT-based optimized structures using the equations specified in the computational details section. Table1 presents the electronic parameters of N-(4-methoxybenzylidene) isonicotinohydrazone and its derivatives.Table 1
Electronic parameters of N-(4-methoxybenzylidene) isonicotinohydrazone and its derivatives calculated at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundsEHaELa∆EgaμaηaЅbωa∆NmaxINH−6.341−1.9184.423−4.1292.2110.2263.8541.867INH1−6.226−1.9024.324−4.0642.1620.2313.8191.879INH2−6.500−1.9914.509−4.2452.2540.2213.9961.883INH3−6.358−2.0224.336−4.1902.1680.2304.0481.932INH4−6.256−1.9864.270−4.1212.1350.2343.9771.930INH5−6.456−2.0454.411−4.2502.2050.2264.0941.927INH6−6.817−2.1764.641−4.4962.3200.2154.3551.937INH7−6.812−2.1674.645−4.4892.3220.2154.3381.933INH8−6.852−2.9193.933−4.8851.9660.2546.0672.484INH9−6.640−2.3784.262−4.5092.1310.2344.7702.115INH10−6.589−2.1154.474−4.3522.2370.2234.2331.945INH11−6.334−1.9664.368−4.1502.1840.2283.9421.900INH12−6.239−1.9234.316−4.0812.1580.2318.8581.891INH13−5.830−1.8224.008−3.8262.0040.2493.6521.909INH14−6.755−2.2304.525−4.4922.2620.2204.4591.985INH15−6.071−1.9294.142−4.0002.0710.2413.8621.931EH ⟶ HOMO energy, EL ⟶ LUMO energy, ∆Eg⟶, µ ⟶ chemical potential, η ⟶ chemical hardness, ω ⟶ electrophilicity index, ΔNmax ⟶ the maximum transferred charge, aunits in eV, and bunits in eV−1.The results show that functionalization of a donor at the terminal of N-(4-methoxybenzylidene) isonicotinohydrazone induces a reduction in the energy gap of INH (see INH1, INH4, INH11, INH12, INH13, and INH15). Similarly, functionalization with an acceptor only raises the band gap in the other cases and decreases it in INH8. Thus, compounds with small band gaps are softer, more reactive, and can show excellent NLO response [47]. The band gaps of all the studied compounds are in the range of 3.933 to 4.645 eV. This reduction in the energy gap of the designed derivatives compared to the synthesized (N-(4-methoxybenzylidene) isonicotinohydrazone) compound is attributed to the introduction of suitable donor and acceptor substituents. Hardness is the ability to resist charge transfer within its environment. The hardness values of all the investigated compounds range from 1.966 to 2.322 eV. Among these compounds, INH8 has the lowest hardness value (1.966 eV) and is therefore the most reactive. Organic materials with high and positive ω and ∆Nmax values have a greater affinity to absorb an electron. However, if a compound has a low amount of these indices, it may be characterized as an electron donor [48]. The maximum transferred charge (ΔNmax) and electrophilicity index (ω) values for all investigated compounds are positive and are in the range of 1.867 to 2.484 eV and 3.652 to 8.858 eV, respectively. The highest ΔNmax value of INH8 (2.484 eV) suggests that this compound has a greater tendency to absorb an electron. Based on the ongoing, INH8 is the most reactive compound and has the highest tendency to absorb an electron.Figure2 shows the HOMO and LUMO distributions of all the investigated compounds.Figure 2
Representation of the HOMOs and LUMOs of the studied compounds as calculated at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.The results show that the HOMOs are distributed on the –OCH3 group and the benzene ring of all the studied compounds. The LUMOs, on their part, are located on the pyridine ring of all the studied compounds except INH2, INH3, INH8, and INH9.


## 3.2. Molecular Electrostatic Potential (MEP) Map

The molecular electrostatic potential (MEP) map is a crucial parameter for describing the electrophilic and nucleophilic centres of a system [49]. On the colour-coded surfaces, the blue region shows the area of low electron density (i.e., the regions of positive potential), while the red region indicates the area of high electron density (i.e., regions of negative potential) [50–52]. Displayed in Figure 3 are the MEP plots of the compounds under investigation.Figure 3
Molecular electrostatic potential plots of the compounds under investigation, calculated at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.These findings show that the red electron-rich sites are centred on the oxygen atom of the carbonyl, the nitrogen atom of the pyridine ring, and the nitrogen atom of the azomethine group in all the studied compounds. In contrast, the blue electron-deficient sites are predominantly on the protons of the azomethine and methoxyl groups (except for INH2, INH3, INH7, and INH15).


## 3.3. Reorganization Energies

Presented in Table2 are important parameters needed to understand the charge transport nature and charge injection.Table 2
Reorganization energies, adiabatic electron affinity, vertical electron affinity, vertical ionization potential, adiabatic ionization potential, and hardness of the studied compounds all in eV, computed at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundsIPaEAaIPVEAVηλelectronλholeINH7.5100.6537.9180.4083.4280.4800.918INH17.4280.6537.8090.4083.7020.4890.859INH27.4560.8707.8910.6253.2930.4400.963INH37.4830.9257.7550.6803.2790.4090.707INH47.5100.7617.7820.5173.3740.4940.634INH57.6190.8708.0270.7073.3740.5780.890INH67.7280.9798.3540.7073.3740.4881.197INH77.7281.0060.2860.7073.3610.4881.181INH87.9181.5788.3541.1973.1690.7030.992INH97.7281.1150.3000.0323.3060.4150.955INH107.6461.0887.8640.7343.2780.5791.007INH117.2920.7617.8640.4893.2650.4950.995INH127.8640.6807.8090.4083.5920.5110.802INH137.1290.5717.4560.2993.2790.5840.845INH147.8641.1978.2720.8163.3330.5630.908INH157.2650.7407.5920.4733.2620.4910.644Note. λelectron/hole: reorganization energies, EAa: adiabatic electron affinity, EAV: vertical electron affinity, IPV: vertical ionization potential, IPa: adiabatic ionization potential, and η: hardness.Small reorganization (λelectron/hole) energy values indicate better charge transport rates and mobility, which give rise to good charge transport properties for the materials [39]. Results from Table 2 show that the increasing trend in the λelectron values is as follows: INH3 < INH9 < INH2 < INH < INH6 = INH5 < INH1 < INH15 < INH4 < INH11 < INH12 < INH14 < INH5 < INH12 < INH13 < INH8. This implies that INH3 (0.409 eV) possesses the best electron transport properties, while INH8 (0.703 eV) has the least. Moreover, the increasing trend in λhole values is as follows: INH4 < INH15 < INH3 < INH12 < INH13 < INH1 < INH5 < INH14 < INH < INH9 < INH2 < INH8 < INH11 < INH10 < INH7 < INH6. This suggests that INH4 (0.634 eV) possesses the best hole transport properties, while INH6 (1.197 eV) has the least. The results also show that the λelectron values are relatively smaller than those of the λhole values. This illustrates the potential of the studied compounds as n-type materials for organic light-emitting devices.A smaller IPa value means easier hole injection ability for the OLED materials, while a larger EAa value facilitates electron injection [8, 53]. Table 2 shows that INH13 (7.129 eV) has the lowest IPa value, while INH8 (1.578 eV) has the highest EAa value. The results also indicate that INH1 is the most stable compound under investigation, with the highest η value (3.702 eV). Good charge transporters for high-performance OLED devices are those with high thermal and chemical stabilities. Thus, the stability of our compounds follows the order: INH8 < INH15 < INH11 < INH10 < INH13 = INH3 < INH2 < INH9 < INH14 < INH7 < INH6 = INH5 = INH4 < INH < INH12 < INH1. Based on the above analyses, the functionalization of N-(4-methoxybenzylidene) isonicotinohydrazone using donor and acceptor groups enhances the performance of the materials in some cases.


## 3.4. Charge Transfer Integrals, Charge Transport Rate, and Mobility of the Studied Compounds

Presented in Table3 are the charge transfer integrals, charge transport rate, and mobility values of the studied compounds. These values were computed using the intermolecular distance of 4.0 Å between the two monomers.Table 3
The charge transfer integrals, charge transport rates, and mobilities of the molecules studied compounds, computed at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
CompoundstelectronatholeakelectronbkholebµelectroncµholecINH0.3360.3442.566 × 10132.752 × 10117.982 × 10−18.561 × 10−3INH10.1280.1593.381 × 10121.078 × 10111.051 × 10−13.353 × 10−3INH20.1170.5124.795 × 10123.843 × 10111.491 × 10−11.195 × 10−2INH30.0480.3131.131 × 10122.019 × 10123.518 × 10−26.281 × 10−2INH40.2020.0197.980 × 10121.597 × 10102.482 × 10−14.968 × 10−4INH50.1150.2521.056 × 10121.969 × 10113.285 × 10−26.125 × 10−3INH60.0230.1211.103 × 10111.979 × 1093.431 × 10−36.156 × 10−5INH70.1010.0632.128 × 10126.311 × 1086.620 × 10−21.963 × 10−5INH80.3460.4412.573 × 10123.178 × 10118.004 × 10−29.886 × 10−3INH90.2120.4322.067 × 10132.970 × 10116.430 × 10−19.239 × 10−3INH100.0460.0281.673 × 10117.329 × 1085.204 × 10−32.280 × 10−5INH110.1050.1572.133 × 10122.604 × 10106.635 × 10−28.100 × 10−4INH120.3410.0261.895 × 10135.195 × 1095.895 × 10−11.616 × 10−4INH130.1100.1489.073 × 10111.079 × 10112.822 × 10−23.356 × 10−3INH140.0120.0921.348 × 10102.181 × 10104.193 × 10−46.785 × 10−4INH150.0900.5381.636 × 10121.153 × 10135.089 × 10−23.586 × 10−1Note. telectron/thole ⟶ charge transfer integral of the electron or hole, kelectron/khole ⟶ charge transport rate of the electron or hole, µelectron/µhole ⟶ mobility of the electron or hole, ain eV, bin s−1, and cin cm2V−1s−1.Large charge transfer integral values improve the mobility and conductivity of OLED materials [16]. The findings in Table 3 show that the telectron ranges from 0.012 to 0.346 eV, while the thole varies from 0.019 to 0.538 eV. INH is found to have the highest electron transport rate with a value of 2.566 × 1013 s−1. This leads to an increase in the mobility of electron transport with a value of 7.982 × 10−1 cm2V−1s−1 and can be used for OLED-based applications. The results in the table also show that the electron mobility values of the different compounds follow the trend: INH > INH9 > INH12 > INH4 > INH2 > INH1 > INH8 > INH11 > INH7 > INH15 > INH5 > INH3 > INH13 > INH10 > INH6 > INH14.The results also indicate that INH15 has the highest hole transport rate (1.153 × 1013 s−1) as compared to the others. The increase in this value also leads to an increase in the hole transport mobility with a value of 3.586 × 10−1 cm2V−1s−1 and can be used in OLED technology. Moreover, the hole mobility values of the different compounds decrease as follows: INH15 > INH3 > INH2 > INH8 > INH9 > INH > INH5 > INH13 > INH1 > INH11 > INH14 > NH4 > INH12 > INH6 > INH10 > INH7. In the present work, the electron transfer integral and charge mobility of the studied compounds are generally higher than their hole transfer integral and charge mobility. So, it can be said that the series of N-(4-methoxybenzylidene) isonicotinohydrazone derivatives are good candidates for electron transfer material and charge mobility in OLED technology.


## 3.5. UV Spectral Analyses via TD-DFT

The UV absorption spectra of the studied compounds were evaluated. The first 10 excited states were calculated at the CAM-B3LYP/6-311G (d, p) level of theory. The calculated absorption wavelength (λabs), excitation energy (Eabs), oscillator strength, and orbital coefficients are summarized in Table 4. It is worth mentioning that only the oscillator strengths of the most intense bands are presented.Table 4
Excitation energies, wavelengths, oscillator strengths, molecular orbitals, and dominant electronic transitions of the studied compounds obtained at the CAM-B3LYP/6-311G (d,p) level of theory in the gaseous phase.
CompoundsExcited stateMO + coefficientEabsλabsƒINHS0 ⟶ S2H ⟶ L (48%)4.610268.390.370INH1S0 ⟶ S5H ⟶ L (50%)4.531273.640.270INH2S0 ⟶ S5H⟶L + 1 (42%)5.178239.420.520INH3S0 ⟶ S4H − 1 ⟶ L (49%)4.769259.950.432INH4S0 ⟶ S10H − 1 ⟶ L + 1 (32%)5.592221.720.329INH5S0 ⟶ S2H ⟶ L (39%)4.597269.700.276INH6S0 ⟶ S2H ⟶ L (58%)4.683264.720.410INH7S0 ⟶ S2H ⟶ L (58%)4.692264.200.411INH8S0 ⟶ S5H ⟶ L + (57%)4.663265.870.478INH9S0 ⟶ S4H ⟶ L + 1 (53%)4.701263.700.445INH10S0 ⟶ S3H ⟶ L + 1 (46%)4.705263.470.426INH11S0 ⟶ S9H − 1 ⟶ L(38%)5.738216.060.329INH12S0 ⟶ S1H − 1 ⟶ L (40%)5.709217.150.354INH13S0 ⟶ S9H − 1⟶L (32%)5.506225.140.298INH14S0 ⟶ S3H ⟶ L + 1 (43%)4.685264.610.445INH15S0 ⟶ S5H ⟶ L + 2 (38%)5.103242.960.344Note.Eabs: excitation energies (in eV), λabs: wavelengths (in nm), ƒ: oscillator strengths, MO: molecular orbital coefficients, H: HOMO, and L: LUMO.The result shows that the oscillator strengths range from 0.270 to 0.520. The most intense absorption band was recorded for compound INH2 with an oscillator strength of 0.520. The findings also show that the oscillator strength increases upon the extension of the conjugation system (see INH2 and INH3). The wavelengths of the investigated compounds are found to range from 216.06 to 273.64 nm. Generally, the functionalization of INH is found to reduce the wavelengths of the studied compounds except for INH1 and INH5. The computedλabs value of N-(4-methoxybenzylidene) isonicotinohydrazone is 268.39 nm and shows good agreement with the experimental value of 283 nm [24].The absorption energies are in the range of 4.531 to 5.738 eV. Functionalization of INH is observed to enhance the energy of the studied compounds except for INH1 and INH5. The shorter wavelengths and higher energies show that the investigated compounds are attributed toπ−π∗ transitions. Lower transition energies accompanied by higher oscillator strength will lead to a greater charge transfer, which consecutively results in robust NLO response (second hyperpolarizability) properties [47]. The recorded UV-Vis absorption spectra of the studied compounds are presented in the supplementary information (SI) file. The peaks at longer wavelength regions (lower energy) are associated with intramolecular charge transfer (ICT), whereas π−π∗ transitions appear in the shorter wavelength regions (higher energy) [54].


## 3.6. Nonlinear Optical Properties

Organic molecules are gaining importance in nonlinear optics as they exhibit good NLO activities because of extendableπ-conjugation and the ease of functionalization of a donor and an acceptor at the terminals of a conjugated molecular system [55]. The NLO properties such as static dipole moment (μ), static isotropic α and anisotropic ∆α polarizability, static isotropic first hyperpolarizability (β), and static isotropic second hyperpolarizability (γ) of the studied compounds are reported in Tables 5–8, respectively. The above-mentioned tensor components were recorded in atomic units (a.u) and converted into electrostatic units (esu) using the conversion factors: 1 a.u. = 0.15 × 10−24 esu for polarizability (αstatic), 1 a.u = 8.6393 × 10−33 esu for first hyperpolarizability (βstatic), and 1 a.u = 0.50367 × 10−39 esu for second hyperpolarizability (γstactic) [56].Table 5
The static electric dipole moment (μ) of the studied compounds, calculated at ω = 0 at B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Speciesμxμyμzμstatic (a.u)μstatic (debye)INH1.6110.364−2.2922.8257.181INH11.027−0.225−2.4562.6726.792INH21.692−0.085−1.9792.6056.623INH31.531−0.076−2.1132.6116.636INH40.0000.0002.6782.6786.807INH51.0820.169−2.0222.3005.847INH60.2680.153−1.6431.6724.250INH70.0000.0001.6921.6924.302INH80.572−1.015−1.4251.8414.680INH90.0000.0002.7372.7376.957INH101.605−0.160−1.5012.2035.601INH111.4420.973−1.7162.4446.212INH120.759−0.521−2.8202.9667.540INH131.624−0.198−2.6513.1157.919INH140.180−0.615−1.6791.7974.569INH151.5150.772−2.0782.6856.825Table 6
Static average polarizabilities of the studied compounds, calculated atω = 0 at the B3LYP-D/6-311G (d, p) level of theory in the gaseous phase.
Speciesαxxαxyαyyαxzαyzαzzα (a.u)α × 10−24 esu∆α (a.u)∆α × 10−24 esuINH233.2478.5703104.8420−45.12915.1361232.0130190.03428.161152.80222.643INH1246.24513.452119.00−41.57919.576243.558202.93430.071150.78422.343INH2325.52843.596171.007−59.578−13.183283.082259.87238.509189.71428.112INH3315.0874.780170.133−58.606−9.602283.879256.36637.989186.80927.682INH4237.661−34.605128.49138.609−24.876266.467210.87331.248160.66723.808INH5234.4879.672104.145−45.27213.797233.287190.64028.249154.38522.877INH6244.88020.954117.990−41.3784.469235.346199.40529.548146.61521.726INH7236.591−22.178125.60945.01657.842255.322205.84130.502149.95422.220INH8254.82616.177121.556−49.10214.430243.722206.70130.630158.26323.452INH9253.230−37.503128.74327.027−31.849233.080205.01830.380151.15822.399INH10254.29819.375127.220−5.23414.372246.456209.32531.018158.67923.513INH11254.87622.234124.974−40.0485.154240.648206.83330.649146.98121.780INH12233.60711.929110.391−38.91719.621235.560193.18628.627146.80721.755INH13243.88917.250115.908−42.24317.463240.765200.18729.664152.15222.546INH14257.87823.986121.423−54.0169.002242.381207.22830.708165.73524.559INH15281.33023.955138.409−47.4873.358255.100224.94633.333160.89123.842α: isotropic polarizability and ∆α: anisotropic polarizability.Table 7
Static first hyperpolarizability of the studied compounds, calculated atω = 0, at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Compoundsβxβyβzβstatic (a.u)βstatic × 10−30 esuINH−683.005187.200785.0311057.269.130INH1−849.40072.728808.7721175.10910.152INH2−631.867−112.204465.456792.7766.849INH3−846.022−360.898625.35361112.2359.608INH4−850.633411.624−1009.2421382.59911.944INH5−780.19694.948885.1911183.75810.226INH6−586.19725.427289.774654.4025.653INH7−563.781−19.462−236.9632611.8655.286INH8−183.556241.853353.656466.1094.026INH9−411.432−6.167−425.3754591.8265.112INH10−372.997229.686539.475694.9216.003INH11−794.90179.312689.9781055.5699.119INH12−901.872−59.775763.1841182.96010.219INH13−1102.43−125.64983.3091266.21510.939INH14−507.054116.024611.955803.1526.938INH15−847.898−112.808648.6821073.5199.274Table 8
The static second hyperpolarizability (γstatic) of the studied compounds, calculated at ω = 0 at the B3LYP-D/6-311G (d,p) level of theory in the gaseous phase.
Speciesγxxxxγyyyyγzzzzγxxyyγxxzzγyyzzγtotal × 10−36 esuINH183239.003854.1387083.702659.5046066.802246.7437.88INH1183722.005950.4590823.404796.2043941.603680.7238.82INH2234874.0020546.5086508.8024211.1063646.4011396.1054.44INH3243315.0025353.4084023.1032513.3064149.1012887.0057.60INH4136059.0010159.80129249.009483.529483.527402.9733.06INH5177961.003555.9595850.102575.2546702.201990.7238.27INH6156375.004737.6080935.104340.6336334.502471.1933.08INH7128524.004901.92107463.004630.4841328.604305.5134.39INH818477.207640.4581610.209315.2552669.305795.2624.51INH9184301.008092.3963934.3013711.8034270.209242.1637.35INH10188585.007622.2782806.507664.5750002.104358.2640.60INH11181608.007284.2793479.205546.2741470.202300.6738.38INH12167395.004662.7587287.703681.2438448.403206.7035.26INH13188566.005535.7694775.705051.4843980.603312.2139.65INH14183228.004196.4589054.404992.8549023.702460.9239.23INH15206706.008567.1585354.209826.6345110.503917.8942.14The molecular dipole moment is the basic property of a molecule, which is used to investigate intermolecular interactions. The higher the dipole moment, the stronger the intermolecular interactions and hence larger hyperpolarizabilities [55]. According to the results in Table 5, the computed dipole moment values of the investigated molecules range from 4.250 to 7.919 Debye. We note that INH13 and INH12 are characterized by the highest value of the total dipole moment; which are 7.919 and 7.541 Debye, respectively. These compounds, therefore, present good NLO responses.Polarizability gives information on the distribution of electrons in the molecule and plays a fundamental role in determining the structure and orientation of a system [56]. The static isotropic α and anisotropic ∆α polarizabilities of all the designed compounds are presented in Table 6.Table6 shows that the amplitudes of α and (∆α) of the N-(4-methoxybenzylidene) isonicotinohydrazone derivatives increase due to the presence of donor and acceptor substituents and the degree of π-conjugation in the system. Moreover, the static isotropic α polarizability values of the studied compounds increase as follows: INH < INH5 < INH12 < INH8 < INH13 < INH1 < INH9 < INH7 < INH11 < INH14 < INH10 < INH9 < INH4 < INH15 < INH3 < INH2. Among all the designed compounds, INH2 has the best isotropic polarizability value while INH has the least. The anisotropic ∆α values follows the order: INH6 < INH12 < INH11 < INH7 < INH1 < INH9 < INH13 < INH < INH5 < INH8 < INH10 < INH4 < INH15 < INH14 < INH3 < INH2. Among all the designed compounds, INH2 also shows the best anisotropic polarizability value. Moreover, the great difference between the isotropic and anisotropic polarizability values of all the compounds shows that polarizability significantly depends on the direction of the applied electric field [47].The first hyperpolarizabilities (second-order response) of the studied compounds are presented in Table7.In Table7, the nonzero value of βstatic shows that the investigated compounds possess first static hyperpolarizability. The first hyperpolarizability of urea (a prototype NLO molecule) was computed at the same level of theory (βstatic = 0.77 × 10−30 esu). The predicted first hyperpolarizability of the studied compounds is much greater than that of urea and has NLO behaviours. Table 7 also presents the calculated values of the components of the first hyperpolarizability and the following order for βstatic has been obtained: INH8 < INH9 < INH7 < INH6 < INH10 < INH2 < INH14 < INH11 < INH < INH15 < INH3 < INH1 < INH12 < INH5 < INH13 < INH4, indicating that INH5 and INH13 possess the highest NLO responses.Presented in Table8 are the second hyperpolarizabilities (third-order response) of the studied compounds.The second hyperpolarizability of para-nitroaniline (reference molecule for the second hyperpolarizability) was computed at the same level of theory (γstatic = 7.615 × 10−36 esu) and compared to those of the studied compounds. The results show that all the studied compounds have second hyperpolarizability values much greater than that of PNA, implying they have good NLO responses. From Table 8, the second hyperpolarizability (γstatic) increases as follows: INH8 < INH4 < INH6 < INH7 < INH12 < INH9 < INH < INH5 < INH11 < INH1 < INH14 < INH13 < INH10 < INH15 < INH2 < INH3. The results also show that the size of the pi-conjugated bridge has a significant effect on the third-NLO response. Among all the designed compounds, INH2 and INH3 possess the best second hyperpolarizability values (i.e., 54.44 × 10−36 and 57.60 × 10−36 esu, respectively.


## 4. Conclusion

DFT and TD-DFT methods have been used to report a theoretical analysis of the charge transport and nonlinear optical properties of novel N-(4-methoxybenzylidene) isonicotinohydrazone derivatives. The reorganization energies of the electronλelectron and hole λhole, charge transfer integral of the electron telectron and hole thole, mobility of the electron µelectron and hole µhole, first hyperpolarizability βstatic, and static isotropic second hyperpolarizability (γ) have been discussed. Frontier molecular orbitals indicate that INH8 is the most reactive, and the band gaps of all the studied compounds are in the range of 3.933 to 4.645 eV. Calculated reorganization energy values indicate that the investigated compounds are electron transport materials. The low values of the reorganization energies reveal that compounds INH3 and INH9, can be considered as moderate electron transport materials with charge mobilities of 3.518 × 10−2 and 8.004 × 10−2 cm2V−1s−1, respectively. In the same vein, the low reorganization energy of the hole reveals that compounds INH4 and INH15 can be considered as moderate hole transport materials. NLO investigations portray that compounds INH2 and INH3 exhibit higher values of static polarizability (isotropic and anisotropic) and second hyperpolarizability, while compounds INH4 and INH13 exhibit a larger value of first hyperpolarizability. The effect of donor/acceptor substituents and the π-conjugation system enhances the NLO and charge transport properties of the studied compounds. These findings are important for the design and applications of new molecules in optoelectronic engineering.



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*Source: 6588603-2023-01-16.xml*