Introduction

Organic materials received much more importance in the emerging field of nonlinear optics [1,2,3], due to their promising structural, optical, and strong intramolecular charge transfer (ICT) properties. These have been known for their low cost, ease of processing, and larger electro-optical coefficients as compared to inorganic materials [4,5,6]. Organic materials have a large number of applications in photonics such as optical data processing, optical data storage, optical communication switches, and cloud computing [7,8,9]. With the help of the materials researcher’s efforts, a large class of organic second-order NLO materials have been introduced in recent years to achieve the expected first hyperpolarizability. The first hyperpolarizability is the key factor for second-ordered NLO materials particularly optoelectronic applications [10, 11]. The most effective way of achieving the first hyperpolarizability is by choosing conjugated π systems by introducing a combination of strong electron donating and withdrawing groups by limited chain length [12]. Organic materials studied extensively confirm that with π conjugated push–pull type system is feasible to modulate for their optical, electronic, and chemical properties by adapting their molecular structure [13]. Higher NLO properties have been demonstrated by D-π-A type NLO organic chromophores. Here, D and A stand for functional groups that donate and accept electrons, respectively, while π denotes a conjugated bridge interaction through π-π* bonds that promote charge transfer and increase NLO activity [14].

Amidst the variety of organic molecules important for nonlinear optical (NLO) applications, certain compounds with strong electron-withdrawing characteristics like 1,3,4-oxadiazoles, thiosemicarbazones, imidazolium, and benzimidazoles are notable due to their exceptional second- and third-order NLO responses. These molecular frameworks display high NLO activity because of their significant ability to facilitate charge transfer within their structure—a crucial feature for NLO materials. A recent study has highlighted the considerable attention garnered by derivatives of 1,3,4-oxadiazoles across diverse fields such as optoelectronics and medicinal chemistry compounds along with dye-sensitized solar cells (DSSC) [15,16,17]. These derivatives are part of the heterocyclic moiety, belonging to the family of organic compounds with significant electron transport properties, high thermal ability, oxidative stability, and strong electron-withdrawing properties. They also exhibit strong fluorescence with good quantum yield, making them valuable in the development of materials for electroluminescent applications and electron-transporting materials [18, 19]. The study highlights the increasing focus on pharmaceutical, optical, biological, optoelectronic, and OLED applications of 1,3,4-oxadiazole derivatives while noting a limited number of works reported on their second nonlinear optical properties. S.S. Oliveira and colleagues investigated the use of different group molecules with 1,3,4-oxadiazoles, reporting second-order NLO properties with a first hyperpolarizability (β) of 24.0 × 10−30 esu [20]. Khemalapure et al. conducted research on the spectroscopic, optical, and NLO properties of 1,3,4-oxadiazole derivatives [21]. Alongamo et al. studied the impact of substituents on the charge transport and nonlinear optical (NLO) properties of 1,3,4-oxadiazole derivatives [22]. Carella et al. explored the use of thiophene rings with 1,3,4-oxadiazole chromophores for second-order NLO properties [23]. Yi-Kai Fang et al. focused on non-conjugated random copolymers with pendant electron-donating 1,3,4-oxadiazole derivative moieties [24]. Homocianu et al. conducted a study and review of fluorinated 1,3,4-oxadiazole derivatives, examining their NLO parameters [25]. In a study by Dhannur et al., advanced DFT methods were used to investigate the NLO properties of D–π–A substituted bis-1,3,4-oxadiazoles [26]. The synthesized molecules were both structurally confirmed through spectroscopic techniques and showed significant NLO activity, with hyperpolarizability values exceeding that of standard benchmarks like urea by 55 times. These exceptional characteristics highlight the potential usefulness of these compounds in NLO applications. Additionally, the research conducted by Homocianu et al. delved into the nonlinear optical properties and metal ion sensing capabilities of a polymer composed of 1,3,4-oxadiazole and bisphenol A units. Utilizing UV–Vis absorption and fluorescence spectroscopies, the solvatochromic method revealed this polymer’s significant NLO parameters (α = 0.54 × 10−23 esu, β = 2.99 × 10−29 esu, and γ = 9.21 × 10−34 esu) [27]. Another study by Silva et al. investigated two 1,3,4-oxadiazole derivatives, demonstrating their substantial second-order optical nonlinearity as seen in their first hyperpolarizability values (106 × 10−34 esu and 126 × 10−34 esu) [28]. These findings collectively underscore the potential of these compounds for advanced optoelectronic applications.

The role of NLO materials is crucial in modern photonic applications, but the challenge lies in finding new compounds with strong NLO response, good thermal stability, and easy processing. Employing the density functional theory method offers significant advantages in designing materials and estimating their potential electronic, optical, and NLO properties [29]. This study aimed to investigate the second-order NLO properties of novel 1,3,4-oxadiazole derivatives using DFT. The specific objectives were to design a series of D-π-A type push–pull chromophores based on 1,3,-4-oxadiazole derivatives; evaluate the impact of different donor groups on the NLO properties of these chromophores; and identify structure–property relationships that may lead to materials with enhanced NLO performance. To achieve this goal, a set of four D-π-A type push–pull 1,3,4-oxadiazole derivative chromophores (Fig. 1) were designed, namely (Z)-4-(5-(4-(bis(4-(dimethylamino) phenyl)amino)styryl)-1,3,4-oxadiazol-2-yl)phthalonitrile, (E)-4-(5-(2-(10-propyl-10H-phenothiazin-3-yl)vinyl)-1,3,4-oxadiazol-2-yl)phthalonitrile, (E)-4-(5-(2-(anthracen-9-yl)vinyl)-1,3,4-oxadiazol-2-yl) phthalonitrile, and (E)-4-(5-(4-(9H-carbazol-9-yl)styryl)-1,3,4-oxadiazol-2-yl) phthalonitrile are abbreviated as TM1, TM2, TM3, and TM4 to achieve second-order NLO properties. Additionally, a series of donors including triphenylamine, phenothiazine, anthracene, and carbazole, together with 1,3,4-oxadiazole as a common withdrawing group, were employed to attain exceptional second-order NLO properties. These substituents were chosen due to their robust electron-donating capabilities, which are well-documented in the literature [30,31,32,33,34,35]. The rationale behind the selection is rooted in their ability to enhance the electron density on the conjugated 1,3,4-oxadiazole core, thereby having the potential to improve the second-order nonlinear optical (NLO) properties of the molecules. Triphenylamine is known for its strong electron-donating nature and its stability, which makes it an excellent candidate for electronic applications [35]. Carbazole is a heteroaromatic compound recognized for its high thermal stability and favorable electronic properties [34]. Carbazole and triphenylamine units are commonly utilized in organic donor materials due to their outstanding optical and electronic properties. The carbazole structure can be extensively modified and is widely used in applications such as organic light-emitting diodes [36, 37]. Phenothiazine provides a unique combination of electron donation capability and steric hindrance that influences molecular packing and electron transport [31]. Additionally, phenothiazine units with strong electron-donating capacity have distinct electronic properties; these have been frequently utilized as donor groups in dye-sensitized solar cells (DSSCs). Anthracene, a polycyclic aromatic hydrocarbon, contributes to extended π-conjugation, potentially increasing NLO responses [32]. Each donor was carefully chosen to explore the effects of different electronic and steric properties on the overall NLO performance of the 1,3,4-oxadiazole derivatives. These substituents not only enhance the intramolecular charge transfer but also contribute to the structural diversity of the compounds, thus offering a broad perspective on structure–property relationships in the context of NLO materials.

Fig. 1
figure 1

1,3,4-oxadiazole derivative chromophores TM1, TM2, TM3, and TM4

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Computational method

In this investigation, the quantum chemical calculations were carried out using the Gaussian 16 program suite [38]. Density functional theory (DFT) was employed for all calculations. Initially, the geometries of chromophores TM1-TM4 were optimized in C1 symmetry using DFT functionals APFD, B3LYP, CAM-B3LYP, and ωB97XD. The choice of APFD and B3LYP functionals was based on their proven reliability in accurately predicting electronic properties across a wide range of molecular systems. Specifically, APFD is known for its balanced treatment of exchange–correlation energy while B3LYP demonstrates general-purpose applicability across diverse chemical systems. For long-range corrected functionals, CAM-B3LYP and ωB97XD were selected to account for significant long-range electron–electron interactions crucial in studying NLO properties. CAM-B3LYP allows tunable range-separation parameters important for studies involving charge transfer states while ωB97XD incorporates dispersion corrections making it adept at modeling non-covalent interactions—an essential factor given our novel 1,3,4-oxadiazole derivatives. By combining these functions, we aimed to achieve a comprehensive analysis ensuring reliability of geometric structures. Moreover, the complementary strengths of these functionals, each meticulously chosen for their proven competencies in different aspects of DFT calculations, coalesce to offer an in-depth and accurate understanding of the second-order NLO properties that are central to our study’s objectives. Further stability analysis was conducted for each wavefunction in the gas phase, with no imaginary frequency found due to the various degrees of freedom of both structure and wavefunction. To examine the nonlinear optical (NLO) behavior and other associated intramolecular charge transfer properties of chromophores TM1–TM4, electrical properties such as dipole moment (μ), polarizability (α), first hyperpolarizability (β), natural bond orbital analysis (NBO), and frontier molecular orbitals (FMO) for the ground state were estimated using the time-independent DFT method. A time-dependent TD-DFT method was utilized to approximate vertical energy transitions for the UV–visible spectra. The estimated properties were derived from both the gaseous phase and five different solvent environments, including acetonitrile, benzene, dichloromethane (DCM), dimethyl sulfoxide (DMSO), and ethanol. The influence of solvents was investigated using the universal solvent model (SMD) [39]. This model efficiently captures polarization effects by considering the dielectric constant and surface tension of the solvent, resulting in a more precise simulation of real-life conditions where the NLO properties would be observed. Throughout the study, the 6–311 +  + G (d, p) level basis set with functionals was utilized to enhance precision and provide a detailed representation of molecular orbitals. In this basis set, the polarization of hydrogen atoms is indicated by d, while all other heavy atoms are represented by p.

Results and discussion

Dipole moment

The static dipole moment is greatly influenced by the structure and the electronegativity of the atoms present in the structure, as well as the induced field [40]. The influence of a polar solvent is also taken into consideration. Using the same level theory, the ground state dipole moment of chromophores TM1–TM4 is estimated. Generally, the dipole moment increases as the polarity of the solvents increases. The dipole moment values for TM1–TM4 are calculated using Eq. (1) and are presented in Table 1, 2, 3, and 4. The order of dipole moment values for TM1–TM4 is TM1 > TM2 > TM4 > TM3.

Table 1 Calculated dipole moment (μ) in Debye, polarizability (α) (in 10−24 esu), and first hyperpolarizability (β) (in 10−34 esu) at 6–311 +  + G (d, p) level basis set for TM1
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Table 2 Calculated dipole moment (μ) in Debye, polarizability (α) (in 10−24 esu), and first hyperpolarizability (β) (in 10−34 esu) at 6–311 +  + G (d, p) level basis set for TM2
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Table 3 Calculated dipole moment (μ) in Debye, polarizability (α) (in 10−24 esu), and first hyperpolarizability (β) (in 10−34 esu) at 6–311 +  + G (d, p) level basis set for TM3
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Table 4 Calculated dipole moment (μ) in Debye, polarizability (α) (in 10−24 esu), and first hyperpolarizability (β) (in 10−34 esu) at 6–311 +  + G (d, p) level basis set for TM4
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$$\begin{array}{ccc}\mathrm{Dipole \;moment},& \mu ={\left({\mu }_{x}^{2}+{\mu }_{y}^{2}+{\mu }_{z}^{2}\right)}^\frac{1}{2}& \mathrm{in \;Debye}\end{array}$$
(1)

The effect of donor functional groups and solvents on all the molecules is evident in the dipole moment values. A higher dipole moment value is observed in TM1 due to the substitution of the triphenylamine functional group, which donates a greater number of partial charges from the donor end. TM2 and TM4 also exhibit moderate donation of partial charges, attributed to the phenothiazine and carbazole functional groups. Conversely, TM3 shows a lower dipole moment value upon substitution of anthracene, as its flat structure contributes to a low partial charge donation compared to other chromophores. Additionally, the dipole moment values increase in solvents, with remarkable values observed in DMSO, following the order of solvent polarity index [41].

Linear polarizability

The linear polarizability (α), also referred to as the first-order NLO response, represents the system’s reaction to an applied electric field [42]. It is associated with intramolecular charge transfer (ICT). When an external electric field interacts with the surplus electrons in these systems, it amplifies the dipole moments, thereby elevating the linear polarizability and first-order hyperpolarizability, which can be calculated using Eq. (2).

$$\begin{array}{cc}\alpha =\left(\frac{1}{3}\right)\left[{\alpha }_{xx}+{\alpha }_{yy}+{\alpha }_{zz}\right]& {\text{esu}}\end{array}$$
(2)

Tables 1, 2, 3, and 4 display the α values for compounds TM1 to TM4. It is evident that the α value for TM4 is 55.31493074 × 10−24 esu in the gaseous phase and 79.87583749 × 10−24 esu in DMSO, which represents the lowest value among the estimated series of compounds. In contrast, TM1 exhibits the most polarizable nature, with significantly higher values of 80.80797773 × 10−24 esu in the gaseous phase and 110.6229904 × 10−24 esu in DMSO. Meanwhile, TM2 and TM3 demonstrate α values of 63.93808397 × 10−24 esu and 65.7275624 × 10−24 esu in the gaseous phase, and 87.43539356 × 10−24 esu and 90.92382203 × 10−24 esu in DMSO, respectively. Overall, the compounds exhibit comparable α values, with the trend being TM1 > TM3 > TM2 > TM4 in both gaseous and solvent phases.

First hyperpolarizability

The first hyperpolarizability is a third-rank tensor represented by a 3 × 3 × 3 matrix. This matrix contains 27 components, which can be reduced to 10 components due to Kleinman symmetry. The first hyperpolarizability is a key factor in determining the strength of second-order nonlinear optical (NLO) materials [43]. The static first hyperpolarizability of the designed molecules TM1–TM4 has been computed using Eq. (3) to analyze their NLO responses, and the results are presented in Table 1, 2, 3, and 4. Initially, we estimated the first hyperpolarizability of TM1–TM4 molecules using the four hybrid functionals mentioned above, both in gas and in five solvents using the solvatochromic method. The results indicated that the order of first hyperpolarizability is TM1 > TM2 > TM3 > TM4 and the first hyperpolarizability increases as the polarity of the solvents increases.

$${\beta }_{{\text{total}}}={\left[{\left({\beta }_{xxx}+{\beta }_{xyy}+{\beta }_{xzz}\right)}^{2}+{\left({\beta }_{yyy}+{\beta }_{xxy}+{\beta }_{yyz}\right)}^{2}+{\left({\beta }_{zzz}+{\beta }_{xxz}+{\beta }_{yyz}\right)}^{2}\right]}^\frac{1}{2}$$
(3)

Due to the substitution of a dimethyl-attached triphenylamine functional group as a donor, the first hyperpolarizability value is higher in TM1. This is attributed to the greater contribution of charges from the lone pair of electrons from nitrogen and methyl groups. The molecule has a good donating capacity among all four molecules. Additionally, TM2 and TM3 are attached with phenothiazine and anthracene respectively, both are good donors due to their donating capacity, resulting in a lower contribution of charges compared to TM1. Furthermore, the first hyperpolarizability of TM4 is the lowest among the four molecules, which can be attributed to its structure and low contribution of charges.

FMO

The HOMO and LUMO, known as frontier molecular orbitals, are widely utilized for assessing the electronic and optical properties of molecules. They provide essential information regarding the spectroscopic and chemical characteristics of molecules [44, 45]. The stability of the molecule is linked to the energy variances of its orbitals. This information, presented in Table 5, along with the molecule’s electronic structure (Fig. 2), aids in evaluating its diverse chemical properties. Here, we have calculated the HOMO–LUMO band gap energies of the TM1–TM4 chromophores at ground state, which are listed in Table 5 and depicted in Fig. 2, showing the FMO for π → π* transitions computed for the ground state of the compounds. Frontier molecular orbitals with energy values closely situated to one another exhibit exceptionally polarizable characteristics, as indicated by the negative charge phase (red) and positive charge phase (green) patterns, suggesting their high reactivity. The HOMO covers the oxadiazole group, while the LUMO extends beyond it, indicating an electrophilic or nucleophilic region, facilitating attainable intramolecular interactions. Given the similar patterns and small energy gaps exhibited by all the molecules, it is probable that they are highly reactive. Furthermore, chemical parameters such as chemical hardness, reactivity, and softness of the molecules were computed using the HOMO–LUMO and are listed in Table 5.

Table 5 Chemical hardness (η) (in eV), chemical softness (σ) (in eV), HOMO, and LUMO (in au) for π → π* interactions calculated at ωB97XD/6–311 +  + G (d, p)
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Fig. 2
figure 2

Frontier molecular orbitals for π → π* interactions calculated at ωB97XD/6–311 +  + G (d, p) in gas phase

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Chemical hardness is a measure of a chemical species’ resistance to changes in its electronic configuration, indicating the stability and electronegativity of its atoms [46, 47]. The chromophores TM1–TM4, listed in Table 5, provide the values of chemical hardness and chemical softness, which are obtained using Eqs. (4) and (5).

$$\eta =\frac{1}{2}\left[{E}_{{\text{LUMO}}}-{E}_{{\text{HOMO}}}\right]$$
(4)
$$\sigma =\frac{1}{\eta }$$
(5)

The HOMO–LUMO band gap exhibits a very low value, leading to softness in nature and high chemical reactivity, along with aromatic and polarizable properties [48]. This low bandgap energy of conjugated chromophores makes them highly suitable for potential optoelectronic applications. Additionally, chemical softness, which is the opposite of hardness, denotes the capacity to attract electron flow. It is associated with a polarizability attribute and can be calculated using Eq. 5. Softness is closely linked to the polarizability of the system, implying that a more polarizable chemical system is expected to be softer [49, 50].

NBO

The natural bond orbital (NBO) tool is utilized to analyze both intra- and inter-molecular interactions, providing valuable insights into the interactions of filled and virtual orbitals. It allows for the precise determination of a molecule’s Lewis structure by maximizing the electron density percentage of an orbital [51,52,53]. Furthermore, it facilitates the extraction of data on variations in charge densities of donor and acceptor protons, particularly in bonding and antibonding orbitals. The tool also calculates intra-molecular charge transfer and determines effective interactions between the Lewis-type occupied NBO orbital (bonding) and non-Lewis unoccupied NBO orbital (anti-bonding) using the same level theory in both gas and solvent phases with detailed results presented in Table 6 as well as Tables S1, S2, and S3 from Supplementary Information. Another useful aspect is that it provides information about interactions in both filled and virtual orbital spaces which enhances analysis of intra- or inter-molecular interactions. Delocalization of electron density between occupied NBO (bond or lone pair) and unoccupied NBO corresponds to stabilizing donor–acceptor interaction can be observed with estimation possible through second-order perturbation theory. Furthermore, conducting second-order perturbation theory on molecules allows for the calculation of stabilization energy using Eq. (6) [54].

$${E}^{\left(2\right)}={q}_{i}\frac{{F}^{2}\left(i,j\right)}{{\varepsilon }_{j}-{\varepsilon }_{i}}$$
(6)

where F2 (i,j) represents the off-diagonal matrix elements, qi gives the donor orbitals occupancy, εj and εi provide the values of donor and acceptor orbital energies, and E(2) estimates the magnitude of the interaction between the donor and acceptor orbitals. There are different types of electronic transitions, in that four different typical electronic transitions are observed σ → σ*, π → π*, LP → σ*, and LP → π* The most significant electronic transitions are found as among the above-mentioned transitions, while is examined as π → π* are the least prominent, LP → σ* and LP → π* and σ → σ*are noticed as slightly dominant transitions. In the case of chromophore TM1 (Fig. 3), the most striking σ → σ* transitions are C33–C35 and C37–C38, with stabilization energies at 3652.23 and 2835.47 kcal mol−1, respectively. Examining the weaker transitions, significant values are also observed at 4.28 and 4.41 kcal mol−1 for transitions C6–C7 and C4–C6, respectively. Notable resonance transitions for discussion include N20 → C2, which shows the highest stabilization energy of 100.80 kcal mol−1, and N20 → C10–C12, exhibiting the lowest stabilization energy of 0.65 kcal mol−1 (Table 6). The most effective transitions are observed at 3652.23 kJ/mol, 2001.29 kJ/mol, 2414 kJ/mol, and 2016.45 kJ/mol in TM1, TM2, TM3, and TM4, respectively. Additionally, two types of donors and three types of acceptors are observed, with the π → π* transitions in both molecules contributing to high polarization, further influencing the NLO activity of the molecule.

Table 6 Some selected most effective second-order perturbation (E2) transitions of TM1 chromophore are listed for evaluation of hyperconjugation energies (kcal/mol) calculated at ωB97XD/6–311 +  + G(d, p)
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Fig. 3
figure 3

Schematic charge in flow in molecule TM1

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MEP

The molecular electrostatic potential (MEP) surfaces are essential in the field of optoelectronics, as they help analyze and understand the electronic structures of organic materials. The distribution of electron density around these molecules is crucial for understanding their reactive behavior. MEP maps use color gradation to display a molecule’s size, structure, and positive, negative, and neutral electrostatic potential areas. These maps can identify regions where charged reagents will electrophilically attack organic compounds. Figure 4 depicts theoretical maps showing the distribution of electrostatic potential on the base ring plane obtained using density functional theory with a level basis set. Additionally, Fig. 5 presents a three-dimensional representation indicating positive nucleophilic sites (in blue), proton-rich electrophilic sites (in red), and electrically neutral regions (in white). The electrophilic cloud predominantly exists on oxygen and nitrogen atoms, encompassing groups such as 1,3,4-oxadiazole. In contrast, the nucleophilic cloud regions extend through the donor region surrounding hydrogen atoms like triphenylamine and carbazole [26]. Notably, the extension around the oxadiazole group has shown a strong positive charge while triphenyl amine exhibits a negatively charged region which signifies intramolecular charge transfer-based dipole moment orientation.

Fig. 4
figure 4

Electrostatic potential surface TM1–TM4 obtained at ωB97XD/6–311 +  + G (d, p)

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Fig. 5
figure 5

Electrostatic potential Curve TM1–TM4 obtained at ωB97XD/6–311 +  + G (d, p)

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UV–Vis spectrum

The UV–Vis absorbance spectra provide valuable insights into the conjugation, transitions, and the nature of charge transfer processes in organic molecules [55]. It is worth noting that all the chromophores TM1–TM4 exhibit absorption maxima (λmax) within the ultraviolet region (Fig. 6 and Figs. S1, S2, and S3).

Fig. 6
figure 6

UV–Vis spectrum of TM1 recorded at ωB3LYP/6–311 +  + G (d, p) with n = 50 (n is number of excited states and wavelength in nm)

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UV–visible spectra were obtained using the TD-DFT method in DMSO, resulting in an enhanced value. Chromophores with donor functional groups containing delocalized π electrons typically exhibit electronic transitions of the n → π* and π → π* types. As shown in Fig. 6, TM1 exhibits absorption at λmax in the ultraviolet region due to the presence of the 1,3,4-oxadiazole ring in the molecule’s structure. The extended aromatic structure reduces the HOMO–LUMO gap, leading to a shift in the wavelength [56]. The oscillator strength indicates the effective number of electrons involved in transitions from the ground state to the excited state, resulting in the absorption area in the spectrum. Smaller oscillator strength leads to new transitions, as reflected in the oscillator strength values mentioned in Table 7. These values were found to be in the range associated with the solvents ethanol, DMSO, DCM, benzene, and acetonitrile, and were correlated with the hyperchromic effect of the TM1 sample in the solvent.

Table 7 UV–Vis spectrum, oscillator strength recorded at ωB3LYP/6–311 +  + G (d, p) with n = 50 (n is the number of excited states)
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Overall, the investigation into the second-order nonlinear optical (NLO) properties of novel 1,3,4-oxadiazole derivatives, conducted through density functional theory (DFT), has yielded promising results that are indicative of their potential in various advanced optoelectronic applications. The study has successfully demonstrated that these derivatives exhibit significant NLO responses, which are highly desirable in the field for the development of efficient and compact optical devices specifically highlighting their utility in organic light-emitting diodes (OLEDs), photovoltaic cells, and as electro-optic modulators due to their promising second-order NLO properties. The theoretical framework provided by DFT has proven to be a powerful tool in predicting and understanding the electronic characteristics that govern the NLO behavior of these materials, laying a foundational basis for further experimental validation and application-driven research.

Conclusion

In conclusion, our study delved into the examination of second-order NLO properties in 1,3,4-oxadiazole derivative chromophores with various donor functional groups. The findings revealed significantly high hyperpolarizability and dipole moment values in TM1 and TM4 molecules when substituted with strong electron-donating groups such as triphenylamine and carbazole in DMSO solvent. Notably, TM1 demonstrated an exceptional first hyperpolarizability (β) of 293,679.0178 × 10−34 esu alongside a dipole moment (μ) of 5.66 Debye and polarizability (α) of 110.62 × 10−24 esu when assessed in dimethyl sulfoxide (DMSO). Furthermore, under benzene solvent conditions utilizing ωB97XD functional with a basis set of 6–311 +  + G(d,p), TM1 exhibited a low energy band gap measuring at 5.33 eV while NBO analysis confirmed the highest charge transfer value at E2 kJ/mol respectively. These molecules exhibit strong absorption maxima in the ultraviolet region and a lower HOMO–LUMO energy gap due to their aromatic structure. The derivatives also demonstrate good thermal stability, indicating the potential for enhancing nonlinear optical (NLO) response through structural tailoring with different electron-rich donor substituents. Moreover, the observed lower energy gap suggests possible intermolecular charge transfer within the π-conjugated molecular system, further supporting their promising NLO candidacy.