NLO potential exploration for D–π–A heterocyclic organic compounds by incorporation of various π-linkers and acceptor units

3.1 Frontier molecular orbital (FMO) analysis

To explain the reactivity, possibility of charge transfer and potential for the light absorption of the molecules, FMO investigation is a remarkable tool (Peng and Yu, 1994). These factors are directly related to the bandgap of HOMO/LUMO orbitals. Herein, HOMO is regarded as an electron donator, which is the highest electronically filled molecular orbital, while LUMO is generally attributed as an acceptor and is empty or unfilled orbital (Chemla, 2012). Molecules with smaller HOMO-LUMO distance are regarded as more reactive, less stable as well as soft compounds. Such molecules exhibited larger possibilities for the intramolecular charge transfer (ICT); hence, more polarized so, will serve as a finer competitor in offering the best NLO response (Dai et al., 2018; Ferdowsi et al., 2018b; Nagarajan et al., 2017; Yamada et al., 2018). In this consideration, energies of HOMO/LUMO, HOMO-1/LUMO + 1 and HOMO-2/LUMO + 2 of DTA1–DTA12 were calculated, and results were tabulated in Tables S13 (a) and S13 (b).

Fig. 3 represented that all the derivatives shown lower HOMO/LUMO energies with smaller bandgap than reference chromophore except DTA6, which expressed HOMO-LUMO energies comparable to reference. Further, Table S13 (a) elucidated that the HOMO/LUMO and bandgap energy (2.13 eV) of the reference compound (JK201) was higher (Khan et al., 2019a) than all its derivatives (DTA1–DTA12). The Eg values of all the designed dyes were decreasing gradually from 2.07 to 1.84 eV. Among DTA1 to DTA4 compounds with FBSA as end caped acceptor moiety, the largest Eg value (2.00 eV) was calculated in DTA2, in which DMT was used as the first π-linker. This Eg was reduced to 1.98 eV in DTA4, then diminished to 1.97 eV in DTA3 and further becomes lessen to 1.88 eV in DTA1 as the first π-spacer changes DPT, FMC and FMB, respectively. The same phenomena was investigated among the ETAA acceptor unit family (DTA5 to DTA8), the compound DTA6 with DMT first π-linker exhibited the huge Eg (2.07 eV). In comparison, the least value was found in DTA5 (1.93 eV), in which FMB was used as the first π-bridge. Similarly, DTA9 - DTA12 compounds with ETMN acceptor decreased in Eg and were observed as DTA10 > DTA11 > DTA12 > DTA9 as their first π-linker changes. Nevertheless, it was also examined that the compounds with FMB as the first π-linker exhibited low bandgap.

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Fig. 3

Graphical representation of HOMO/LUMO energies of entitled chromophores.

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On the other hand, DMT first π-spacer species showed a larger HOMO/LUMO energy difference. Among all the designed dyes, in compound DTA9, the least Eg was studied. The combined effect of electron-rich and planar π-linker FMB (5,6-difluoro-4,7-dimethylbenzo[c] thiadiazole) (Eaton, 1991; Peng and Yu, 1994) and powerful acceptor moiety ETMN(2-(5-methylene-4-oxothiazolidin-2-ylidene)malononitrile), collectively reduced the distance between HOMO and LUMO (1.84 eV) in DTA9 than from its reference dye(2.13 eV). Overall, calculated Eg of the organic dyes DTA1–DTA12 was increased in the following order: DTA9 < DTA12 < DTA11 < DTA1 < DTA10 < DTA5 < DTA3 < DTA4 < DTA7 < DTA2 < DTA8 < DTA6.

Along with the magnitude of the energy gap of orbitals, the capability of species to undergo ICT towards acceptor from the donor through π-spacers is also a significant aspect for NLO structure–function relationships (Khalid et al., 2020a). Surfaces of FMOs were utilized to reveal the transfer of charges, as displayed in Fig. 4 and Fig. S1. In all designed dyes, the HOMO was predominantly located over the donor DMFA part and partially on the π-bridge. LUMO charge density was mainly presented over the terminal acceptor units and partly over the π-spacers (Fig. 4). Similarly, for HOMO-1, the electronic cloud is located majorly over the π-bridge and acceptor units and minorly over the donor part, while for LUMO, it is concentrated over the acceptor and π-spacers (see Fig. S1).

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Fig. 4

The contour of HOMO and LUMO orbitals of the studied dyes.

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Fig. 4

The contour of HOMO and LUMO orbitals of the studied dyes.

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This facilitation indicated the efficient charge transfer by π-conjugates from the D moiety towards A unit ensures that all the analyzed dyes (DTA1-DTA12) would be significant NLO materials.

3.2 Global reactivity parameters

The Eg (E_LUMO-E_HOMO) is the most significant factor for the evaluation of the global reactivity parameters (GRPs) such as global hardness (η), global softness ( $\sigma$ ), global electrophilicity index (ω) electron affinity (EA), ionization potential (IP) (Fukui, 1982) electronegativity (X) and chemical potential (μ) (Chattaraj et al., 2006; Lesar and Milošev, 2009; Parr et al., 1978; Parr et al., 1999). The energy necessary to extract the electron from the HOMO orbital is equal to the ionization potential, which expressed the electron-donating and electron-accepting ability of an atom. This parameter is used to measure the electrophilic strength of compounds. Furthermore, the HOMO/LUMO energy gap was directly related to chemical potential, hardness, and compound stability while inversely associated with reactivity. Therefore, molecules with smaller Eg were regarded as more reactive, less stable and soft molecules considered far more polarized and serve as a finer competitor in offering the best NLO response (Dai et al., 2018; Ferdowsi et al., 2018a; Khalid et al., 2020a). Thus, global reactivity parameters are appealing to researchers to conduct large-scale analysis. The calculated GRP of investigated compounds are shown in Table 1.

Above table elucidated that reference chromophore have the greater value of hardness (η = 0.039 a.u) as well as chemical potential (μ = -0.140 a.u) while greater values for global softness (σ = 12.775 a.u) than all its derivatives. These GRP results indicated that JK-201 is more stable and less reactive, hence showed lower NLO response as compared to its derivatives. Interestingly all the designed dyes expressed least values of hardness (η = 0.034–0.038 a.u) as well as chemical potential (μ = -0.151 to-0.139 a.u) while greater values for global softness (σ = 13.15–14.77 a.u). Among designed compounds, DTA9 exhibited higher value of softness (14.778 a.u) so, it shows highest reactivity. The decreasing order of softness; DTA9 > DTA12 > DTA11 > DTA1 > DTA10 > DTA5 > DTA3 > DTA4 > DTA2 > DTA8 > DTA6. > JK-201. Hence, all the molecules exhibited higher value of softness which indicated more reactivity as well polarizability resulting excellent NLO response.

3.3 UV–Vis spectra

Employing TD-DFT computation, absorption spectra of the designed compounds have been calculated to understand the effect of bridging core moieties and acceptor units on spectral properties. The calculated results of absorption wavelength (λ_max), transition energy (E_ge), transition moment (M_x^gm), oscillator strength (f_os), transitions nature and light-harvesting efficiency (LHE) of the designed compounds (DTA1-DTA12) were presented in Tables 2.

Table 2 elucidated a significantly close relationship was presented between experimental and theoretical value, which supported the selected methodology for DFT analysis was appropriate enough. Interestingly, all the designed compound (DTA1-DTA12) exhibited a larger value of λ_max than their reference molecule (JK-201) 484.7 nm (Khan et al., 2019a) except DTA2 and showed absorbance spectra in the visible region as shown in the spectrum (Fig. 5). It was seen that λ_max values are greatly influenced by preferable planarity and more electron richness π-spacer and end-capped electron acceptor motifs, which in turn push the absorption spectra towards redshift (Ans et al., 2019; Khalid et al., 2020b; Paek et al., 2010). So, DTA2 exhibited lower absorption properties due to the poor electron-withdrawing nature of DMT as no electronegative atom was presented in its structure compared to other π-spacers (Figs. 1a and 1b). The simulated spectra of designed compounds existed between 462.5 and 539 nm. Among all entitled molecules, the larger computed λ_max finding was found in the compounds (DTA11, DTA7 and DTA3) having FMC as first π-spacer (Table 2) as FMC $\pi$ spacer enhances the conjugation hence, stabilized the molecule which in result showed redshift. Furthermore, molecules (DTA2, DTA6 and DTA10) with DMT π spacer exhibited the least value of λ_max with the same acceptor units. Additionally, it was also analyzed that the dyes with ETMN acceptor units were red-shifted while FBSA acceptor unit containing molecules exhibited blue shift (Table 2). The ETMN acceptor had a cyclic structure with a more powerful electron-withdrawing cyano (–CN) group. Resonance due to a five-member ring and strong electron-withdrawing –CN group (Ali, 2021) enhanced the stability by lowering the Eg value and show maximum absorption properties as compared to FBSA, which contain fewer electron-withdrawing (CF_3, SO₃H) groups as compared to cyano. The reducing order for λ_max of the designed compounds is: DTA11 > DTA12 > DTA7 > DTA8 > DTA9 > DTA5 > DTA10 > DTA6 > DTA3 > DTA4 > DTA1 > DTA2. Transitions in the DTA1-DTA12 were arisen from HOMO to LUMO, which was according to the principle of most donor- π-acceptor organic molecules. Chief donation in these excitations belongs to the HOMO → LUMO (31–52%) and HOMO-1 → LUMO supply (31–51%). So, it was cleared that by the structural modelling of the parent compound (JK-201) in 1st π-spacer and acceptor parts, λ_max can be enhanced in derivatives which would be appealing NLO novel dyes.

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Fig. 5

Absorption spectra of entitled compounds (DTA1- DTA12) obtained by TD-DFT method using CAM-B3LYP/6-31G(d,p) level.

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LHE is a significant component that expresses the optical efficiency of the designed compounds, which can be obtained by using f_os, provided by the TD-DFT computations. It is considered that the more excellent photocurrent response is investigated by the compound, which has greater LHE. Using Eq. (3), the LHE of the designed dyes was calculated (Xie, 2001) and results were displayed in Table 2.

Oudar and Chemla formulated a two-state model (Oudar and Chemla, 1977) extensively utilized in the literature to analyze NLO response containing the critical excited and ground state e in sum-over-state expression. In this model, an interaction was formed between the charge transfer transition and 2nd order polarizability, the origin of push–pull architecture for modelling remarkable NLO compounds.

Eq. (4) showed two-state model expression, where (β_CT) first hyperpolarizability, (Δμ_gm) dipole moment difference, (f_gm) oscillator strength and ( ${\mathrm{E}}_{\mathrm{g}\mathrm{m}}^3$ ) cube of transition energy among ground and mth excited state. Eq. (4) revealed that β_CT directly relates to the product of Δμ_gm and f_gm and inversely related with the transition energy.

So, the molecules with optimum NLO behavior had a larger magnitude of Δμ_gm and f_gm and smaller ${\mathrm{E}}_{\mathrm{g}\mathrm{m}}^3$ . Herein, Δμ_gm, f_gm, and ${\mathrm{E}}_{\mathrm{g}\mathrm{m}}^3$ were calculated from spectral analysis, and results were shown in Table 3. The results indicated that among derivatives, the higher value for ${\mathrm{E}}_{\mathrm{g}\mathrm{m}}^3$ DTA3 (2.7 eV) was found, while a smaller value was exhibited in DTA12 (2.3 eV). Moreover, to further enhance the NLO finding, the relationship between the two-state model (β_CT) and β_total values for all dyes (DTA1-DTA12) is displayed in Fig. 6. The rise and fall in the graph indicate the effect of different π-spacer and terminal acceptor units on β_total values related to the rise and fall predicted by two-level model (β_CT) results. It is evident from Fig. 6 that the β_total values of studied compounds DTA1, DTA5, DTA6, DTA7, DTA8, DTA10 and DTA11 are in broad agreement with two-state model (β_CT) results which support our claim of their potential to be used as efficient NLO compounds.

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Fig. 6

Relationship between the β_total values and the corresponding Δμ_gmf_gm/ ${\mathrm{E}}_{\mathrm{g}\mathrm{m}}^3$ values for investigated compounds (DTA1-DTA12).

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3.4 Nonlinear optical (NLO) properties

In optoelectronic devices, telecommunication, networking and signal manipulation, NLO products are extensively utilized. The optical behavior depends upon the electrical properties of the entire molecule, which are successively related to the linear (<α>) and nonlinear (β_total) responses. Furthermore, it will be entrancing to see how these NLO properties vary with modifying π-linkers and acceptor units. Herein, NLO responses of entitled dyes (DTA1-DTA12) were estimated, and results were displayed in Tables 2 and 3.

Table 3 revealed that the linear polarizability (<α>) values of the parent compound are lesser (914.08 a.u.) (Khan et al., 2019a) than its derivatives (DTA1-DTA12). Among all the designed molecules, the species with FMC as 1st π-spacer DTA3 and DTA11 exhibited a huge value of <α> 1183.91, 2868.08 and 1391.12a.u., respectively while FMB containing molecules expressed the least values except DTA5 in the ETAA family (Table 3). Overall, the investigation revealed that dyes with ETMN acceptor unit (DTA9-DTA12) manifested an enormous value of <α> . However, compounds structurally tailored with FBSA acceptor moiety (DTA1-DTA4) have the least linear polarizability values with the same π linkers. Among all the dyes, the greater value was investigated in DTA5 (2868.08 a.u), and compound DTA1 exploited a smaller value (939.89 a.u) for linear polarizability. Nevertheless, average polarization of all the explored dyes increases in the following order: DTA5 > DTA11 > DTA7 > DTA12 > DTA10 > DTA8 > DTA3 > DTA6 > DTA9 > DTA4 > DTA2 > DTA1.

The literature study disclosed that average polarizability was affected by energy gap values. It was evident that a smaller bandgap and larger linear polarizability designated greater hyperpolarizability, referring to the large NLO values (Mohankumar et al., 2015; Qin and Clark, 2007). Equation (5) illustrates the calculation of dipole polarizability (along the x-axis):

Herein, ${\mathrm{M}}_{\mathrm{X}}^{\mathrm{g}\mathrm{m}}$ represents the transition moment, and E_gm refers to the transition energy between ground $\to$ n_th excited state. A direct relationship exists between <α> and ${\mathrm{M}}_{\mathrm{X}}^{\mathrm{g}\mathrm{m}}$ whereas an inverse relation is seen with the E_gm. The transition dipole moment demonstrates the electronic transition effects and interactions of dyes with certain electromagnetic waves of the given polarization. Generally, it was investigated that a molecule with higher ${\mathrm{M}}_{\mathrm{X}}^{\mathrm{g}\mathrm{m}}$ value and minor E_gm value presented greater hyperpolarizability values (Khan et al., 2019b). Therefore, for the assessment of attractive NLO properties of species, dipole polarizabilities were found as a quantitative estimation. As the first hyperpolarizability endorsed the estimation of NLO behavior of compounds which was successively related with the intermolecular charge transfer (ICT) towards A unit from D moiety via π-linkers. Such interaction was studied in our designed compounds, as displayed in Fig. 3. Electron density interacts with the external field, which enhanced the dipole moment, leading to higher first-order hyperpolarizability. The calculated results of second-order polarizability of entitled dyes were explored in Table S14 while their graphical representation is done in Fig. 7.

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Fig. 7

Graphical representation of hyperpolarizability of entitled chromophores.

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These DFT investigations explained that the calculated 2nd order polarizability (β_total) for all the designed dyes (DTA1-DTA12) were more significant than that of their parent compound (JK-201), 104093.90 a.u. (Khan et al., 2019a). Fig. 7 explored that the chromophores with ETMN acceptor moiety and DPT spacer expressed remarkable β_total values than other acceptors and spacers units. Further, among FBSA, ETAA and ETMN terminal acceptor unit families, compounds with DPT 1st π-spacer DTA4, DTA8 and DTA12 expressed larger hyperpolarizability174280.17, 188317.42 and 268494.70 a.u, respectively. Furthermore, these values decrease as the 1st π-spacer DPT is replaced with FMC.DMT and FMB, respectively. Moreover, it was also examined that dyes with FMB π-bridge manifested the least values except in the FBSA acceptor unit family, in which molecule DTA2 with DMT spacer explored low value (Fig. 7). Additionally, the dyes with ETMN acceptor units and the DPT first π-spacer exhibited greater hyperpolarizability than others. Might be more electron-withdrawing groups fluoro (-F) on spacer and cyano (–CN) group on acceptor unit collectively created a robust pull–push architecture which stabilized the band gap between orbitals hence showed excellent results. This increase in the hyperpolarizability values might be due to the combined effect of powerful A units and the delocalized π-electrons that stabilize the molecule by lowering their orbitals bandgap and enhanced the polarizability. Overall, the decreasing order for β_total of all theoretically designed dyes was: DTA12 $<$ DTA11 $<$ DTA10 $<$ DTA9 $<$ DTA8 $<\mathbf{D}\mathbf{T}\mathbf{A}7<$ DTA4 $<$ DTA-3 $<\mathbf{D}\mathbf{T}\mathbf{A}6<$ DTA1 $<$ DTA2 $<$ DTA5.

Additionally, hyperpolarizability findings of our designed dyes (DTA1-DTA12) were also compared with urea (β_total = 43 a.u), an organic reference compound (Kanis et al., 1994) and found considerably larger in entitled molecules. It was examined that in all investigated dyes from DTA1 to DTA12, β_total values were observed to be 3609, 3546, 3816, 4053, 3451, 3713, 4308, 4540, 5333, 5659, and 6244 times higher, respectively than urea.