Computational Study on Optoelectronic Properties of Donor-Acceptor Type Small π-Conjugated Molecules for Organic Light-Emitting Diodes (OLEDs) and Nonlinear Optical (NLO) Applications

Abstract

Recently, donor-acceptor type molecule that contains electron-rich (D) and electron-deficient (A) moiety has emerged as an interesting approach of molecular design strategy to develop organic light-emitting diodes (OLEDs) and non-linear optical (NLO) devices. In this work, we report a theoretical investigation based on two donor-acceptor (D-A) type small π-conjugated molecules based on dithieno [3,2-b: 2′,3′-d] pyrrole (DTP) and anthracene derivatives. All of the theoretical calculations were performed by Density Functional Theory (DFT) approach at B3LYP/6-31 g(d) level of theory. The structural, electronic, optical and charge transfer properties were investigated. The effect of acceptor blocks (DPA and DTA) on the molecular characteristics was elucidated. The obtained results clearly show that the studied compounds exhibit non-coplanar structures with low electronic band gap values. These relevant structures exhibited important optical absorption and intense emission in the green-yellow region. NLO investigation based on static polarizability (α0), first-order hyperpolarizability (β0) and second-order hyperpolazabilty (ɣ0) demonstrated that the studied materials exhibit excellent NLO properties. Thus, the designed materials showed promising capabilities to be utilized in OLED and NLO applications.

1. Introduction

Recently, several categories of conjugated materials have gained significant interest due to their relevant optoelectronic characteristics for the development of a wide range of organic electronic devices [1, 2, 3]. Remarkably, organic luminescent materials are increasingly attractive in the manufacture of organic light-emitting diodes (OLEDs) and non-linear optical (NLO) devices [4, 5, 6].

OLEDs are desirable electronic devices due to their valuable advantages of full color emission, high brightness, flexibility and operation stability [7, 8, 9, 10, 11]. OLEDs were greatly developed in electronic fields and showed their successful applications in digital displays, mobile phones and flat panels in TV screens [12]. Various functional units, such as fluorene [13], carbazole [14] and anthracene [15] were utilized to develop efficient luminescent materials for their prominent photoluminescence properties and simple modifications. Among these functional units, anthracene and its derivatives were widely studied as potential building blocks in the development of active materials for OLED devices [16].

Apart from OLEDs, recent studies have demonstrated the potential application of conjugated materials in NLO devices [17, 18]. NLO materials have reached large interest of the scientific community for prosperous use in technological areas such as telecommunications, optical information processing and data storage [19, 20, 21]. NLO studies have shown the design of promising organic materials for nonlinear effect based on the introduction of highly delocalized electron fragments and additional electron donor and acceptor groups for enhancing the molecular conjugation [22].

Previous works have shown that D-A (Donor-Acceptor) systems dispose a successful architecture for non-linear optics and OLEDs. Where, D-A systems exhibit large charge transfer (CT) in which the electrons located in the electron rich donor unit undergo an intra-molecular charge transfer (ICT) to the electron deficient acceptor unit [23, 24]. The present CT phenomenon leads to excellent optoelectronic characteristics that encourage the use of D-A systems in NLO and OLED applications.

Dithieno [3,2-b: 2′,3′-d] pyrrole (DTP) material has been recognized as one of the most efficient building blocks with high electron donation capacity [25, 26]. DTP building blocks have been widely incorporated into a variety of materials for the aim of reducing the band gap, improving the mobility of charge carriers, and reinforcing solution and solid state fluorescence.

Equally, anthracene has attracted significant attention to the construction of organic luminescent materials due to its unique features. Where, anthracene derivatives such as 9,10-diphenylanthracene (DPA) and 9,10-di(thiophen-2-yl)anthracene (DTA) have exhibited remarkable electronic and light-emitting properties to be applied in optical applications [27, 28].

In the present work, we have developed a theoretical investigation based on new D-A type small molecules for NLO and OLED applications. As mentioned in Figure 1, we have used DTP as an electron donor block and derivatives from DPA and DTA as an electron acceptor block. The addition of a strong electron withdrawing group as cyano group is for the reason of enhancing the polarization and improving the π-electrons delocalization [29].

Figure 1.

Molecular structures of the investigated compounds.

A theoretical computational study using density functional theory (DFT) approach introduce excellent tools to predict the optoelectronic properties of molecular systems as well as the design of new materials for OLED and NLO devices [30]. Hence, the designed materials will be theoretically investigated and discussed to envisage the reliability for OLED and NLO applications.

2. Computational methods

Theoretical calculations were performed using Density Functional Theory (DFT) approach implemented in Gaussian 09 software [31]. Previous studies have shown that DFT//B3LYP/6-31 g(d) method gives better accuracy in investigating the photo-physical properties of materials based on DTP and anthracene [32, 33]. Structural properties such as dihedral angles, torsion angles and bridge bond lengths were firstly investigated based on the geometry optimization of M1 and M2 in their ground states. Vibrational calculations were carried out to confirm the stable conformers with no imaginary frequencies. Frontier molecular orbitals (FMOs) and electron density difference (EDD) contour plots were carried out to examine the electron delocalization within the conjugated frameworks. The absorption and emission spectra were simulated using Time Dependent DFT (TD-DFT) at B3LYP/6-31 g(d) level. Photoluminescence color coordinates of M1 and M2 were determined using International Commission on Illumination (usually abbreviated CIE for its French name, Commission internationale de l’éclairage) process. Bilayer OLED devices are designed based on the optoelectronic properties of the studied molecules. Hole and electron charge transfer properties (${\mathrm{\lambda }}_{\mathrm{h}},{\mathrm{\lambda }}_{\mathrm{e}}$) were carried out on neutral, anionic and cationic states. The NLO properties involving the electric dipole moment (μ), the polarizability (α), the first order hyperpolarizability (β) and the second order hyperpolarizability (γ) were investigated.

3. Results and discussion

3.1 Ground state optimized geometries

The development of high performance luminescent materials is principally based on the enhancement of π-electrons delocalization within the conjugated architectures. In fact, the geometric structure gives an idea about the delocalization of the π-electrons as well as the charge transfer (CT) within the conjugated structure [34].

Hence, the ground state geometries of the studied materials were optimized using DFT//B3LYP/6-31 g(d) method in gaseous phase. The optimized geometries of M1 and M2 are illustrated in Figure 2 and the geometric parameters involving bond lengths, torsion angles and dihedral angles are listed in Table 1.

Figure 2.

Ground state optimized geometries at B3LYP/6-31 g(d) level for the studied molecules.

	M1	M2
Bond length (Å)
L1	1.46	1.44
L2	1.49	1.48
L3	1.49	1.48
Torsion angle (deg.)
ϴ1	119.96	119.88
ϴ2	119.83	119.68
Torsion angle (deg.)
Φ	25.67	17.24

Table 1.

Optimized ground state geometry parameters of the studied molecules.

The considered materials exhibit non-coplanar structures (Figure 2). There are large torsion angles around 119° between anthracene and phenyl ring in M1 and between anthracene and thiophene ring in M2 (Table 1) which is a characteristic property of compounds based substituted anthracene [23, 35].

Furthermore, as mentioned in Figure 1, the characteristic bridge bonds between the donor and acceptor blocks (L1) and between the different groups of the acceptor units (L2 and L3) were calculated to have an idea about the charge transfer (CT) in the conjugated backbone. The calculated lengths of bond L1 were found equal to 1.46 and 1.44 Å for M1 and M2, respectively. While, the bond lengths of L2 and L3 were found about 1.49 Å for M1 and about 1.48 Å for M2. The calculated values are located in the interval between C-C single bond length (C-C = 1.54 Å) and C=C double-bond length (C=C = 1.33 Å) showing the high π-electron delocalization and interesting intra-molecular charge transfer (ICT) within the framework [36].

The structural analysis suggests that the studied compounds exhibit good conjugated structures with high π-electron delocalization, which is important for applications in organic electronic devices.

3.2 Frontier molecular orbitals (FMOs)

The electronic properties of the studied molecules are examined based on the frontier molecular orbital (FMOs) analysis. The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) contour plots were carried out using the DFT//B3LYP/6-31 g(d) method at the optimized ground state geometries. The energy values of HOMOs, LUMOs and band gap energies are listed in Table 2. The HOMOs and LUMOs distributions are illustrated in Figure 3.

Compound	$E_{{\text{HOMO}}-1}$ (eV)	$E_{{\text{HOMO}}}$ (eV)	$E_{{\text{LUMO}}}$ (eV)	$E_{{\text{LUMO}}+1}$ (eV)	$∆E_{{gap}}$ (eV)
M1	−5.36	−5.04	−1.88	−1.41	3.16
M2	−5.57	−4.97	−2.16	−1.64	2.81

Table 2.

DFT//B3LYP/6-31 g(d) calculated electronic properties of M1 and M2 molecules.

Figure 3.

Frontier molecular orbitals in the optimized ground state for the studied molecules.

As depicted in Figure 3, the HOMOs are mostly located over the DTP unit while the LUMOs are distributed over the DPA and DTA acceptor units that indicate the important electron charge transfer from the donor to acceptor moieties. Hence, the FMOs analysis has shown the considerable charge transfer taking place within the designed molecules.

The band gap energies are calculated from the difference between the HOMO and LUMO energy levels at DFT//B3LYP/6-31 g(d) method. The band gap energies are about 3.16 eV and 2.81 eV for M1 and M2, respectively. These lower values of band gaps with the FMOs distributions demonstrate the presence of a significant intra-molecular charge transfer (ICT) that leads to enhance the electronic properties [37].

Density of states (DOS) is a helpful tool to examine the delocalization of π-electrons in the compound. The DOS plots were determined by DFT//B3LYP/6-31 g(d) method at the ground state geometry and illustrated in Figure 4. DOS plots of M1 and M2 show a large overlapping of electronic energy levels that indicates the high electron delocalization. In fact, the high electron delocalization within these materials could be explained by the mutual reactions of donor and acceptor constructive blocks.

Figure 4.

Density of states (DOS) plots of the studied materials.

To better understand the delocalization of π-electrons, electron density difference (EDD) was simulated between the ground state (S₀) and the first excited state (S₁). As seen in Figure 5, the EDD plots contain blue regions referring to electron density depletion and purple regions referring to electron density increment.

Figure 5.

Electron density difference (EDD) contour plots of the studied materials.

Hence, the regions of electron increment density are mainly located over the DPA and DTA blocks. While, the DTP block presents the region of depleted free carriers (depletion region). These observations decline the effective electron transfer from donor to acceptor units within the studied materials.

3.3 Optical properties

3.3.1 Optical absorption properties

The optical absorption properties of M1 and M2 have been investigated based on the simulated UV–Vis optical absorption spectra using TD-DFT method at 6-31 g(d) basis set. The obtained optical absorption curves with their Gaussian fitting peaks are given in Figure 6. The simulated corresponding maximum absorption wavelengths (${\mathrm{\lambda }}_{\max }^{\mathrm{abs}}$), the electronic transition energy (Eex), the oscillator strength (f), the full-width at half maximum (FWHM) and the main electronic transitions are listed in Table 3.

Figure 6.

Optical absorption spectra of M1 and M2 with fitting Gaussian peaks obtained at DFT//B3LYP/6-31 g(d) level.

Compound	${\lambda }_{\mathit{max}}^{\mathit{abs}}$(nm/eV)	f (a.u)	FWHM (nm)	Main electronic transitions
M1	442/2.80	0.05	76.96	H$\to$L (99%)
	396/3.12	0.38	56.33	H-1$\to$L (93%), H$\to$L + 1 (4%)
	353/3.51	0.71	33.46	H$\to$L + 2 (81%), H-2$\to$L (9%)
M2	406/3.08	0.63	58.70	H-1$\to$L (85%), H$\to$L + 2 (12%)
	373/3.32	0.67	35.09	H$\to$L + 2 (85%), H-1$\to$L (12%)

Table 3.

Maximum absorption wavelengths${\lambda }_{\mathit{max}}^{\mathit{abs}}$ (nm), electronic transition energy, Eex (eV), oscillator strength f (a.u), full-width at half maximum FWHM (nm) and main electronic transitions calculated at B3LYP/6-31 g(d) level.

As it can be seen from Figure 6, the studied molecules exhibit large and intense absorption bands in the visible zone ranging from 300 nm to 500 nm. These electronic transitions are defined as π$\to$ π* transitions associated with the electron migration from the HOMOs mainly located over the DTP units to the LUMOs mainly concentrated over the anthracene units [38].

From Table 3, the maximum absorption wavelengths (${\mathrm{\lambda }}_{\max }^{\mathrm{abs}}$) of M1 and M2 are found at 442 nm and 406 nm, respectively. The full-width at half maximum FWHM referring to the main absorption band for M1 is found higher than that of M2 (FWHM (M1) = 76.96 > FWHM (M2) = 58.70). This result shows the role played by the acceptor block in improving the optical absorption properties.

From the optical absorption analysis, it is obvious that the acceptor block configuration contributes significantly in enhancing the absorption properties of conjugated materials.

3.3.2 Emission properties

The emission properties of M1 and M2 are simulated on their optimized geometries at the first excited state by means of TD-DFT//B3LYP/6-31 g(d) method. The emission spectra with their fitting Gaussian peaks are depicted in Figure 7 and the corresponding emission characteristics are listed in Table 4.

Figure 7.

Emission spectra of M1 and M2 with fitting Gaussian peaks obtained at DFT//B3LYP/6-31 g(d) level.

Compound	${\lambda }_{{max}}^{{em}}$(nm/eV)	f (a.u)	FWHM (nm)	Main transition	$\tau$ (ns)
M1	478/2.59	0.34	75.35	L$\to$H (98%)	10.12
	351/3.53	0.27	37.44	L$\to$H-2 (90%)
M2	554/2.23	0.85	95.65	L$\to$H (99%)	5.46
	441/2.81	0.21	41.86	L$\to$H-1(63%)
	393/3.15	0.18	57.49	L + 1$\to$H (40%)
	344/3.60	0.15	30.52	L + 1$\to$H-1 (94%)

Table 4.

Calculated maximum emission wavelengths ${\mathrm{\lambda }}_{\max }^{\mathrm{em}}$ (nm), fluorescent energy${\mathrm{E}}_{\mathrm{flu}}$(eV), oscillator strength f (a.u), full-width at half maximum FWHM (nm), main electronic transitions, stokes shift (nm) and radiative lifetime ($\mathrm{\tau }$).

As it can be seen from Figure 7, the studied materials exhibit large emission bands with maximum emission wavelengths of 478 nm and 554 nm for M1 and M2, respectively. As mentioned in Table 4, the emission spectrum of M2 exhibits larger FWHM comparing to M2 which indicates the effect of acceptor moiety in enhancing the emission properties.

The photoluminescence chromaticity coordinates of M1 and M2 were carried out according to the CIE 1931 diagram. As illustrated in Figure 8, the CIE coordinates are found upon (x: 0.45, y: 0.45) and (x: 0.32, y: 0.43) for M1 and M2, respectively. Hence, M1 displays a pure green color while M2 displays a pure yellow color.

Figure 8.

CIE color coordinates for the studied materials (right), schematic structure of proposed bilayer OLED based studied materials (left).

From the emission investigation, it is revealed that the studied materials are promising materials for OLED applications. Indeed, OLEDs as they are promising organic electronic devices present the subject of intense research. The efficient OLED operation requires balanced charge injection, charge transport and charge recombination within the electronic device [39].

The considered materials exhibit appropriate optoelectronic characteristics allowing their use as emitting layers in two layers OLED device. Alq₃ (Tris (8- hydroxyquinoline) aluminum) is a suitable material to act as an electron transport layer [40] with respect to the LUMO energy levels of M1 and M2 (See Figure 8).

Radiative lifetime ($\mathrm{\tau }$) introduces the average time of the stay of a molecule at the excited state before a photon-emission. The lower value of $\mathrm{\tau }$leads to a relevant emission of the conjugated material. The radiative lifetime$\mathrm{\tau }$could be determined according to the following expression [41]:

$$\mathrm{\tau }=\frac{{\mathrm{C}}^3}{2{\left({\mathrm{E}}_{\mathrm{flu}}\right)}^2\mathrm{f}}$$E1

Where, c, ${\mathrm{E}}_{\mathrm{flu}}$ and $\mathrm{f}$ represent the velocity of light, the fluorescent energy and the oscillator strength, respectively.

The radiative lifetime values are of 10.12 ns and 5.46 ns for M1 and M2, respectively. The small values of $\mathrm{\tau }$denote the efficient light emission of these materials. The findings of the present report corroborate a slight difference in radiative lifetime values which are explained by the effect of DPA and DTA acceptor blocks within the conjugated structures.

According to these results and compared to some previous studies reported in Refs. [28, 42], it is revealed that M1 and M2 exhibit promising optoelectronic properties for high performance OLED devices.

3.4 Charge transfer properties

Many factors are responsible for high performance organic optoelectronic devices such as hole/electron charge transfer balance. The reorganization energies of holes and electrons ($\mathrm{\lambda }$_h and $\mathrm{\lambda }$_e) together with the ionization potential (IP) and the electron affinity (EA) have been calculated to evaluate the hole/electron transfer abilities. The reorganization energies were carried out from neutral, cationic and anionic geometries, as detailed in Figure 9.

Figure 9.

Calculation details of reorganization energies from neutral cation and anion states.

The reorganization energies of holes and electrons can be calculated following the expression above [43]:

$${\mathrm{\lambda }}_{\mathrm{h}}/{\mathrm{\lambda }}_{\mathrm{e}}=\left({\mathrm{E}}_0^{\pm }-{\mathrm{E}}_{\pm }^{\pm }\right)+\left({\mathrm{E}}_{\pm }^0-{\mathrm{E}}_0^0\right)$$E2

Hence, ${\mathrm{E}}_0^{\pm }$, ${\mathrm{E}}_{\pm }^0$, ${\mathrm{E}}_{\pm }^{\pm }$ and${\mathrm{E}}_0^0$represent the cation/anion energy of cation/anion at neutral geometry, the energy of neutral structure in the cation/anion state, the energy of cation/anion in the cation/anion state and the energy of the neutral structure, respectively. Charge transfer parameters have been determined using DFT//B3LYP/6-31 g(d) method and the results are presented in Table 5. Based on the obtained results, it is found that M1 exhibits higher hole and electron transfer abilities regarding the lower reorganization energies of hole and electron.

Compound	$\mathit{IP}$	$\mathit{EA}$	$\left(E_0^{+}-E_{+}^{+}\right)$	$\left(E_{+}^0-E_0^0\right)$	$\left(E_0^{-}-E_{-}^{-}\right)$	$\left(E_{-}^0-E_0^0\right)$	${\lambda }_h$	${\lambda }_e$
M1	6.02	0.94	0.171	0.129	0.283	0.144	0.300	0.427
M2	6.00	1.17	0.248	0.158	0.298	0.224	0.406	0.522

Table 5.

Calculated charge transfer parameters (expressed in eV) of M1 and M2 at DFT//B3LYP/6-31 g(d) level of theory.

To get insights into the charge transport properties, the ionization potential (IP) and the electron affinity (AE) were carried out for better evaluating the electron extraction and attraction abilities, respectively [44]. In comparison with M2, M1 exhibits relatively lower EA (0.94 eV versus 1.17 eV) which demonstrates that our materials exhibit low performance of grasping electrons. However, the low values of IP (6.02 eV for M1 and 6.00 eV for M2) indicated the high ability of these materials to grasp hole (See Table 5). It is possible to better improve the mobility of charge carriers through the modification of the conjugate structure [45].

Overall, the charge properties analysis of M1 and M2 shows that they are considered as promising materials for organic optoelectronic applications.

3.5 Nonlinear optical (NLO) properties

The principle of nonlinear optics represents the interaction between an incident electromagnetic field with a particular material leading to the generation of an electromagnetic field modified in wave number, phase or frequency [17]. NLO materials are increasingly applied in emerging technological fields such as telecommunications, optical memory, optical information processing, etc. [46].

NLO properties produced from the high delocalization of electrons within the molecule increase while increasing the molecular conjugation [47]. Further, the presence of electron donor blocks (D) and electron acceptor blocks (A) contributes to the improvement of the NLO properties [48, 49, 50]. Studies have shown that nonlinear organic optical materials possess higher optical nonlinearity compared to inorganic materials [51].

The electric dipole moment$\mathrm{\mu }$, the polarizabilities$\mathrm{\alpha }$, the first ($\mathrm{\beta }$) and the second-order hyperpolarizability ($\mathrm{\gamma })$describe the nonlinear optical response of an isolated molecule within an electric field [52]. The total dipole moment${\mathrm{\mu }}_{\mathrm{tot}}$, the static polarizability${\mathrm{\alpha }}_0$, the static first hyperpolarizability${\mathrm{\beta }}_0$ and the static second order hyperpolarizability ${\mathrm{\gamma }}_0$are calculated using the expressions above [22, 53]:

$${\mathrm{\mu }}_{\mathrm{tot}}={\left({{\mathrm{\mu }}_{\mathrm{x}}}^2+{{\mathrm{\mu }}_{\mathrm{y}}}^2+{{\mathrm{\mu }}_{\mathrm{z}}}^2\right)}^{\frac{1}{2}}$$E3

$${\mathrm{\alpha }}_0=\frac{1}{3}\left({\mathrm{\alpha }}_{\mathrm{xx}}+{\mathrm{\alpha }}_{\mathrm{yy}}+{\mathrm{\alpha }}_{\mathrm{zz}}\right)$$E4

$${\mathrm{\beta }}_0={\left[{\left({\mathrm{\beta }}_{\mathrm{xxx}}+{\mathrm{\beta }}_{\mathrm{xyy}}+{\mathrm{\beta }}_{\mathrm{xzz}}\right)}^2+{\left({\mathrm{\beta }}_{\mathrm{yyy}}+{\mathrm{\beta }}_{\mathrm{yzz}}+{\mathrm{\beta }}_{\mathrm{yxx}}\right)}^2+{\left({\mathrm{\beta }}_{\mathrm{zzz}}+{\mathrm{\beta }}_{\mathrm{zxx}}+{\mathrm{\beta }}_{\mathrm{zyy}}\right)}^2\right]}^{\frac{1}{2}}$$E5

$${\mathrm{\gamma }}_0=\left(1/5\right)\left[{\mathrm{\gamma }}_{\text{xxxx}}+{\mathrm{\gamma }}_{\text{yyyy}}+{\mathrm{\gamma }}_{\text{zzzz}}+2{\mathrm{\gamma }}_{\text{xxyy}}+2{\mathrm{\gamma }}_{\text{yyzz}}+2{\mathrm{\gamma }}_{\text{zzxx}}\right]$$E6

DFT approach is used as a reliable method for the determination of NLO properties of organic materials [54]. To get insights into the NLO properties, theoretical calculations were performed on the ground state optimized geometries of M1 and M2 at DFT//B3LYP/6-31 g(d) level of theory and the results are listed in Table 6.

	M1	M2		M1	M2		M1	M2		M1	M2
${\mathbf{\mu }}_{\mathit{x}}$	0	0	${\mathit{\alpha }}_{\mathit{xx}}$	63.382	74.513	${\mathit{\beta }}_{\mathit{xxx}}$	5.006	5.457	${\mathbf{ɣ}}_{\mathbf{\text{xxxx}}}$	69.828	95.548
${\mathbf{\mu }}_{\mathit{y}}$	0	0	${\mathit{\alpha }}_{\mathit{xy}}$	5.051	−6.979	${\mathit{\beta }}_{\mathit{xxy}}$	1.042	−1.122	${\mathbf{ɣ}}_{\mathbf{\text{yyyy}}}$	42.211	40.665
${\mathbf{\mu }}_{\mathit{z}}$	7.383	7.362	${\mathit{\alpha }}_{\mathit{yy}}$	55.263	55.263	${\mathit{\beta }}_{\mathit{xyy}}$	0.220	0.139	${\mathbf{ɣ}}_{\mathbf{\text{zzzz}}}$	831.140	624.809
${\mathbf{\mu }}_{\mathit{tot}}$	7.383	7.362	${\mathit{\alpha }}_{\mathit{xz}}$	−33.103	−36.709	${\mathit{\beta }}_{\mathit{yyy}}$	0.056	−0.034	${\mathbf{ɣ}}_{\mathbf{\text{xxyy}}}$	3.191	1.728
			${\mathit{\alpha }}_{\mathit{yz}}$	−5.787	5.383	${\mathit{\beta }}_{\mathit{xxz}}$	−8.816	−7.756	${\mathbf{ɣ}}_{\mathbf{\text{xxzz}}}$	247.105	241.440
			${\mathit{\alpha }}_{\mathit{zz}}$	109.672	97.457	${\mathit{\beta }}_{\mathit{xyz}}$	−1.979	1.656	${\mathbf{ɣ}}_{\mathbf{\text{yyzz}}}$	11.081	10.138
			${\mathit{\alpha }}_{\mathbf{0}}$	76.106	75.744	${\mathit{\beta }}_{\mathit{yyz}}$	−0.475	−0.347	${\mathbf{\gamma }}_{\mathbf{0}}$	293.186	253.527
						${\mathit{\beta }}_{\mathit{xzz}}$	18.993	14.347
						${\mathit{\beta }}_{\mathit{yzz}}$	4.340	−3.168
						${\mathit{\beta }}_{\mathit{zzz}}$	−36.233	−24.125
						${\mathbf{\beta }}_{\mathbf{0}}$	51.851	38.145

Table 6.

Calculated electric dipole moment μ_tot (D), polarizability α₀ ($\times {10}^{-24}$ esu), first-order hyperpolarizability β₀ ($\times {10}^{-30}$ esu) and second-order hyperpolarizability${\mathrm{\gamma }}_0$($\times {10}^{-36}$ esu) of the studied materials at DFT//B3LYP/6-31 g(d) level.

From Table 6, the first- and second-order hyperpolarizabilities of M2 are found lower than those of M1 explained by the distinct electron delocalization in the conjugated structures. Thus, as compared to M2, it is important to note that M1 presents the best NLO properties.

Urea is a prototypical organic molecule used as a threshold comparison value in the study of the NLO properties of molecular materials [55]. The NLO parameters of urea calculated at DFT//B3LYP/6-31 g(d) level of theory are found of: ${\mathrm{\mu }}_{\mathrm{tot}}$ = 4.259 D, ${\mathrm{\alpha }}_0=$3.749 × 10–24 esu and ${\mathrm{\beta }}_0=$0.557× 10–30 esu and ${\mathrm{\gamma }}_0$ = 0.746× 10–36 esu.

Compared to urea, the high values of NLO parameters of M1 and M2 confirm the design of high performance nonlinear optical materials.

4. Conclusion

In this study, we reported a DFT study based on structural, optoelectronic and nonlinear optical (NLO) properties of D-A small π-conjugated molecules based on DTP and anthracene. The optimized structures have shown the non-planarity of the investigated molecules M1 and M2 arising from the anthracene derivatives (DPA and DTA) conjugated configuration. FMOs analysis shows the appropriate HOMO/LUMO energy levels with the low band gap energies. To support the FMOs analysis, EDD contour plots have been computed to identify the donor and acceptor moiety within M1 and M2 structures. The TD-DFT study demonstrated the role played by the acceptor block in improving the absorption properties of the studied materials. The emission properties revealed an intense emission in the pure green and pure yellow for M1 and M2, respectively. These molecules have shown their promising abilities to be used in OLED devices. The charge transfer properties analysis attested the relevant hole/electron transport abilities of these materials. Computed static polarizability (${\mathrm{\alpha }}_0$), first-order hyperpolarizability (${\mathrm{\beta }}_0$) and second-order hyperpolazabilty (${\mathrm{ɣ}}_0$) indicated the excellent NLO properties of M1 and M2. This NLO response suggested these compounds to be used as potential candidates for NLO applications. Overall, this study provided an insight into a promising D-A conjugated architecture with the role of the acceptor block on enhancing the optoelectronic performances of organic materials.

Acknowledgments

This research was supported by the Ministry of Higher Education and Scientific Research, Tunisia.

Conflict of interest

The authors declare no conflict of interest.