Impact of doping on the optoelectronic, electronic and nonlinear optical properties and on the reactivity of photochromic polymers containing styrylquinoline fragments: Hartree-Fock and DFT study

Abstract

Hartree-Fock (HF) and Density Functional Theory (DFT) studies were conducted to assess the impact of potassium doping on the thermodynamic, optoelectronic, electronic and nonlinear optical properties and on the reactivity of photochromic polymers containing styrylquinoline fragments. Doping was carried out on the virgin monomer (M1) and on the derivative monomer (M2) with the nitro group NO₂. Three doped monomers were investigated including, the monomer M3 obtained from M1 by substituting the H atom with a potassium, the monomer M4 by substituting two H atoms and the monomer M5 obtained from M2 by substituting the H atom. Findings proved that the use of potassium and the nitro group is an excellent process to improve the electronics properties of styrylquinoline virgin monomers. In fact, the energy gap decreases from 3.82 eV for M1 to 3.02 eV and to 2.92 eV for M3 and M4, respectively; while the decrease from 3.43 eV for M2 to 2.52 eV for M5 was observed, thus demonstrating the good semiconductor character of the obtained compounds with relevant applications in the manufacture of solar cells. Likewise, the fundamental gap decreases from 6.50 eV for M1 to 5.34 eV and to 4.62 eV for M3 and M4, respectively; while the decrease from 6.11 eV for M2 to 5.21 eV for M5 was observed; thus demonstrating an improvement in the reactivity of our doped monomers. In addition, potassium doping is an appropriate method to enhance optoelectronic properties of styrylquinoline virgin monomers. Thus, the refractive index of our doped monomers is greater than that of glass, which is a reference in optic and can be used under high electric fields of the order of $1.90\times {10}^9$ Vm⁻¹ for monomer M4 up to $7.01\times {10}^9$ Vm⁻¹ for M3 and to $10.89\times {10}^9$ Vm⁻¹ for M5. Finally, the strong enhancement of the linear and nonlinear optical (NLO) properties that we observed leads us to conclude that these doped monomers can be appropriate candidates in devices requiring good NLO properties.

Styrylquinoline; Doping; HF/DFT; Nonlinear optical properties; Electronic properties; Energy gap

1. Introduction

In recent decades, semiconductor polymers have attracted wide attention as being a class of materials that may enable the development of flexible and biocompatible electronic devices, thus pushing the limits of electronic toward applications that cannot be achieved with inorganic materials alone [1], [2], [3]. One of the most studied class of this semiconductor polymer is the conjugated polymers, which constitutes a vital class of material for extensive industrial applications [4], [5]. Indeed, the development of conjugated polymers, including double and single bonds has led to potential applications in optoelectronic devices such as light-emitting diodes (LED), field-effect transistors (FET), photovoltaics (PV), nonlinear optical devices, memory storage devices, energy storage photo detectors, and chemo- and bio-sensors [4], [6], [7], [8], [9], [10], [11]. Despite all these potential applications of semiconductor polymer, there remains a concern that can be formulated as: how can the electronic properties of semiconductors be optimized in order to enhance the performance of assimilated devices? In fact, conjugated polymers in the pristine state are neutral and usually semiconductors or insulators with low conductivity [4]. Therefore, doping is the unique, central, underlying and unifying method which enables the distinction of conducting polymers from other types of polymers [12], [13].

Nowadays, after decades of research, we notice that conjugated polymers with an interchanging sequence of suitable acceptor and donor units in the main chains can show a decrease in its energy band-gap due to interactions of the intramolecular charge transfer. Likewise, the electrical properties of semiconductor polymers strongly depend on the density of charge carriers. During doping, charge carriers are created and move along the polymer chain. As a result, the conductivity increases by several orders of magnitude [12]. Moreover, doping produces changes in the electronic, electrical, magnetic, optical and structural properties of the polymer, giving rise to new applications of doped material in many areas. Therefore, doping has quickly become a powerful tool for optimizing the performance of organic electronic devices, such as organic field effect transistors (OFET), organic photovoltaics (OPV) solar cells and organic light-emitting diodes (OLED) [1], [2], [3], as well as organic thermoelectric materials [1], [14]. Doping of conductive polymers have mainly been achieved by redox doping, which involves the partial addition (reduction) or removal (oxidation) of electrons to or from the π system of the polymer backbone [15], [16], [17].

Our study aims to improve the excellent properties of these photochromic materials, in particular their potential to control digital on/off switching due to the occurrence of trans-cis (E/Z) isomerization by photo-irradiation of said materials. [18]. Trans-cis isomerization was first investigated in photochromic compounds such as azobenzenes, azines, stilbenes, cinnamoyls, diarylethenes [19], [20], [21]. However, according to M. F. Budyka [22] and O. Kharchenko et al. [23], polymers containing styrylquinoline moieties can be a potential substitutes for azobenzenes, due to their ability to reversibly transform between their trans and cis form when exposed to light or thermal stimulation. This material is an asymmetric organic molecule [23] and π-conjugated polymer, for which we decided to investigate the impact of doping on its thermodynamic, electronic, optoelectronic and optical properties. D. Guichaoua et al. [24] conducted numerical simulations and UV irradiations to investigate the modulation of NLO properties of a photochromic styrylquinoline-based polymers. Our previous work on these compounds [25] allowed us to investigate the structural, optoelectronic, thermodynamic and nonlinear optical properties of the virgin styrylquinoline monomer (M1) and the derived monomer (M2). To our knowledge, no other study has been carried out in this molecular compound based on styrylquinoline fragment to improve the optoelectronic and electronics properties of the material and optimize NLO properties. Therefore, we chose the appropriate dopant based on the works of C. D. D. Mveme et al. [26] and G. W. Ejuh et al. [27] on doping with halogens (chlorine or fluorine). However, these halogens did not produce a significant improvement in the properties of the studied compounds. We have also used the radicals CN, OH and COOH without much success. Finally, based on the works of C. C. Fonkem et al. [28], we carried out doping with alkaline (Lithium, sodium or potassium). Except for potassium, other dopants produced an insignificant impact on the optoelectronic and linear and nonlinear optical properties of our reference monomers. Our choice therefore fells on potassium as a dopant.

The main objective of this work is to perform HF and DFT calculations to investigated the effect of potassium doping on optoelectronic, electronic, linear and nonlinear optical properties of methacrylate monomers containing styrylquinoline moieties. Doping was carried out on the virgin monomer (M1) and on the derived monomer (M2). The structural and thermodynamics properties of our doped monomers were also established. Before beginning our studies, we first described the theoretical background and methodology.

2. Methodologies and details of theoretical calculations

2.1. Details of theoretical calculations

Physical properties of materials such as electric displacement (D), electric field in the material (E), relative permittivity of the material (${\epsilon }_r$), induced polarization (P), average electric susceptibility (${\chi }_e$) and refractive index (n) were calculated using equations available in the literature [25].

Linear and nonlinear optical properties such as dipole moment (μ), average polarizability ($\bar{\alpha }$) and anisotropy (Δα), molar refractivity (MR), first order hyperpolarizability (β) and second order hyperpolarizability (γ) of our studied systems were calculated using equations found in literature [25], [29]. In addition, electronic and optoelectronic properties are deduced from NLO parameters through equations found in the literature [25]. Thus, the first order (${\chi }^{(1)}$), second order (${\chi }^{(2)}$) and third order (${\chi }^{(3)}$) electric susceptibility tensors are defined by [30], [31]

$${\chi }_{ij}^{(1)}=\frac{{\alpha }_{ij}}{{\epsilon }_{0}V},{\chi }_{ijk}^{(2)}=\frac{{\beta }_{ijk}}{2{\epsilon }_{0}V},{\chi }_{ijkl}^{(3)}=\frac{{\gamma }_{ijkl}}{6{\epsilon }_{0}V}$$ (1)

where ${\alpha }_{ij}$, ${\beta }_{ijk}$ and ${\gamma }_{ijkl}$ are the polarizability and first and second hyperpolarizability tensor components and V the volume of our monomer. Atomic unit were translated into SI units and electrostatic units using conversion factors available in the literature [32], [33].

The energy gap ($E_g$) which allows discussing the potential applications of a material as a semiconductor has been calculated using the following equation

$$E_g=E_{LUMO}-E_{HOMO}$$ (2)

where $E_{\mathit{LUMO}}$ is the energy of the lowest unoccupied molecular orbital and $E_{\mathit{HOMO}}$ is the energy of the highest occupied molecular orbital. Some electronic and global reactivity parameters were evaluated using the vertical approximation for ionization potential (IP) and the electron affinity (EA) [34], [35], [36], [37], [38].

2.2. Computational methods

Hartree-Fock and Density Functional Theory were used in this research work to investigate the impact of doping on the structural, thermodynamic, optoelectronic, electronic and nonlinear optical properties of our reference monomers M1 and M2 [25]. Doping was carried out by substituting hydrogen atoms with those of potassium. All calculations were done in gas phase using the quantum chemical software Gaussian 09 [39]. Structure modeling and visualization of the studied molecules were achieved using the Gauss View 6.0.16 software [40]. Our findings were based on the HF, DFT/B3LYP, DFT/ωB97XD and DFT/B3PW91 methods with the 6-311G(d,p) as basis set. Calculations started with the geometry optimization of our doped monomers at the ground state. Frequency calculations were also performed. The location of the electronic population was obtained by calculating the HOMO and LUMO levels. NLO properties such as average polarizability, first and second order hyperpolorizability and dipole moment were assessed. Both static and dynamic nonlinear responses were evaluated for an incident wavelength of 1059.6 nm. Optoelectronic parameters were deduced from nonlinear optical parameters through Eq. (1).

Within the framework of this study, we retain as basic compounds two photochromic monomers based on styrylquinoline: the main or virgin styrylquinoline monomer denoted M1 and the derivative monomer denoted M2 obtained by replacing a hydrogen atom in the monomer M1 with the nitro group NO₂. Fig. 1 shows the optimized structure of the two monomers [25]. Next, we carried out the doping of our two monomers with potassium. Therefore, two doped monomers were obtained from M1: the monomer M3 by substituting the hydrogen labeled 36 (Fig. 1M1) with potassium and the monomer M4 by substituting the hydrogens labeled 27 and 36 (Fig. 1M1) with potassium. The last doped monomer denoted by M5 was obtained from the monomer M2 by substituting the hydrogen labeled 27 (Fig. 1M2) with potassium.

Figure 1.

Optimized and labeled structures of our reference monomers obtained using DFT/B3LYP method, according to P. Noudem et al. [25]. The blue color stands for nitrogen, the red for oxygen, the dark gray for carbon and the white for hydrogen atoms.

3. Results and discussions

3.1. Optimized structures

The optimized structures of our doped monomers are shown in Fig. 2, in the case of HF (Fig. 2a, 2c and 2e) and DFT/B3LYP (Fig. 2b, 2d and 2f) methods. As for the reference monomers [25], we did not observe any negative frequency after the optimization. Geometric parameters such as bonds length and bond angles were determined and reported in the supplementary material (S): Tables S.1, S.2 and S.3 for bonds length and Tables S.4, S.5 and S.6 for bond angles. Small differences were observed on the bonds length, as well as on the number of C=C bonds and on their distribution along the chain, and finally on the presence or absence of the double bond in the 9-22 junction, C−N. Indeed, using the DFT/B3LYP method, in monomer M3 (Fig. 2a and 2b), the C−C bond length in the 15–17 junction changes to 1.4118 Å and in the 16–17 junction to 1.4168 Å, compared to the virgin monomer M1 where these bonds length are of 1.3923 Å and 1.3963 Å, respectively. Similar behavior is observed when moving from M1 to M4. However, the variation of these bonds length is 0.08% at most, when moving from M2 to M5, as compared to 1.47% when moving from M1 to M3 or M4.

Figure 2.

Optimized structures of the doped monomers. (a), (c) and (e) HF method; (b), (d) and (f) DFT/B3LYP method. The purple color stands for potassium. We indicated in (b) the conventions adopted for the vibrational analysis.

With regard to the bond angles, small variations were observed, of the order of 0.70% at most for monomers M3 and M4 and about 0.50% at most for M5 monomer, regardless of the calculation method used.

3.2. Vibrational analysis

In order to verify the stability of our studied monomers, vibrational analysis was performed using DFT/B3LYP method. Indeed, DFT/B3LYP is an efficient, accurate and less computationally time-consuming method for determining the vibrational frequencies of compounds [41], [42]. No imaginary frequency was observed in the IR and Raman vibrational spectra as shown in Fig. 3 for monomers M1, M2 and M3. According to D. Fouejio et al. [43], this shows that the stability points on the potential energy surfaces are local minima and therefore our studied monomers are stables. The IR and Raman spectra of doped monomers M4 and M5 can be found in the supplementary material (S): Fig. S.1. In Fig. 3, we found that the intensity of the vibrational modes of monomer M2 and M3 is highest than that of monomer M1, which is probably due to the presence of the nitro group (NO₂) in M2 and that of potassium in M3. The values of some vibrational modes are collected in Table 1, Table 2, Table 3 for monomers M1, M2 and M3, respectively. The values of monomers M4 and M5 can be found in the supplementary material (S): Tables S.7 and S.8. We are interested by stretch (υ), twist (τ), in-plane (δ) and out-of-plane (γ) deformations of some selected bonds of our monomers. Our analysis is made by comparison with the vibrational spectroscopy study of the 2-[(E)-2-phenylthenyl]quinoline-5-carboxylic acid [44], which differs from the monomer M1 by the absence of the methacrylate functionalization. As shown in Fig. 2b for monomer M3, we assign in this work, the label “${\mathit{P}\mathit{h}\mathit{i}}_{\mathit{I}\mathit{I}}$” for mono-substituted benzene, “${\mathit{P}\mathit{h}}_{\mathit{I}}$” for benzene in quinoline ring and “Ring” for nuclear with nitrogen in quinoline. In the following section, we will analyze some vibrational modes in detail.

Figure 3.

IR intensity ((a) and (c)) and Raman activity ((b) and (d)) of monomers M1, M2 and M3 obtained using DFT/B3LYP method.

Table 1.

Some selected vibrational frequencies (cm⁻¹), IR intensities, Raman scattering activities and interpretations of monomer M1 obtained using DFT/B3LYP method.

Frequencies	IR intensity	Raman activity	IRa	Ramana	Interpretations
3144	16.928	116.752	-	3145	υC-H
3120	16.221	74.163	-	-	υC-HI
3096	11.438	58.777	-	-	υC-H
3040	10.431	130.841	3046	3054	υC-HII
1640	71.142	4138.345	1600	1600	υC=C, υC=O
1592	35.914	204.253	-	-	υPhI, υPhII
1544	60.258	312.118	1513	1514	υPhI
1408	6.362	888.841	-	-	υPhI, δCH
1368	45.484	587.324	1364	1376	δCHII
1312	105.276	105.276	1300	-	υC-O, υC-C
1272	404.669	404.669	1252	1261	υC-N, δC-HI
1232	27.199	945.109	-	1242	υC-C, δC-H
1208	8.864	435.566	-	1196	υC-C, δC-HI
1176	7.914	122.355	1169	-	δC-HII, δPhII
1024	62.075	166.342	-	-	υPhII, δPhI
904	12.945	52.682	-	-	γCHII, γC-H
832	26.971	23.959	838	836	γC-C, γC-HI
808	19.829	27.346	814	-	υPhI, δPhI
776	53.233	41.368	773	791	τRing, γCHI
664	5.151	8.741	656	662	τPhI, τRing
640	9.336	12.364	620	618	δPhII
560	4.987	4.052	-	554	δC=O, δPhI
520	9.440	17.738	-	518	τC-O, δPhI

^aExperiment values provided by R.T. Ulahannan et al. [44].

Table 2.

Some selected vibrational frequencies (cm⁻¹), IR intensities, Raman scattering activities and interpretations of monomer M2 obtained using DFT/B3LYP method.

Frequencies	IR intensity	Raman activity	IRa	Ramana	Interpretations
3152	16.194	130.876	-	3145	υC-H
3120	14.111	64.737	-	-	υC-HI
3096	13.803	64.180	-	-	υC-H
3040	10.138	124.873	3046	3054	υC-HII
1640	170.478	8904.71	1600	1600	υC=C, υC=O
1592	146.767	607.981	-	-	υPhI, υPhII
1544	45.607	715.531	1559	-	υPhII, δC-HII
1448	29.257	479.507	1427	1420	υPhII
1376	688.778	2585.355	1364	1376	δC-HII
1272	95.347	770.299	1252	1261	υC-N, δC-HI
1176	7.240	219.936	1169	-	δC-HII, δPhII
1128	136.732	1055.824	1144	-	δC-HI, δC-C
1024	70.205	54.194	-	-	υPhII, δPhI
808	22.681	35.380	814	-	υPhI, δPhI
776	32.491	22.323	773	791	τRing, γC-HI
616	19.598	10.630	-	-	δPhI, γC=O

^aExperiment values provided by R.T. Ulahannan et al. [44].

Table 3.

Some selected vibrational frequencies (cm⁻¹), IR intensities, Raman scattering activities and interpretations of doped monomer M3 obtained using DFT/B3LYP method.

Frequencies	IR intensity	Raman activity	IRa	Ramana	Interpretations
3144	26.262	151.851	-	3145	υC-H
3096	52.675	335.612	-	3107	υC-H
3064	40.175	239.083	-	-	υC-HII
3040	14.205	116.655	3046	3054	υCHII
1680	-	6254	-	-	υC=N
1640	267.412	6186.498	1600	1600	υC=C, υC=O
1504	52.380	2013.369	1487	-	υC-C, δC-C
1472	27.859	836.731	-	-	υPhI, δC-HI
1448	26.714	546.594	1427	1420	υPhII, δC-HII
1376	828.301	5100.310	1364	1376	δC-HII
1232	75.123	4924.703	-	1242	υC-C, δC-H
1128	465.763	2335.051	1144	-	δC-HI, δC-C
1088	75.995	452.114	-	1079	υPhII, δC-HII
960	39.990	79.537	-	-	γC-HII, δC-HI
720	26.735	100.482	-	727	γC-C, δC=O
568	11.907	326.446	570	573	τC-O

^aExperiment values provided by R.T. Ulahannan et al. [44].

With regard to C=O bond, in the carboxylic acids spectra, its stretching vibration gives rise to a broad band of the order of 1600 – 1700 cm⁻¹ and the in-plane deformation frequency is expected at 725 ± 95 cm⁻¹ [44]. Our calculated stretching vibration (C19=O20 bond) was observed both on IR and Raman spectra at 1640 cm⁻¹ for monomers M1, M2, M3 and M5, while the in-plane deformation was observed at 720 cm⁻¹ for our doped monomers and at 560 cm⁻¹ for monomer M1. In addition, another in-plane deformation was observed at 568 cm⁻¹ for monomer M5. Finally, out-of-plane deformation appears at 616, 568, 520 cm⁻¹ for monomers M2, M3 and M4, respectively.

As regards the C−H bond, due to stretching vibrations of the bond, its exhibits for all aromatic compounds, a weak frequency band of the order of 3100 – 3000 cm⁻¹ [44]. Our calculated stretching vibration of monomers M3 and M5 were observed both on IR and Raman spectra at 3040 cm⁻¹ and 3064 cm⁻¹, which is in agreement with the experimental values. Likewise, this stretching vibration was observed at 3128 cm⁻¹, 3088 cm⁻¹ and 3064 cm⁻¹ for monomer M4 and at 3120 cm⁻¹ and 3040 cm⁻¹ for our reference monomers M1 and M2. In-plane bending vibrations are usually observed between 1000 – 1300 cm⁻¹ [45]. In mono-substituted benzenes they are expected between 1230 – 1280 cm⁻¹ and 1170 – 1000 cm⁻¹ [44]. Our findings reveal small discrepancies with these experimental data. On the other hand, out-of-plane vibrations are expected below 1000 cm⁻¹ [46] or specifically between 750 – 1000 cm⁻¹ [45]. In this study, out-of-plane vibrations were observed at 960 cm⁻¹ for monomers M3 and M5 and at 776 cm⁻¹ for M1 and M2, this last frequency is closer to that of 745 cm⁻¹ obtained by R.T. Ulahannan et al. [44].

Regarding the C=C vibrations, from a theoretical point of view, carbon-carbon ring stretching vibrations occur between 1625 – 1430 cm⁻¹ [45]. It is also well known that quinoline has three bands around 1600 cm⁻¹ [46]. As shown in Fig. 3b and 3d, in Raman spectra, the band near 1600 cm⁻¹ is sharp and strong. Our calculated stretching out-of-ring mode was observed both on IR and Raman spectra at 1640 cm⁻¹ for monomers M1, M2, M3 and M5, which is closer to the experimental value 1600 cm⁻¹ [44]. This mode was observed at 1632, 1608 and 1576 cm⁻¹ for monomer M4.

With regard to C−C bond, our calculated stretching vibration was observed at 1312 and 1232 cm⁻¹ for monomer M1, at 1504 cm⁻¹ for M3, M4 and M5 and at 1232 cm⁻¹ for M3 and M5. Out-of-plane deformation was observed at 720 cm⁻¹ for our doped monomers and at 832 cm⁻¹ for the virgin monomer M1.

As regards the C=N bond, ring stretching vibration band occurs between 1600 – 1500 cm⁻¹ [45] and between 1660 – 1480 cm⁻¹ for conjugated cyclic systems [46]. This mode was observed in this work for monomer M5 at 1536 cm⁻¹ on IR spectra and at 1688 cm⁻¹ both on IR and Raman spectra. For monomer M4, the mode was observed both on IR and Raman spectra at 1680 cm⁻¹. Finally, for monomer M3, the mode was observed at 1680 cm⁻¹ on IR spectra and at 1688 cm⁻¹ on Raman spectra.

In view of the findings of the vibrational frequencies of our selected bonds, it can be concluded that they altogether agree with those reported in the literature.

3.3. Optoelectronic properties

Some optoelectronic parameters of our doped monomers such as those listed in the methodology section were calculated using HF, DFT/B3LYP, DFT/B3PW91 and DFT/ωB97XD methods. The values of these parameters are reported in Table 4. The dipole moment (μ) is related to the electric field in the material by the equation $\mu =\alpha E+\beta E^2+\gamma E^3+\cdots$. μ can be induced as a result of the application of an external electric field or is permanent due to the non-coincidence between the barycenter of the positive and negative charges of the molecule; our study concerns this last case. Regarding the induced electric polarization, it is the macroscopic quantity associated with the dipole moment; it is given by the equation $P=\mu /V$. Whereas the electric field is given by $E=\mu /\bar{\alpha }$.

Table 4.

Average electric field (E), electric polarization (P), average electric susceptibility (χ_e), relative dielectric constant (ε_r), dielectric constant (ε), refractive index (n) and electric displacement (D) of doped styrylquinoline monomers.

Monomer M3
Methods/Parameters	E×109Vm−1	P×10−2Cm−2	D×10−2Cm−2	ϵ×10−11	ϵr	χe	n
HF	9.468	26.120	34.492	3.643	4.120	3.120	2.030
B3LYP	7.008	27.715	33.912	4.839	5.473	4.473	2.339
B3PW91	7.452	20.844	27.433	3.681	4.164	3.164	2.040
ωB97XD	8.001	26.527	33.601	4.200	4.750	3.750	2.179
Monomer M4
HF	3.198	7.959	10.786	3.373	3.815	2.815	1.953
B3LYP	1.904	7.449	9.133	4.797	5.426	4.426	2.329
B3PW91	1.972	7.426	9.170	4.649	5.258	4.258	2.293
ωB97XD	1.664	4.083	5.553	3.338	3.776	2.776	1.943
Monomer M5
HF	15.115	43.372	56.737	3.754	4.245	3.245	2.060
B3LYP	10.891	40.717	50.346	4.623	5.228	4.228	2.287
B3PW91	11.389	31.731	41.801	3.670	4.151	3.151	2.037
ωB97XD	12.734	48.726	59.985	4.711	5.328	4.328	2.308

From Table 4, we found that, except for monomer M4, the substitution of the hydrogen by potassium in the basic monomers M1 and M2 strongly improves the optoelectronic properties of the resulting compounds. As a matter of fact, the electric field, electric polarization and electric displacement decrease when we move from HF to DFT methods. This behavior was also observed on the reference monomers [25]. Concerning the average electric field of our doped materials, the highest values are obtained using HF method and the lowest by DFT/ωB97XD. Moreover, the strongest variations are observed when we move from the reference monomers to the doped monomers. The increase is at least 97% for monomers M3 and M5 regardless of the calculation method used. On the contrary, for monomer M4, a decrease of 30.38%, 45.68%, 44.41% and 58.33% is observed using HF, DFT/B3LYP, DFT/B3PW91 and DFT/ωB97XD methods, respectively. Similar behavior was observed for the electric polarization and electric displacement. Regarding the electric polarization, the increase is at least 115% for M3 and at least 101% for M5, whatever the calculation method. As regards the electric displacement, the increase is at least 114% for M3 and at least 102% for M5, regardless of the method. In the case of monomer M4, the highest decrease of the electric polarization of about 62% is obtained using DFT/ωB97XD method and the lowest of about 20% using DFT/B3LYB method. Meanwhile, for the electric displacement, the highest decrease of about 62% is obtained using DFT/ωB97XD method and the lowest of about 26% using DFT/B3LYB. The substitution of the hydrogens labeled 27 and 36 of monomer M1 with potassium, produces a compensation effect in the monomer M4, which impacts on the distribution of the charges (on the electron density), thereby causing a strong decrease in the dipole moment as can be seen in Table 7; which therefore does not contribute to improving the optoelectronic properties of this monomer.

Table 7.

Dipole moment (μ), average polarizability ($\bar{\alpha }$), anisotropy of polarizability (Δα), molar refractivity (MR), first total static hyperpolarizability (β_T) and averaged second static hyperpolarizability ($\bar{\gamma }$) of doped styrylquinoline monomers.

Monomer M3
Methods/Parameters	μ (D)	$\bar{\alpha }$ (×10−24 esu)	Δα (×10−24 esu)	MR (esu/mol)	βT (×10−30 esu)	$\bar{\gamma }$ (×10−36 esu)
HF	13.028	41.258	43.372	104.089	12.312	174.287
B3LYP	12.300	52.624	67.688	132.766	135.711	810.202
B3PW91	12.575	50.594	63.344	127.645	82.692	645.004
ωB97XD	12.110	45.380	50.488	114.490	25.667	330.496
Monomer M4
HF	4.826	45.250	49.264	114.162	9.481	320.855
B3LYP	3.985	62.770	88.214	158.362	40.874	1769.489
B3PW91	3.847	58.480	78.557	147.539	31.765	1677.172
ωB97XD	2.805	50.563	58.910	127.567	24.367	603.958
Monomer M5
HF	21.752	43.145	45.740	108.851	4.763	173.039
B3LYP	20.420	56.216	76.044	141.829	26.016	1130.730
B3PW91	20.650	54.365	71.903	137.157	34.922	994.358
ωB97XD	20.304	47.806	55.037	120.611	8.452	364.695

Based on values in Table 4, we found that, just as for the reference monomers M1 and M2 [25], the refractive index of the doped monomers is higher than that of the reference materials in optoelectronic such as glasses [47], regardless of monomers and method used. However, small variations in the refractive index are observed during doping. For monomer M3, the increase is of the order of 4.54%, 16.82%, 0.83% and 6.58% obtained respectively at the HF, DFT/B3LYP, DFT/B3PW91 and DFT/ωB97XD levels. Concerning the monomer M4, the increase is of the order of 0.59%, 16.32% and 13.31% obtained using HF, DFT/B3LYP and DFT/B3PW91, respectively; while a decrease of 4.98% is observed using DFT/ωB97XD. Finally, for monomer M5, the decrease is 0.85% obtained using DFT/B3PW91; while an increase of 7.45%, 8.54% and 10.50% is observed using HF, DFT/B3LYP and DFT/ωB97XD methods, respectively.

By comparing our findings with those in the literature [32], [48], [49], [50], [51], we can conclude that just like for the reference monomers [25], our doped monomers based styrylquinoline are excellent candidates for optoelectronic and could have applications in OPVs, optical switches and OLEDs or could be used within a strong electric field.

3.4. Electronic properties and chemical descriptors

In order to investigate the impact of doping on the semiconductor properties and on the reactivity of our reference monomers, several parameters such as E_LUMO, E_HOMO, E_g, IP, EA, the fundamental gap (E_f), chemical potential (μ_CP), chemical hardness (η), electrophilicity index (ω) and electronic charge transfer (ΔN_max) were calculated and summarized in Table 5. The frontier molecular orbitals of the studied monomers are shown in Figure 4, Figure 5, Figure 6. They provide realistic qualitative information on the susceptibility of electrons from the HOMO level to be transferred to the LUMO level. Red iso-surfaces represent the negative domains of the molecular orbitals of high electron density, while green iso-surfaces represent the positive domains of the molecular orbitals of low electron density. As shown in these figures, the frontier molecular orbitals of the studied monomers are mainly localized on the potassium atoms. Indeed, the analysis of these frontier molecular orbitals reveals that, unlike the basic monomers where electrophilic and nucleophilic sites are equally distributed along the molecular chain, charge distribution is strongly impacted by potassium doping. This is accompanied by the presence of domains of high electron density on potassium and on neighboring atoms. In the case of monomer M4, one of the potassium seems to have no effect.

Table 5.

Electronic properties and global reactivity descriptors of doped styrylquinoline monomers. All parameters are given in eV.

Monomer M3
Methods/Parameters	ELUMO	EHOMO	Eg	IP	EA	Ef	μCP	η	ω	ΔNmax
HF	−0.393	−6.588	6.195	4.951	0.511	4.440	−2.731	2.220	1.680	1.230
B3LYP	−1.743	−4.633	2.890	6.142	0.822	5.320	−3.482	2.660	2.279	1.309
B3PW91	−1.583	−4.604	3.021	6.155	0.811	5.343	−3.483	2.672	2.270	1.304
ωB97XD	−0.283	−6.531	6.248	6.574	0.027	6.547	−3.301	3.274	1.664	1.008
Monomer M4
HF	−0.308	−5.886	5.577	4.917	0.323	4.595	−2.620	2.297	1.494	1.140
B3LYP	−1.629	−4.273	2.644	5.508	0.959	4.549	−3.233	2.274	2.298	1.422
B3PW91	−1.308	−4.223	2.915	5.503	0.883	4.620	−3.193	2.310	2.207	1.382
ωB97XD	−0.198	−6.122	5.924	5.917	0.485	5.432	−3.201	2.716	1.886	1.178
Monomer M5
HF	−0.587	−7.076	6.489	5.840	0.713	5.126	−3.277	2.563	2.094	1.278
B3LYP	−2.495	−5.069	2.573	6.548	1.351	5.197	−3.950	2.598	3.002	1.520
B3PW91	−2.527	−5.048	2.522	6.541	1.333	5.209	−3.937	2.604	2.976	1.512
ωB97XD	−0.693	−6.997	6.304	6.547	0.645	5.902	−3.596	2.951	2.191	1.219

Figure 4.

HOMO-LUMO molecular orbitals of doped styrylquinoline monomer M3.

Figure 5.

HOMO-LUMO molecular orbitals of doped styrylquinoline monomer M4.

Figure 6.

HOMO-LUMO molecular orbitals of doped styrylquinoline monomer M5.

The electrical conductivity (σ) of a material is linked to its energy gap through the relation $\sigma \propto \exp (-E_g/2k_{B}T)$, where $k_B$ is the Boltzmann constant, T the absolute temperature and $E_g$ the energy gap calculated using Eq. (2) [52]. Consequently, the decrease of $E_g$ leads to an increase of the electrical conductivity. The values of $E_g$ in Table 5 show that doping improves the conductivity of the reference monomers M1 and M2. On the other hand, the value of the HOMO-LUMO gap decreases sharply when moving from HF or DFT/ωB97XD to DFT/B3LYP or DFT/B3PW91. As for the reference monomers M1 and M2 [25], the values of the energy gap of the doped monomers obtained using HF and DFT/ωB97XD methods remain quite high. However, E. Shakerzadeh et al. [53] in their work showed that the functional B3PW91 leads to good results of the energy gap. Our findings obtained using DFT/B3LYP and DFT/B3PW91 show very slight differences; therefore, the results obtained by the two methods can be used interchangeably. Hence, the doping of our reference monomers allows the energy gap to go from 3.82 eV for M1 to 3.02 eV for M3 and to 2.92 eV for M4, and from 3.43 eV for M2 to 2.52 eV for M5. Which leads to a reduction of the energy gap at least 26%, 31% and 32% when moving from M1 to M3, M1 to M4 and from M2 to M5, respectively regardless of the calculation method. Therefore, our doped monomers are better semiconductors than the reference monomers. Thus, we suggest that these methacrylate monomers containing styrylquinoline moieties and doped with potassium, can find applications in PLEDs (Polymer Light-Emitting Diodes) or OLEDs [54] due to their energy gap between 2 and 3 eV [55]. Indeed, according to studies carried out by L. Fugikawa Santos et al. [54], in the manufacture of PLEDs – OLEDs, monomer M3 can be a substitute for PFO (Poly(9,9-di-n-octylfluorenyl-2,7-diyl)) with E${}_{\mathrm{g}}=3.0$ eV, M4 for PPV (Poly(p-phenylene vinylene)) with E${}_{\mathrm{g}}=2.7$ eV, while M5 can be an alternative for MEH-PPV (Poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene]) with E${}_{\mathrm{g}}=2.2$ eV.

The ionization potential (IP) is the energy required to extract an electron from the HOMO level. It also provides information on the stability and reactivity of the molecule. The lower the ionization potential, the more reactivity of the molecule; while a high ionization potential indicates a more stable molecule. Our reference monomers M1 and M2 have minimum ionization potential of 7.09 eV and 7.32 eV [25], respectively, which gives them fairly good stability. The results in Table 5 show that, the IP and EA values decrease upon doping, thus leading to a decrease in the stability and to an increase in the reactivity, and as well as a reduction of the fundamental gap. The IP values of our doped monomers are comparable to the ionization potential of some semiconductor polymers already used in the industry, such as MEH-PPV [54]; which allows the production of energy-efficiency polymer photovoltaic cells [56], [57]. Therefore, it can be concluded that our doped monomers are good candidates for the manufacture of photovoltaic cells. Concerning the electron affinity of our doped monomers, their values are all positive whatever the calculation method and fall within the range 0.02 eV and 1.40 eV.

As regards the fundamental gap (E_f), in the case of organic molecules, it differs from the HOMO-LUMO gap [35]. Indeed, the fundamental gap connects the ionization potential and the electron affinity and is defined by $E_f=IP-EA$ and is also linked to the chemical hardness by the relation $E_f=2\eta$. Thus, in terms of electronic transition, the fundamental gap is well suited to describe the reactivity of a molecular system [43]. As shown in Table 5, doping reduces the fundamental gap. The decrease of E_f is at least 9%, 31% and 16% when moving from monomer M1 to M3 and to M4, and from monomer M2 to M5, respectively whatever the calculation method. The strong variations are obtained using HF method, where the fundamental gap goes from 7.33 eV for M1 to 4.44 eV for M3 and to 4.60 eV for M4, and from 7.29 eV for M2 to 5.13 eV for M5.

Concerning the chemical hardness, it accounts for the resistance of a chemical compound against change in its electronic structure. It allows to describe the reactivity and the stability of a molecule. An increase in η leads to an increase in stability and a decrease in reactivity. According to the values in Table 5, μ_CP increase and η decrease during doping of monomers M1 and M2 no matter the calculation method. Thus showing that the stability of doped monomers decreases, while its reactivity increases. Furthermore, increasing the chemical potential during potassium doping, improves the ability of electrons to escape from our monomers [58]. Finally, the electrophilicity index decrease during doping, thus showing the improvement of the electron donor character of our doped monomers.

As regards the charge transfer, natural bond orbital (NBO) was performed to better understand the direction and extent of charge transfer between our alkali atom with styrylquinoline. For this purpose, the NBO charges were calculated on all atoms of the studied system. NBO analysis is a powerful tool to study the nature of intra-molecular and intermolecular interactions as well as charge transfer between the atoms of any complex [59], [60], [61]. For our investigated monomers, charge transfer occurs from the alkali atom to the styrylquinoline and results in a positive charge on the potassium. In addition, the C19-labeled carbon located in the methyl methacrylate (MMA) subunit exhibits a positive charge. Thus, the MMA is also involved in the charge transfer that appears on our studied monomers. The NBO charge values of the monomer M3 range from −0.588 e to +0.859 e. The highest positive charge of 0.859 e and 0.824 e is observed in the potassium labeled 41 and in the carbon labeled 19 of the MMA group, respectively. Concerning the M4 monomer, the double potassium doping does not affect the range of NBO charge values; however, 3 atoms exhibit high net positive charge: 0.860 e for potassium labeled 40, 0.843 e for potassium labeled 41 and 0.824 e for carbon labeled 19. Regarding the M5 monomer, the NBO charge values range from −0.587 e to +0.881 e. The highest positive charge of 0.512 e, 0.881 e and 0.822 e is observed in the nitrogen labeled 43 of the nitro group, in the potassium labeled 40 and in the carbon labeled 19, respectively. Thus, there is a very small increase in NBO charge values with the coaction of the alkali donor and the nitro group acceptor. Finally, for the monomers studied, the potassium metal atom has the highest net positive charge, confirming electron transfer from metal atom to organic complex [60], [61].

3.5. Thermodynamic properties

The values at normal pressure and room temperature of the electronic energy (EE), zero point vibrational energy (ZPVE), enthalpy (H), Gibbs free energy (G), thermal energy (E_Th), heat capacity (C_v) and entropy (S) of our doped monomers were calculated and given in Table 6.

Table 6.

Thermodynamic properties of doped styrylquinoline monomers. Values are given in kcal/mol.

Monomer M3
Methods/Parameters	EE (×103)	ZPVE	H (×103)	G (×103)	ETh	Cv (×10−3)	S (×10−3)
HF	−1009.063	208.567	−1008.841	−1008.889	222.034	79.133	164.142
B3LYP	−1013.328	197.278	−1013.117	−1013.166	211.313	83.855	165.886
B3PW91	−1013.559	194.595	−1013.35	−1013.400	208.847	85.041	168.646
ωB97XD	−1013.266	195.164	−1013.056	−1013.106	209.413	84.984	168.331
Monomer M4
HF	−1384.643	200.049	−1384.428	−1384.481	214.985	84.384	181.494
B3LYP	−1389.4	189.328	−1389.184	−1389.238	204.745	88.878	181.195
B3PW91	−1389.627	186.555	−1389.424	−1389.479	202.252	90.216	183.718
ωB97XD	−1389.297	187.071	−1389.094	−1389.148	202.788	90.156	184.436
Monomer M5
HF	−1136.779	211.055	−1136.553	−1136.606	226.094	87.111	178.763
B3LYP	−1141.652	199.118	−1141.437	−1141.49	214.818	92.21	181.651
B3PW91	−1141.924	196.232	−1141.712	−1141.766	212.134	93.534	182.774
ωB97XD	−1141581	196.903	−1141.368	−1141.422	212.805	93.423	182.783

From Table 6, we notice that EE, ZPVE, H, G and E_Th values decrease during doping whatever the method, while C_v and S values increase at the same level. Regarding the Gibbs free energy, it is a fundamental parameter for the thermodynamic stability of a compound at a given temperature T and pressure P. Lower the Gibbs free energy, the more stability of the compound. The values of G in Table 6 show a strong decrease during doping. The decrease percentage is at least 59.1, 118.1 and 49.2 when moving from M1 to M3, M1 to M4 and from M2 to M5, respectively no matter the calculation method. The lowest value of our doped monomers is −1389.479 × 10³ kcal/mol followed by −1141.766 × 10³ kcal/mol and by −1013.400 × 10³ kcal/mol obtained for the monomer M4, M5 and M3, respectively using DFT/B3PW91 method. Therefore, M4 is the most thermodynamically stable doped monomer followed by M5. Furthermore, the fact that the monomer M5 is thermodynamically more stable than M3, both being doped once with potassium, is in agreement with the relative stability of the reference monomers M1 and M2 [25]. In addition, the enthalpy of our doped monomers are all negative, making it possible to conclude that they are thermodynamically stable. A similar behavior on the values of the electronic energy was observed. With regard to thermal energy, the decrease observed during doping confirms the improvement in the stability of the doped monomers. As with the Gibbs free energy, the lowest values are obtained using DFT/B3PW91 method regardless of the doped monomer. As regards the heat capacity, slight increases were observed during doping. The variations are at least 6.7%, 13.2% and 6.0% when we move from M1 to M3, M1 to M4 and from M2 to M5, respectively no matter the calculation method. A similar behavior on the entropy values has also been observed.

3.6. Linear and nonlinear optical properties

The linear and nonlinear optical parameters such as dipole moment (μ), average polarizability ($\bar{\alpha }$), anisotropy of polarizability (Δα), first order hyperpolarizability (β), second order hyperpolarizability (γ) and molar refractivity (MR) of our doped monomers were calculated and summarized in Table 7 in the case of static mode.

As with the reference monomers M1 and M2 [25], the results in Table 7 show that the linear optical parameters of our doped monomers vary slightly with the computational method, while the nonlinear optical parameters are highly dependent on the computational method. Based on the work of Jeng-Da Chai et al. [62], DFT/ωB97XD takes into account exchange, correlation and long range interactions and allows accurate evaluation of NLO parameters. Likewise, HF method offers good precision in the determination of NLO properties [63], [64]. The comparison of our findings with experimental data or with literature results will therefore be based on these two methods. From the findings in Table 7, we found that except for the dipole moment in the case of the M4 monomer and the first-order hyperpolarizability in the case of the M5 monomer, the linear and nonlinear optical parameters increase during doping whatever the method. Regarding the polarizability, which represents the ease with which the electronic cloud of a molecule can be deformed under the effect of an electric field or another molecule, we observed an increase at least 14%, 25% and 11% when we move from M1 to M3, from M1 to M4 and from M2 to M5, respectively, regardless of the calculation method. A similar behavior on the values of the molar reactivity, which is a measure of the total polarizability of one mole of a substance, was observed. While strong increases were observed on the anisotropy of polarizability; the variations are found between 26.4% – 48.8%, 43.6% – 94.0% and 20.3% – 39.5% when moving from M1 to M3, M1 to M4 and from M2 to M5, respectively no matter the method. As with the reference monomers M1 and M2 [25], there is also a higher anisotropy of polarizability with respect to the polarizability of at least 105% for M3, 109% for M4 and 106% for M5 regardless of the method. According to the results in Table 7, it can be concluded that the substitution of hydrogen atoms with potassium atoms is a suitable method to improve the total polarization of our investigated molecules.

As regards the dipole moment, the polarity of a molecule comes from the non-homogeneous distribution of its electronic cloud, thus the dipole moment gives a measure of the polarity of the compound. The results in Table 7 show that potassium doping strongly improves the values of μ of monomers M3 and M5, while in the case of monomer M4, the double potassium doping produces rather an opposite effect. Indeed, the values of μ of monomer M3 are at least 2.34 times greater than that of monomer M1 whatever the calculation method. The same applies to the monomers M5 and M2, meanwhile for the monomers M4 and M1, the dipole moment values of M1 are at least 1.15 times greater than those of M4.

Regarding the total static hyperpolarizability, we found that, except for monomer M5 in the case of the first hyperpolarizability, potassium doping significantly enhances the nonlinear response of our reference monomers M1 and M2. The greatest increases were achieved with DFT/B3LYP followed by DFT/B3PW91 and the lowest with HF. The percentage of variations are found between 80.9 – 747.4 and 39.3 – 155.2 for ${\beta }_{\mathrm{T}}$ when moving from M1 to M3 and from M1 to M4, respectively; and 321.6 – 510.7, 676.1 – 1233.8 and 199.3 – 285.8 for $\bar{\gamma }$ when moving from M1 to M3, from M1 to M4 and from M2 to M5, respectively. However, the association of potassium with the nitro group NO₂ (monomer M5), instead produces a decrease in ${\beta }_{\mathrm{T}}$ of at most 52% and at least 33% compared to the monomer M2. Likewise, compared to the impact of the nitro group [25], it is clear that potassium doping better improves NLO properties of our virgin monomer. This greater improvement for second order hyperpolarizability, favors the use of the resulting monomers in the third harmonics generation (THG). Comparing our results with those of M. Niu et al. [65] on the enhancement of the NLO properties of the inorganic compound Al₁₂N₁₂ by doping with an alkali atom (Li, Na, K), we find that for the potassium case the value of ${\beta }_T=654.87\times {10}^{-30}esu$ obtained by M. Niu et al. is 4.82 times higher than our value obtained for monomer M1 using DFT/B3LYP method and 25.20 times higher than our result for monomer M5. Alkali and superalkali doping [66], [67] thus appear to be a promising approach for the improvement of NLO properties of the organic and inorganic compounds.

In order to complete our study and to better understand the relationship between structure property and NLO processes, we performed the calculations of NLO parameters in dynamic mode. In fact, to suggest applications in SHG or THG, the materials must be non-centrosymmetric and the calculations should be carried out in dynamic mode (frequency-dependent) at a specific wavelength. For this purpose, the frequency-dependent first order hyperpolarizability $\beta (-2\omega ,\omega ,\omega )$ and second order hyperpolarizability $\gamma (-2\omega ,\omega ,\omega ,0)$ at wavelength $\lambda =1059.6$ nm were calculated and collected in Table 8, Table 9 respectively. From these tables it is noted that just like for the static hyperpolarizability, the potassium doping of the reference monomers leads to a very strong increase of the dynamic hyperpolarizability using DFT/B3LYP and DFT/B3PW91 methods, whereas this increase remains quite reasonable for HF and DFT/ωB97XD. Indeed, the average first hyperpolarizability of monomer M3 is 3.1, 5.5, 278.5 and 32.9 times greater than that of monomer M1 using HF, DFT/ωB97XD DFT/B3LYP and DFT/B3PW91 methods, respectively; that of M4 is 0.9, 1.6, 452.6, and 66.7 times greater than that of M1 and the value of ${\beta }_{\mathrm{T}}$ of monomer M5 is 0.5, 0.8, 1.9 and 3.2 times greater than that of M2 at the same conditions of calculation. Similarly, the average second hyperpolarizability of monomer M3 is 6.0, 9.8, 3442.8 and 54.9 times greater than that of monomer M1 using HF, DFT/ωB97XD DFT/B3LYP and DFT/B3PW91 methods; that of M4 is 12.2, 22.2, 923.0, and 667.2 times greater than that of M1 and the value of $\bar{\gamma }$ of monomer M5 is 5.3, 8.1, 127.6 and 60.5 times greater than that of M2 at the same conditions of calculation.

Table 8.

Some selected components of the frequency-dependent first order hyperpolarizability β(−2ω,ω,ω) values at ω = 0.043 au = 1059.6 nm for monomers M3, M4 and M5. Values are given in 10⁻³⁰ esu.

Monomer M3
Methods/Parameters	βxxx	βyyy	βzzz	βx	βy	βz	βT
HF	5.306	3.971	8.726	7.631	11.298	25.857	29.231
B3LYP	284.229	307.902	6414.440	2204.265	2336.789	8528.850	9113.762
B3PW91	40.704	43.455	710.831	246.242	283.489	973.819	1043.707
ωB97XD	10.256	8.650	55.182	25.152	39.872	101.832	112.214
Monomer M4
HF	−13.477	−0.838	−1.527	−7.779	−2.351	−3.591	8.884
B3LYP	−11891.800	−13.143	323.249	−14327.918	802.388	3666.311	14811.310
B3PW91	1468.810	−39.082	−87.188	1945.210	−490.027	−675.298	2116.600
ωB97XD	−30.660	−1.424	−27.598	−14.714	2.622	−28.125	31.849
Monomer M5
HF	−3.536	1.663	−1.687	−0.450	−4.231	6.187	7.509
B3LYP	−46.757	−4.964	258.201	−102.039	−101.623	334.438	364.127
B3PW91	−12.713	−17.412	−456.908	119.505	−264.276	−507.146	584.226
ωB97XD	−6.291	2.944	7.717	−3.502	−8.257	26.301	27.789

Table 9.

Some selected components of the frequency-dependent second order hyperpolarizability γ(−2ω,ω,ω,0) values at ω = 0.043 au = 1059.6 nm for monomers M3, M4 and M5. Values are given in 10⁻³⁶ esu.

Monomer M3
Methods/Parameters	γxxxx	γyyyy	γzzzz	γxxyy	γyyzz	γxxzz	$\bar{\gamma }$
HF	57.633	47.086	1207.390	13.831	112.254	146.371	371.404
B3LYP	−19018.800	11600.200	−3712280.000	−21937.600	−301472.000	−581254.000	−1105805.160
B3PW91	928.730	1048.050	54245.400	650.014	7271.290	6853.030	17154.170
ωB97XD	136.533	137.023	4338.250	55.955	441.725	493.575	1318.863
Monomer M4
HF	2531.400	59.082	80.154	252.891	34.520	254.930	751.063
B3LYP	−1104940.000	−589.428	−1611.460	−71727.500	−808.116	−115061.000	−296466.824
B3PW91	714788.000	1571.220	7692.640	58372.200	3873.240	97220.200	208596.628
ωB97XD	4304.980	349.779	2593.250	806.507	662.183	2371.500	2985.678
Monomer M5
HF	35.311	22.239	1131.840	8.339	105.456	113.980	328.988
B3LYP	1365.390	1000.020	151589.000	752.826	11980.300	12725.200	40974.212
B3PW91	445.893	691.115	70484.400	373.762	6808.140	4306.000	18919.442
ωB97XD	85.027	67.904	3824.300	30.864	348.856	351.024	1087.744

As regards the monomer M3, the NLO response is predominant in the z direction, a direction in which the methacrylate group and its various functions (acid, alkene) are located, which suggests that the material enhances its dynamic hyperpolarizability by reacting its carbon chain out of the main plane of the molecule. In the presence of two potassium, monomer M4, the preferred direction of the NLO response is the x-axis. In the monomer M4, the presence of two potassium leads to a greater involvement of the charges in the methacrylate which is accompanied by a strong deformation of its electronic cloud. With regard to monomer M5 which already contains a nitro group, able to deactivate the aromatic cycle, to reduce the electron density and to promote a high intramolecular charge transfer [24], [25], the presence of potassium, as an electron donor, slightly enhances the NLO response of monomer M2. In addition, we found that beyond the passage of the system from the push type with the only presence of the nitro group to the push-pull type, with the simultaneous presence of a strong donor (K) and a strong acceptor (NO₂), there is a decrease in the first total hyperpolarizability. We believe that this decrease can be explained by the fact that the presence of potassium causes a shadowing effect on the impact of the nitro group, preventing it from relocating the maximum number of bonds in its direction and vice versa.

By comparing NLO parameters of our doped monomers with those of the organometallic complexes [24] and urea [68], [69] which is the reference molecule for NLO properties, it is clear that, these new materials based on styrylquinoline and potassium would be excellent candidates in devices requiring good NLO properties.

3.6.1. Electric susceptibility

Electric susceptibility is a physical property that link the electric polarization to the electric field. This property was calculated in this work using Eq. (1). The results of the first order average susceptibility (${\chi }_{\mathrm{e}}$) are reported in Table 4. From this table, we found a slight enhancement in ${\chi }_{\mathrm{e}}$ when moving from M1 to M3. The rate of increase is found between 2.2% and 48.6%. Regarding the monomer M4, a decrease of 12.8% was observed using DFT/ωB97XD, while an increase was observed with the other three methods. With regard to monomer M5, a decrease of 2.2% was observed using DFT/B3PW91, while an increase was observed with the other three methods.

In order to better understand and analyze the impact of potassium doping on the nonlinear response of our reference monomers M1 and M2, the second (χ⁽²⁾) and third (χ⁽³⁾) order susceptibility were also calculated in dynamic mode and the findings are summarized in Table 10, Table 11, respectively. From Table 10, we found that the values of second order total susceptibility (${\chi }_{tot}^{(2)}$) strongly increase when we move from M1 to M3. This increase is at least 202% whatever the calculation method. Similar behavior is observed for M4 and M5 with DFT/B3LYP and DFT/B3PW91 methods. While a decrease of 24.6% was observed when moving from M1 to M4 using HF method; and of 46.0% and 8.8% when we move from M2 to M5 using HF and DFT/ωB97XD, respectively. Regarding the third order total susceptibility (${\chi }_{tot}^{(3)}$), very large increase were observed during potassium doping. The percentage of variation is at least 299 regardless of the monomer and the calculation method. By comparing our ${\chi }_{tot}^{(2)}$ values with that of ${\chi }_{tot}^{(2)}=1pm/V$ of quartz [70] and our ${\chi }_{tot}^{(3)}$ values with that of ${\chi }_{tot}^{(3)}=2\times {10}^{-22}{m}^2{V}^{-2}$ of silica [71], [72], which are the reference for SHG and THG, respectively, we can suggest that our reference and doped monomers would be excellent candidates in the development of NLO materials.

Table 10.

Some selected components of the frequency-dependent second order susceptibility ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ values at ω = 0.043 au = 1059.6 nm for doped styrylquinoline monomers. Values are given in pmV⁻¹.

Monomer M3
Methods/Parameters	χ(2)xxx	χ(2)yyy	χ(2)zzz	χ(2)x	χ(2)y	χ(2)z	χ(2)tot
HF	6.693	5.009	11.007	9.626	14.252	32.617	36.873
B3LYP	402.950	436.512	9093.730	3124.979	3312.858	12091.321	12920.549
B3PW91	42.451	45.321	741.351	256.815	295.661	1015.630	1088.519
ωB97XD	14.135	11.921	76.054	34.665	54.953	140.349	154.659
Monomer M4
HF	−13.984	−0.869	−1.584	−8.071	−2.439	−3.726	9.218
B3LYP	−13985.330	−15.456	380.156	−16850.322	943.647	4311.758	17418.814
B3PW91	1783.817	−47.464	−105.887	2362.388	−595.120	−820.125	2570.535
ωB97XD	−28.071	−1.303	−25.268	−13.471	2.401	−25.751	29.161
Monomer M5
HF	−4.436	2.086	−2.117	−0.565	−5.308	7.763	9.421
B3LYP	−58.660	−6.228	323.932	−128.016	−127.494	419.577	456.823
B3PW91	−12.290	−16.834	−441.729	115.535	−255.496	−490.298	564.817
ωB97XD	−9.499	4.445	11.653	−5.288	−12.468	39.713	41.959

Table 11.

Some selected components of the frequency-dependent third order susceptibility ${\chi }^{\left(3\right)}(-2\omega ,\omega ,\omega ,0)$ values at ω = 0.043 au = 1059.6 nm for doped styrylquinoline monomers. Values are given in 10⁻²² m²V⁻².

Monomer M3
Methods/Parameters	χ(3)xxxx	χ(3)yyyy	χ(3)zzzz	χ(3)xxyy	χ(3)yyzz	χ(3)xxzz	χ(3)tot
HF	8.084	6.604	169.347	1.940	15.745	20.530	52.093
B3LYP	−2998.025	1828.595	−585184.577	−3458.130	−47522.483	−91625.868	−174313.394
B3PW91	107.700	121.537	6290.559	75.379	843.214	794.710	1989.280
ωB97XD	20.923	20.999	664.829	8.575	67.694	75.639	202.113
Monomer M4
HF	292.056	6.816	9.248	29.177	3.983	29.412	86.653
B3LYP	−144488.297	−77.077	−210.724	−9379.500	−105.674	−15046.037	−38767.704
B3PW91	96523.004	212.173	1038.793	7882.421	523.032	13128.348	28168.314
ωB97XD	438.264	35.609	264.003	82.106	67.413	241.428	303.954
Monomer M5
HF	4.926	3.102	157.888	1.163	14.711	15.900	45.893
B3LYP	190.468	139.500	21146.186	105.017	1671.214	1775.125	5715.773
B3PW91	47.932	74.293	7576.851	40.178	731.854	462.881	2033.780
ωB97XD	14.275	11.401	642.069	5.182	58.570	58.934	182.623

4. Conclusion

HF and DFT methods were used in this work to investigate the impact of potassium doping on the structural and thermodynamics parameters, optoelectronic, electronic and nonlinear optical properties of two photochromic polymers containing styrylquinoline moieties and denoted M1 and M2. Thermodynamic findings of our doped monomers revealed thermodynamically stable materials with significant reactivity that is suitable for reactions with other compounds. In fact, potassium doping decreases the enthalpy of our doped monomers and promotes their thermodynamic stability. Furthermore, the findings of the geometric optimization indicate that doping does not change the molecular structure of studied monomers, but leads to a reduction in the number of C=C bonds and promotes a strong delocalization of these bonds along the chain of doped monomers. The analysis of the optoelectronic properties revealed that the substitution of hydrogen by potassium in our reference monomers, strongly improves the optoelectronic properties of the obtained compounds. Thus, the refractive index of our doped monomers is greater than that of glass, which is a reference in optics and can be used under strong electric fields of the order of 1.90×10⁹ Vm⁻¹ for monomer M4 up to 7.01×10⁹ Vm⁻¹ for M3 and to 10.89×10⁹ Vm⁻¹ for M5. Furthermore, potassium doping is an excellent process to improve electronics properties of styrylquinoline virgin monomers. In fact, the energy gap decreases from 3.82 eV for M1 to 3.02 eV and to 2.92 eV for M3 and M4, respectively; while the decrease from 3.43 eV for M2 to 2.52 eV for M5 was observed, thus demonstrating the good semiconductor character of the obtained compounds. Likewise, the fundamental gap decreases from 6.50 eV for M1 to 5.34 eV and to 4.62 eV for M3 and M4, respectively; while the decrease from 6.11 eV for M2 to 5.21 eV for M5 was observed; thus demonstrating an improvement in the reactivity of our doped monomers. Based on the largest values of the first and second order hyperpolarizability of the doped monomers, these compounds are promised materials for NLO devices. Finally, based on the consistency of our findings, we believe that our studied monomers could be subject to further experimental studies, find the same applications as methacrylate polymers, namely: use in optical devices [73], manufacture of dental prostheses, ocular implants [74] and in orthopaedic surgery [75].

Declarations

Author contribution statement

David Fouejio; P. Noudem: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

C.D.D. Mveme: Conceived and designed the experiments; Analyzed and interpreted the data.

S.S. Zekeng: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.

J.B. Fankam Fankam: Analyzed and interpreted the data.

Funding statement

Prof. A.N. Singhwas supported by the Council of Scientific and Industrial Research (CSIR), India, for its financial support through Emeritus Professor scheme [grant no. 21(0582)/03/EMR-II].

Data availability statement

Data included in article/supp. material/referenced in article.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

Supplementary content related to this article has been published online at https://doi.org/10.1016/j.heliyon.2022.e11491.

No additional information is available for this paper.

Supplementary material

The following Supplementary material is associated with this article:

PNoudem_KDE_Supplementary_Mmaterial.pdf

In the supplementary material, the optimized geometry parameters of doped monomers M3, M4 and M5 calculated using HF, DFT/B3LYP and DFT/B3PW91, DFT/ωB97XD with 6-311G(d,p) basis set, are presented in Tables S.1, S.2 and S.3 respectively and the bonds angles are given in Tables S.4, S.5 and S.6 respectively. In addition, the IR and Raman spectra of doped monomers M4 and M5 are depicted in Fig. S.1, and the values of some vibrational modes of monomers M4 and M5 are given in Tables S.7 and S.8.