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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

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 1.90×109 Vm−1 for monomer M4 up to 7.01×109 Vm−1 for M3 and to 10.89×109 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.


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 donor units in the main chains can show a decrease in its energy bandgap 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 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 -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.

Details of theoretical calculations
Physical properties of materials such as electric displacement ( ), electric field in the material ( ), relative permittivity of the material ( ), induced polarization ( ), average electric susceptibility ( ) and refractive index ( ) were calculated using equations available in the literature [25].
Linear and nonlinear optical properties such as dipole moment ( ), average polarizability ( ) and anisotropy (Δ ), molar refractivity (MR), first order hyperpolarizability ( ) and second order hyperpolarizability ( ) 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 ( (1) ), second order ( (2) ) and third order ( (3) ) electric susceptibility tensors are defined by [30,31] (1) = 0 , (2) = 2 0 , where , and are the polarizability and first and second hyperpolarizability tensor components and 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 ( ) which allows discussing the potential applications of a material as a semiconductor has been calculated using the following equation where LUMO is the energy of the lowest unoccupied molecular orbital and 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 ( ) and the electron affinity ( ) [34,35,36,37,38].

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/ B97XD 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 NO 2 . 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.

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 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.  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.
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.

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 (NO 2 ) in M2 and that of potassium in M3. The values of some vibrational modes are collected in Tables 1, 2 and 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 ( ), twist ( ), in-plane ( ) and out-of-plane ( ) 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 " " for mono-substituted benzene, " " 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.
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    Table 4. Average electric field ( ), electric polarization ( ), average electric susceptibility ( ), relative dielectric constant ( ), dielectric constant ( ), refractive index ( ) and electric displacement ( ) of doped styrylquinoline monomers. 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-ofring 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.

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/ B97XD methods. The values of these parameters are reported in Table 4. The dipole moment ( ) is related to the electric field in the material by the equation = + 2 + 3 + ⋯. 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 = ∕ . Whereas the electric field is given by = ∕ .
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/ B97XD. 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/ B97XD 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/ B97XD 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/ B97XD 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.
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/ B97XD 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/ B97XD. 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/ B97XD 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.

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 ( CP ), chemical hardness ( ), electrophilicity index ( ) and electronic charge transfer (ΔN max ) were calculated and summarized in Table 5. The frontier molecular orbitals of the studied monomers are shown in Fig. 4, 5 and 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.
The electrical conductivity ( ) of a material is linked to its energy gap through the relation ∝ exp(− ∕2 ), where is the Boltzmann constant, the absolute temperature and the energy gap calculated using Eq. (2) [52]. Consequently, the decrease of leads to an increase of the electrical conductivity. The values of 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/ B97XD 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/ B97XD 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 g = 3.0 eV, M4 for PPV (Poly(p-phenylene vinylene)) with E g = 2.7 eV, while M5 can be an alternative for MEH-PPV (Poly[2-methoxy-5-(2-ethylhexyloxy)-1,4phenylenevinylene]) with E 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 = − and is also linked to the chemical hardness by the relation = 2 . 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 leads to an increase in stability and a decrease in reactivity. According to the values in Table 5, CP increase and 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

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.
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 × 10 3 kcal/mol followed by −1141.766 × 10 3 kcal/mol and by −1013.400 × 10 3 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.

Linear and nonlinear optical properties
The linear and nonlinear optical parameters such as dipole moment ( ), average polarizability ( ), anisotropy of polarizability (Δ ), first order hyperpolarizability ( ), second order hyperpolarizability ( ) 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/ B97XD 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 varia- Table 7. Dipole moment ( ), average polarizability ( ), anisotropy of polarizability (Δ ), molar refractivity (MR), first total static hyperpolarizability ( T ) and averaged second static hyperpolarizability ( ) of doped styrylquinoline monomers.   [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 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 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 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 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 NO 2 (monomer M5), instead produces a decrease in 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 Al 12 N 12 by doping with an alkali atom (Li, Na, K), we find that for the potassium case the value of = 654.87 × 10 −30 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 (frequencydependent) at a specific wavelength. For this purpose, the frequencydependent first order hyperpolarizability (−2 , , ) and second order hyperpolarizability (−2 , , , 0) at wavelength = 1059.6 nm were calculated and collected in Tables 8 and 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/ B97XD. Indeed, the average first hyperpolarizability of monomer M3 is 3.1, 5.5, 278.5 and 32.9 times greater than that of monomer As regards the monomer M3, the NLO response is predominant in the 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 -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 (NO 2 ), 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.

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 ( e ) are reported in Table 4. From this table, we found a slight enhancement in 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/ B97XD, 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 ( (2) ) and third ( (3) ) order susceptibility were also calculated in dynamic mode and the findings are summarized in Tables 10  and 11, respectively. From Table 10, we found that the values of second order total susceptibility ( (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/ B97XD, respectively. Regarding the third order total susceptibility ( (3) ), very large increase were observed during potassium doping. The percentage of variation is at least 299 regardless of the monomer and the calcula- Table 11. Some selected components of the frequency-dependent third order susceptibility (3) (−2 , , , 0)  tion method. By comparing our (2) values with that of (2) = 1 ∕ of quartz [70] and our (3) values with that of (3) = 2 × 10 −22 2 −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.

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 1.90×10 9 Vm −1 for monomer M4 up to 7.01×10 9 Vm −1 for M3 and to 10.89×10 9 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].

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.