Theoretically studying the optoelectronic properties of oligomers based on 2.7-divinyl-cabazole

This work consists of theoretically studying the electronic and optical properties of 9(4-octyloxyphenyl)-2.7-divinyl-carbazole (PCrV) oligomers. This study has been undertaken using the density functional theory (DFT) method at the B3LYP/6-31G (d,p) level and BP86/6-31G (d,p) level of theory. To evaluate the PCrV-basis systems properties, the structural optimization without geometrical restrictions was performed on the total potential energy surface (TPES). In order to ensure good absorption of radiation, the interest was in increasing the efficiency of the organic photovoltaic cell. For this effect, the (HOMOLUMO) gap energy of such compounds was reduced in terms of geometric and electronic structure. The BP86 functional gives good results at the energy gap level, while other parameters using the B3LYP functional give the best results.


Introduction
The growing energy needs of daily lives on the one hand, and the strong growth of the world population on the other are leading to a search for new sources of energy (hydroelectricity, wind, sun), as well as the mastery of materials with new properties (semiconductors, aluminum, composites, rare earths, etc...). In addition to the speed of technological development, especially plastic-based technology, and the development of computational performance, facilitates he realization of new organic materials, the discovery and improvement of new properties of semiconductor organic materials, and the expansion of the field of use, especially in the field of photovoltaic (Baek et al., 2012;Bourass et al., 2017;Toub, 2007).
Polymeric (Fukuta et al., 2015;Huang, 2015;Scharber and Sariciftci, 2013) (organic) solar cells are becoming more and more important in the field of scientific research. These cells have many potential advantages over inorganic solar cells (Koh et al., 2008;Tarascon, 2011;Zeyada et al., 2016), such as relatively low cost, lightweight, interesting electronic properties, good mechanical properties and ease of processing. However, the main limitations of this type are the low power-to-energy conversion efficiency and the relative instability compared to silicon-based solar cells. However, this efficiency depends on highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and energy gap properties.
Derivatives of 2.7-carbazole (Blouin et al., 2008;Chen et al., 2014;Zhao et al., 2010) are organic materials (these oligomers) possessing the properties of a semiconductor, known by their high stability due to the presence of nitrogen atoms, by their wide range of industrial applications thanks to their important physicochemical property. The addition of alkyl chains on the nitrogen atom increases the solubility, which facilitates the synthesis of these oligomers.
The interest is in increasing the efficiency of the organic photovoltaic cell, seeking to decrease the gap energy (HOMO-LUMO), to characterize these compounds in terms of geometrical and electronic structures to ensure a good absorption of radiation.
This work consists in theoretically studying the electronic and optical properties of oligomers based on 9-(4-octyloxyphenyl)-2.7-divinylcabazole (PCrV) (Fig. 1) using the density functional theory (DFT) method under two different functionals with the same base (6-31G [d,p]). The optical properties are obtained by the time-dependent density functional theory (TD-DFT) method, in order to show the reliability of one of these functionals, and their fairness with the experimental results (Leclerc et al., 2006).
The calculated band gap energy of these oligomers is between 0.87 eV and 2.9 eV at the BP86/6-31G (d,p) base of the DFT method, while at the B3LYP/6-31G (d,p) base of the same method the gap energy is between 1.75 eV and 3.86 eV. However, the experimental gap energy is 2.8 eV. Absorption properties, optical properties and electron density are also studied.

The studied systems
The basic molecule 9-(4-octyloxyphenyl)-2.7divinylcabazole was chosen, to which was linked a radical R, which was changed to obtain the different systems studied. The different R groups were introduced to study their effects on the electronic structure and on the optoelectronic properties. Below are the structures of the R groups and the abbreviation of different oligomers (Fig. 2
The geometrical structures of the neutral molecules were optimized without constraints, the convergence of all calculations was confirmed by the absence of negative frequencies.
The energy levels HOMO, LUMO (gap energy) are calculated from the optimized structures. Photovoltaic parameters are obtained from the optimized geometries. In order to calculate the optical properties by the TD-DFT method (Boussaidi et al., 2016;Jacquemin et al., 2009;Laurent and Jacquemin, 2013), with the two functionals (B3LYP and BP86) at the atomic base 6-31G (d,p) from the optimized structures under the same functionals.

Geometrical study
The geometrical study of the oligomers carried out at the level of the functionals B3LYP and BP86 of the DFT method under the atomic base 6-31G (d,p). The grafting of the R groups increasing the number of atoms of each oligomer causes the total energy of each system to decrease, i.e., the oligomers stabilize more and more. Note that the distances d1 and d2 represent, respectively, the charge transfer bridge between the donor part (D) and the spacer (vinyl) with the groups R, and q1 and q2 are the dihedral angles between the donor (D) and the spacer on the one hand and the groups R and the spacer on the other hand (Fig. 3). The values obtained from the optimization are grouped in Tab. 1. According to Tab. 1, it is possible to observe that the values of the bonds obtained from the calculations do not undergo a great change, generally the lengths are close to that of carbon-carbon (1.48 Å). In resonance, especially the values obtained by the B3LYP functional, the d2 bond ( Fig. 3) of the PCrV oligomer is a C-H single bond, and the closest value to the experimental one is that obtained by the B3LYP functional.
The introduction of the vinylene bond in the πconjugate system (Kim et al., 2016;Nazim et al., 2015) is an efficient strategy to modulate the electronic properties of the systems to lower the gap energy. It is also a good method to obtain coplanar molecules due to the relatively small dihedral angle between the vinyl group and the grafted R groups (Fig. 2).
The increase in the value of the dihedral angle contributes to the loss of coplanarity between donor and acceptor. In order to exploit these geometrical and structural parameters of the studied molecules internucleus distances (di) and dihedral angles (i), the most stable conformations are obtained after optimization in their fundamental state using the DFT method. The results obtained are illustrated in Fig. 4a. It is noticed that the dihedral angle i between the electron donor groups and the spacer for all compounds varies between 0.5 and 2.75°. Regardless of the study functional (B3LYP and BP86) except the dihedral angle of the PCrV-BiTTP oligomer for both functionals (0.01° for the B3LYP functional and 0.35° for the BP86 functional), i.e., the PCrV-BiTTP oligomer is almost coplanar, when the geometries are optimized by the B3LYP functional. On the other hand, for both functionals (B3LYP and BP86) the values of the dihedral angle q2 between the spacer and the R groups for the PCrV-BiTTP oligomer is 0.02° for B3LYP and 0.03 for BP86. The values of the other oligomers show that the compounds studied have a noncoplanar structure especially for compounds having the PP, TTP, PT groups, this is probably due to the steric effect of the R groups.

Optimized structures
The optimized molecular structures are shown in Fig. 5. The structures have been optimized in its neutral state by the DFT method under the base 6-31g (d,p) with the functionals B3LYP and BP86 in order to obtain the optoelectronic and photovoltaic properties.

Electronic properties
The theoretical knowledge of the HOMO and LUMO energy levels of the components is fundamental for the study of organic solar cells. Electronic properties are of paramount importance for the study of this type of molecules. Among these properties, it is mentioned the LUMO, HOMO levels, and the energy gap (Davidson et al., 1984;Jabha and Abdellah, 2018;Kato et al., 2014;2015), the latter being one of the most important factors in the control of physical and photovoltaic properties. The theoretical and experimental gap energy values of the PCrV and PCrV-T oligomers were compared, which are, respectively, 2.78 and 2.6 eV (Leclerc et al., 2006) (Fig. 6).
The values plotted in the graph shown in Fig. 6 demonstrate that the energy gap decreases when the R groupings, R ≠ H, on the carbon skeleton are added. This phenomenon is apparent specifically for R = BiTTP and R = TTN.
One of the most important parameters for determining the quality of -conjugate compounds is the value of the gap. More than the energy gap close to that of a semiconductor, the more the compose quality is candidate for use in the manufacture of electronic devices. For this reason, the most efficient strategy to have good molecules is to increase the aromaticity of these compounds by introducing R groups. All the calculations made by DTF under the functional B3LYP with the atomic base 6-31G (d,p), show a decrease of the energy gap of the oligomers, but for the oligomers PCrV and PCrV-T a band gap far from the experimental one of these molecules is obtained. On the other hand, the calculations made by the BP86 functional of the DFT method under the atomic base 6-31G (d,p) show a proximity of the calculated gap energy and the experimental band gap, as well as the decrease of the gap energy Eg of the oligomers.  shows that the band gap is generally low for all systems studied, the observed decrease in the band is due to the addition of the conjugated R group.
These results are confirmed by the propagation of the electron density. This phenomenon appears very clearly below (see Fig. 11). The electron density of LUMO is higher around the R unit for systems with smaller energy gap and precisely for the oligomers PCrV-BiTTP, PCrV-TTN, PCrV-TTP. This feature precisely allows these systems (PCrV-BiTTP, PCrV-TTN, PCrV-TTP) to be used to produce and manufacture electronic devices for photovoltaics.

Electrochemical properties
According to the optimization of structures by the DFT method with the atomic base 6-31G (d,p) and at the functional levels B3LYP and BP86, several chemical parameters were determined, namely: the electronic chemical potential μ, the electronegativity and the global hardness (Ayers, 2007;Cherkasov et al., 1998;Miranda-Quintana et al., 2016;Zhou and Parr, 1989).
The electronegativity (Eq. 1) is opposite of the chemical electronic potential μ (Eq. 2), the latter and the global hardness (Eq. 3) are calculated from the energies of the molecular orbital boundaries according to the following relationships (Khalid et al., 2020;Parr and Pearson, 1983;Zhou and Parr, 1989) In Tabs. 2 and 3, the electronic and chemical parameters obtained from the optimized structures are presented, namely: HOMO and LUMO energies, chemical potential, overall hardness and electronegativity of the compounds (PCrV-R) and the Bis-PCBM acceptor. From these results (Tabs. 2 and 3), it can be seen that the Bis-PCBM compound has the lowest chemical potential value (-4.95 eV) compared to the other compounds.  Table 3. HOMO (eV) and LUMO (eV) energies, chemical potential (eV), overall hardness (eV) and electronegativity (eV) obtained by BP86/6-31G (d.p).  Figure 8 shows that all systems studied have a donor character with a small difference in the ability to release electrons easily. The passage of electrons will take place from the compounds with the highest chemical potential to the one with the lowest chemical potential, therefore, since the value of the chemical potential of Bis-PCBM is smaller in comparison to the other compounds, it can be deduced that Bis-PCBM will behave as an electron acceptor while the others will behave as electron donors.

Electronegativity of the different compounds
Comparing the different values of electronegativity shown in Fig. 9, it can be noticed that Bis-PCBM is the molecule with the highest value of electronegativity (Tabs. 2 and 3). Therefore, the molecule with the highest electronegativity value is likely to attract electrons strongly. Here, Bis-PCBM is the electron accepting molecule.

Global hardness of different molecules
According to Fig. 10, the oligomer with the highest global hardness (PCrV and PCrV-T). These molecules hardly undergo any rearrangement of their electronic structure and will have the lowest reactivity.  The oligomer PCrV-BiTTP can easily undergo a change of their electronic structure by chemical reaction, probably leading to the creation of covalent bonds, so it is easier to polymerize this molecule. Figure 11 presents the electron density of the HOMO and LUMO orbitals of the studied oligomers. These give a qualitative and rational indication of the electronic properties of the studied oligomers.  HOMO (a, c, e, g, i, k, m, o) and LUMO (b, d, f, h, j, l, n, p) orbitals of the studied compounds. Figure 11 shows that the electron density is spread over the entire carbon skeleton at the HOMO level, and an almost complete shift towards the R group at the LUMO level. Also note the absence of electron density on the carbon chain bound to the nitrogen (N) in carbazole. Thus, this chain has no optical effect. Its main role is the solubilization and stability of the system.  Table 4 shows the values of the excitation energy Eex (eV), the absorption maximum (Jabha and Abdellah, 2018;Leliège et al., 2013) λmax (nm) and the oscillator strength (Fos) for all the molecules studied. These calculated values are obtained by the methods TD-B3LYP/6-31G(d,p) and TD-BP86/6-31G(d,p). To study the optical properties, the structures by the B3LYP/6-31G(d) method were optimized. The UVvisible spectra ( Fig. 12a and b) of the studied compounds were calculated using the TD-DFT method. In Tab. 4, the calculated values of maximum absorption wavelengths (lmax), excitation energies (Eex) and oscillator forces (Fos) were presented.

Optical proprieties
Molecules with an energy gap below 3.05 eV (PCrV-TT, PCrV-TP, PCrV-PP, PCrV-TTP, PCrV-TTN, PCrV-BiTTP) have absorption maxima for both computational functions (B3LP and BP86), thus reflecting the HOMO-LUMO transition. In addition, the simulated absorption spectra ( Fig. 12a and b) of all compounds studied have a shoulder, which can be attributed to the intramolecular charge transfer band caused by the R group introduced into the skeleton of the structures of these molecules. This indicates that these organic materials could absorb the maximum amount of incident light radiation, in particular the molecules PCrV-BiTTP, PCrV-TTN and PCrV-TTP. This property is beneficial to increase the photoelectric conversion efficiency of the solar cell containing these types of molecules.
The excitation in the S1 state corresponds exclusively to the promotion of an electron from the HOMO to the LUMO, and to the greatest oscillation force (Fos < 1) that comes from the S0→S1 electronic transition.
The excitation in the S1 state corresponds to HOMO→LUMO + 1, and the high values of the oscillation force (Fos > 1) in these compounds comes from the S0→S2 electronic transition.  All the compounds studied show simulated wavy absorption spectra; this can be attributed to the intermolecular transfer charge in the structures of these molecules. This indicates that these organic materials could absorb the maximum of the incident light radiation. The energy range for all the structures studied is generally in the visible field.
From the absorption spectra (Fig. 12b), the electronic transitions of the double spectral band for all molecules belong to the visible field and in particular for the oligomers PCrV-BiTTP, PCrV-TTP. That is to say, the low energy radiation can excite the electrons of the system.
Concerning the energy absorption, it was found that some studied molecules absorb in the ultraviolet while others in the infrared, this factor is important for a good photovoltaic application of these molecules.

Photovoltaics proprieties
The theoretical values of the open circuit voltage, Voc, have been calculated from the following expression (Eq. 4 and Eq. 5) (Boussaidi et al., 2016;Bourass et al., 2017): The

Conclusions
In this paper, quantum chemical studies on the geometry and electronic properties of several compounds based on 2.7-divnyl-carbazol are carried out to show the variation effects of alkyl R groups.
The approach of increasing the conjugation length in the skeleton of these oligomers offers good optoelectronic and photovoltaic properties for the studied systems. This is clearly justified by the results obtained which show low bandgap values especially for the molecules PCrV-BiTTP, PCrV-TTP and PCrV-TTN. Add to this the high values of the absorption maxima λmax as well as the good location of the HOMO and LUMO levels of these molecules. These results lead to suggest these materials as good candidates for applications in organic solar cells.
Two functionalities were used to describe the geometrical and optoelectronic properties to compare the results, and the BP86 function was found to give good results at the energy gap level, while other parameters using the B3LYP function give the best results.

Data availability statement
All data sets were generated and analyzed in the current study.

Funding
Not applicable