New Organic Dyes with Low Bandgap Based on Heterocyclic Compounds for Dye-sensitized Solar Cells Applications

In this paper, a theoretical study has been carried out. This study concerns four organic dyes with structure D–π–A on the base of triphenylamine; we choose thiophene and thieno [3, 4-b] pyrazine group as a donor and the group cyanoacrylic acid as an acceptor bridged by four conjugated spacers consisting of phenyl, pyrrole, thiophene, and furan. Our studied dyes' ground state geometric and electronic properties are calculated after optimization in their fundamental states with DFT / B3LYP / 6−311G (d, p). Using this method, EHOMO, ELUMO, bandgap energy, λmax, chemical reactivity indices, dipole moment, the Voc, molecular electrostatic potential (MEP), the LHE, the free injection energy (ΔGinj), the regeneration energy (ΔGreg), and the total reorganization energy (λtot) for all these dyes have been calculated and discussed. The optical properties such as Etr, the maximum wavelength (λmax), and the corresponding oscillator strengths have been carried out by the TD−DFT method at CAM–B3LYP/6–311G (d, p). The calculated results for all these dyes indicate that all these latters can be considered favorable candidates for an efficient DSSC sensitizer.


Introduction
Solar energy becomes the most competitive alternative to substitute fossil fuels to satisfy the increasing energy demand [1]. Photovoltaic refers to directly converting light harvested to electrical energy employing a semiconductor material [2]. Therefore, the development of new photovoltaic devices becomes indispensable. Different new photovoltaic systems have been developed and are going through the process to be commercialized [3]. Thus, enormous researchers focus their efforts to develop solar cell elements, principally for solar cells DSSC type [4]. The dye-sensitized solar cells (DSSC), The DSSC, since they have been first reported by O'Regan and Grätzel et al. in 1991 [5], have been pulled tremendous attention thanks to low cost, lightweight nature, and high performance of photovoltaic to develop flexible photovoltaic devices [2][3][4][5]. The DSSC devices consist of four units: photoanode [6], cathode [7], electrolyte, and sensitizer [8]. The photoanode consists of a unit, different π-linkers join the two units D and A as example phenyl, thiophene, pyrrole and furan [37].
The objective of this work is to study the influence of π-bridges on the electronic and photovoltaic parameters of the four organic dyes named DA-Phe (D1), DA-Pyr (D2), DA-Thi (D3), and DA-Fur (D4). Several important parameters can affect dye performances like energy levels HOMO and LUMO, energy bandgap, dipole moment, E00, which means the lowest excitation energies, Light-Harvesting Efficiency (LHE), energy corresponding to open-circuit voltage noted (Voc), the free energy of injection (ΔG inj ) and the regeneration energy (ΔG reg ) have been conducted. The electrochemical, photovoltaic, and absorption parameters of the studied compounds (dyes) are systematically investigated using the DFT and TD-DFT quantum methods. The chemical structure of the studied dyes is shown in figure 1.

Computational details.
The DFT using the functional (B3LYP) [38] at the 6-311G (d) basis set [39] have been utilized for optimizing the geometries in their fundamental state and also theoretically computing of the electronic, optic, and photovoltaic parameters for the designed dyes having a D-π-A structure to possible use in DSSCs. Gaussian 09 software package [40] has been used to achieve the theoretical calculations. The time-dependent quantum method TD-DFT [41] with the functional CAM-B3LYP [42] is applied to calculate optical parameters and the absorption spectra. The HOMO, LUMO, bandgap, wavelength λmax, and oscillator strength (f) have been carried out using quantum calculations.
Various parameters can determine the performance of a DSSC, one the most generally used parameter is power conversion efficiency (PCE) noted (η), this latter parameter depends on several other parameters such as short-circuit current density (Jsc), Fill Factor (FF), opencircuit voltage (Voc) and the incident solar power (Pin) [43]. The power conversion efficiency can be expressed by the following formula: The V oc parameter (open-circuit voltage) can be estimated as [44]: = − (2) Where ELUMO is the energy level, LUMO of the dye and (ECB) is considered as the energy of the conduction band (CB) of the semiconductor (commonly TiO2 ) (ECB = -4.0 eV) [45].
In DSSCs, the Jsc is generally estimated as follows [46]: Here, the parameter LHE (λ) is linked to the oscillator strength (f) at a designated maximum wavelength, Φinject is considered as electron injection within the conductance band of the TiO2, and ηcollect parameter signifies charge collection efficiency. To know the theoretical relation betwixt the Jsc and PCE, several parameters like Φinj, LHE, and reorganization energy (λtot) are examined. The LHE can be determined as [47].
( ) = 1 − 10 − (4) For studied dyes, the injection driving force ΔG inj has been calculated by the expression [48]: = * − (5) E dye* denotes the oxidation potential of the dye in an excited state, and it can be determined as follows [49]: * = − 00 (6) E dye signifies the oxidation potential of the dye in the neutral state (Edye = -EHOMO), while E00 is considered as the vertical transition energy which corresponds to max [50].
The regeneration driving force (ΔG reg ) is expressed as follows [51]: is denoted as redox potential of the electrolyte I -/I -3 (−4.80 eV) [52]. The positive and negative states of dyes are optimized through the DFT method, aiming to determine the reorganization energies (λtot) [53]. It is noted that to have a high value of Jsc, a low value of reorganization energy (λtotal) is needed; that could be determined by adding the hole reorganization energy to the electron one [12] as follows [54]: Noted that 0 ± designate the energy of cation (anion), which is determined in the neutral state from their optimized structure, ± ± indicate the energy of cation (anion) determined in the cationic (anionic) state from the optimized structure, ± 0 is the calculated energy at the cationic (anionic) state of the neutral molecule. Finally, 0 designates the computed energy at the fundamental state of the neutral molecule. Moreover, the cations and anions concerning the creation of "electron holes". The two parameters of the dyes, such ionization potential (IP) and the electronic affinity (EA) have been carried out as follows: Several global reactivity parameters have been introduced in the chemical literature [55] example the chemical potential (µ), electronegativity (χ) [56] and hardness (ƞ) [57,58].
Knowing the values HOMO and LUMO energy levels for such a compound, these various parameters can be calculated via the following formulas [59,60]: -µ = (E HOMO + E LUMO ) /2; (11) -ƞ = (ELUMO -EHOMO) /2; (12) -χ = -(EHOMO + ELUMO) /2; (13) Figure 2 display the chemical structures of the investigated molecules. Using DFT/B3LYP/6-311G (d, p), all molecular geometries have been carried out [61]. The data in figure 2 exhibits that all organic dyes possess nearly planar conformations [62]. In D-π-A type compounds, the π-conjugated group exists as a linker for intermolecular charge transfer (ICT), the bonds between D and π-spacer (L1), between and A and π-spacer (L2) furnish an account of the interrelationships among themselves [63]. To gain from intramolecular charge transfer in the D-π-A type compounds, a short link length of the bridge is needed. The critical bonds lengths (L1 and L2) and the dihedrals angles (Ф1 and Ф2) of investigated molecules in their ground state and excited one are collected in table 1. As illustrated in figure 1, the dihedral angle between the donor and -spacer is named 1 while and these betwixt the acceptor and -spacer is 2.  It is remarked from the results exhibited in the table above that the bond lengths values L1 for all dyes in their ground state (S0) are 1.43 Å; that is to say, the bond lengths are between C-C bonds which facilitates the ICT process of the dyes. For all the dyes, L2 change significantly, and their values are 1.41 Å for D2 and D4 and are 1.42 Å for D1 and D3 [64]. It implies that the interplay midst acceptor moiety and π-spacer are barely influenced by the interactions D-π [65]. From Table 1, it can be observed that Φ2 in all compounds in their fundamental state is similar (179°); whereas Φ1 values of all molecules are similar (179°), except for D1 (168.18°). These obtained values indicate that all molecules have planar geometry except for the dihedral angle betwixt the donor and π-spacer for D1 dye, which is somewhat twisted likely because of the existence of steric effects between the two groups donor and acceptor [66,67]. It is believed that this planar molecular structure ought to ameliorate the transfer of electrons from the D to A across the π-spacer unit for these dyes [68]. Therefore, the insertion of phenyl moiety as π-spacer is unfavorable to the molecular planarity and the effect of conjugation [69]. Finally, for these studied compounds in the excited state (S1) the getting values of Li and Φi are almost analogous compared to those in the ground state (S0).

Molecular orbitals.
Generally, the choice of the appropriate donor group and acceptor one is required to ameliorate the light-gathering capacity of DSSCs [62]. So, in dyes with the D-π-A type, the electron-donating ability (D) can affect the electrochemical properties [61]. Regarding D-π-A type organic dyes, a high value of the energy level HOMO is provided by a stronger electrondonating group. In contrast, the great electron-accepting group supplies a low energy level ELUMO. To provide a profound vision into the outbuilding of the electronic properties on the structure of molecules [70], it is helpful to theoretically determine the energy levels HOMO and LUMO for any molecule, seeing that this knowledge informs whether the proposed dyes meet the basic requirements for a photosensitizer from DSSC [71]. The analysis of the HOMO and LUMO energies levels and the relevant energy gap of our studied dyes are given in figure  3. The FMO diagram is presented in figure 4.  Figure 3 indicates that the electrons of HOMO are mainly distributed on the donor moiety, raft whereas a high electron density is exhibited on the π-spacer moieties as well as the acceptor one for any dyes. This means that there is an electron delocalization [70]. On the first hand, the HOMO possesses a π-bonding character in the sub-fragments as well as a πantibonding one betwixt successive sub-fragments [72]; on the other hand, the LUMO's exhibit a π-antibonding character in the sub-fragments as well as a π-bonding character betwixt the sub-fragments [73]. Generally, the molecule containing a more density of HOMO ought to own a great ability to provide electrons [74], while the one occupied by more density of LUMO is more comfortable acquiring the electrons [75]. HOMO's electron density transfers to the LUMO one during photoexcitation of the sensitizer producing a great transition of the ICT.  [23]. Furthermore, the obtained values of the bandgap are between 1.67 and 1.78 eV. This implicates that the studied dyes can be used in DSSCs [2]. It can be remarked that the Egap decreases as follows: D2 > D1 > D4 > D3. Subsequently, the Egap of these dyes is weak. This is probably influenced by π-conjugated donor units and the π-bridge ones leading to a rise in the charge transfer betwixt the donor group and the acceptor one.

Quantum chemical parameters.
To better understand the reactivity in molecular systems in their ground state [76], electronic chemical potential (μ), global hardness (ƞ), and electronegativity (χ) are estimated using the DFT method. The chemical potential (μ) may represent an electron's propensity to leave an equilibrium system [77]; Whereas chemical hardness (a) is known to be a marker for measuring stability and reactivity that are related to intramolecular charge transfer resistance (ICT) [74]. Electronegativity (χ) is the opposite value of the chemical potential and can be defined as the system's electron-donor property [66]. These quantum parameters are determined from the energy levels of HOMO and LUMO.
According to the obtained results figured in Table 2, the chemical potentials of the four molecules are superior to the value of TiO2. This means that electrons can readily skip to the TiO2 from these dyes, showing that these molecules behave as optimal donors' groups of electrons for solar cells applications. It should be noted that as the chemical hardness decreases, the conversion efficiency increases [78]. The four dyes' chemical hardness ascending order is as follows: D3 < D4 < D1 < D2. The electronegativity values of all dyes are lower than those of TiO2 one, indicating that TiO2 is capable of pulling the electrons of these compounds. The electronegativity values of all dyes are 4.23 eV, 4.17 eV, 4.27 eV, and 4.26 eV, respectively. The potential chemical values are greater than TiO2 for the investigated dyes. This signifies that electrons readily jump from the Di dyes to the TiO2 [70]. Finally, from table 2, the computed values of dipole moment (ρ) parameter for D1, D2, D3, and D4 dyes are 7.18 eV, 4.87 eV, 6.80 eV, and 8.84 eV. The obtained dipole moment values for D1, D3, and D4 are comparatively higher than those for D2, indicating that the latter are more reactive [66].

Electrostatic potential (ESP).
We conducted calculations for the electrostatic potentials of the investigated dyes with DFT-B3LYP/6-311G. (d, p). The MEP is a plot showing the electrostatic potential, charted onto the constant electron density surface [79], that focuses on predicting the physicochemical properties such as the reactive sites for the attack of the electrophilic nucleophilic [80]. MEP offers a 3D vision system for recognizing the electrostatic impact of a molecule [81]. Furthermore, it provides a tool for analyzing the related polarity of the compounds [82]. The ESP maps of the designated dyes are illustrated in figure 5.
ESP values are displayed in different colours. The blue region indicates electron-poor regions, whereas the red region indicates an electron-rich field [70]. The map color code falls between the two values -5.628 e -2 (deepest red) and 5.628 e -2 (deepest blue) for D1, −0.128 e 0 (deepest red) and 0.128 e 0 (deepest blue) for D2, -5.855 e -2 (deepest red) and 5.855 e -2 (deepest blue) for D3, -6.020 e -2 (deepest red) and 6.020 e -2 (deepest blue) for D4. For the donor and acceptor elements, their energy levels HOMO and LUMO influence whether an effective charge transfer will occur between the donor Di and acceptor (TiO2) [70]. The study results show that all dyes' energy level LUMO is far superior to that of the CB for TiO2 (-4.0 eV) [23]. This indicates that HOMO and LUMO energies levels can be influenced by photo-excited electron transfer from these investigated dyes. Hence, a study of the impact of varying the π-spacer of these dyes on the electronic properties has been achieved.
Therefore, D4 presents a great HOMO value (-5.10 eV), designating that the furan unit presents powerful electron-donor conduct relative to other π-spacers [20]. It has been shown that the furan unit shows an important oxidation potential, which makes it more effective as a dye sensitizer [83]. Lastly, it can be noticed that the energy levels values LUMO of all investigated compounds are insignificantly influenced by replacing π-spacer groups. This exhibits that this parameter is linked to the acceptor group (cyanoacrylic acid).
Using equations in the Computational detailssection, different parameters like f, LHE, Eex, E dye * , ΔG inj , ΔG reg , λtotal, and Voc for the four dyes have been studied and listed in table 3. Using quantum methods DFT and TD-DFT, the optical parameters such as f, LHE, and Eex have been computed. Evaluating the performances of an organic dye depends on an important parameter that is the LHE. Here, all the resulting values of the LHE parameter for the four dyes are betwixt 0.89 and 0.93. Since the LHE values of these dyes are in a close range, these dyes give approximately the same photocurrent response.
A feeble negative value of G inj and a small value of G reg are needed the acceptable sensitizers. Moreover, lower G reg is sufficient to prevent the recombination process and minimize dye degradation [51]. From Table 3, all studied dyes have a negative value of ΔG inj ; this can be explained by the excited state occupying the upper conduction band of Titanium dioxide. This reveals that the electron injection process from dye to TiO2 is spontaneous. It can be observed that D 3 has a greater ΔG inj value (maximal value -0.99 eV), while D 1 has the smallest one (minimal value -1.13 eV). This study indicates that D1 has the greatest driving force of electron injection in all designed dyes, whereas D3 has the least.
On the other hand, the regeneration energy (ΔR reg ) for any dyes is positive, indicating that the sensitizer fundamental state situates under the electrolyte redox couple, which is why electron recombination is suppressed [84,85]. For designed dyes, the ΔGreg value of D3 (3.00 eV) is the greater value than others, suggesting that D3 regenerates more rapidly than other dyes [66]. Consequently, D1 electron injection could be quicker than other dyes, and on the other hand, the D3 dye regeneration rate could be quicker than the other designed dyes [86].
Besides the short-circuit current density Jsc, the PCE (η) could also be affected by another parameter, that is, the energy corresponding to the open-circuit voltage (Voc). Based on Eq. (2), the computed Voc values for any dyes range between 0.57 V and 0.72 V (see Table  3). The estimated values theoretically of Voc decrease as follows: D2 > D1 > D4 > D3. It can be noticed that D2 has a larger Voc value than other dyes, while D3 has the tiniest one. These results advise that photoexcited electrons in the dyes might jump into the conduction band of TiO2, which helps increase the effectiveness of photoconversion in photovoltaic systems.
In addition, the reorganization energy (λtot) is a necessary factor in deciding the equipoise properties for hole and electron transport, whereas petty λtot is capable of accelerating charge carrier transport speeds, and the converse is true for larger reorganization energy [87]. Therefore, to analyze the correlation betwixt the Jsc and the electronic structure, the calculating of the λtot is also necessary [65]. As cited above in the Computational details part, the λtot consists of the hole (λh) and electron (λe) energies. Thus, the small λtot could improve the Jsc. The findings listed in table 3 indicate that computed λtot of designed dyes are between 0.497 eV to 0.524 eV and decrease as follows D2 < D3 < D4 < D1. It is shown that the dye D2 has the smallest λtot energy, whereas D1 possesses the largest one.
Moreover, The appropriate and balanced transport of both injected electrons and hole is critical in determining the performance of electronic devices [88]. Thus, the energy barrier for the electron and hole injection in a given dye can be determined by computing the DFT of the ionization potential and electron affinity [65]. The major challenge that the application in the LEDs is the need to achieve an n-type conjugated molecule to boost electron injection and transport. Also, It is a challenge for organic electronic devices to boost hole injection/transport when a p-type conjugated molecule at low ionization potential is used [89]. It is shown from Table 3 that the energies needed for holes' injection in these dyes are: 5.930, 5.890, 5.812, 5.920, and 5.930 eV, respectively. They are all low. This is coherent with the analysis of HOMO energy [90].

Optical properties.
It is necessary to study the absorption spectrum, which is a crucial property of a DSSC dye [2]. It is important to measure the absorption spectrum of the studied compounds for use in DSSCs to decide whether a material is acceptable for photovoltaic applications [75]. Indeed, wide and large visible absorption properties are necessary to have a good photovoltaic compound. The optical properties like ETr, f, and λabs of the studied dyes have been investigated using CAM-B3LYP/6-311G (d, p) [91]. These parameters are displayed in table 4, and absorption spectra are presented in figure 6. The absorption spectra arising from the excited state (S1) are assigned to the HOMO-1→ LUMO transition for the four dyes. These absorption bands were allocated to ICT betwixt electron donor and the acceptor [63]. The greatest absorption peak of these dyes is localized around 593 nm for D3. The obtained values of wavelength λmax for the considered dyes decrease as follows: D3 (593.59 nm) > D2 (590.14 nm) > D4 (574.64 nm) > D1 (557.70 nm). The dyes give a bathochromic absorption when crossing from D 3 (559.59 nm) to D 1 (557.70 nm) which may be attached to the increment of the π-conjugation during replacing the phenyl ring by pyrrole or thiophene ring in the π-spacer [20]. From figure 6, the absorption spectra exhibit two peaks: one is a huge peak situated betwixt 500 and 900 nm, and another one is located among the 300-450 nm wavelength region. This means these molecules possess a single band within the visible region ( where λmax> 400 nm). This is probably because of the rise in conjugation length through the π-spacer part [92]. As a result, it can be deduced that these studied dyes may be useful as donor compounds in photovoltaic devices.

Conclusions
In this work, several geometric, electronic, photovoltaic, and optical properties of four D1-D4 dyes have been theoretically investigated using quantum chemical methods DFT and TD-DFT. Modifying the chemical structures of investigated materials may considerably adjust and ameliorate both electronic and optical properties. Their electronic properties are investigated for our conjugated dyes based on triphenylamine, thiophene, and thieno [3, 4-b] pyrazine as the donor and various π-spacer groups the mentioned method above. It is found that changing the acceptor moiety ameliorates the photovoltaic properties of the investigated dyes by destabilizing and stabilizing the HOMO and LUMO levels, respectively. This leads to decreasing the Eg value, growing the geometrical planarity, increasing the absorption wavelength λmax, and improving the injection of electrons and dye regeneration.
Computations show that the obtained values of the bandgap are from 1.67 to 1.78 eV. This implicates that the investigated dyes possess the ability to be used in DSSCs. The energies levels LUMO of these dyes are located above the CB of the TiO2, proposing that transferring a photoexcited electron from Di toward TiO2 can be advantageous in photovoltaic materials. Calculated values of Voc for these dyes vary between 0.57 V and 0.72 V, meaning that these are enough to be an effective injection of electrons possibly. The obtained values of wavelength λmax for the investigated dyes D1, D2, D3, and D4 are 557.70 nm, 590.14 nm, 593.59 nm, and 574.64 nm, respectively.
In summary, the most suitable dye that can be applied in photovoltaic devices like donor of electrons in solar cell DSSCs type is a small bandgap, broad wavelengths, relevant FMO levels, great values of LHE and ΔG inj , as well as the lowest λtot. Therefore, our studied dyes Di are suitable to perform this function

Funding
This research received no external funding.