Comparison in optoelectronic properties of triphenylamine-imidazole or imidazole as donor for dye–sensitized solar cell: Theoretical approach

In the present work, the structural and electronic properties of the D-D'-π-A organic dye with two donors have been calculated theoretically by DFT/TD-DFT method. In order to prove their efficiency as sensitizers, a comparative study was performed with a serie of D-π-A architecture with one donor. The results of light harvesting efficiency (LHE), open circuit voltage (Voc), free energy injection ( ∆𝐺 𝑖𝑛𝑗 ), free energy dye regeneration ∆𝐺 𝑟𝑒𝑔 , excited-state lifetimes for the two series reveal that the D-D'-π-A dyes are promising for the design of new sensitive dyes in solar cells.


I. Introduction
In the last decades, since the works of Grätzel and O'Regan in 1991 [1], dye-sensitized solar cell (DSSC) has been given special interest from experiment and theory researchers. DSSC mainly consist of redox electrolyte, counter electrode, photo-anode, dye sensitizers adsorbed on the TiO2 semiconductor surface. The sensitizers play a vital role for sunlight harvesting and electrons performance. So far there are two classes of dyes, organic and organometallic [2][3][4][5]. Organic sensitizers have shown several merits, lower cost, simple synthesizing process [6][7][8] and flexibility in tailoring molecular structures in order to enhance electronic and optophysical characteristics [9][10][11][12].
Dye sensitizers should fulfill several requirements regarding the efficiency. (i) Their optical absorption should cover a wide section of the visible spectrum and extend up to the near IR region. (ii) To ensure effective electron transfer and efficient dye regeneration, LUMO energy levels have to be above the TiO2 semiconductor conduction band (CB) (-4.0 eV) and the HOMO levels below the redox potential of the I -/I3electrolyte (-4.8 eV) [13][14][15]. Thus, there is a close link between the electronic structure, HOMO, LUMO, gap energy and the photo-tocurrent conversion efficiency (PCE).
During the photoexcitation, the electron is transferred from the HOMO, which is located on the donor to the LUMO which is on the acceptor moiety [16].
The organic chromophore consists mainly of three components; a donor moiety linked to an acceptor one via a bridge. The role of each component is vital. The modulation by adding one donor or acceptor moieties may result in multipolar models and consequently exert a significant impact on the sensitizer performances. The use of multi-donors has been proven as a good strategy for delaying charge recombination and enhancing the open-circuit photovoltage [17,18].
Among all, several models multidonor have been synthesized or designed theoretically, D-Dπ-A, (D-π-A) 3L2, in order to improve the performance and the efficiency of the dye to absorb more energy from solar spectrum [19][20][21][22]. The computation tools have contributed a lot in this field in studying the different molecular designs, to deepen in optoelectronic studies of the different molecules in order to be able to present them as effective candidate dyes [23,24], as well as to propose them to the experimenter to be synthesized it.
Recently S. Sambathkumar et al [29], synthesized and characterized a novel dye serie of D-D'-π-A design, the triphenylamine -imidazole has been used as a donor entity in order to boost the optoelectronic properties and to better absorb the solar spectrum.
In this paper, we have designed two series of dyes, one based on two donors (Triphenylamine -imidazole), the second based on one donor (imidazole), possessing three different acceptor units by following D-D'-π-A and D-π-A approach respectively

II. Methods
In this work, we have carried out all the calculations using DFT [30,31] and TD-DFT [32,33] together with the GAUSSIAN 16 software package [34]. The geometries have been optimized with DFT by Becke's three-parameter hybrid functional combined with the correlation function of Lee, Yang, Parr B3LYP [35] and the base 6-31G (d, p) [36].
In addition, the vibrational frequencies were calculated; all the frequencies are positive, this indicates that the geometries obtained through optimization correspond to the potential energy surface minima.
Then, the excited states have been calculated using TD-DFT all through CAM-B3LYP [37] functional and the 6-31G (d, p) base in the N, N-dimethylformamide solvent (DMF).
It is clear that the CAM-B3LYP functional together with the 6-31G (d, p) basis have been selected as the best overall functional-basis set which reproduces the most the experimental data [38,39].
The calculation results have enabled us to obtain the geometric parameters, the energies of the frontier molecular orbitals (HOMO and LUMO), the absorbance spectral study of the dyes as well as the photovoltaic parameters.

III. Results and discussion
The investigated dyes with D-D'-π-A and D-π -A architectures are schematized in Fig1. The first serie which is synthesized [29] includes two donors triphenylamine-imidazole named (SD1, SD2, TPAB5) and the second serie is hypothetical consists mainly of imidazole as a donor entity named (SD1', SD2', TPAB5').
In order to get insights on the added donor effect on the geometrical and optoelectronic parameters on the first serie, we have studied and analyzed through DFT and TD-DFT the HOMO, LUMO, distribution of (MOs) along the molecule backbone, light harvesting efficiency, energy electron injection, energy regeneration and life excited states. In addition, we have carefully reported the effect of the electron withdrawing group on the optoelectronic and photovoltaic properties.

III.1Optimizations of the ground state of molecules
The Selected geometrical parameters shown in Fig. 3 and Fig. 4 are listed in Table 1. From Table 1 we show that the bond length for the two dyes series decreases in this direction: d2> d3> d1. The bond length d3 remains unchanged because this is the distance between the two donor moieties, which doesn't change at the same time away from the acceptor moiety. At the same time, d2 is very sensitive to the variation of the acceptor group in the sensitizer from the strongest (cyanoacrylic) to the weakest (nitrophenyl acetonitrile) via the medium (rhodanine acetic acid).
At this point the ɸ1, ɸ2, ɸ3 represent the dihedral angles respectively between the D-π, π-A and D-D' units. Also from the same table, we notice a kind of deviation from the molecular plane of the donor-π unit for SD1, however the planarity is maintained between D-π for the dyes SD2 and TPAB5. The values of the dihedral angles ɸ3 in the dyes SD1, TPAB5 indicate that the donor-donor groups are co-planar in this structure. Idem for SD2. It results in an excellent delocalization of the electrons in these structures.

III.2 Electronic properties
The energy of HOMO and LUMO plays a very important role in the charge transfer between the donor and acceptor part, HOMO is the orbital which mainly acts as an electron donor and LUMO is the orbital which acts as an electron acceptor.
It is possible to obtain the required properties for the dyes for maximum DSSC conversion efficiency, while improving their electronic properties via HOMO and LUMO orbitals [40][41][42].
Those orbitals distributions displayed in Fig. 2

III.3 UV-Vis spectra and electronic transitions
The study of the excited states of the two donors-based dyes (SD1, SD2, and TPAB5) and the mono-based dyes (SD1', SD2' and TPAB5') has been carried out with TD-DFT methods for the first twenty excited state.
Furthermore, to take into account the solvent effect, we have considered the N, Ndimethylformamide (DMF) for solvent phase calculation and polarizable continuum model (CPCM) as method [43]. The results in Table 3  During the structural modification, the two donors-based dyes (SD1, SD2 and TPAB5) have presented red-shifts at 404nm, 432nm, 380nm respectively, further shifts towards blue were observed with mono donor-based dye (SD1', SD2' and TPAB5'). Consequently, we can notice herein that those results revealed that the nature of acceptor unit strongly affects the absorption spectra. The rhodanine acetic acid units giving rise to the largest absorption wavelengths 432nm for SD2, and absorption wavelengths 380 nm decrease with cyanoacrylic for TPAB5. An outstanding agreement between the theory and the available experimental values has been verified for the wavelength absorbance maxima. We can see in Table 3, the HOMO→LUMO transition dominates the absorption band of the absorption spectrum, with contribution > 50 percentage for all the studied dyes.

III.4 Light harvesting efficiency and open circuit voltage
Efficient sensitizers to be used in DSSCs should have a large light-harvesting efficiency (LHE), which can be expressed briefly as equation (1) [44], light-harvesting efficiency and other photovoltaic parameters have been described in detail in our previous works [45].
Where f is the oscillator strength at maximum wavelength λmax.
The open circuit photovoltage in DSSCs can be calculated from the expression [46]: The result values of the oscillator strength f, the light harvesting efficiency (LHE) and the open circuit voltage (Voc) are saved in Table 3. From this table it is clear that added of second donor moiety lead to significant impact on oscillator strength. The LHE has to be as high as possible to maximize the photocurrent response. The LHE values for two donors based-dyes (SD1, SD2 and TPAB5) are higher than the ones of the mono donor chromophore (SD1', SD2', and TPAB5'). Finally, the calculated Voc follows the same trend as that of LHE.
From, it is concluded that the adding up of a second donor in a dye improves its performance.

III.5 Electron injection and dye regeneration
The charge transfer within the sensitizer takes place in two stages, the electrons injection into the semiconductor conduction band then the regeneration of the dye ground state.
The electrons injection is measured by ∆ free energy injection and the regeneration of the dye by ∆ free energy regeneration. The simulated values for ∆ , ∆ are collected in Dye regeneration ability is calculated through the formula: According to the calculated values of ∆ reported in Table 4, they are all greater than (0.4 eV) [43]. That shows that all dyes can be regenerated.

III.6 Excited-state lifetime
Where ∆E is the excitation energy of the different electronic states (cm -1 ) and f the oscillator strength corresponding to the electronic state.

III.7 Dipole moment in ground and excited state
The  Table 4. The calculated dipole moments in the excited state are greater than the ground state for the investigated D-D-'π-A and D-π-A dyes see Table 4. We also note that the dipole moment based on imidazole-

VI. Conclusion
In present work, we have studied and compared by DFT/TD-DFT the optoelectronic properties of two and mono donor-based dyes in order to demonstrate the value-added of a second donor, and effect of different anchoring groups, to ensure their ability as promising sensitizers in DSSC.
We have carried out a theoretical study on the dyes synthesized namely, SD1, SD2, and