Effect of the Alkyl Chain Length Incorporated into Donor Part on the Optoelectronic Properties of the Carbazole Based Dyes : Theoretical Study

In this paper, we report a theoretical study using density functional theory (DFT) and timedependent (TD-DFT) for R-D-π-A systems with various alkyl chains (R). Results show that the LUMO of the dye lies above the semiconductor conduction band, promoting the injection of electrons; the lower HOMO level promotes dye regeneration. The incorporation of methyl chain (CH3) has a significant reduction in the gap energy, improved red-shift absorption spectrum and increase the molar extinction coefficient at the maximum absorption wavelength compared to D. While, the increase in alkyl chain length from C2H5 to C6H13 present a relatively reduce of gap energies, low effect on the wavelength (438 nm) and converged excitation energies.


INTRODUCTION
Dye Sensitized Solar Cells (DSSCs) have been widely investigated since the first report by O'Regan and Grätzel in 1991 [1], due to their easy and low cost fabrication procedure [2], environment friendliness, greater structural flexibility, higher molar extinction coefficient, and reasonably good power conversion efficiency [3][4].These characteristics make them a possible competitor to traditional inorganic silicon for photovoltaic cells.Ru-complex dyes are unsuitable for cost-effective and environment friendly photovoltaic systems because they contain the noble metal ruthenium; expensive resources and the difficult purification process of metal limit their widespread application in DSSCs [2].
Most organic dyes are composed of a push-pull Donor-π-Acceptor (D-π-A) structure due to its effective better intramolecular charge transfer characteristics [5].Organic dyes having carbazole and its derivatives [6] and triphenylamine [7][8][9] as the donor moiety have been reported to show remarkable efficiency in DSSC devices.The carbazole donor has been usually used for building block in push-pull D-π-A structure for the organic sensitizers and optical materials because of their strong donating ability [17][18].Thiophene and its derivatives are choosing as the best candidates for the π-conjugated systems, in particular bithiophene.They exhibits the best charge transport properties, due to reduced band gap energy and better photoconversion of electric current [19].Cyano-acrylic acid is the most commonly used as acceptor moiety due to the existence of the cyanide group that has a strong electron accepting ability [20].We use π-bridge spacers to link the donor and acceptor.The π-bridge help to relay the electron density and facilitate charge separation upon excitation.Therefore, engineering of organic sensitizer with a reduced tendency toward aggregation is paramount.A successful approach was introduced by incorporating some alkyl chains into the organic framework, which not only suppresses aggregate formation but also enhances the molar extinction coefficient of the organic sensitizer [21] In this study, we have designed a series of R-D-π-A type of organic dyes with thiophene-carbazole as the electron donor (D), bithiophene as the πconjugated bridge and cyanoacrylic acid as the electron acceptor (A).Keeping all other units fixed and varying the alkyl group (R) from CH 3 to C 6 H 13 , we elucidated the effect of the different alkyl chain on the geometric, electronic, and optical properties of such dye for their use as sensitizers in solar cells.

MATERIAL AND METHODS
The ground state of the dye optimized with Density Functional Theory (DFT) using the B3LYP functional [22] and 6-31G (d,p) basis set with the Gaussian 09 [23].The structures are minima on the potential energy surface and their harmonic vibrational frequencies are positive of all compounds.Moreover, the excited state calculations were carried using Time-Dependent (TD-DFT) with the same hybrid functional and basis set to simulate the UV-Vis absorption spectra in chloroform solvent by using the polarizable continuum model of solvation (CPCM) [24].The energy levels of the molecular orbital and the isodensity plot were extrapolated in isolated state to show the electronic density distribution that used for description of optic and electronic properties of donor-π-acceptor sensitizers.

RESULTS AND DISCUSSION
In order to gain insight of the effect of different alkyl chains on the geometrical, electronic and optical properties of organic dyes, we have studied, in this work, a dye based on carbazole donor and Bithiophene Bridge.The dye namely D was substituted by different C n H 2n+1 alkyl chains (with n = 0 to 6) on the donor part (Scheme 1) and the theoretical study was optimized using DFT and TD-DFT methods.

Geometrical properties
The geometrical values of all studied dyes are shown in Table 1.The calculated ground-state bond lengths for all studied dyes are about 1.39; 1.44; 1.46 and 1.42 Ǻ for d 1 , d 2 , d 3 and d 4 respectively.These distances are in range of 1.38-1.44Å showing significant C=C character, which improved the intramolecular charge transfer [25].The dihedral angles values (Table 1) shown that the optimized geometry of all sensitizers is not totally planar, in particularly, θ 1 and θ 3 , which show an important decrease inside plan for the dyes substituted by the methyl chain CH 3 .Although, for the same dye D-CH 3 , θ 2 and θ 4 present a significant decrease in outplan.Moreover the substitution by C n H 2n+1 (n=2 to 6) showed a little variation in the dihedral angle.These results mean that the incorporation of the methyl chain into thiophene donor unit induced an important distortion of the dihedral angle.However, the increase in alkyl chain length from C 2 H 5 to C 6 H 13 has a little variation on the dihedral angles.

Electronic properties
Table 2 represents the electronic properties (including the HOMO, LUMO and Gap energies values) of the dye D substituted with different chain alkyl and compared with the corresponding experimental results.The calculated HOMO, LUMO and gap energy levels of D and D-C 6 H 13 are in quite good agreement with the experimental analogues compounds DWH1 and DWH2 obtained by J-F Huang and all [26], Indicating the validation of the functional (B3LYP) and the method (DFT).
The D-CH 3 dye (2.37 eV) with incorporation of the methyl chain shows a reduction in the gap energy of 0.11 eV compared with D (2.48 eV).Whereas when the length of the alkyl chain was varied, HOMOs and LUMOs energy values display a very little variation that giving the Gap energy values about 2.36eV.These results indicate that the incorporation of methyl chain CH 3 results in a small Reduction of the gap energy that improves the electronic properties of the dye.Moreover, the dye substituted by the alkyl chain CH 3 to C 6 H 13 showed similar electronic properties, which can lead to similar overall efficiencies.These results are also obtained by Y-H Lee et al [29], they found that there is no variation in the gap energy (2.82 eV) when the alkyl chain was increased from C 4 H 9 to C 12 H 25 .

Absorption spectra
The UV-visible absorption spectra reported for all studied dyes in chloroform solvent are revealed in Figure 1.The summarized data including wavelength absorption, oscillator strength, light harvesting efficiency and molar extinction coefficient are shown in Table 3.These results show that all studied dyes exhibits three principal bands.The peaks positioned at lower energy region appearing at about 578-604 nm are attributed to the intramolecular charge transfer (ICT) between the thiophene-carbazole donor and the cyanoacrylic acid.The intense peaks at about 432-438 nm can be assigned to the localized π-π* transition with an important oscillator strength of 0.9-1.Whereas the peak at 300 nm has a flow form, it is unclear and presents a very small oscillator strength (0.06-0,1).
The band appeared at 432 nm for D and that at 438 nm for D-C 6 H 13 are in good agreement with experimental data λ max (D namely DWH1 in his work)=434 nm and λ max (D-C 6 H 13 namely DWH2 in his work)=436 nm [26], implying that the TD-B3LYP functional is valid for reproducing the absorption bands.D-CH 3 peak at 438.27 is red-shifted by 6.28 nm compared to the D peak at 432 nm, which indicate that the introduction of methyl chain on the thiophene donor is very important for improved the red-shift absorption spectrum and also increase the molar extinction coefficient (Table 3) at the maximum absorption wavelength compared to D. While the variation of the alkyl chain length from CH 3 to C 6 H 13 has a low effect on the wavelength (438 nm), the value of Light Harvesting Efficiency (LHE≈0.9),(table 3 and figure 1).Q-Y Yu and al [27] also obtain these results.The latter found that the compound C6 (λ max =503 nm) with the C 6 H 13 alkyl chain and the compound C9 (λ max =504 nm) with presented the nearby wavelength absorption.The difference between the molar extinction coefficient of D-CH 3 and D-C 6 H 13 at the maximum absorption is also small (about 479 M -1 cm -1 ) that is comparable with the experimental difference between C 4 and C 12 (about 923 M -1 cm -1 ) [29], which indicate the marginally effect obtained with C 6 H 13 compared to CH 3 .
The UV-visible absorption data showed that there is an important decrease in the excitation energies (eV) from dye D to D-CH 3 .The excitation energies almost converged by varying from dye D1-CH 3 to C 6 H 13 (Figure 2).These lower and converged excitation energies of dyes D-C n H 2n+1 (n=2 to 6) may be responsible for showing higher and similar efficiencies over dyes D and D-CH 3 .So, we can use just the methyl alkyl chain instead of the longest, in the theoretical investigation, in order to minimize the calculation times.
Therefore, the incorporation of long alkyl chain in organic sensitizers can be used experimentally to decrease the undesirable formation of dye aggregates on the surface of the semiconductor and to decrease recombination processes between TiO 2 electrons and electrolyte species.The long alkyl chain is also used to enhance the stability of sensitizers, increase the solubilization of the dyes structure and improve the lifetimes of DSSC devices [30].

Molecular orbital calculations
We plotted the electron spatial distribution of the HOMO-2, HOMO, and LUMO molecular orbitals involved in the electron transitions of the studied dyes in Figure 4.The HOMO-2 and HOMO orbitals display anti-bonding character between two adjacent fragments and bonding character within each unit.While the LUMO orbital exhibits bonding character between the two adjacent fragments and anti-bonding character within each unit.
The electron densities of the HOMO levels in all the studied dyes are mainly originated from the πorbitals of the donor consisting by carbazole and thiophene.The HOMO-2 electron densities are localized in the bithiophene bridge and cyanoacrylic acid acceptor.While the LUMO levels are largely dominating contributions from the π*-orbitals of the cyanoacrylic acid and the nearby π-linkers, which facilitate the electron charge transfer from the donor to acceptor.The contribution of electronic transition from HOMO to LUMO is ~99% for all dyes.The HOMO eigenvalues of all the dyes (Figure 3) were lower than the redox potential (-4.8 eV) of the I -/I 3- redox couple [31], which facilitates effective dye regeneration from its oxidized state.More the LUMO is above the conduction band TiO 2 semiconductor (-4.00 eV) [32], so the electron injection from the excited state of the dye to the conduction band of TiO 2 would be facilitated.Depend on figure 3, there was little variation in the LUMO and LUMO energies with increasing the alkyl chain length from CH 3 to C 6 H 13 and the energy values almost converged.Such electronic distribution of the HOMOs and LUMOs indicates that HOMO−LUMO excitation moves the electron from the donor part to the cyanoacrylic acid through the π-linker groups, ensuring efficient charge separation and electron injection.

CONCLUSION
The theoretical calculation obtained by the DFT/B3LYP/6-31G(d,p) for the ground state optimization and TD-DFT/B3LYP/6-31G(d,p) for the excited state have shown that the introduction of CH 3 methyl chain has an important reduction in the gap energy, improved red-shift absorption spectrum and increase the molar extinction coefficient at the maximum absorption wavelength.However, increase in alkyl chain length from C 2 H 5 to C 6 H 13 present a relatively reduce of gap energies, has a low effect on the wavelength (438 nm), has almost converged excitation energies.Therefore, the long alkyl chain can be used experimentally to decrease the undesirable formation of dye aggregates on the surface of the semiconductor and to decrease recombination processes between TiO 2 electrons and electrolyte species.

Figure 1 .
Figure 1.Absorption spectra of D substituted by different alkyl chains in chloroform.
[26]Experimental data[26] Variation of excitation energy with the increase of alkyl chain length.H CH 3 C 2 H 5 C 3 H 7 C 4 H 9 C 5 H 11 C 6 H 13