Introduction

Over the past decade, environmental problems related to nonrenewable energy sources, such as petroleum and coal, have become matters of serious concern due to their negative impact in the atmosphere. Therefore, in the global motif of sustainable development, enormous research endeavors have been devoted to harvest the clean and renewable energy such as wind energy and solar energy [1]. Dye-sensitized solar cells (DSSCs) are perceived as one of the most promising renewable energy source in comparison to that of other clean energy sources. DSSCs have attracted considerable interest since their invention by O’Regan and Grätzel [2, 3] and in particular due to their low manufacturing cost, environment friendliness, and ease of fabrication. In addition, DSSCs exposed the possibility of designing flexible solar cells [4,5,6]. In DSSC, organic dye/sensitizer is excited by absorption of solar light. The photo-excited electrons of the dye are injected into the conduction band of the semiconductor and prior to charge recombination, the oxidized dye is restored to its neutral state by I− in the electrolyte solution. The injected electron on the semiconductor passes through the external circuit to the counter electrode, where it reacts with I3 − to regenerate I−. For an efficient DSSC, dye sensitizer must absorb strongly the entire visible and near-IR spectrum of the solar radiation. Furthermore, the energy alignment of the lowest unoccupied molecular orbital (LUMO) of the dye with the conduction band of the semiconductor also requires fine-tuning to inject electrons efficiently and the highest occupied molecular orbital (HOMO) of the dye should be lying sufficiently below the energy level of redox couple to regenerate the dye. From the viewpoints of stability and efficiency, ruthenium polypyridine (N719, N3, black dye) [3, 7,8,9,10,11,12] complexes are the best performing dyes for DSSCs due to their broad absorption in the visible region. Metal-to-ligand charge transfer (MLCT) is responsible for absorption in the visible region in those dyes. To improve the light-harvesting efficiency in the near-IR region of the solar spectrum, some attempts have been made to tune the MLCT absorption band to higher wavelength by modifying the bipyridyl ligand with various substituents [13,14,15]. By employing this approach, although the absorption maximum red-shifted to higher wavelength, the molar absorption coefficient remained still moderate. Some researchers used tandem cells, wherein photoanode captures the most of the visible spectrum and the photocathode captures the red and near-IR region [16,17,18,19]. Although this approach resulted in enhancing the open-circuit voltage, the short-circuit current density was limited in comparison to DSSCs. Despite these advances, the rarity of Ru, environmental issues, and high cost of Ru have stimulated researchers to discover cheaper and environment friendly metal-free sensitizers. In general, metal-free dyes contain a donor (D), π-linker, and acceptor (A) groups, respectively, which are called as D-π-A dyes or push-pull molecules. One of the biggest advantage of D-π-A dyes is their abundances and synthesis in few easy steps. The other features of these dyes are (i) higher molar absorption coefficient vis-à-vis metal-based dyes and (ii) tunable absorption in the visible to near-IR region upon suitable molecular engineering. The D-π-A dyes, such as cyanine- [20], hemicyanine- [21], perylene- [22], coumarin- [23], porphyrin- [24, 25], indoline- [26], carbazole- [27], triphenylamine- (TPA) [28,29,30,31], pyrene- [32], and phenothiazine [33]-based dyes have been studied and showed satisfactory performances in DSSC. According to the literature, TPA is the most preferred donor moiety due to its tunable electron donating ability. Recently, ferrocenyl substituted TPA [34] and ferrocenyl bisthazole-linked TPA-based molecular system [35] were reported to exhibit power conversion efficiencies (PCE) of 4.96 and 6.33%, respectively. Misra et al. [31] demonstrated the tuning ability of TPA donor moiety by introducing the positional isomers of pyridine. Metal-free organic dyes based on derivatives of carbazole and triphenylamine (TPA), with thiophene-based π-bridge/linker, have exhibited a power conversion efficiency (PCE) up to 12.8%, while using cobalt(III/II) tris(2,2′-bipyridine) as the redox couple [36, 37], which is close to the value achieved with the Ru-based dyes [7, 10, 12]. Highest efficiency reported till date is 14.3%, while employing two metal-free carbazole and modified TPA-carbazole-based dyes (ADEKA-1 and LEG4) with silyl and carboxyl anchoring groups, and cobalt(III/II) tris(1,10-phenanthroline) complex redox electrolyte [38].

Thiophene-based π-linker oligomers and polymers have been widely explored in DSSCs because of their electronic tunability and chemical and environmental stability [39,40,41,42]. Although there are plenty of reports using thiophene as a spacer in organic dyes [43,44,45], use of oligothiophene moiety as spacer is still rare [46,47,48,49]. Oligothiophene moiety shows higher electronic conjugation and coplanarity than benzenoid moieties [50, 51]. Therefore, incorporating oligo(2,5-thiophene) as the spacer of dipolar arylamine/cyanoacrylic acid sensitizers have been explored by Thomas et al. [52]. According to Thomas et al. [52], incorporation of arylamine donor at the C2 and C3 positions of thiophene ring hinders the back electron transfer from TiO2 to the electrolyte through the delocalization of positive charge between C2 and C3 substituents upon electron injection. In the literature, the density functional theory (DFT) [53,54,55,56] is widely used to understand the electronic structure and photophysical properties of the dyes. We have employed DFT to those dyes developed by Thomas et al. [52] and calculated their highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) energies, and the bandgap (E g, difference between HOMO and LUMO). Time-dependent DFT (TD-DFT) calculations have been performed to get the photophysical properties of excited state geometries such as maximum absorption wavelength, oscillator strength, and percentage contributions of electronic transition from occupied to virtual orbitals. TD-DFT calculation and evaluation of natural bond orbital (NBO) analysis of dye-(TiO2)8 cluster of these dyes are the main aspect of this present study.

Computational methods

Kohn-Sham DFT calculations have been employed to optimize the ground state geometries of the dyes using Beck’s three-parameter hybrid functional combined with Lee, Yang, and Parr correlation functional (B3LYP) with the 6-31G(d,p) basis set [57,58,59]. The frequency calculations were performed to confirm the stationary nature of the optimized geometries at energy minimum using the same level of theory. The absence of imaginary frequencies confirms that all the dyes are optimized at minimum ground state energy. The Cartesian coordinates of all the optimized geometries have been provided in the supporting information. From the optimized ground state geometry, the HOMO, LUMO, and band gap energy have been evaluated and frontier orbital analysis was carried out for optimized structures. To get insight into the photophysical properties of the dyes, TD-DFT calculations have been performed and the vertical excitation energies, oscillator strengths (f), and the compositions in terms of excitations between occupied and virtual orbitals were calculated from the excited state geometries. The B3LYP functional [59] has been widely employed among the other functional in DSSC-related works [28, 60,61,62,63]. However, the B3LYP functional generally underestimates the excitation energies of charge transfer transitions for large π-conjugated systems [32, 64, 65]. Therefore, by taking consideration of long-range correction factor, the coulomb-attenuating method (CAM-B3LYP) functional [66] has been introduced for establishing suitable intramolecular charge transfer (ICT). Polarizable continuum model (PCM) [67, 68] was used to consider the solvent environment effect during the calculation. The geometry optimization of the dyes and TD-DFT calculations were carried out using the Gaussian 09 software suit [69].

To investigate the electron injection mechanism from the dye to the semiconductor interface, the calculations of the prototype model systems (i.e., dye-TiO2 anatase (101) interface) were implemented using the DMol3 software [70, 71] in the Materials Studio 2017 version. Cyanoacrylic acid moiety was used as an anchoring group. The geometry optimizations of dye-(TiO2)8 clusters were carried out using the generalized gradient-correlated approximation (GGA) method of the Perdew-Burke-Ernzerhof (PBE) [72] functional with the double numeric-polarized (DNP) basis set. It is to be noted that the DNP basis set is the highest quality set available in DMol3, and it is comparable with the 6-31G(d,p) basis set of the same size [73, 74]. The TD-DFT calculations of dye-(TiO2)8 clusters were performed using the CAM-B3LYP/6-31G(d,p) method in vacuum by taking the ground state DMol3 optimized geometry.

Results and discussion

Structures of the dyes

The chemical structures of the five dyes (D1 to D5) are shown in Fig. 1a. The optimized geometries of the five dyes were obtained using the B3LYP/6-31G(d,p) method and presented in Fig. S1, and their corresponding frequency analyses have been shown in Fig. S2. Similarly, the optimized geometry of the dye-(TiO2)8 clusters are given in Fig. 1b. In all the dyes, TPA and cyanoacrylic acid (CA) act as donor and acceptor, respectively, and thiophene is used as spacer moiety between TPA and CA. D1 and D2 are 2, 5-disubstituted thiophene-based dyes and D3 to D5 contain 2, 3, 5-trisubstituted thiophene-based congeners. The C2 and C3 positions of the thiophene ring are substituted with thiophene-TPA moiety. D1, D2-D3, D4, and D5 contain 2, 3, 4, and 5 thiophene spacers in total. The IUPAC name of the five dyes is presented in Table S1.

Fig. 1
figure 1

a The chemical structures of the dyes (D1 to D5). b The optimized geometries of dye-(TiO2)8 cluster of the dye (D1 to D4)

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Energy level alignment and dye regeneration kinetics

The calculated energy of HOMO (E HOMO), LUMO (E LUMO), and E g of all five dyes are summarized in Table 1 using the B3LYP/6-31G(d,p) method. The experimental E HOMO, E LUMO, and E g values, taken from the work of Thomas et al. [52], are given in the parenthesis next to the theoretical values for comparison. However, it is to be noted that solid-state packing effects are not included in the DFT calculations, which tend to affect the HOMO and LUMO energy levels in a thin film compared to an isolated molecule as considered in the calculations. In spite of that, the energy of HOMO and LUMO values estimated is reasonably close to the experimental values. The energy level diagram of all five dyes along with the conduction band (CB) energy level of TiO2 and redox potential energy of I3 −/I− redox electrolyte (−4.8 eV vs. vacuum) [75] is shown in Fig. 2. The energy of the LUMOs of all five dyes lie above the CB of TiO2 (−4.0 eV vs. vacuum) [76, 77], resulting in an effective electron injection from the LUMO of the dye into the CB of TiO2. Likewise, the energy of the HOMOs of all five dyes is located below the energy level of the I3 −/I− redox electrolyte. However, for regeneration of the oxidized dye, the sufficient driving force (\( {E}_{I_3^{-}/{I}^{-}}-{E}_{\mathrm{HOMO}} \)) is required and the calculated values of “\( {E}_{I_3^{-}/{I}^{-}}-{E}_{\mathrm{HOMO}} \)’” were tabulated in Table 1. The maximum and minimum driving force for dye regeneration were found for D1 (0.25 eV) and D5 (0.07 eV), respectively. It is important to have sufficient driving force for dye regeneration as it can influence the back electron transfer kinetics between the injected electrons in the CB of TiO2 with the oxidized dye and I3 −. The decreasing order of the driving force of dye regeneration energy is D1 > D3 > D2 > D4 > D5. It is palpable from Fig. 2 that D4 and D5 offer very less driving force for dye regeneration kinetics as compared with the other three dyes. The relative position of HOMO of D1 to D3 is sufficiently negative to that of the redox energy of the electrolyte, thereby enhancing the chance of dye regeneration. Experimentally, D1 is clearly seen as the best performing dye in DSSC with an efficiency of 6.15% [52].

Table 1 The calculated HOMO, LUMO, bandgap energy, and driving force for dye regeneration (in eV) of five dyes obtained using the B3LYP/6-31G(d,p) method. The experimentally measured values [1] are given in the parenthesis
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Fig. 2
figure 2

The energy level diagram of five dyes including the conduction band of TiO2 and redox potential energy level of I3 −/I− couple

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Projected density of state analysis

The projected density of state (PDOS) calculation has been carried out for all five dyes using the B3LYP/6-31G(d,p) method. PDOS analysis offers a qualitative information about electron density of dyes at different moieties such as donor, π-linker, and acceptor. The presence of ICT in the dyes during photoexcitation can be explained by examining the HOMO and LUMO of dyes, i.e., the relative ordering of occupied and virtual orbitals. During photoexcitation, the charge transfer occurs from the donor moiety to the acceptor moiety as the PDOS in the donor shift to the acceptor located on the virtual orbital (LUMO). It is crucial for ICT that the HOMO must localize on the donor moiety and the LUMO must localize on the acceptor moiety. Figure 3 presents the plot of the PDOS of the donor, π-linker, and acceptor for the five dyes at HOMO and LUMO. It is seen that for all five dyes, the electron density on HOMO (55 to 70% in donor and 25 to 44% in π-linker) shifts to LUMO (52 to 63% in π-linker and 36 to 43% in acceptor). This indicates that during ICT, there is some amount of electron retention on the π-linker moiety which is well agreed to the frontier orbital diagram of dyes shown in Fig. 4.

Fig. 3
figure 3

The projected density of states (PDOS) plot of the five dyes at a HOMO and b LUMO

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Fig. 4
figure 4

Frontier molecular orbitals (HOMO-1 to LUMO) of D1 to D5 obtained using the B3LYP/6-31G(d,p) method

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Natural bond orbital analysis of dye-(TiO2)8 cluster

Furthermore, natural bond orbital (NBO) analysis was performed using the ground state geometry of all the five dyes to confirm the direction of the flow of electron in photoanode. Generally, the positive NBO value indicates the electron donating ability and negative NBO value about the electron accepting ability of a group. The NBO values of the donor, π-linker, and acceptor have increased in THF as compared to vacuum. In order to get the NBO charges in solvent medium, the polarized continuum model (PCM) is used. This method creates the solute cavity via a set of overlapping spheres and which stabilizes the dye molecules. Therefore, the polarity of the dye molecule increased in THF as compared with vacuum. Table S2 compares the NBO values obtained in THF and vacuum. The positive NBO value of TPA and negative NBO value of CA indicate TPA and CA to be effective electron donor and acceptor, respectively. Therefore, for all five dyes, the charge separation state can be established upon photoexcitation and the electron can be shifted from TPA to the CA part via ICT.

The direction of electron flow in a DSSC device is from dye to the CB of semiconductor. Hence, to get insight into the electron transfer mechanism at the dye-TiO2 interface, NBO analysis of the dye-(TiO2)8 cluster was performed by employing the ground state optimized structure obtained using the B3LYP/6-31G(d,p) method. Figure 5 shows the frontier orbital diagram of the dye-(TiO2)8 cluster. The NBO values of the dye-(TiO2)8 cluster are summarized in Table 2. The positive NBO values are observed for TPA and π-linker moieties and negative NBO values are noticed for CA-(TiO2)8 moiety. The reasonable higher negative NBO values on CA-(TiO2)8 moiety have been observed for D1 (−0.657), D3 (−0.655), and D4 (−0.642), which indicates the possibility of electron injection from the LUMO of the dye to the CB of the TiO2. D2 and D5 are having the least NBO value at the CA-(TiO2)8 moiety, indicating poor electron injection into the CB of TiO2. Therefore, D1, D3, and D4 would show higher power conversion efficiency as compared to D2 and D5, which is correlating perfectly with the experimental data [52] (experimental order of the efficiency of DSSCs made of those dyes: D1 > D4 > D3 > D2 > D5). Hence, based on the (\( {E}_{I_3^{-}/{I}^{-}}-{E}_{\mathrm{HOMO}} \)) and NBO value at CA-(TiO2)8 moiety, the expected order of performance of the dyes is D1 > D3 > D4 > D2 > D5.

Fig. 5
figure 5

Frontier orbital diagram of dye-(TiO2)8 cluster

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Table 2 The natural bond orbital (NBO) analysis of five dye-(TiO2)8 cluster obtained using the B3LYP/6-31G(d,p) method
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UV-vis absorption spectra

TD-DFT calculation has been carried out to get insight into the photophysical properties of the dyes using the CAM-B3LYP/6-31G(d,p) method. The simulated UV-Vis absorption spectra in THF solvent are displayed in Fig. 6 by considering 30 lowest singlet-singlet (S 0 to S 1) transitions. The simulated UV-Vis absorption spectra show the reasonable agreement with the experimentally observed absorption spectra reported by Thomas et al. [52]. The comparison of the experimental and simulated absorption spectra has been shown in Fig. S3. The first band around 200–400 nm corresponds to π-π* transition for D1 and D2. For example, electron density, both in HOMO and LUMOs (LUMO + 1, LUMO + 3 and LUMO + 4), are almost on the donor part (Fig. S4(a)) for D1. For D3 to D5, this band is overlapped with the ICT band (400–700 nm). The extent of overlap of the π-π* band with the ICT band, in three substituted dyes, is more for D4 and D5 than D3. This overlaps indicates the possibility of π-π* transition influencing the ICT transition in the excited state of the dyes. For example, the frontier orbital diagram of D4 corresponding to the oscillator at 273, 305, and 342 nm are shown in Fig. S4(b). This clearly shows the presence of electron clouds on the donor and π-linker both in ground and excited states. From Fig. 6, it can be seen that the aforementioned π-π* transition band intensity is more for D3 to D5 than D1 and D2, which is due to the addition of the extra substituent at the C3 position of the 2,3-substituted thiophene ring. The larger extinction coefficient of the ICT band in D1 than in D3 (or in D2 than in D4) may be attributed due to the loss in coplanarity between the electron donor (at the C2 position of the thiophene) and the electron acceptor because of the presence of the C3 substituent. The photophysical properties such as computed maximum wavelength (λ c , in nm), experimentally observed maximum wavelength (λ max, in nm), oscillator strength (f), and the percentage of the major transitions are presented in Table S3. The λ c (in THF solvent) of D1 to D5 are 473, 494, 470, 478, and 490 nm, respectively, which show a close match to the λ max of the experimentally observed values [52]. The blue-shift in λ c of D3 and D4 as compared with D1 and D2 is ascribed due to the loss in coplanarity, which hinders the ICT, by addition of the substituent at the C3 position. The percentage transition ascribed to HOMO to LUMO is maximum for D1 (70%) among all the dyes. The TD-DFT calculations of dye-(TiO2)8 cluster were performed to get the UV-Vis absorption spectra of the five dyes using the CAM-B3LYP/6-31G(d,p) method in vacuum. The simulated UV-Vis absorption spectra of dye-(TiO2)8 cluster are shown in Fig. S5. The spectra show a dramatic red shift as compared to the spectra obtained in solvent medium due to the increased delocalization of the π* orbital of the conjugated framework caused by the interaction between the carboxylate group and the Ti4+ ions [78]. The higher f for D1 and higher driving force for dye regeneration coupled with high NBO value of CA-(TiO2)8 moiety steers D1 to perform better in DSSC.

Fig. 6
figure 6

Computed UV-Vis absorption spectra of five dyes in THF solvent obtained using the CAM-B3LYP/6-31G(d,p) method

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Calculation of photovoltaic parameters pertain to DSSCs’ performance

Light-harvesting efficiency (LHE (λ)) [79] at a particular wavelength (associated with oscillator strength, f) is provided in Eq. 1:

$$ \mathrm{LHE}=1-{10}^{- f} $$
(1)

Φ inject, the electron injection efficiency is proportional to the f and free energy of electron injection (∆G inject) which is expressed by [80]:

$$ {\varPhi}_{\mathrm{inject}}\propto f\left(\Delta {G}_{\mathrm{inject}}\right) $$
(2)

Therefore, higher negative value of ∆G inject corresponds to greater electron injection efficiency. ∆G inject can be calculated as the difference between excited state oxidation potential (\( {E}_{\mathrm{OX}}^{{\mathrm{dye}}^{\ast }} \)) of the dye and the ground state reduction potential (E CB) (Table 3) of the conduction band (CB) of the TiO2 (E CB = −4.0 eV [76]) and is expressed by [65]:

$$ \Delta {G}_{\mathrm{inject}}={E}_{\mathrm{OX}}^{{\mathrm{dye}}^{\ast }}-{E}_{\mathrm{CB}} $$
(3)
Table 3 The calculated excited and ground state oxidation potential (\( {E}_{\mathrm{OX}}^{{\mathrm{dye}}^{\ast }} \)and \( {E}_{\mathrm{OX}}^{\mathrm{dye}} \)), the electronic vertical transition energy (∆E) associated with the λ max, LHE, ∆G inject, and open-circuit voltage (V OC) of the dyes
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\( {E}_{\mathrm{OX}}^{{\mathrm{dye}}^{\ast }} \) can be estimated using Eq. 4:

$$ {E}_{\mathrm{OX}}^{{\mathrm{dye}}^{\ast }}={E}_{\mathrm{OX}}^{\mathrm{dye}}-\Delta E $$
(4)

where \( {E}_{\mathrm{OX}}^{\mathrm{dye}}\ \left(\mathrm{i}.\mathrm{e}.,-{E}_{\mathrm{HOMO}}\right) \) is the ground state oxidation potential of the dye [81] and ∆E is the electronic vertical transition energy associated with the λ max (Table 3).

∆G inject and LHE values are presented in Table 3. All the dyes displayed sufficient exergonicity as the calculated ∆G inject values were negative (process to occur spontaneously), which is facilitating the electron injection from E LUMO of the dye to the CB of TiO2. LHE is also more than 90% for all the dyes considered in this study, i.e., all dyes can be able to harvest light to generate electricity. Scharber et al. [82] carefully analyzed a series of organic solar cell devices employing 26 polymer donor moieties having a common acceptor and different HOMO levels. Based on their study, they have proposed an empirical equation (Eq. 5). It is to be noted that the V OC loss of 0.3 V indicated is empirical and the actual loss could be greater or smaller than 0.3 V. In this study, we have chosen 0.3 V to predict the trend in the V OC variation among the five dyes studied and the emphasis is not on finding the exact V OC values [35]:

$$ {V}_{\mathrm{OC}}=\left|{E}_{\mathrm{HOMO}}\left(\mathrm{donor}\ \mathrm{or}\ \mathrm{dye}\right)\right|-\left|{E}_{\mathrm{LUMO}}\left(\mathrm{acceptor}\right)\mathrm{of}\ {\mathrm{TiO}}_2\right|-0.3 $$
(5)

The calculated V OC are presented in Table 3. The decreasing order of V OC is D1 > D3 > D2 > D4 > D5. Please note, our model does not consider the kinetics of back electron transfer; hence, the calculated V OC are only an indicative value, depending upon the dye molecule’s size and substitution that they bear the extent of back electron transfer kinetics may vary. Experimentally, D3 and D4 showed a higher V OC value than D1, because of the effect of substitution at the C3 position of the thiophene ring, which may retard the back electron transfer, hence improving the open-circuit voltage. Therefore, it can be concluded that D1 is the best performing dye in DSSC, due to the highest driving force of dye regeneration and the highest negative NBO value of CA-(TiO2)8 moiety coupled with reasonably higher open-circuit voltage.

Conclusions

The dyes comprising of oligothiophene as spacers, TPA as donor at C2- and C3-sites of thiophene, and cyanoacrylic acid as acceptor have been investigated by using the B3LYP/6-31G(d,p) method and the UV-Vis absorption spectra have been simulated by using the TD-DFT methods with the PCM model to simulate the solvent environment. Although, substitution at the 3-position of the thiophene ring may retard the back electron transfer, the loss of coplanarity affected the intramolecular charge transfer. The electron injection is possible by all five dyes as the LUMO of all the dyes are above the CB of TiO2, indicating a thermodynamically favorable charge transfer from the dyes to the CB of the TiO2. The NBO analysis of the dye-(TiO2)8 cluster showed that the higher negative NBO value of the dye-(TiO2)8 cluster for D1 indicates feasibility of intermolecular charge transfer from the TPA moiety to the CB of TiO2. The highest driving force for dye regeneration and higher NBO value of CA-(TiO2)8 moiety coupled with reasonable higher open-circuit voltage make D1 to be the clear winner among all the dyes studied for the DSSC application. The outcomes of this theoretical study are clearly explaining the experimental data obtained. Hence, the reason behind the poor performance of D2 and D5 is their poor electron injection ability.