Introduction

Dye-sensitized solar cells (DSSCs) have been actively pursued in the search for new renewable energy sources, as they have many advantages over silicon-based solar cells, including low cost, easy production, and flexibility [1–9]. DSSCs have been extensively studied since O’Regan and Grätzel published their seminal work in 1991 [10]. These devices are generally composed of organic or inorganic dyes adsorbed on an inorganic n-type semiconductor, a platinized counter electrode, and a redox electrolyte [11]. The highest power conversion efficiencies (PCEs) of DSSC devices have been achieved by using metal-based dyes [12–24]. Among various DSSCs, those derived from ruthenium(II)–polypyridyl complexes have shown the best photostability as well as photocurrent conversion efficiencies [25]. Such dyes possess the highest PCEs because of their photochemical and electrochemical properties. However, it can be difficult to synthesize and purify the preferred Ru(II)–polypyridyl complexes [26]. Dyes based on heavy-metal ions are not environmentally friendly, and sources of ruthenium are limited [27]. Thus, metal-free sensitizers such as organic dyes have been studied and explored with a view to developing a new class of sensitizer dye molecules [13, 28–31]. In some cases, the utilization of organic dye molecules as efficient DSSCs is hindered by their low stability, difficult syntheses, and the formation of aggregates on the semiconductor surface [13, 32]. However, efforts have been made to synthesize efficient organic dye molecules in order to achieve higher DSSC performance [13, 32]. Metal-free organic dyes have a D–π–A dipolar architecture, where a π-electron-rich moiety (D) is linked to a π-electron-poor end group (A) through a π-spacer. The choice of anchoring group also plays a crucial role in the efficiency of the DSSC [33]. Recent reports have revealed that modifying metal-free organic dyes structurally as well as electronically can significantly improve their absorption and overall efficiency, making them more useful for application in DSSCs [26].

A solar energy to electricity conversion efficiency of 6.8 % was achieved using an organic dye containing diarylamine as the donor unit, fluorene and thiophene as π-spacers, and cyanoacrylic acid as the anchoring group [34]. The performance of a DSSC is dependent on several different parameters, so the development of an efficient dye is a considerable challenge to both experimental and theoretical chemists [33].

DFT methods have been used to calculate the structural properties, electronic bands, optical excitation spectra, and charge-transport properties of organic/inorganic hybrid materials [35]. DFT and TDDFT methods have been found to be reliable tools for designing new dyes with appropriate optical, electrochemical, and physical properties for application in DSSCs [36]. Reports have suggested that CAM–B3LYP/6-31 + G* in combination with the conductor-like polarizable continuum model (CPCM) accurately reproduces the vertical transition energies of D–π–A organic dyes [37–39]. The nature of the anchoring group as well as the strength of coupling of the dye molecule to the semiconductor surface significantly influence the efficiency of the DSSC. Strong dye coupling reduces the possibility of desorption, enhances the cycle of use of the solar cell, and faciliates electron injection from the photoexcited singlet/triplet state(s) of the dye to the conduction band of the semiconductor. The electron injection rate is an important influence on the efficiency of a DSSC [40]. This injection rate can be calculated quantum chemically with reasonable accuracy by a range of methodologies [14, 36, 41–45]. Reports also suggest that the donor group of the dye molecule has a significant effect on solar cell performance. A wide variety of organic dyes containing various electron donors, such as dialkylamine groups [46, 47], coumarins [48–51], carbazole [52, 53], quinoxaline [54, 55], difluorenylphenylamine [56–62], julolidine [63], an electron-donating diphenyl amine moiety containing a methoxy group [64], di(p-tolyl)phenylamine [65], pyrrolidino, and ullazine [66], have been explored in DSSC design.

In the work reported in the present article, we performed a computational study to investigate the influence of cyclic asymmetric benzotripyrrole derivatives (2–6) as donor groups on DSSC efficiency. Phenyl-substituted derivatives of cyclic asymmetric benzotripyrrole can be prepared by the electropolymerization of indole-5-carboxylic acid and 5-cyanoindole [67] and the reaction of indole with nitrosobenzene in the presence of an acid [68]. Ruiz et al. have shown that asymmetric compounds present redshifted absorption and emission maxima compared to the corresponding symmetric compounds [69]. Asymmetric compounds also show improved fluorescence quantum yields [69]. The experimental results for organic dye 1 with diphenylamine as a donor group were found to be in good agreement with the corresponding computational results [34, 70, 71]. Therefore, in the present study, we used 1 as a reference dye to examine the efficiencies of a series of designed dyes (Fig. 1). The calculations were performed at the same level of theory as employed for 1, and they predicted that the designed dyes 3, 4, and 6 possess higher efficiencies than reference dye 1 [70]. The designed dyes were compared with other recently reported donor systems that have a nitrogen atom in the middle of the ring system [66, 71, 72]. These comparisons highlighted the importance of the position of the nitrogen atom in the donor molecule.

Fig. 1
figure 1

Structures of organic dyes 1–9

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Methods

Evaluation of key parameters

The energy conversion efficiency (η) of solar cell device can be determined using the following equation:

$$ \eta =\mathrm{F}\mathrm{F}\frac{V_{OC}{J}_{SC}}{P_{inc}}, $$
(1)

where V oc is the open-circuit photovoltage, J sc is the short-circuit current density, FF is the fill factor, and P inc is the solar power incident on the cell.

The short-circuit current density, J sc, in a DSSC is determined by the following equation [70]:

$$ {J}_{\mathrm{s}\mathrm{c}}={\int}_{\lambda}\mathrm{L}\mathrm{H}\mathrm{E}\left(\lambda \right){\varPhi}_{\mathrm{inject}}.{\eta}_{\mathrm{collect}}.{\eta}_{\mathrm{regen}}{I}_{\mathrm{s}}\left(\lambda \right).\mathrm{d}\lambda, $$
(2)

where LHE(λ) is the light-harvesting efficiency at a given wavelength, calculated as LHE = 1 – 10−f; f is the oscillator strength. Φinject is the electron-injection efficiency and η collect denotes the charge-collection efficiency. Φinject is closely related to the driving force ΔG inject (for the injection of electrons from the excited states of dye molecules to the semiconductor substrate), which is calculated as the difference between the oxidation potential of the excited dye (E dye*) and the reduction potential of the CB of TiO2 (E CB, −4.00 eV) [73]:

$$ \varDelta {G}_{\mathrm{inject}}={E}^{\mathrm{dye}*}-{E}_{\mathrm{CB}}. $$
(3)

E dye* can be expressed as [74]

$$ {E}^{\mathrm{dye}*}={E}^{\mathrm{dye}}-{\lambda}_{\max }, $$
(4)

where E dye is the redox potential of the ground state of the dye and λ max is the vertical transition energy. The regeneration efficiency (η regen) of the oxidized dye is associated with the regeneration driving force (ΔG regen). ΔG regen is the difference between the oxidation potential of the dye and the redox potential of the electrolyte I−/I3 − (4.58 eV) [75]. Thus, J sc will increase with increasing LHE and ΔG inject. The value of J sc also increases when the value of ΔG regen is decreased.

The V oc of a DSSC is determined using the following equation [73]:

$$ {V}_{\mathrm{oc}}=\frac{E_c+\varDelta \mathrm{C}\mathrm{B}}{q}+\frac{kT}{q} \ln \left(\frac{n_{\mathrm{c}}}{N_{\mathrm{CB}}}\right)-\frac{E_{\mathrm{redox}}}{q}. $$
(5)

Here, q is a unit of charge, E c is the conduction band edge of the semiconductor substrate, k is the Boltzmann constant, T is the absolute temperature, n c is the number of electrons in the conduction band, N CB is the density of accessible states in the conduction band, and E redox is the reduction–oxidation potential of the electrolyte. ΔCB is the shift in the edge of the conduction band of the semiconductor when the dye is adsorbed at its surface [76].

Computational details

We applied DFT using Becke’s three-parameter hybrid functional and the correlation formula of Lee, Yang, and Parr (B3LYP) [77, 78] for the gas-phase geometry optimization of compounds 1−9 before and after they were bound to the TiO2 surface. The dyes were fully optimized using the 6-31G* basis set for the atoms C, H, O, N, and S and the effective core potential (ECP) basis set LANL2DZ for Ti atoms. Positive vibrational frequencies were obtained, confirming that the optimized molecular structures corresponded to energy minima. An earlier report had shown that this method could provide a reasonable prediction of the geometry—comparable to that optimized at the MP2 level of theory, but with a much lower computational cost [37]. The absorption spectra of the optimized dyes were obtained in the solvent tetrahydrofuran (THF) [79, 80] at the CPCM–CAM–B3LYP/6-31 + G* [81] level of theory. The long-range corrected functional CAM-B3LYP showed the best agreement of λ max with the experimentally observed results among all of the DFT functionals tested (Table S1 of the “Electronic supplementary material,” ESM). We utilized the CAM-B3LYP functional in this study, as this method has been extensively employed to calculate the vertical transition energies of D–π–A dye molecules [38, 39, 82]. The oxidation potentials of the optimized free dyes were calculated at the CPCM-B3LYP/6-311G** level of theory for the neutral and the cationic dyes in the ground state [77]. Dipole moments of the TiO2-bound dyes were calculated at the CPCM–B3LYP/6-31G* level of theory. Ti(OH)3H2O was used as a model in earlier reports, and the results obtained with this model provided a reasonable explanation for the electronic and physical properties of TiO2 [70]. This model also showed good agreement (in terms of electronic and physical properties) with a larger nanocluster, (TiO2)6 [83, 84]. All quantum chemical calculations carried out in the present work were performed using Gaussian 09 [85].

Results and discussion

Molecular design and geometries

The optimized geometries of the studied dyes 1–9 are shown in Fig. 2. The dye molecules anchored on the semiconductor TiO2 model system are shown in Fig. S1 in the ESM. The basic unit of each dye molecule is D–π–A, where D is the donor group, which was always a cyclic asymmetric benzotripyrrole derivative. The phenyl-substituted derivative of cyclic asymmetric benzotripyrrole was prepared by the electropolymerization of indole-5-carboxylic acid and 5-cyanoindole [67]. The reaction of indole with nitrosobenzene in the presence of an acid also gives similar products [68]. Ruiz et al. ascertained that asymmetric compounds showed redshifted absorption and emission maxima compared to the maxima of the corresponding symmetric compounds [69]. Cyanoacrylic acid was used as an anchoring as well as an electron-acceptor group in dye molecules 2–6. Fluorene and thiophene groups were attached between the chromophore and the anchoring group as π-spacer units. Such π-spacers are widely used in DSSCs to shift the absorption band into the visible region via extended π-conjugation [86]. Fluorene is a well-documented π-spacer that is used in organic dyes due to its photophysical and electrochemical properties [87]. This compound also influences DSSC efficiency due to its high molar extinction coefficient and light-harvesting properties [88–90]. Thiophene spacers have also been adopted for use in DSSCs due to their high polarizability, tunable spectroscopy, and electrochemical properties [91].

Fig. 2
figure 2

Optimized geometries of the free dyes 1–9, calculated at the B3LYP/6-31G* level of theory

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The effect of the choice of donor group on the geometrical structures of the designed dyes was examined (see Fig. 1 and Scheme 1). Some of the geometric parameters of the studied dyes (1–9) are listed in Table 1. The process of transferring an electron from the donor moiety to the semiconductor surface is facilitated (and thus solar cell efficiency can be increased) by D–π–A coplanarity. The calculated dihedral angles (θ) of 1–9 indicate that the constituent units in each of the dyes 2–6 and 9 are almost coplanar (Table 1 and Scheme 1). These dye molecules therefore show stronger π-conjugation effects than the other dye molecules studied here.

Scheme 1
scheme 1

D–π–A organic dyes: θ is the dihedral angle between the donor and spacer units (shown in red); r 1, r 2, r 3, and r 4 are bond lengths

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Table 1 Selected bond lengths (r 1, r 2, r 3, and r 4, in Å), dihedral angles (θ, in degrees), and the HOMO–LUMO energy gaps (HLGs, in eV) of the designed dyes 1–9
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The frontier molecular orbitals of dyes 1–9 in the ground state are given in Fig. 3. Upon analyzing the frontier molecular orbitals, it was observed that the highest molecular orbital (HOMO) was mainly localized on the donor group and the fluorene spacer unit (Fig. 3) while the lowest unoccupied molecular orbital (LUMO) was mainly localized on the thiophene spacer and the acceptor group in the dye molecules (Fig. 3). The calculated energy levels of dyes 1–9, along with the conduction band of the TiO2 surface and the redox couple triiodide/iodide, are given in Fig. 4. Electron transfer from the dye molecule to the semiconductor occurs via two different mechanisms: type I or indirect injection and type II or direct injection [92, 93]. The type I process involves two steps: an excitation from the ground state to the excited state of the dye molecule that occurs through the absorption of a photon, and the transfer of an electron to the conduction band of the semiconductor nanoparticle (NP). The type II process involves a single step, in which the electron is transferred from the ground state of the dye to the conduction band of the semiconductor upon photoabsorption. It is known that, for the indirect mechanism to operate, the LUMO level must be above the conduction band of TiO2 (E CB, −4.00 eV) to allow effective electron injection, and the HOMO level should be lower than the redox potential of I−/I3 − (−4.80 eV) [73, 94]. The studied dyes utilize the indirect mechanism for electron transfer to the semiconductor nanoparticle (Fig. 4). It is clear from Fig. 4 that the HOMOs are situated below the redox potential of the I−/I3 − electrolyte (−4.80 eV), and that the LUMOs of all dyes lie above the conduction band of the TiO2 surface [73, 94]. Thus, all of the designed dyes show favorable electron injection properties. Among the series of dye molecules, 6 has the lowest HOMO–LUMO energy gap (HLG), which facilitates electron excitation as well as longer-wavelength light absorption (Fig. 4).

Fig. 3
figure 3

HOMO–LUMO diagrams of dyes 1–9 calculated at the CAM–B3LYP/6-31 + G*//B3LYP/6-31G* level of theory in the gas phase; surfaces shown in the diagrams correspond to an isosurface value of 0.02

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Fig. 4
figure 4

Energy diagram showing the HOMO–LUMO gaps for dyes 1–9 (plotted along the x-axis), TiO2, and the electrolyte (I3 −/I−)

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Absorption spectra

The calculated maximum absorption wavelength (λ max), the corresponding electronic transition configurations, the oscillator strengths (f), and the light-harvesting efficiencies (LHEs) of dyes 1–9 are listed in Table 2. The absorption spectrum of an organic dye is dependent on the conjugation present in the molecule, the dihedral angle between the donor and spacer groups, and the HOMO–LUMO energy gap for the probable transition. The degree of conjugation in the dye molecule influences the optical properties of the DSSC, and thus its efficiency [66, 71]. We also exploited the effect of π-conjugation at the appropriate position of the donor group to enhance DSSC efficiency. The calculated absorption spectrum of dye 2 was found to be 420 nm (Table 2). We attached two pyrrole groups to the phenyl ring of dye molecule 2 to create dye 3 (Fig. 1), enhancing the absorption wavelength. The absorption maximum of dye 3 was found to occur at 439 nm, suggesting increased conjugation in 3 than in 2 (Table 2, Fig. S3 in the ESM). The calculated dihedral angles for 2 and 3 corroborate the notion that the constituent units in 3 are more coplanar than those in 2 (Table 1). The calculated smaller HOMO–LUMO energy gap of dye 3 (4.17 eV) compared to that of dye 2 (4.77 eV) also shows the effect of the enhanced conjugation in the former case (Fig. 4, Table 1). One phenyl ring was then attached to the pyrrole unit of dye 3 to give dye 4 (Fig. 1). The calculated results revealed that dye 4 has a comparable absorption maximum (λ max = 440 nm) to that of dye 3 (Table 2 and Fig. S3 in the ESM). Incorporation of a phenyl ring into dye 4 to yield dye 5, however, shifted the absorption maximum to a lower wavelength (434 nm). Geometrical analysis of the optimized dye 5 suggested that the dihedral angle between the nitrogen atoms is larger (N1CCN2 = −2.6°) than in dye 4 (N1CCN2 = −0.4°) (Fig. 1). This distortion in the ring plane decreases the conjugation in dye 5 compared to dye 4. This interrupted conjugation is reflected in the HOMO–LUMO energy gaps (HLGs) of the dyes. The HLG value of compound 5 (4.26 eV) is higher than that of 4 (4.13 eV) (Fig. 4, Table 1). To minimize the geometrical distortion in dye 5, we changed the position of the phenyl ring attached to the pyrrole unit of dye 4 to generate dye 6 (Table 2). Dye 6 showed a longer-wavelength absorption maximum (443 nm) due to better conjugation, which decreased the HOMO–LUMO gap. The computed absorption maxima of dyes 7–9 are also given in Table 2. The absorption maxima of dyes 7–9 occurred at smaller wavelengths than those of dye 6 and reference dye 1.

Table 2 Calculated wavelengths of maximum absorption λ max (in nm and in eV in parentheses), oscillator strengths f, light-harvesting efficiencies (LHEs), and the nature of the transitions for dyes 1–9
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Photovoltaic performance

Factors influencing J sc

An important parameter of the dyes in relation to enhancing the efficiency of a DSSC is J sc, which is directly related to the light-harvesting efficiency (LHE) and electron-injection rate (Φinject) of the dye (Eq. 2). The efficiency of a DSSC increases with increasing LHE and Φinject of the dye molecule. The calculated results for LHE, the electron-injection driving force (ΔG inject), and the electron-regeneration driving force (ΔG regen) are given in Table 3. The electron-injection driving force (ΔG inject) can be calculated by relaxing or fixing the TiO2 surface. An earlier study showed that a fixed surface of semiconducting TiO2 yields reasonably close results to those observed experimentally [70]. Therefore, we assumed a fixed surface for calculations of the electron-injection driving force. The calculated LHE and oscillator strength values were found to increase with the degree of conjugation in the system (Table 2). The designed dyes (2–6) showed higher LHE values than reference dye 1 (0.98). Such LHE values are similar to some of the LHE values obtained for highly efficient organic dye molecules reported in the literature [95, 96]. These designed dye molecules (2–6) also show better LHE values than dye 10 (LHE = 0.98, η = 4.92 %), which is reported to be inferior to dye 1 (LHE = 0.99, η = 6.78 %) [70]. The ΔG inject values of compounds 1–9 are given in Table 3. The calculated ΔG inject value of reference compound 1 is −1.62 eV. It is known that ΔG inject is related to J sc and that the J sc value of a dye increases with increasing ΔG inject. The asymmetric benzotripyrrole donor dyes presented higher ΔG inject values than that of 1 (Table 3). However, there is another factor, ΔG regen, which also influences J sc [97]. The larger the value of ΔG regen, the lower the J sc of a cell. We also calculated the ΔG regen values for dyes 1–9, as shown in Table 3. The calculated values suggest that dyes 3–6 have lower ΔG regen values than dye 1. Therefore, dyes 3–6 should have higher J sc values than dye 1. Furthermore, we compared the most promising dye, 6, with other recently reported donor dye molecules (7–9) that have a donor nitrogen atom in the middle of the ring system. The computed results suggest that dye 6 should have a larger J sc than dyes 7–9 due to the different positions of the nitrogen atoms in their ring systems; this difference leads to improved optical and electronic properties for 6. The location of the nitrogen atom at a peripheral site in the ring in 6 significantly enhances λ max, ΔG inject, and ΔG regen compared to the systems where the nitrogen is positioned in the middle of the ring (7–9). Therefore, it appears that the efficiency of organic dye molecules can be tuned by varying the position of the donor nitrogen atom in the ring system.

Table 3 Calculated values of the redox potential (E dye, eV), driving force for electron injection (ΔG inject, eV), and driving force for electron regeneration (ΔG regen, eV) for dyes 1–9
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Factors influencing V oc

The overall power conversion efficiency of a solar cell also depends on the open-circuit photovoltage (V oc) according to Eq. 1. It is known that the value of V oc for a dye molecule can depend on the conduction band (CB), which is associated with the dipole moment of the molecule [98]. Grätzel and coworkers showed that the large vertical dipole moment (μ normal) of an adsorbed dye molecule pointing away from the TiO2 surface can significantly enhance V oc and affect the efficiency of a dye-sensitized solar cell [99]. A Ti(OH)3H2O model of the semiconductor surface was employed in a study and was found to adequately reproduce the properties of the semiconductor surface [70]. We expanded on this model of the TiO2 surface by using a (TiO2)6 cluster model to examine the dipole moments, absorption spectra, and the main configurations of the spectra for dyes 4 and 6 as representative cases (Fig. S4, Tables S2–S4). The calculated results revealed that the trends afforded by the (TiO2)6 cluster model were similar to those obtained with the simpler Ti(OH)3H2O model. The following equation can be used to calculate the shift in E c for the semiconductor upon the adsorption of a dye molecule:

$$ \varDelta \mathrm{C}\mathrm{B}=\hbox{-} \frac{q{\mu}_{\mathrm{normal}}\gamma }{\varepsilon_0\varepsilon }, $$
(6)

where μ normal is the dipole moment of an individual dye molecule perpendicular to the surface of the semiconductor substrate, γ is the surface concentration of the dye, and ε 0 and ε represent the vacuum permittivity and the dielectric permittivity, respectively. It is evident from Eqs. 5 and 6 that increasing the μ normal and n c values of a dye will enhance the V oc. Table 4 presents the values of n c obtained by calculating the difference in the charge on the TiO2 surface between the ground state (S0) and excited state (S1) for dyes 1–9. We also calculated the μ normal values for the studied dyes (Table 4 and Fig. 5). The calculated μ normal and n c values suggest that dyes 3, 4, and 6 should have much higher V oc values than reference dye 1. The dyes with donor units (7–9) that have a nitrogen in the middle of the ring showed lower μ normal and n c values than dye 6.

Table 4 Computed atomic charge distributions (in units of e) on the donor, π-spacer, acceptor, and TiO2 surface for dyes 1–9 adsorbed on the TiO2 substrate in the ground state (S0) and excited state (S1), as calculated at the CPCM–B3LYP/6-31G* level
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Fig. 5
figure 5

Vertical dipole moments of dyes 3, 4, and 6, as calculated at the CPCM–B3LYP/6-31G* level of theory. The TiO2 surface was considered to be parallel to the yz-plane

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Conclusions

In this work, we investigated a series of metal-free organic dyes (2–6) theoretically, and showed that their application in DSSCs should lead to improved efficiency. Cyclic asymmetric benzotripyrrole derivatives were modeled as the donor groups in these dye systems. The phenyl derivative of cyclic asymmetric benzotripyrroles can be obtained synthetically in the laboratory [67]. The results of our calculations indicate that dye 2 has lower efficiency than reference dye 1. The role of conjugation was examined, and the cyclic asymmetric benzotripyrrole unit was found to yield higher DSSC efficiency. Dyes 3 and 4 were predicted to have superior LHEs, ΔG inject values, vertical dipole moments, and electron injection compared to reference dye 1. The V oc values of dyes 3 and 4 were enhanced because of an improved electron-transfer process and higher vertical dipole moments compared to dye 1. Dyes 3 and 4 also showed higher J sc values than dye 1. The designed dye 6 presented the highest λ max (443 nm) among the studied series of dye molecules due to its increased conjugation, which influences the HUMO–LUMO energy gap. The calculated LHE, ΔG inject, μ normal, and Δq values suggest that dye 6 should permit the largest improvement in DSSC efficiency among the series of dye molecules 1–6. We also compared the photophysical properties of dye 6 with those of other reported dyes 7–9 that have a donor nitrogen atom is in the middle of the ring system. The computed results predicted that designed dye 6 should possess a higher incident photon to current conversion efficiency (IPCE) than the reported dyes 7–9. The locations of the nitrogen atoms in the donor groups in the designed dye molecules were found to be an important influence on DSSC efficiency, with peripheral locations of the nitrogen atoms leading to enhanced efficiency. Such results may contribute towards the development of more efficient dyes for solar cell applications.