Introduction

Since 1991, the dye-sensitized solar cell (DSSC), often called the “Grätzel cell” [1] has attracted the extensive interest of many researchers from both a fundamental and a practical perspective [2–24] as a low-cost and high efficiency solar electricity system. In DSSC, the dye, as photosensitizer, plays a major role in absorbing sunlight and transporting electrons into the conduction band of the semiconductor, transforming solar energy to electricity. So far, DSSC sensitized by Ru-containing compounds have achieved the highest solar to electricity conversion efficiency (∼11 %) [25, 26]. Even though such DSSCs possess high efficiency, disadvantages in this system also exist. The main problem is that the sensitizer used in DSSC are noble metal compounds that are limited in amount causing of high product costs. In addition, toxicity to humans and the environment is found. Thus, non-metallic organic dyes as well as natural dyes have attracted interest in this field due to their cheapness, abundance and environmental friendliness.

Recently, DSSC using some organic dyes as sensitizers have been reported with efficiency as high as 9.8 % [27]. Regarding natural dyes, a group of cyanin [28–39], carotenoid [40, 41], tannin [42], chlorophyll [43] and coumarin dye and its derivatives [44–46] have been utilized as sensitizers. A promising approach to improve the performance of DSSC is to search for new dyes or structural modification of existing dyes. A natural dye can be extracted from many parts of vegetables, flowers and trees, and some dyes can be extracted from insects. Recent work has reported DSSC performance using dyes extracted from the fungus Monascus, with the highest overall conversion efficiency of 2.3 % being reached [47]. Theoretical work has also supported experimental results [48]. Thus, dyes derived from fungi as well as small-scale insects are interesting to test for photosensitization in DSSC. Carminic acid (CA) can be extracted from the body and eggs of the cochineal insect (Dactylopius coccus). Lac dye (LA) is a natural reddish dye stuff extracted from stick lac, which is a secretion of the insect Coccus laccae (Laccifer Lacca Kerr). Both dyes have been used extensively as a natural food additive, cosmetics and, especially, as a colorant for silk and cotton dyeing. The pigments belong to the group of anthraquinones, which are water-soluble and can be extracted with water or alcohols. The main pigment in cochineals is CA while LA contains several pigments (Lac A–E) as shown in Fig. 1. Photosensitization and photocurrent switching in CA/TiO2 hybrid material has been reported [49]. There is evidence that a CA/TiO2 system may be a good starting point for the development of photofuel cells [50]. There are several advantages to apply this kind of insect dye as a photosensitizer in DSSC, including its molecular structure, which is composed of several potential anchoring groups (-COOH and -OH) that can bind with TiO2 surface; stability to a wide range of pH, light and heat; nontoxic to the environment and natural abundance.

Fig. 1
figure 1

Chemical structures of carminic acid (CA) and lac dyes (LA)

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According to DSSC performance, the electronic structure of the dye and energy level of the semiconductor have to be matched in order to satisfy the electron transfer process. An understanding of electronic, optical, and redox properties of the dye is necessary. Thus, in this work, the electronic structure, optical properties, oxidation potential and electron injection force relevant to charge transfer of CA and LA were investigated using density functional theory (DFT) and time dependent (TD) DFT.

Computational methods

The ground-state geometries of CA and LA were optimized with DFT method at the B3LYP/6-31+G(d,p) level of theory [51–55]. The free energy change (in eV) for electron injection from dyes to TiO2 surface can be expressed as [56]:

$$ \Delta {G^{inject }}=E_{OX}^{dye* }-E_{CB}^{{Ti{O_2}}} $$
(1)

where \( E_{OX}^{dye* } \) is the oxidation potential of the dyes in the excited state. Based on the Rehm and Weller equation [57], \( E_{OX}^{dye* } \) can be estimated by

$$ E_{OX}^{dye* }=E_{OX}^{dye }-{E_{00 }}+{\omega_r} $$
(2)

where \( E_{OX}^{dye } \) is the oxidation potential of the dyes in the ground state while E 00 is adiabatic energy difference between excited and ground states and ω r is a coulombic stabilization term. As noted in a previous work [58], the latter term can be negligible, so \( E_{OX}^{dye* } \) is estimated approximately as \( E_{OX}^{dye }-{E_{00 }} \). \( E_{CB}^{{Ti{O_2}}} \) corresponds to the conduction band of the TiO2 semiconductor. The \( E_{CB}^{{Ti{O_2}}}=-4.0\,\mathrm{eV} \) [59] used in this work was obtained from experiment because the presented value was observed under conditions in which the semiconductor is in contact with aqueous redox solution at fixed pH [60]. Recently, Preat et al. [61] proposed an equation to calculate ΔG inject reliably in the relaxed excited state; the ΔG inject calculated by unrelaxed paths differs from that of the relaxed path by approximately 0.5 eV. The latter work concluded that calculation using the unrelaxed path is reliable. Thus, in this work, ΔG inject for the dyes was estimated using the unrelaxed path. Single-point calculations at the same level of theory were employed for solvent-effect computations using the polarizable continuum model (PCM) of Tomasi and coworkers [62–68]. The integral-equation formalism (IEF) PCM [62, 65] was used in single-point calculations for the PCM solvent effect. The molecular cavity models used in the PCM models are UAKS [69]. Electronic transitions were examined by single-point calculations using the ground-state geometries performed at TDDFT/B3LYP/6-31+G(d,p) in vacuo and TDDFT/IEF-PCM(UAKS)/B3LYP/6-31+G(d,p) level in water. To analyze the acidity of the carboxylic and hydroxyl groups of the dyes, deprotonation energies (ΔE H) for each carboxylic and hydroxyl groups (atomic labeled in Fig. 1) were computed based on the following equation:

$$ \varDelta {E_H}={E^{+}}-{E_H} $$
(3)

where E + and E H represent the total energy of the cationic and neutral forms of the dye molecules. All calculations were performed with the Gaussian 03 program package [69]. The program Molekel was utilized to generate molecular graphics [70].

Results and discussion

Ground state structure and optical properties

The ground state geometries of carminic acid (CA) and all lac dyes (LA) were optimized at B3LYP/6-31+G(d,p) level. The frontier molecular orbital (MO) energies including highest-occupied molecular orbital (HOMO), lowest-unoccupied molecular orbital (LUMO) and energy gap (ΔE H−L) computed in vacuo and water are listed in Table 1. E HOMO of all dyes were more positive (expect for CA) while their E LUMO were more negative going from vacuo to water media. MO energies of CA in this work are close to the previous work based on the same calculation method [71]. As can be seen, differences in the chemical structures of LA_A, B, C and E are their substituents on the phenyl ring D, thus E HOMO and E LUMO of these four dyes are not much different. A similar result has also been found in their ΔE H−L (in vacuo). LA_D shows lowest E HOMO and E LUMO. Thus, it is noted that phenyl ring D substitution on ring A stabilizes E HOMO and E LUMO of LA_A, B, C and E by their π-conjugate systems leading to lower ΔE H−L. The highest and higher values of ΔE H−L of LA_D and CA may due to sugar moiety substitution and un-substitution, respectively. The ΔE H−L of all dyes are narrower in water media than in vacuo due to the stabilization of their MOs by the polar environment. ΔE H−L of all dyes (in water) are, in decreasing order: LA_D > CA > LA_E > LA_B > LA_A > LA_C.

Table 1 The highest occupied molecular orbital energies (E HOMO), the lowest occupied molecular orbital energies (E LUMO) and energy gap (ΔE H−L) of carminic acid (CA) and all lac dyes (LAs) computed at the B3LYP/6-31+G(d,p) level
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The UV–vis spectra of all dyes were simulated by single-point calculation using the B3LYP/6-31+G(d,p)-optimized structures computed at TDDFT/B3LYP/6-31+G(d,p) level. The λmax for all dyes, considering as absorption maxima, were obtained from absorption spectra generated from TDDFT computation as shown in Table 2. The results show a ∼23–35 nm red shift of λmax from vacuo to water media for all dyes. The computed values are ∼13–28 nm lower than the experimental values. The λmax of LA_A is similar to those of crude laccaic acid (containing of LA_A, B and C), in which their λmax were reported to be 490 nm, while absorption maxima at 485 and 493 nm were found for LA_E and CA, respectively [72].

Table 2 Maximum absorption wavelengths (λmax) for UV–vis absorption spectra of CA and all LAs in various media computed at TD/DFT/B3LYP/6-31+G(d,p) level
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The isovalue plots of five MO (HOMO−2 to LUMO+1) levels for all dyes together with their ΔE H−L are shown in Fig. 2. The HOMO-2 orbitals of all lac dyes (except for LA_D) are localized separately at the phenyl ring A and ring C, especially on the -COOH1 and -OH3 groups. For, HOMO-1 orbital, more electron distribution is found on the phenyl ring while a much lesser distribution is found on ring C. As can be seen, the phenyl rings D of LA_A, B, C, and E, as well as the sugar ring of CA were perpendicular to the planar core. At HOMO orbital, energies are contributed mainly on ring A, collapsing to ring B with a conjugated double bond. The energies located mainly on ring B and C of the LUMO are in accordance with the charge movement from the ring A at HOMO. The LUMO+1 of LA_A, B, C, E is not very different from their LUMO, in which the node of energy is found at –COOH2 as well as –COOH1.

Fig. 2
figure 2

Isovalue plot of frontier molecular orbital (MO) of CA and LAs and their corresponding energy gap, E gap (eV) in vacuo and in water (in parenthesis)

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The first three vertical singlet states, major transition characters and oscillating strength of the absorption bands in the UV–vis region for all dyes computed by single-point calculation using TDDFT/B3LYP/6-31+G(d,p) are presented in Table 3. It can be observed that the first transition of all dyes is the HOMO→LUMO found both in water and vacuum environments. HOMO→LUMO+1 is found as second and third characters for all dyes. HOMO-2→LUMO and HOMO-3→LUMO can be observed in the transitions of all dyes. The HOMO→LUMO+1 can be considered as the possible transition due to its high charge distribution located on both two carboxyl groups with high corresponding oscillating strength and transition character. The possible binding modes of the dye–TiO2 system are shown in Fig. 3. The bi-coordinated mode formed by the hydroxyl oxygen of –OH3 and carboxyl oxygen of –CΟΟΗ1 and Ti(IV) (Fig. 3a) were proposed previously for CA [49]. However, for LA_A,B,C,E, the bi-coordinated binding mode may be formed by either -COOH1 or -COOH3 and Ti(IV) due to the nodal charge distribution, which is found on both groups at LUMO+1 orbital. The ability of the anchoring group to chelate with Ti(IV) depends on the deprotonation energy for all –OH and –CΟΟΗ groups, as tabulated in Table 4. Deprotonation energies (ΔE H) of the dye were computed from the energy difference between their neutral and cationic forms of various deprotonate sites. The ΔE H of the first three anchoring groups of LA_A, B, C and E are, in increasing order: –CΟΟΗ1 < –ΟΗ2 < –CΟΟΗ3. These computed parameters confirmed the predicted doubly bi-coordinated mode (Fig. 3b) based on the lower difference in deprotonation energy between –CΟΟΗ3 and –CΟΟΗ1 groups (∼20 kcal mol−1). This kind of binding mode will enhance greater charge transfer from the dye to the TiO2 surface than another mode in the case of the HOMO→LUMO+1 with more intensive occurrence.

Table 3 Vertical singlet states, transition character and oscillating strength (with f > 0.01) of absorption bands in UV–vis region of CA and all LAs computed at the TDDFT/B3LYP/6-31+G(d,p) level
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Fig. 3a,b
figure 3

Proposed binding modes of interaction between LA and Ti(IV). a Bi-coordinated mode, b doubly bi-coordinated mode

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Table 4 Deprotonation energiesa (in kcal mol−1) of various anchoring groups of CA and all LAs
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Excited state oxidation potential and electron injection force

Electron transfer from excited state of the dye to conduction band of semiconductor depends on the excited state oxidation potential. \( E_{OX}^{dye } \) is estimated as the negative E HOMO based on Koopman’s theorem [73]. \( \Delta {G^{inject }} \) and \( E_{OX}^{dye* } \) are computed from Eqs. 1 and 2, respectively. The computed \( E_{OX}^{dye } \), \( E_{OX}^{dye* } \) and ΔG inject of all dyes in vacuo and water are tabulated in Table 5. LA_D possesses the highest \( E_{OX}^{dye* } \) and lowest ΔG inject in both two phases due to the effect of un-substitution on ring A as described above. This means that LA_D is less responsive to the photosensitization and charge transport process in both two phases. On the other hand, the most positive response in photosensitization and dynamic charge flow is LA_C. ΔG inject and \( E_{OX}^{dye* } \) computed in water are different from the value computed in vacuo due to the polarization effect on E HOMO. The charge transfer due to photosensitization of all dyes is spontaneous.

Table 5 The computed ΔG inject, \( E_{OX}^{dye* } \) and \( E_{OX}^{dye } \) (all in eV) for of CA and all LAs
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Thermodynamically, the spontaneous charge transfer process from the dye excited state to the conduction band of TiO2 requires LUMO energy with more positive potential than \( E_{CB}^{{Ti{O_2}}} \) (−4.0 eV), while HOMO energy with more negative than redox potential of the \( {{{{{\mathrm{I}}^{-}}}} \left/ {{\mathrm{I}_3^{-}}} \right.} \) electrolyte (±4.80 eV) [74] requires spontaneous charge regeneration. The energy level diagram of the HOMO and LUMO of the dyes and E cb of TiO2 and redox potential of the electrolyte is depicted in Fig. 4. The LUMOs of all dyes lies over the E cb of TiO2 while their HOMOs are lower than the reduction potential of electrolyte. Thus, all of them possess a positive response to charge transfer and regeneration related to the photosensitization process.

Fig. 4
figure 4

Schematic energy diagram of CA and LAs, TiO2 and electrolyte \( \left( {{{{{{\mathrm{I}}^{-}}}} \left/ {{\mathrm{I}_3^{-}}} \right.}} \right) \). E HOMO and E LUMO of the dyes are in water environment

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Relationship between electronic structure of the dyes and photovoltaic performance

The overall efficiency (η) of the DSSC can be calculated from the integral of short-circuit photocurrent density (J SC), open circuit potential (V OC), the fill factor (ff) and the intensity of light (I s), expressed by

$$ \eta =\frac{{{J_{SC }}{V_{OC }}ff}}{{{I_s}}} $$
(4)

From this expression, J SC, V OC, and ff are obtained only by experiment. The relationship among these values and electronic structures of the dyes is still not well understood. However, the relationship between V OC and E LUMO of the dyes based on electron injection from LUMO of the dye to E cb of TiO2 can be expressed as [75]:

$$ e{V_{OC }}={E_{LUMO }}-{E_{cb }} $$
(5)
$$ {V_{OC }}=\frac{{{E_{LUMO }}-{E_{CB }}}}{e} $$
(6)

According to this expression, the higher the E LUMO, the larger the V OC found. The approximated V OC values based on Eq. 6 for the dyes are tabulated in Table 6. The trend of the V OC of the dyes was found to be similar to \( E_{OX}^{dye* } \) and ΔG inject. As mentioned in a previous work [49], where CA–TiO2 was found to be a good photovoltaic system, all LAs (except for LA_D) will give higher overall efficiency than CA without consideration of any other factors. LA_C and LA_D are found to be the best and the worst sensitizers, respectively, while LA_E, A and B are also expected to show good overall efficiency of their DSSCs.

Table 6 Estimated open-circuit voltage (V OC) and light harvesting efficiency (LHE) of CA and all LAs
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One factor relates to efficiency of DSSC is the performance of the dyes in response to incident light. Based on the light harvesting efficiency (LHE) of the dyes, this value has to be as high as possible to maximize the photocurrent response. The LHE can be expressed as [76]

$$ \mathrm{LHE}=1-1{0^{-A }}=1-1{0^{-f }} $$
(7)

where A (f) is the absorption (oscillating strength) of the dyes associated to the absorption energy (E 00). The computed LHEs for all dyes are shown in Table 6. Based on the result, LA_D is the worst responder to incident light among these dyes. Finally, it can be concluded that all the dyes have HOMO−LUMO energy levels matching the E CB level of TiO2 and the reduction potential of the electrolyte but LA_C, A, and B are suggested as photosensitizers according to their good computed \( E_{OX}^{dye* } \), ΔG inject and V OC values in which these parameters are believed to relate to overall efficiency of DSSC.

Conclusions

The ground state geometries, electronic structures, and photoelectrochemical redox properties of carminic acid and five lac dyes were evaluated using DFT and TDDFT calculations. The results show that the major electronic transition of all dyes is HOMO→LUMO, while HOMO→LUMO+1 is expected to be the minor transition. All the dyes show favored electron injection (negative ΔG inject) from their excited states to the conduction band edge of TiO2. The \( E_{OX}^{dye } \), \( E_{OX}^{dye* } \) as well as ΔG inject of these lac dyes are quite similar except for LA_D. The calculation result suggests that, based on their good computed redox properties, most lac dyes can be used as efficient photosensitizers in DSSC. In addition, they also show a strong interaction with TiO2, possible via doubly bi-coordinated mode bound to Ti(IV). Their stabilities to thermal degradation and pH are advantage that make this kind of natural dye promising for use as photosensitizers in DSSC.