DFT study of anthocyanidin and anthocyanin pigments for Dye-Sensitized Solar Cells: Electron injecting from the excited states and adsorption onto TiO₂ (anatase) surface

1 Introduction

Dye-sensitized solar cells (DSSC) based on organic dyes adsorbed on nanocrystalline TiO₂ electrodes have attracted considerable attention in recent years because of their high incident solar light → electricity conversion efficiency and low cost of production [1, 2]. The driving force in these is the interfacial electron injection from the dye to the semiconductor. Upon absorbing light, the dye molecules are excited from their ground state, which is located energetically in the semiconductor band gap, to an excited state that is resonant with the TiO₂ conduction band. The electron is then transferred to the semiconductor on the ultrafast time scale [3]. The relative yields and rates of electron injection, recombination, and decay of the dye-excited state influence the efficiency of the solar cell [4]. Therefore, improving the efficiency of the solar devices is possible only when the rates and mechanisms of the competing reactions are known and understood. This in turn requires knowledge of the electronic structure of the dyes both, before and after binding to the semiconductor surface [5]. The photochemical properties of different organic sensitizers have extensively been investigated in an attempt to design dyes with maximal visible light absorption coupled to long-lived excited states. However, major effort is still needed in both developing new sensitizers and finding optimal working conditions to improve the photon → current conversion efficiencies [6, 7, 8]. In this framework, natural dyes as photosensitizers for DSSCs are very attractive because they are of low cost, abundant in supply and sustainable [9]-[12]. Specifically, several types of natural dyes belonging to anthocyanin have been performed. The anthocyanins belong to the group of natural dyes responsible for several colors in red-blue range, found in fruits, flower and leaves of plants. The dyes extracted from grape, mulberry, blackberry, red Sicilian orange, Sicilian prickly pear, eggplant and radicchio have shown a monochromatic incident photon to current efficiency (IPCE) ranging from 40 % to 69 %. Short circuit photocurrent densities (J_sc) up to 8.8 mA/cm², open circuit voltage (V_oc) ranging from 316 to 419 mV and solar conversion efficiency of 2.06 % [13, 14, 15]. Despite several experimental results about the performance of anthocyanin pigments in DSSC, there are no systematic calculations of their electron transference mechanism from the excited states and adsorption onto TiO₂ surface to the best of our knowledge. Within this framework, the main objectives of this paper are to explore, using theoretical calculations, the electronic properties of anthocyanidin and anthocyanin pigments after and before adsorption onto TiO₂ (anatase) surface. The characterization of electronic properties for dyes in gas phase was carried out using the level of theory CAM-B3LYP, employing the 6-31+G(d,p) basis set. The absorption spectra, excited states and electronic injection parameters were obtained and analyzed at TD(CAM-B3LYP)/6-31+G(d,p). Finally, the adsorption energies onto anatase surface model were obtained and analyzed at density functional theory (DFT) level using generalized gradient-corrected approximation (GGA)(Perdew–Burke–Ernzerhof [PBE]) functional and double numerical basis set with polarization (DNP).

2 Theory and computational details

The sunlight-to-electricity conversion efficiency (η) of solar cell devices is determined by open-circuit photovoltage (V_OC), short-circuit current density (J_SC) and the fill factor (FF), as compared to incident solar power (P_inc) [1, 16, 17]:

J_SC is determined by the following equation:

where η_collect is the charge collection efficiency, for the same DSSCs differing only in the dye. As is the case for the organic dyes under study, it is reasonable to assume that this parameter is constant. Light harvesting efficiency (LHE (λ) is the fraction of the incident photons that are absorbed by the dye. LHE is related to the oscillator strength (f) at a given wavelength. By the following equation, while the larger f, the stronger LHE [18]:

The Φ_inject parameter evinces the electron injection efficiency and is related to the driving force ΔG_inject of electrons injecting from the excited states of dye molecules to the semiconductor substrate. It can be estimated as [19]:

EOXdye∗ is the excited state oxidation potential of the dye. ECBTiO2 is the energy conduction band of the TiO₂ semiconductor (–4 eV). EOXdye∗can be determined using following formula:

In eq. 5) λmaxICT is the energy of intermolecular charge transfer (ICT).

DFT and time-dependent density functional theory (TDDFT) calculations were performed to determine geometries, electronic structures and electronic absorption spectra of anthocyanin dyes. All the calculations, in gas phase, were performed using GAMESS package [20]. All calculations were performed by employing CAM-B3LYP/6-31+G(d,p). On the basis of eqs 3, 4, 5), we calculated LHE and ΔGinject parameters and analyzed the efficiency of anthocyanin dyes for electron injection from dye’s excited state to TiO₂ (anatase) surface [21, 22].

The adsorption of dyes on the anatase cluster was performed with DFT calculations using DMol³ program [23]. The model employed herein to represent the (100) surface of anatase consists of 30 TiO₂ units, terminated with 12 hydrogen atoms, which modeled a TiO₂ nanoparticle [24]. The initial structure has been taken from the crystal of TiO₂ anatase [25]. This model has a diameter of about 1 nm, that has to be compared to nanoparticles of about 2–6 nm used in experiments, and has been used in theoretical study of electronic absorption spectrum of organic compound supported on TiO₂, with application in DSSC [3].

The (TiO₂)₃₀ configurations were fully optimized using the GGA. The PBE functional was used to account exchange–correlation effects with DNP basis set. The core electron was treated with DFT-semicore pseudopotentials (DSPPs). After optimization, the adsorption energies (E_ads) on the (TiO₂)₃₀ cluster were obtained. The latter value was obtained using the equation:

where ETiO2+AmA is the total energy of anthocyanin–(TiO₂)₃₀ complex, ETiO2 is the energy for the anatase surface model and EAnth is the energy for the anthocyanin molecule [26]. Following the above expression, a positive value of E_ads indicated a stable adsorption.

3 Results and discussion

3.1 Geometric optimization and intramolecular charge transferences of anthocyanin dyes

The anthocyanin chromophores molecule (cyaniding, delphinidin, peonidin and cyanin) used to carry out the calculations are displayed in Figure 1. They have a positive charge on the molecule, which enables it to absorb light and thus have color [13]. As observed in Figure 1, cyanidin and delphinidin differ in the number of hydroxyl groups present in the molecule, while peonidin has a substituted –OH group. Cyanin has a glucoside group. From level of theory CAM-B3LYP/6-31+G(d,p) all structures showed a planar geometric, which facilitates the electronic delocalization in all the structure. The glucoside group in cyanine dye led a small deviation in the torsion angle for the [C3-C2-C1´- C2´] bond (14°).

Figure 1:

Anthocyanin chromophores molecules (cyanidin, delphinidin, peonidin and cyanin) studied in this work.

3.2 Frontier molecular orbitals, absorption spectra and LHE

The ground state first singlet excited state excitation process can be mainly assigned to the HOMO–LUMO transition, which correspond to a π-π* excited singlet state. For the sake of characterizing electronic properties, it is useful to examine the distribution patterns of molecular orbitals [27, 28]. On the other hand, an important thermodynamic requirement of the dyes to be used in DSSC technology is that the HOMO level of the sensitizer has to be sufficiently positive in the redox potential for efficient regeneration of the oxidized dye molecule to its original state by the iodide electrolyte and the LUMO energy of the dye has to be sufficiently higher than the conduction band edge of the semiconductor (E_CB). To demonstrate their characteristic electronic structure, the HOMO–LUMO shape from the anthocyanin molecules at CAM-B3LYP/6-31+G(d,p) methods in gas phase, are shown in Figure 2, and the energy parameter, including solvent (water) effects with IEFPCM model, are shown in Table 1. With exception of cyanin, the distribution pattern of HOMO and LUMO spreads over the whole molecule, as expected, in both, gas phase and water, which lead an efficient electronic delocalization [13]. In fact, the electronic density is shifted from the catechol moiety in ring B to the benzopyran system (ring A and C) (see Figure 1). Independently of the substituted groups, in gas phase, the energy values for the HOMO and LUMO orbitals are close to the average –10.46 eV and –5.65 eV, respectively, in agreement with others reports [29], which underestimate the value corresponding to the conduction band of the anatase (–4 eV). When the effects of solvent are account, these values are increased up to –7 eV < –4 eV < –2 eV range [30]. Therefore, the LUMO energy is sufficiently higher than the conduction band edge of TiO₂, and HOMO level is lower than the redox potential of I−/I3− electrolyte to regenerate the oxidized dye (–4,6 eV) [31, 32].

Figure 2:

HOMO–LUMO shape from the anthocyanin molecules at CAM-B3LYP/6-31+G(d,p) theory level in gas phase.

Table 1:

Computed HOMO, LUMO and energy gap (eV) in the gas phase and water at CAM-B3LYP/6-31+G(d,p) level.

	Gas phase			Water
Molecule	EHOMO	ELUMO	Egap	EHOMO	ELUMO	Egap
Cyanidin	–10.5803	–5.7686	4.8117	–5.6660	–2.6172	5.0489
Delphinidin	–10.4320	–5.6154	4.8166	–5.6405	–2.5796	5.0608
Peonidin	–10.3659	–5.6734	4.6925	–5.6008	–2.6107	4.9901
Cyanin	–10.4992	–5.5578	4.9414	–5.7030	–2.5908	5.1122
Average	–10.4693	–5.6538	4.8156	–5.6526	–2.5996	5.0530

The calculations of the wavelength of maximum absorption (λ_max) and others spectroscopic parameter in water are shown in Table 2 at TD(CAM-B3LYP)/6-31+G(d,p). Absorption spectra for anthocyanin molecules in gas phase and water are shown in Figure 3. The prediction of absorption spectra for structures studied lead two maximum wavelength in 200 nm–250 nm range, and 400 nm–450 nm range, as expected [30, 32, 33]. The λ_max values associated with the intramolecular charge transference (ICT), and HOMO → LUMO transition, is in the order cyanidin (446 nm) > peonidin (445 nm) > delphinidin (442 nm) > cyanin (438 nm). From delphinidin molecule, the lack of a hydroxyl group lead a two extra maximum wavelength, associated with the transitions HOMO-4 → LUMO (229 nm) and HOMO → LUMO+2 (205 nm). Similarly, the substitution of a glucoside group in cyanin structure, lead a two extra maximum wavelength, associated with the transitions HOMO → LUMO+1 (250 nm) and HOMO-1 → LUMO+1 (237 nm).

Figure 3:

Absorption spectra for anthocyanin molecules in gas phase and water at TD(CAM-B3LYP)/6-31+G(d,p) theory level.

Table 2:

Wavelength of maximal absorption (λ_max/nm), excitation energies (E_e/eV, in water, TD(CAM-B3LYP)/6-31+G(d) level), electronic transition configurations (Assignment), oscillator strengths (f) (f > 0.1) and LHE for anthocyanin dyes.

Molecule	λmax	Assignment	Ee	f	LHE
	446.2	HOMO → LUMO (0.68)	2.78	0.742	0.8187
Cyanidin	229.2	HOMO-4 → LUMO (0.56)	5.41	0.244
	205.6	HOMO → LUMO+2 (0.49)	6.03	0.283
	442.2	HOMO → LUMO (0.67)	2.80	0.744	0.8198
Delphinidin	228.4	HOMO-2 → LUMO+1 (0.37)	5.43	0.321
	206.2	HOMO → LUMO+3 (0.46)	6.01	0.322
	445.7	HOMO → LUMO (0.66)	2.78	0.767	0.8290
Peonidin	228.4	HOMO-2 → LUMO+1 (0.36)	5.43	0.309
	207.1	HOMO → LUMO+2 (0.36)	5.99	0.437
	438.7	HOMO → LUMO (0.68)	2.83	0.723	0.8107
Cyanin	250.8	HOMO → LUMO+1 (0.63)	4.94	0.264
	237.6	HOMO-1 → LUMO+1 (0.37)	5.22	0.264

According to the eqs 1 and 2), LHE is one of the key factors in DSSC. It represents the fraction of the incident photons that are absorbed by the dye. The LHE of the dye should be as high as feasible to maximize the photo-current response. As observed in Table 2, the calculated LHEs are all near unity. Methoxy group in peonidin molecule lead the largest oscillator strength and LHE. On the other hand, from delphinidin molecule, the lacks of a hydroxyl group lead a decreased in the LHE. Similarly, when a glucoside group is substituted in cyanin structure, a decreased in the LHE value is found.

3.4 Chemisorption on TiO₂-anatase

Tetragonal structure of anatase may be described using two cell edge parameters, a and c, and one internal parameter, d (the length of the Ti−O apical bond) [34]. In this paper, the (TiO₂)₃₀ configurations were optimized using the GGA. The results for the geometric parameters described before were a = 3.566 Å, c = 10.707 Å and d = 1.899 Å, which were comparable with experimental values (a = 3.782 Å, c = 9.502 Å, d = 1.979 Å) and others theoretical DFT methodology, where cluster approach methodology had been used [34, 35, 36].

In dye-TiO₂ adsorption, the adsorption of dyes through terminal –H atom can be either physisorption (via hydrogen bonding between an oxygen atom on TiO₂ surface and a hydrogen atom of the dye) or chemisorption (an H atom dissociates and the bond is formed between oxygen atoms and the surface titanium atoms of TiO₂). In this paper, we have chosen the second option. The adsorption complex was first fully optimized using the PBE functional together with the double-numerical with polarization performed in the DMol³ program. The optimized structures of anthocyanin–(TiO₂)₃₀ adsorption complexes are show in Figure 4 and the important optimized bond length and adsorption energy (E_ads) are listed in Table 4. The bond distances between Ti and O atom of dyes were calculated to be in the range of 1.89–1.97 Å. The adsorption energy (E_ads) of anthocyanin–(TiO₂)₃₀ complex was calculated to be from 17 to 24 eV, indicating the strong interactions between the dyes and the anatase (TiO₂) surface. Table 4 shows that a systematic change in the sunlight-to-electricity conversion efficiency (η) was observed as predicted from adsorption energies. Therefore, the higher adsorption energy resulted in the stronger electronic coupling strengths of the anthocyanin–(TiO₂)₃₀ complex, which corresponded to higher observed η as expected [37, 38].

Figure 4:

Optimized structures of anthocyanin–(TiO₂)₃₀ adsorption complexes at PBE/DNP theory level. Important optimized bond length are shown in Å.

Table 4:

Important optimized bond length Ti-O (Å), adsorption energy (E_ads/eV) and sunlight-to-electricity conversion efficiency, η(%) for anthocyanin–(TiO₂)₃₀ adsorption complexes.

Molecule	Ti-O	Eads	η (%)
Cyanidin	1.93	17.624	0.37
Delphinidin	1.97	18.749	0.56
Peonidin	1.89	17.889	0.62
Cyanin	1.95	24.107	0.66

In order to explore the possible intramolecular charge transference between anthocyanin dyes and anatase surface, HOMO and LUMO shape were examined by the DFT (PBE) calculations with DNP basis set. Numerical basis set was used because of its reasonable computational cost. Figure 5 shows the frontier molecular orbitals of anthocyanin–(TiO₂)₃₀ adsorption complex in vacuum. The HOMO and LUMO shape showed the electrons delocalized predominantly on the anthocyanin structure while the LUMO + 1 shape is localized into the (TiO₂)₃₀ surface. Therefore we expected an electronic injection from HOMO to LUMO + 1 in the anthocyanin–(TiO₂)₃₀ adsorption complex, after the light absorption.

Figure 5:

The HOMO (blue/green) and LUMO + 1 (blue/yellow) shapes of anthocyanin–(TiO₂)₃₀ adsorption complexes at PBE/DNP theory level.

Conclusions

We explored the electronic properties of anthocyanidin and anthocyanin pigments after and before adsorption onto TiO₂ (anatase) surface. The characterization of electronic properties for dyes in gas phase and water was carried out using CAM-B3LYP/6-31+G(d,p) methods. The absorption spectra, excited states and electronic injection parameters were obtained and analyzed at TD(CAM-B3LYP)/6-31+G(d,p). The adsorption energies onto anatase surface model were obtained and analyzed at DFT level using GGA(PBE) functional and numerical DNP basis set. For all isolated dyes, the distribution pattern of HOMO and LUMO spreads over the whole molecule, as expected, in both, gas phase and water, which lead an efficient electronic delocalization. The LUMO energy is sufficiently higher than the conduction band edge of TiO₂, and HOMO level is lower than the redox potential of I−/I3− electrolyte to regenerate the oxidized dye. The calculated LHEs are all near unity. Methoxy group in peonidin molecule lead the largest oscillator strength and LHE. The water presence lead a higher spontaneous electronic inject process, with ΔG_inject average of –1.14 eV. The negative ΔG_inject is an indication of spontaneous electron injection from the dye to TiO₂. For the anthocyanin molecules studied, the ΔG_inject order is peonidin < delphinidin < cyanin < cyanidin. The adsorption energy (E_ads) of anthocyanin–(TiO₂)₃₀ complex was calculated to be from 17 to 24 kcal/mol, indicating the strong interactions between the dyes and the anatase (TiO₂) surface. Therefore, the higher adsorption energy resulted in the stronger electronic coupling strengths of the anthocyanin–(TiO₂)₃₀ complex, which corresponded to higher observed η as expected. The HOMO and LUMO shape showed the electrons delocalized predominantly on the anthocyanin structure while the LUMO + 1 shape is localized into the (TiO₂)₃₀ surface. Therefore we expected an electronic injection from HOMO to LUMO + 1 in the anthocyanin–(TiO₂)₃₀ adsorption complex, after the light absorption.