The influence of a dye–TiO₂ interface on DSSC performance: a theoretical exploration with a ruthenium dye

Abstract

Density functional theory (DFT) and time-dependent DFT (TD-DFT) approaches were applied to explore the influence of a dye–TiO₂ interface on DSSC performance by taking a heteroleptic Ru(II) dye as an example. Our analysis was based on the interpretation of the dye–TiO₂ geometry, electronic structure, and light harvesting and utilization. The results indicate that an alkaline electrolyte is necessary if the solar cell was fabricated with an Ru dye coordinated to 2,5-bis(N-pyrazolyl)pyridine and bipyridine ligands. The higher average thermodynamic driving force of the a@(TiO₂)₅(OH) structure ensures a better electron injection ability. Proper modification of the acceptor ligand (4-carboxyl-pyridine fragment) not only expands the absorption coverage, but also improves the ability to capture more photons within effective absorption bands. Despite the absorption coverage being further expanded within the c@(TiO₂)₅(OH) geometry, the relatively weaker molar absorption coefficient reduces the light harvesting capability. The extra absorption bands in the lower energy region indicate more photons will be captured in the b@(TiO₂)₅(OH) structure, therefore leading to a higher short-circuit current density. Our results elucidate the effect of the dye–TiO₂ interface on DSSC performance and supply a promising way to estimate and screen possible candidates for DSSC application.

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1 Introduction

Due to growing demands for energy, accompanied by increasing environmental pollution and consumption of fossil fuels, the search for alternative pollution-free and renewable energy sources has become a subject of great interest. Dye-sensitized solar cells (DSSCs) have attracted attention globally because of their high photoelectric conversion efficiency, pollution-free mode of action, and bargain price since the breakthrough work reported by O'Regan and Grätzel in 1991.¹ In recent years, the status of DSSCs has gradually risen to replace that of traditional solar cells. They have become a promising alternative to conventional amorphous silicon and other inorganic semiconductor-based photovoltaic devices,^2–4 though their low current conversion slows down their further application. This is especially true when compared with other solid solar cells, such as the perovskite solar cell, which attains a conversion efficiency as high as 20%. From the point of view of the DSSC operating mechanism, the overall efficiency of DSSCs is controlled by the following: (a) the light harvested; (b) electron injection; (c) electron collection on the dye-semiconductor interface; and (d) dye regeneration.^3,5,6 Abundant efforts have been made to overcome the bottleneck of DSSC performance by covering one or more of the above aspects. Recently, experimental investigations and theoretical design of Ru(II) center sensitizers have made great progress either by extending the π-conjugation,⁷ evaluating the role of ancillary ligands,⁸ or exploring the connection style of the dye on the semiconductor.⁹ Philippopoulos et al.¹⁰ synthesized and evaluated a series of heteroleptic Ru(II) sensitizers and finally concluded that the photovoltaic performance depends remarkably on the number of COOH functional groups. Our previous contribution¹¹ indicated that it is not only the number of COOH groups, but also the substituent position on the electron donor or acceptor ligand that determines the amount of light harvested and the charge injection efficiency, thus affecting the overall efficiency of the DSSC. However, all of these conclusions are based on the electronic properties of a single dye molecule without considering other facts such as the dye-semiconductor interface, due to the computing capacity limit at that time.

Additionally, the study of different substitution sites for the auxiliary anchoring group is rarely mentioned. Considering the direct connection of the anchor group with the semiconductor, it is a crucial element of the dye–TiO₂ interface to determine whether the DSSCs are high-efficiency or not. Generally speaking, the interface between the dye and semiconductor plays a vital role in reaching a higher photoelectric conversion efficiency. This is because the interface determines the position where the electron injection happens and where the charge transfer starts. There have been plenty of studies devoted to investigating the interaction between dyes and TiO₂ surfaces and the charge transfer mechanism acting between them.^12–28 In our current contribution, we push the previous study further by considering the dye–semiconductor interface to explore how the dye–TiO₂ interface structure affects the efficiency of DSSCs.

2 Computational details

2.1 DFT and TD-DFT calculations

In this work, all the calculations were performed using the Gaussian 09 program package.²⁹ All ground state geometries of the dye and dye@TiO₂ were fully optimized with density functional theory (DFT) at the B3LYP³⁰/LanL2DZ; 6-31G(d) level of theory, which has been successfully applied for the theoretical investigation of ruthenium dyes.^11,31,32 Then at the same level of theory the harmonic vibrational frequencies were computed in order to check the nature of the stationary points, namely to check if all the frequencies were real. The electronic properties of the dye and dye@TiO₂ in their excited states were explored by a time-dependent density functional theory (TD-DFT) approach. In order to select a proper functional to estimate the excitation energy, we have compared the results of the excited state based on the B3LYP, CAM-B3LYP,³³ and LC-BLYP³⁴ with LanL2DZ and 6-31G(d) hybrid basis sets. All the information for the discussion is collected in the ESI.† Solvent effects were considered by using the Polarizable Continuum Model (PCM) of SCRF procedure for dimethylsulfoxide (DMSO).

2.2 The efficiency of DSSCs

At any given wavelength λ, the incident photon to current efficiency (η_IPCE(λ)) is a function of the light harvesting efficiency (η_LHE(λ)), and the efficiency of charge injection (φ_inject) from the electronic excited state to the conduction band of TiO₂, combined with the charge collection efficiency (η_c). (If the dye is different in the main body, but similar in the dye–TiO₂ interface, the η_c can be considered to be the same.) Thus the η_IPEC(λ) can be expressed as:

η_IPCE(λ) = φ_injectη_LHE(λ)η_c (1)

Here, φ_inject depends on the thermodynamic driving force (D) of electrons injecting from the excited states of the dye to the semiconductor substrate.

φ_inject ∝ D (2)

Obviously, accompanied by an increase of D, the efficiency of the charge injection would be higher, assuming the injection takes place at or near the Franck–Condon region. D can be expressed as:³⁵

D = E* − E_cb = E⁰ + ΔE − E_cb (3)

where, E* is the redox potential in the excited state; E⁰ is the redox potential in the ground state, which can be calculated in accordance with the Nernst equation;¹¹ ΔE is the vertical excitation energy which can be obtained from TD-DFT calculations; and E_cb is the conduction band edge of TiO₂.

The light harvesting efficiency at the given wavelength λ can be calculated as:^36,37

η_LHE(λ) = 1 − 10^−Γσ(λ) (4)

where, Γ is the surface loading of sensitizers (mol cm⁻²) grafted onto the semiconductor. In the current work, Γ is set to 1.6 × 10⁻⁷ mol cm⁻² according to a previous publication on Ru-based dyes.¹⁰ σ(λ) is the molecular absorption cross-section (cm² mol⁻¹). It is a function related to the molar absorption coefficient (ε(λ)) and can be expressed as follows:^36,38

σ(λ) = 1000ε(λ) (5)

3 Results and discussion

3.1 Geometry of the dye–TiO₂ interface

As illustrated in Fig. 1, for clarity, we label the three Ru(II) complexes [Ru(bpp-1)(bpy)Cl]⁺, [Ru(bpp-2)(bpy)Cl]⁺, and [Ru(bpp-3)(bpy)Cl]⁺ (bpp = 2,6-bis(N-pyrazolyl)pyridine, bpp-1 = 1,1′-(4-carboxypyridine-2,6-diyl)bis(1-H-pyrazole-5-carboxylic acid), bpp-2 = 1,1′-(4-carboxypyridine-2,6-diyl)bis(1-H-pyrazole-3-carboxylic acid), bpp-3 = 1,1′-(4-carboxypyridine-2,6-diyl)bis(1-H-pyrazole-4-carboxylic acid), bpy = 2,2′-bipyridine) as a, b, and c, respectively. Accordingly, we label the corresponding dye-semiconductor structures as a@(TiO₂)₅, b@(TiO₂)₅, and c@(TiO₂)₅, referring to Fig. 2.

Fig. 1 Schematic representation of dyes a, b, and c.

Fig. 2 Optimized dye@(TiO₂)₅ structures calculated at the B3LYP/LanL2DZ; 6-31G(d) level.

The TiO₂ surfaces are generated from the optimized bulk geometry exposing the most thermodynamically stable surface: (101) in the case of anatase. In general, nanoparticle surfaces apply the anatase (101) surface to simulate the semiconductor, because this surface has a smaller surface energy and a high efficiency for DSSCs.^39,40 In the current work, anatase Ti₅O₂OH₂₂ (101) models from crystal structures are adopted as the surface of the TiO₂ film. In this model, the covalent bonds of the O atoms are saturated by extra H atoms, giving the Ti₅O₂OH₂₂ semiconductor model. This method not only maintains bond-orientation in the crystal but also avoids the confusion of multiplicity and charge in the whole system. Additionally, these Ti atoms can be divided into two types: one is five-coordinate and the other is six-coordinate. The five-coordinate Ti atoms are located at the anatase (101) surface, which is used as the adsorption site. Meanwhile the six-coordinate Ti atoms make up the bulk of the TiO₂ crystal. The calculated bond lengths d_l/d₂ between the two carboxylate oxygens and connected titanium atoms on the TiO₂ films of the a@(TiO₂)₅, b@(TiO₂)₅, and c@(TiO₂)₅ systems are: 2.137/2.298 Å, 2.193/2.247 Å, and 2.192/2.255 Å, respectively. These are comparable with the Ti–O bond lengths in the dye–TiO₂ interfaces calculated for larger cluster models, such as 2.12/2.10 Å for the (TiO₂)₂₅₆ model,⁴¹ 2.08/2.08 Å for the (TiO₂)₃₆ model,⁴² and 2.216/2.166 Å, 2.121/2.172 Å for the (TiO₂)₂₈ model.⁴³ This indicates that such small scale models could be sufficient to simulate the real physical properties of TiO₂, and this strategy has been successfully applied in a previous study.^32,44–46 Additionally, the angles of θ₁ and θ₂ as shown in Fig. 2 are 129.7°/131.4°, 134.2°/134.6°, and 134.3/134.5° in a@(TiO₂)₅, b@(TiO₂)₅, and c@(TiO₂)₅, respectively. From the point of view of bond lengths and angles, it can be concluded that the three dye–TiO₂ interfaces are similar in geometry though the auxiliary anchoring groups are attached to different sites. Meanwhile, the dye–TiO₂ interface is where the excited charge will be captured or collected by the semiconductor. Therefore, the similar dye–TiO₂ interface geometry would lead to essentially the same charge collection efficiency (η_c) among a, b, and c.

Meanwhile in a real DSSC system, the dye–TiO₂ interface may not only be affected by the electrolyte, but may also be affected by temperature and other environmental factors. As a result, the hydrogen atoms of the anchoring group of the dye molecule may be dissociated. We have calculated all possible dye–TiO₂ structures which may arise from dehydrogenation processes. The calculations indicate that there are no significant changes in the bond length and angle on the dye–TiO₂ interface. From this point of view, we may speculate that, whether dehydrogenated or not, this has little effect on the geometry of the dye–TiO₂ interface.

3.2 Electronic structure properties

The appropriate energy level layout of the dye is one of the prerequisites for a fast charge transfer. For DSSC systems, the lowest unoccupied molecular orbital (LUMO) should be higher in energy than the lower edge of the conduction band of TiO₂ (E_LUMO > −4.0 eV), which should guarantee efficient electron injection from the excited dye into the semiconductor substrate. Meanwhile the highest occupied molecular orbital (HOMO) should lie between the upper edge of the valence band of TiO₂, and the redox potential of I⁻/I₃⁻ (in the current case, −4.60 eV > E_HOMO > −7.20 eV), which should guarantee efficient dye regeneration and that the excited dyes get an electron from the electrolyte rapidly. The calculated HOMO and LUMO energy values are tabulated in Table 1. The results indicate that the dye itself fully matches the above-mentioned energy level requirements, namely, there are possibilities that dyes a, b, and c could act as sensitizers in DSSCs.

Table 1 The HOMO and LUMO energy levels (in eV) for all dyes and dye–TiO₂ interfaces.

Dye	a	a@(TiO2)5(2H)	a@(TiO2)5(1H)	a@(TiO2)5(OH)
ELUMO	−3.10	−4.06	−3.79	−3.48
EHOMO	−6.08	−6.33	−5.88	−5.44

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Dye	b	b@(TiO2)5(2H)	b@(TiO2)5(1H)	b@(TiO2)5(OH)
ELUMO	−3.11	−4.08	−3.87	−3.69
EHOMO	−6.04	−6.25	−5.68	−5.21

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Dye	c	c@(TiO2)5(2H)	c@(TiO2)5(1H)	c@(TiO2)5(OH)
ELUMO	−3.06	−4.04	−3.91	−3.77
EHOMO	−6.06	−6.26	−5.71	−5.49

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The dye itself alone does not constitute a real DSSC. The sensitizer should be attached to TiO₂ and soaked in the electrolyte at least. The energy levels of all possible dye–TiO₂ structures are listed in Table 1. The calculations reveal that the HOMO and LUMO energy levels are pushed down to an even lower position by attaching the TiO₂ fragment, meaning that dyes a, b, and c might not be capable of DSSC application from the point of view of their energy levels. However, if the electrolyte can be tuned into an alkaline environment, the energy value of the LUMO would be higher than −4.0 eV, as shown in the last two rows in Table 1, which means that the alkaline electrolyte solution is necessary when building DSSCs with the dyes a, b, or c, otherwise the cell may not work. Therefore, in the following sections, we only talk about the dye–TiO₂ structures in the forms of a@(TiO₂)₅(OH), b@(TiO₂)₅(OH), c@(TiO₂)₅(OH), that is to say, all the hydrogens of the carboxyl groups are dissociated.

As is known to us, the open-circuit photovoltage (V_oc) is also a crucial parameter to evaluate the efficiency of a DSSC device. Proper charge population improves the V_oc. The correlation of charge population and experimental V_oc indicates that when more charges are populated in acceptor groups it results in a larger V_oc.⁴⁷ The molecular orbital composition reveals that more than 90% of the charge would populate the bpp ligands in a, b, and c. In particular, as the substituent positions of the –COOH group change on pyrazole fragments in a, b, and c, more and more charges (from 60% in a, to 68% in b, and 79% in c, see Table 2 and Fig. 3) populate the 4-carboxyl-pyridine fragment (abbreviated as, cpy), which acts as a charge acceptor fragment and a tunnel to transfer charge from the dye to the conduction band of the semiconductor. Therefore, it can be predicted that the V_oc could be further improved if the cell is fabricated with dye c.

Table 2 The composition of the HOMO and LUMO for all of the isolated dyes

Dye	Orbital	Composition
		Ru	Cl	bpy	cpyra^a	cpy^b
a Refers to 1-H-pyrazole-3-carboxylic acid or something similar.b Refers to 4-carboxyl-pyridine.
a	LUMO	0.08	0	0	0.31	0.60
	HOMO	0.64	0.16	0.13	0.07	0
b	LUMO	0.08	0	0	0.22	0.68
	HOMO	0.66	0.16	0.12	0.06	0
c	LUMO	0.08	0	0	0.12	0.79
	HOMO	0.66	0.17	0.12	0.06	0

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Fig. 3 The HOMO and LUMO diagrams of dyes a, b, and c at the PCM-B3LYP/Lanl2DZ; 6-31G(d) level of theory.

Moreover, in order to better understand the nature of the charge transfer process, we present several important orbitals in Fig. 4. As shown in Fig. 4, in the current case, the HOMO is primarily populated on the dyes, whereas the LUMO is delocalized onto the TiO₂. This kind of electronic structure is consistent with dye@TiO₂ electronic character in DSSC application. In other words, the electronic properties of a dye@TiO₂ system can also be described by the smaller (TiO₂)₅ cluster model.

Fig. 4 The HOMO and LUMO diagrams of dye@(TiO₂)₅ at the PCM-B3LYP/Lanl2DZ; 6-31G(d) level of theory.

3.3 Light harvesting and utilization

The DSSCs that are currently used to turn sunlight into electricity can only absorb and use a small fraction of that light, which means that an abundant amount of solar energy goes unused. Harvesting more energy from sunlight requires a broad band absorption which can cover as much as possible of the solar spectral irradiance in the visible and near infrared region. In this work, the fitted Gaussian type absorption curves of the dye–TiO₂ interfaces are illustrated in Fig. 5 and the corresponding character vertical excitations calculated from TD-DFT are listed in Table 4. The half-width at half height is set to 0.1 eV in gaussview, so that the character molar extinction values can be compared with the experimental values. At first glance, the molar absorption coefficients decrease but the absorption bands are widened in b and c as compared with that of a. But one cannot take it for granted that all the absorption bands in the lower energy region really contribute to the photon to electricity transfer process. According to the operation mechanism of DSSCs, to guarantee a beneficial charge transfer process, on the one hand, the value of the redox potential of the dye in the excited state, E*, should be higher in value than the conduction band of the semiconductor; on the other hand, the energetics of the excited states should be high enough to provide a thermodynamic driving force (D) to accomplish the charge injection (namely, a larger D is better). If the vertical excitations which contribute to the absorption band satisfy the above-mentioned requirements, then the exact absorption band is the so-called valid absorption band. And only the valid absorption band has the ability to contribute the final photon to the electricity conversion efficiency.

Fig. 5 The absorption spectrum at the B3LYP/LanL2DZ; 6-31G(d) level in DMSO solvent.

The redox potentials of a, b, and c in the ground state are calculated to be −5.08 V, −4.85 V, and −5.36 V, which are 1.08 V, 0.85 V, and 1.37 V below the conduction band of TiO₂, respectively, as shown in Table 3. Therefore, the vertical excitation energy should not be less than 1.08 eV in a, otherwise the final excited state would not have enough energy to transfer the electron to the conduction band of TiO₂. As reported in Table 4, the main excitation energies are greater than 1.08 eV, therefore all absorption bands of a are valid. Similarly, the absorption bands of b and c in the current case are all effective. From this point of view, it can be deemed that the electronic structure of the dye–TiO₂ interface will be changed significantly by proper modification of the acceptor segment. In addition, according to eqn (2), the average driving force of a, b, and c goes in the order of a (1.82) > b (1.49) > c (1.11), indicating that a would be optimal in the performance of the charge injection.

Table 3 Calculated redox potential (E⁰, in V) and Gibbs free energy (ΔG_sol, in au)

Dye@(TiO2)5	a@(TiO2)5(OH)	b@(TiO2)5(OH)	c@(TiO2)5(OH)
ΔGsol	0.187	0.178	0.197
E^0	−5.083	−4.852	−5.365

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Table 4 Selected calculated excitation energies (ΔE, eV), wavelengths (λ, nm), oscillator strengths (f), and driving forces (D, eV) for all of the dye@(TiO₂)₅ complexes

Dye@(TiO2)5	Excitation^a (|CI coeff.|)	ΔE	D	λ	f
a H represents HOMO, L represents LUMO.
a@(TiO2)5(OH)	H → L+9(0.63)	2.35	1.27	527	0.1056
	H−1 → L+6(0.71)	2.52	1.44	492	0.0691
	H−1 → L+16(0.45)	3.32	2.24	374	0.0375
	H → L+18(0.77)	3.41	2.33	364	0.0146
b@(TiO2)5(OH)	H−1 → L+1(0.94)	1.59	0.74	779	0.0484
	H−3 → L+1(0.74)	1.86	1.01	666	0.0209
	H−1 → L+6(0.88)	2.24	1.39	553	0.0903
	H−3 → L+6(0.88)	2.50	1.65	496	0.0740
	H → L+16(0.63)	2.84	1.99	437	0.0674
	H−13 → L+1(0.89)	3.06	2.21	406	0.0371
c@(TiO2)5(OH)	H−5 → L+1(0.95)	1.89	0.53	656	0.0127
	H−5 → L+5(0.85)	2.25	0.89	552	0.0196
	H−5 → L+6(0.78)	2.33	0.97	533	0.1852
	H−3 → L+14(0.35)	2.92	1.56	425	0.0365
	H → L+17(0.44)	2.98	1.62	416	0.0256

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However, the weak molar absorption coefficient of c may limit light harvesting and utilization. There is another factor we should take into account, the η_LHE(λ). We have shown the η_LHE(λ) profile of each dye in Fig. 6, and it is obvious that b@(TiO₂)₅(OH) covers a wider range and a higher η_LHE(λ) at 600–900 nm than the others. But only taking into account η_LHE(λ) does not make any sense, because the photon number varies with the change in wavelength.

Fig. 6 The plot of the η_LHE(λ) curves for all structures.

The DSSC is used to convert an excited photon into an electric current. If more photons were captured, there would be more electrons to be excited, thereby resulting in more charges being injected into the conduction band of TiO₂, and finally improving the short-circuit current density (J_sc) of the solar cell. J_sc is related to the integral photon flux density (Φ(λ)) over the whole absorption coverage. The Φ(λ) is defined as the number of photons per second per unit area and per unit wavelength, and it can be evaluated using the following equation at a given wavelength (λ),

thus, the total photon number per second per unit area within the whole spectrum coverage can be calculated using the following equation:where, P(λ) is the spectral power density in W m⁻² m⁻¹; and E is the energy of the photon at the wavelength of light (λ).

E can be expressed as:

where, h is Planck's constant, 6.626 × 10⁻³⁴ J s; and c is the speed of light, 3.0 × 10⁸ m s⁻¹.

Additionally, the maximal photon generated current (J_ph) can be expressed as:

where, q is the elementary charge, 1.6 × 10⁻¹⁹ C.

Here, the flow of electric charge across a surface per second per unit area over the whole spectrum is equivalent to the maximum short-circuit density (J^max_sc) the cell can produce.

On the one hand, the experimentally determined sun irradiance is too complicated to be expressed within a simple formula; on the other hand, the spectral irradiance of the sun is well approximated by the emission of a blackbody with a temperature of about 5778 K.⁴⁸ Hence, the power density at the given wavelength can be rewritten as:

where, R is the radius of the sun, 0.695 × 10⁹ m; D is the distance from the sun to the earth, 1.496 × 10¹¹ m; κ is the Boltzmann's constant, 1.3806488 × 10⁻²³ J K⁻¹; and T is the temperature of the blackbody. Here, T = 5778 K.

In fact, the radiation absorbed by dyes is not absolutely complete, and with the consideration of the practical conditions, we introduce η_LHE(λ) for obtaining the actual absorption. From eqn (6) and (10), the exact part of the photon flux density (Φ(λ)) generated by the dyes per second per unit area at the given wavelength (λ) can be rewritten as (λ in m):

Finally, the J_ph for a@(TiO₂)(OH), b@(TiO₂)(OH), and c@(TiO₂)(OH) can be obtained according to eqn (9). The J_ph which can be generated by a@(TiO₂)(OH), b@(TiO₂)(OH), and c@(TiO₂)(OH) within the absorption coverage between 300–900 nm is calculated to be 15.1 mA cm⁻², 31.2 mA cm⁻², and 16.0 mA cm⁻², respectively. As mentioned above, the flow of electric charge across a surface per second per unit area over the whole spectrum is equivalent to the short-circuit density (J^max_sc), therefore, it can be inferred that the b@(TiO₂)(OH) structure can generate the largest J^max_sc. That is to say, the J^max_sc of the solar cell will be further improved if the cell is fabricated with b as compared to the other two structures.

4 Conclusion

DFT and TD-DFT approaches were applied to explore the influence of the interface between the dye and the semiconductor on DSSC performance. In this work, dye–TiO₂ structures with the (TiO₂)₅ cluster model were investigated theoretically. Though the dye–TiO₂ structure remains as it was when H⁺ dissociates from the –COOH anchoring group due to the change of pH in the electrolyte environment, the LUMO of the dye–TiO₂ structure was pushed to a higher energy level, which is advantageous for a rapid charge transfer process. More charge would populate the charge acceptor ligand (4-carboxyl-pyridine fragment) if the auxiliary anchoring group on the pyrazole fragment is located far away from the Ru(II) core. A higher average thermodynamic driving force indicates that the a@(TiO₂)₅(OH) structure is more conductive to electron injection. Though the absorption coverage is further expanded within the c@(TiO₂)₅(OH) geometry, the relatively weaker molar absorption coefficient hinders the improvement of light utilization. With the help of solar radiation's power density, our calculation reveals that a larger J^max_sc is obtained within the absorption coverage between 300–900 nm in the b@(TiO₂)₅(OH) structure, namely a higher short-circuit current density could be expected if the solar cell is fabricated with dye b in an alkaline electrolyte. In a nutshell, we hope that this theoretical investigation will be helpful for improving and designing new sensitizers in DSSCs, so as to satisfy the growing demands of the DSSC field.

Acknowledgements

This work was supported by the State Key Development Program for Basic Research of China (Grant No. 2013CB834801), the Natural Science Foundation of China (Grant No. 21573088 and 21203071), and the China Post-Doctoral Science Foundation (Grant No. 2015T80297).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra16173a

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