Rational modifications on ruthenium terpyridine sensitizers with large J_sc for dye-sensitized solar cells: combined DFT and relativistic TDDFT studies

Abstract

In this work, we designed a series of ruthenium sensitizers DX2–DX5 derived from a phosphine-coordinated ruthenium sensitizer DX1 with a surprisingly high short-circuit photocurrent density (J_sc) of 26.8 mA cm⁻² for dye sensitized solar cells (DSSCs), with the aim of enhancing the light harvesting ability in the near-infrared (NIR) region and further increasing the J_sc. Density functional theory (DFT) and relativistic time-dependent DFT calculations have been performed to evaluate the optical and photovoltaic properties of these Ru dyes, taking the effect of spin–orbit coupling (SOC) into consideration. The intrinsic causes for varied J_sc and open-circuit photovoltage (V_oc) have been systematically discussed through investigating the light harvesting efficiency, electron injection driving force, dye regeneration driving force, electronic coupling and conduction band energy shift. The calculated results reveal that the designed DX5 has increased light harvesting efficiency in the NIR region and a higher conduction band energy shift compared with other sensitizers. That is, DX5 may have improved J_sc and V_oc, which makes DX5 serve as a promising sensitizer for future DSSC applications.

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1. Introduction

Dye-sensitized solar cells (DSSCs) represent a promising alternative to the conventional silicon solar cells because of their low cost, easy production, flexible fabrication and high conversion efficiencies.^1–7 Unlike silicon solar cells, DSSC are mainly composed of different components such as mesoporous semiconductors, sensitizers, electrolytes, and it needs optimization of each component and interaction among different materials to improve the overall efficiency. As known to all, the dye sensitizer plays an important part in designing DSSCs with higher efficiency, and researchers have devoted many efforts to developing new and efficient sensitizers. Among various organic/inorganic dyes, Ru(II)-polypyridyl complexes, such as N3,⁸ N719 (ref. 9) and N749,¹⁰ have been proved as the most successful charge transfer sensitizers, achieving higher conversion efficiency of 9–11%. Up to now, Ru(II)-polypyridyl complexes have shown many advantages as efficient sensitizers, such as a wider absorption spectrum, long excited-state lifetime, suitable HOMO and LUMO energy levels and good molecular stability. However, there is a major disadvantage in Ru(II) sensitizers, the lower light harvesting ability in near-infrared region (NIR) compared with those of organic dyes. Hence, how to harvest NIR photons more efficiently has still been a challenge for researchers to increase efficiency of Ru(II) sensitizers.

Recently, Kinoshita et al. have reported a tandem-type DSSC using a newly synthesized sensitizer—trans-dichloro-(phenyldimethoxyphosphine) (2,2′;6′,2′′-terpyridyl-4,4′,4′′-tricarboxylic acid)ruthenium(II) (coded as DX1), which yielded a high short-circuit photocurrent density (J_sc) of 26.8 mA cm⁻².¹¹ The increased J_sc is ascribed to exploiting near-infrared spin-forbidden singlet-to-triplet transitions in Ru(II) dye, which induces the enhanced absorption intensity in the NIR. The explanation is very surprising compared with general understanding. Meanwhile, Fantacci et al. have comparatively investigated the impact of Spin–Orbit Coupling (SOC) on the optical and photovoltaic properties of Ru(II) sensitizers by employing scalar relativistic (SR)- and SOC-based time-dependent density functional theory (TDDFT).¹² Their study indicates that the SOC-induced spectral broadening slightly enhances the light-harvesting efficiency by inducing a redistribution of the singlet–singlet transitions intensity. After that, Fantacci and his co-workers presented the same methodology to compute the effect of relativity on the absorption spectra of Ru(II) and Os(II) polypyridyl complexes,¹³ and they found that the employed computational approach could be useful in designing new and efficient sensitizers, which have enhanced absorption in the red region of the solar spectrum.

In this article, we designed four derivatives (presented in Chart 1) based on the original sensitizer, DX1, with a goal of enhancing the light harvesting ability in NIR region and further increasing the J_sc of solar cells. In DX2 and DX3, the Cl ligands are substituted by one or two Br ligands to increase the heavy atom effect and accordingly enhance spin–orbit effect; while for DX4 and DX5, one or two C atoms in terpyridyl ligand are replaced by N atoms at different positions and the other parts in DX1 are kept to enhance the MLCT molar extinction coefficient (ε) in NIR. Herein, we have investigated the photoelectronic properties and cell performance of Ru(II) complexes taking SOC into consideration to provide more accurate results and screen suitable Ru(II) sensitizers. In particular, our attention has been focused on the optical properties of the dyes including electronic structure and absorption spectra, in order to figure out the change in light harvesting ability in NIR region which have important effect on J_sc. We also analyzed other factors affecting performance of DSSCs such as driving force, conduction band energy shift and so on.

Chart 1 Molecular structures of DX1–DX5.

2. Theoretical methodology

In this work, the ground-state geometries of all three dyes were optimized in gas phase using hybrid GGA functional PBE0 (ref. 14) with 6-31G^* basis set for H, C, N, O, S, P, Cl, Br atoms and Stuttgart-Dresden 11-electron effective core potential (ECP) designated as SDD^15–18 for Ru atom. To be in accord with experimental results, we simulated the fully protonated DX1_3H in this work and the other four dyes were in the same protonation state. All the fully optimized structures of the Ru(II)-polypyridyl dyes investigated are displayed in Fig. S1† and the calculations mentioned above were performed in the Gaussian 09 program package.¹⁹ Based on the optimized structures, we then performed TDDFT calculations to obtain spectroscopic properties in N,N-dimethylformamide (DMF) solvent using the B3LYP exchange–correlation functional within the Amsterdam density functional program package (ADF 2013).^{12,13,20–23} E_dye was also calculated at B3LYP levels in N,N-dimethylformamide (DMF) through single point energy calculation in ADF program package, in order to obtain the electron injection driving force.²⁴ The ZORA/TZP basis set for all the atoms was employed.²⁵ The relativistic effects were taken into consideration through the ZORA Hamiltonian in scalar approximation as implemented in the ADF code.²⁶ We also calculated excitation energies with the SOC effects as a perturbation to scalar relativistic calculation. The “Conductor-like Screening Model” (COSMO) was employed to simulate the solvent effects of DMF in TDDFT relativistic calculations.²⁷

For discussing the dye–TiO₂ interactions, (TiO₂)₃₈ cluster obtained by appropriately “cutting” an anatase slab exposing the majority (101) surface was considered to model the TiO₂ nanoparticle effects, since the (TiO₂)₃₈ cluster stands for a good compromise between accuracy and computational cost and its lowest excitation energy is in good agreement with the experimental bandgap.^28–32 SIESTA package was used to optimize dye/(TiO₂)₃₈ systems in gas phase.^33–35 We adopted the deprotonated form d2/(TiO₂)₃₈ (which is shown in Chapter 3.1.2) as the stable model in our following calculation, referring to the results of Shih-Hung Liu and co-workers³⁶ (d2 means deprotonated adsorptions with two carboxylic group anchors). In other words, the dye molecule is anchored on the TiO₂ surface through two carboxylic groups in terpyridyl ligand and one of carboxylic group is deprotonated (one H atom in dye molecule is transferred to TiO₂ surface). In order to evaluate the extent of the total shift of the TiO₂ conduction band, the electron densities and partial density of states (PDOS) were also calculated by performing single-point B3LYP calculations in DMF solution with the C-PCM solvation model on the optimized dye–TiO₂ model.³⁷ The basis set for metal atoms is SDD and for non-metal atoms is 6-31G^* within the Gaussian 09 package.

3. Results and discussions

In DSSCs, the overall conversion efficiency (η) of the device is directly related to the short-circuit photocurrent density (J_sc), the open-circuit potential (V_oc), the fill factor (FF) and the intensity of the incident light (I_s) which is defined as below:

η = J_scV_ocFF/I_s (1)

Therefore, J_sc and V_oc are the two key factors determining η, which are the main objects to be thoroughly discussed in this work. We will investigate whether the modulation on molecular structure of the Ru(II) sensitizers can enhance the light harvesting ability in NIR region firstly, then we will estimate the change of electron injection efficiency (Φ_inject) and conduction band energy shift among five sensitizers, and finally screen out desired sensitizers with better performance from the theoretical point of view.

3.1 Evaluating J_sc

As we know, J_sc is defined as:

J_sc = e∫_λLHE(λ)Φ_injectη_collectη_regI_s(λ)dλ (2)

where LHE(λ) represents the light harvesting efficiency, which is related to the oscillator strength (f) at a specified wavelength, determined as:^38,39

LHE(λ) = 1 − 10^−ε(λ)bc (3)

ε(λ) is the molar absorption coefficient at certain wavelength and b, c denote the thickness of film and the concentration of dye, respectively. To facilitate discussing LHE(λ), b and c are taken as 10 μm and 500 mmol L⁻¹, respectively, which are typical values for Ru dyes.^12,40 Φ_inject is related to the driving force (ΔG_inj) of the electron injection from the excited states of dyes to the TiO₂ surface and electronic coupling between the LUMO of dyes and the TiO₂ conduction band. η_collect is the charge collection efficiency which is assumed as a constant in the same DSSCs device only except for different dyes. The regeneration efficiency of the oxidized dye, η_reg, is in connection with the regeneration driving force, ΔG_reg.

In general, ΔG_inj can be expressed as:⁴¹

ΔG_inj = E^dye* − E_C (4)

where E_C denotes the conduction band energy level of semiconductor and the experimental value is −4.00 eV (vs. vacuum).⁴² E^dye* is the excited state oxidation potential of the sensitizer and determined by E^dye* = E^dye + λ_max (E^dye: oxidation potential of the dye in ground state; λ_max: the vertical transition energy) when the electron injects from the photoinduced excited states of the dyes to the semiconductor before the vibrational relaxation.^41,43–45 ΔG_reg is defined as:

ΔG_reg = E_redox − E_dye (5)

E_redox is the redox potential of I⁻/I₃⁻ (−4.58 eV).⁴⁶

3.1.1 Light harvesting efficiency (LHE). Since we designed four dyes with the purpose of enhancing absorption in NIR region of the spectrum, we started this Section by investigating the light harvesting ability of the dyes and then evaluated the change of J_sc.

We make a comparison between computed and experimental absorption spectra for DX1 in Fig. S2† to prove the reliability of theoretical method. We can find that the overall trends of the both spectra are same although the simulated spectrum has a slight blue shift compared with the experimental one. The deviation of calculated spectrum (776 nm) from experimental value (792 nm) at the first electronic absorption peak is considered acceptable. In Fig. 1, the simulated spectra by SOC-TDDFT method of DX1–DX5 in DMF are reported to provide further insight into LHE. The main SOC-calculated transitions and their nature in terms of the constituting SR transitions are listed in Table 1. Herein, our attention is mainly focused on the region of λ > 600 nm because the visible and near infrared light could be utilized as solar power more effectively and our purpose of design is to enhance LHE in NIR region. Combined Fig. 1 with Table 1, it could be seen that DX2–DX5 all show similar electron transition characters compared with DX1 in absorption spectrum. Taking DX1 for example, the SOC-TDDFT eigenvectors suggest that the absorption band within the investigated range originates from two sets of transitions. Each transition is decomposed into the SR calculated singlet–singlet (S_n) and singlet–triplet (T_n) excitations (see Table 1). The S₁ (1.649 eV, f = 0.043) state is mixed with T₂ (1.653 eV, f = 0.000) state which generate two major SOC transitions, ST₄ (1.597 eV, f = 0.043) and ST₇ (1.705 eV, f = 0.039). The two SOC transitions are assigned to a MLCT from HOMO to LUMO and HOMO−1 to LUMO.

Fig. 1 Calculated absorption spectra in DMF for the full protonated DX1–DX5 by SOC-TDDFT method.

Table 1 Main SOC-calculated transitions along with the transition energies (eV nm⁻¹) and transition nature in terms of the constituting SR transitions for DX1–DX5 in DMF

SOC transitions	SR contribution		SR composition
DX1
ST4 1.597/776	52% S1	1.649/752(f = 0.043)	H → L
(f = 0.043)	48% T2	1.653/750(f = 0.000)	H−1 → L
ST7 1.705/727	48% S1	1.649/752(f = 0.039)	H → L
(f = 0.039)	52% T2	1.653/750(f = 0.000)	H−1 → L
DX2
ST4 1.583/783	48% S1	1.661/747(f = 0.038)	H → L
(f = 0.038)	51% T2	1.657/748(f = 0.000)	H−1 → L
ST7 1.728/718	51% S1	1.661/747(f = 0.041)	H → L
(f = 0.041)	48% T2	1.657/748(f = 0.000)	H−1 → L
DX3
ST4 1.576/787	48% S1	1.660/747(f = 0.036)	H → L
(f = 0.036)	51% T2	1.656/749(f = 0.000)	H−1 → L
ST7 1.740/713	51% S1	1.660/747(f = 0.039)	H → L
(f = 0.039)	48% T2	1.656/749(f = 0.000)	H−1 → L
DX4
ST4 1.466/846	38% S1	1.532/809(f = 0.027)	H → L
(f = 0.027)	60% T2	1.513/820(f = 0.000)	H−1 → L
ST7 1.573/788	60% S1	1.532/809(f = 0.039)	H → L
(f = 0.042)	39% T2	1.513/820(f = 0.000)	H−1 → L
DX5
ST4 1.438/862	36% S1	1.504/824(f = 0.022)	H → L
(f = 0.022)	61% T2	1.483/836(f = 0.000)	H−1 → L
ST7 1.543/804	62% S1	1.504/824(f = 0.037)	H → L
(f = 0.037)	37% T2	1.483/836(f = 0.000)	H−1 → L

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Table 1 shows that the wavelength of maximum absorption, in λ > 600 nm, is red-shifted from 776 nm (1.597 eV) for DX1 to 862 nm (1.438 eV) for DX5 and the red-shifted spectrum matched with solar spectrum better, which may achieve higher light harvesting efficiencies. Although the absorption intensity decreased within the low-energy region from DX1 (f = 0.043) to DX5 (f = 0.022), there is another relatively strong absorption peak for DX5 at about 804 nm which can make up for the loss in absorption intensity. Besides, it is clearly shown in calculated spectra that, in lower-energy region (500–600 nm), the newly designed sensitizer DX5 shows stronger absorption intensity than DX1, which is helpful to increasing the LHE of DX5. In order to obtain an intuitive comparison in light absorption ability among all dyes, we simulated the LHE curves of DX1–DX5 in Fig. 2 on the basis of eqn (3). According to theoretical background, in order to get a higher J_sc, the dyes used in DSSCs should have a larger LHE, and a larger ε(λ) could lead to a larger LHE. From Fig. 2, the onsets of the LHE curves are above 1000 nm. It is obvious that the LHE curve of DX4–DX5 is red-shift about 100 nm compared with those of DX1–DX3, which indicates that DX4–DX5, especially for DX5, with broadened LHE curve, may exhibit the overall improvement in light harvesting ability, which can lead to a higher J_sc for DX4–DX5 as compared to DX1. Meanwhile, DX2 and DX3 might show similar LHE to that of DX1, which are lower than that of DX4 and DX5.

Fig. 2 The LHE curves of DX1–DX5.

3.1.2 Electron injection efficiency (Φ_inject). Another way to enhance J_sc is to improve Φ_inject. As mentioned above, Φ_inject is related to the ΔG_inj and electronic coupling strength. We first explored the characteristic electronic properties of dyes and plotted the distribution of frontier molecular orbitals and energy levels in Fig. 3 before analyzing the factors influencing Φ_inject. These results show that DX1–DX5 have similar electron distributions: the HOMO orbitals are localized on the central Ru atom and the Cl or Br ligands, and the LUMO orbitals are almost delocalized over the terpyridine ligands. The distribution in this way will favor the electron injection from the dye photo-excited state to the semiconductor surface via carboxyl groups. From the calculated energy levels of the DXn dyes (Fig. 3), we note that the energy levels of HOMO and HOMO−1 orbitals (<−5.5 eV) are sufficiently lower than the I⁻/I₃⁻ redox couple (−4.58 eV), ensuring a fast regeneration of the oxidized dyes. Meanwhile, the energy levels of LUMOs (>−3.5 eV) are higher than the CB of TiO₂ (−4.0 eV), which could ensure an effective electron injection from the dyes to TiO₂. Compared with DX1, the substitution of Cl atom by Br atom (DX2 and DX3) does not shift the energy of HOMO, HOMO−1 and LUMO much, but replacing one or two C atoms with one or two N atoms (DX4, DX5) in terpyriding ligands make LUMO energy levels downshift about 0.2–0.3 eV and HOMO energy levels decrease about 0.1 eV. Therefore, the energy gaps between HOMO and LUMO for DX4 and DX5 (depicted in Fig. 3) are smaller than those of DX1–DX3, which is in agreement with the red-shifted light absorption discussed in 3.1.1 Section.

Fig. 3 Electron density diagrams and calculated energy levels of the frontier molecular orbitals of DX1–DX5 relevant to the absorptions in DMF (isodensity value = 0.02 a.u.).

Then ΔG_inj for each dye was calculated to estimate Φ_inject following eqn (4) and the results are listed in Table 2. The absolute values of ΔG_inj of all the five dyes are greater than 0.2 eV, the lowest energy for electron injection, as shown in Table 2, which indicates that the driving force for electron injection from the dye to semiconductor is sufficient.⁴⁷ The regeneration driving force ΔG_reg is also discussed, which is in connection with J_sc by affecting η_reg. The driving forces for dye regeneration of all five dyes range between 0.67 and 0.82 eV. Daeneke and his co-workers have demonstrated that when dye regeneration driving forces are in the range of 29–101 kJ mol⁻¹ (ΔE = 0.30 − 1.05 eV), the reaction rates do not change a lot.⁴⁸ Therefore, we can consider the driving forces for dye regeneration among DX1–DX5 are similar.

Table 2 Key parameters for ΔG_inj and ΔG_reg

Dye	Edye (eV)	λmax (eV)	E^dye* (eV)	ΔGinj (eV) unrelaxed	ΔGreg (eV)
DX1	−5.25	1.98	−3.27	0.73	0.67
DX2	−5.26	1.97	−3.29	0.71	0.68
DX3	−5.27	1.96	−3.31	0.69	0.69
DX4	−5.32	2.34	−2.98	1.02	0.74

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As for the electronic coupling strength, we note that in DX1/TiO₂ configurations (as depicted in Fig. 4), the optimized O1–Ti1 and O2–Ti2 distances between carboxylic oxygen atoms of DX1 and titanium atoms of the TiO₂ cluster are 1.92 and 2.13 Å, respectively. This reflects a strong electronic coupling between the dye molecule and TiO₂, which is a key requirement for efficient electron–hole separation.⁴⁹ The O–Ti distances of the other dye/TiO₂ complexes are shown in Table 3, which are similar to those of DX1/TiO₂, indicating the electronic coupling strengths of these systems are approximately equal. Therefore, we can demonstrate that the electron injection driving force, electronic coupling strength and dye regeneration driving force for DX1–DX5 are similar, suggesting that the Φ_inject is not much different among five sensitizers. In addition, we have tried different binding patterns for DX4/TiO₂ and DX5/TiO₂ with respect to pyrimidine and triazine ring, respectively. The optimized configuration of DX5/TiO₂ complex is shown in Fig. S3† and the corresponding O1–Ti1 and O2–Ti2 distances are collected in Table S1.† Comparing the bond lengths between DX4(DX5) and TiO₂ in Table S1† with the corresponding data in Table 3, we can find the distances between the compounds and TiO₂ with one binding point located on the pyrimidine or triazine ring are larger than the data with binding patterns as in Fig. 4. It indicates weaker electronic coupling strength between dyes and TiO₂ in the case of binding points located on pyrimidine and triazine ring for DX4 and DX5, respectively.

Fig. 4 Optimized configuration of DX1/TiO₂ complex. The left structure represents a magnified image of the selected part of DX1/TiO₂ (dashed circle). The distances between O atoms of DX1 and Ti atoms of the TiO₂ are also shown.

Table 3 The O1–Ti1 and O2–Ti2 distances of the DX/TiO₂ complexes (the unit is Å)

	DX1	DX2	DX3	DX4	DX5
O1–Ti1	1.92	1.92	1.91	1.92	2.03
O2–Ti2	2.13	2.12	2.13	2.14	2.19

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Based on the discussion above, we can draw a conclusion that it is propitious that solar cells made with DX4–DX5 may show an improved J_sc compared with DX1–DX3. However, we also need to discuss another important element influencing the efficiency, V_oc, to gain a comprehensive estimation of the performance of DX4–DX5.

3.2 Evaluating V_oc

As mentioned above, V_oc is another key element influencing the efficiency of solar cell. And V_oc is defined as below:

In the equation, kT and q are physical constants of the thermal energy and the unit charge, respectively. E_redox is oxidation potential of the redox couple in the electrolyte and N_CB is the accessible density of conduction band states which are both usually assumed as constants for the same material. n_c is the electron number in the conduction band. Hence, it is apparent that E_CB (the conduction band edge of semiconductor) is one of key factors determining V_oc. E_CB is sensitive to many elements and can be summed up from various contributions:³⁷

ΔE_CB,tot = ΔE_CB,solv + ΔE_CB,ions + ΔE_{CB,sensitizer} (7)

This indicates that the total shift of the TiO₂ conduction band (CB) could be associated with the shift induced by the solvent (ΔE_CB,solv), the ions presented in the electrolyte (ΔE_CB,ions) and the adsorbed sensitizers (ΔE_{CB,sensitizer}).⁵⁰ For the same DSSCs with different sensitizers, we can assume ΔE_CB,solv and ΔE_CB,ions remain approximately constants and focus our attention on ΔE_{CB,sensitizer} solely, which is in connection with the sensitizer structure.

3.2.1 Conduction band energy shift, ΔE_CB. As discussed above, V_oc is related to the total shift of E_CB. Thus, the ΔE_CB after dye adsorption was calculated to estimate the change of V_oc in the following part. We calculated the Partial Density of State (PDOS) of TiO₂ in order to evaluate the extent of ΔE_CB after adsorption and then to estimate the change of V_oc on the basis of optimized dye/TiO₂ adsorption mode. We performed a linear fit of the PDOS profile in a range of 20%–80% at the maximum height and took the intercept of this line with x energy axis as CB edge (shown in Fig. 5 and S4–S7†).⁵⁰ The calculated CB shifts for DX1–DX5 in DMF are listed in Table 4. From the data in Table 4, we note that the shift of E_CB could be induced to different extent upon sensitizer adsorption. ΔE_CB (0.278 eV) for DX5 is much higher than other four dyes, while DX2, DX3, DX4 have comparable ΔE_CB with that of DX1. Thus, we can reach a conclusion that replacing two C atoms in terpyriding ligands with two N atoms may cause an increased CB shift after adsorption, which may lead to a higher V_oc for DX5.

Fig. 5 Schematic representation of the model used to evaluate the CB shift caused by the sensitizer adsorption for DX1 in DMF (the black line represents the DOS of (TiO₂)₃₈ cluster. The blue line represents the contribution of (TiO₂)₃₈ cluster to the total DOS).

Table 4 Calculated CB shift (ΔE_CB, eV) for the dyes adsorbed onto the (TiO₂)₃₈ cluster in DMF

Dye	DX1	DX2	DX3	DX4	DX5
ΔECB	0.232	0.229	0.237	0.229	0.278

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4. Conclusions

Four ruthenium sensitizers derived from DX1 with different ligands were designed and investigated by DFT and TDDFT methods, aiming to increase the light harvesting ability in NIR region and further improving the J_sc of solar cells. The SOC-TDDFT method was also employed to give more accurate description on optical properties of Ru sensitizers. The elements affecting J_sc together with V_oc were evaluated through the electronic structures, photovoltaic properties and so on. Our study has revealed that by replacing C atoms in terpyridyl ligand with N atoms (DX4, DX5), we successfully increase the dye's light harvesting efficiency, especially in NIR region; however, the substitution of Cl atoms by Br atoms (DX2, DX3) has less influence on LHE. Taking both J_sc and V_oc into consideration, we find DX5 is the best among all the five DX dyes due to not only its increased LHE (resulting in a higher J_sc) but also the improved ΔE_CB (leading to an improved V_oc). We also hope that this work will assist in the experimental synthesis of Ru-contained sensitizers with enhanced conversion efficiency.

Acknowledgements

The authors gratefully acknowledge financial support from NSFC (21131001, 21203019, 21363025 and 21273030), SRFDP and RGC ERG Joint Research Program (20120043140001) and the Science and Technology Development Planning of Jilin Province (20150101008JC).

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Footnote

† Electronic supplementary information (ESI) available: The fully optimized structures of DX1–DX5 in gas phase by PBE0. Schematic representations of the models used to evaluate the CB shift caused by the sensitizer adsorption for DX2–DX5 in DMF. See DOI: 10.1039/c5ra17237c

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