First principles study of ruthenium(II) sensitizer adsorption on anatase TiO₂ (001) surface

Abstract

We present a systematic investigation of the adsorption behavior of the highly efficient ruthenium(II) sensitizer (N3) on the anatase TiO₂ (001) surface based on density functional theory. Three preferable configurations can be formed by exploiting two or three carboxylic groups attached to the TiO₂ surface, with their adsorption energies differing slightly. The interplay of N3 with the (001) surface is considerably stronger than that of N3 with the (101) surface, resulting in a larger dye coverage on the (001) surface. The energy gap of the N3 sensitizer, determining the absorption spectrum, decreases about 0.12 eV upon adsorption, suggesting an even larger range for the absorption spectrum than for the isolated N3 molecule. Moreover, the higher conduction band minimum of the TiO₂ (001) surface with N3 adsorption, compared with that of the (101) surface, indicates the higher open circuit potential. These results provide a clue to understand the high solar light-to-electricity conversion efficiency of dye sensitized solar cells with TiO₂ nanocrystals exposing a high percentage of {001} faces.

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1 Introduction

Dye sensitized solar cells (DSSCs) have attracted an enormous amount of interest over the past decades due to their low cost and high efficiency in converting solar energy to electricity.^1,2 In contrast to the conventional p–n junction photovoltaic devices where the semiconductor assumes both the task of light absorption and charge carrier transport,³ a DSSC uses a dye sensitizer to absorb the solar radiation and transfer the photo-excited electrons to its wide band gap semiconductor electrode. In this way, the absorption light wavelength is extended to the visible region, which constitutes most of the solar radiation. The overall conversion efficiency (η) of the DSSC is defined as: η = (i_ph)(V_oc)(ff)/I_s, where i_ph is photocurrent density at short circuit, V_oc is the open circuit voltage of the cell (the difference between the quasi-Fermi level of the semiconductor under illumination and the redox potential of the mediator), ff is the fill factor and I_s is the intensity of the incident light. Therefore, to improve the efficiency, the product of V_oc and i_ph should be optimized. In a photovoltaic device, the photoanode is perhaps one of the most important components, which directly determines the photocurrent (i_ph), open-circuit photovoltage (V_oc) and cycling performance of the cell. In general, photoanode materials now are mainly composed of a metal oxide semiconductor like ZnO,⁴ SnO₂,^5,6 Nb₂O₅,⁷ and TiO₂,^8,9 due to their good stability against photocorrosion and excellent electronic properties. Among them, anatase TiO₂, with the highest recorded efficiency of 13%, is considered to be one of the best photoanode materials in DSSCs.¹⁰

In order to obtain higher efficiency, considerable efforts have been made towards morphological control of TiO₂ crystals, like nanoparticles, nanorods¹¹ and nanotubes.¹² The TiO₂ surfaces are in direct contact with the dye molecules and offer anchoring sites for sensitizers. Transmission electron microscopy indicates that anatase TiO₂ powders primarily have {101} faces exposed and {001} facets to a lesser degree.¹³ Work on these different crystal facets suggests that the latter {001} facet is more reactive than the former {101} facet and plays a key role in the reactivity of anatase nanoparticles.^14,15 On the other hand, it was only in 2008 that TiO₂ single crystals with a high percentage of {001} facets (47%) were fabricated.¹⁶ Since then, TiO₂ crystals with even higher percentages of {001} facets have been reported gradually.^17,18 These achievements provide a new insight into DSSCs fabrication and make it possible for preparing sensitized TiO₂ photoanodes with a high percentage of {001} facets exposed. In recent years, some experiments have shown that the DSSCs, with TiO₂ nanocrystals exposing a high percentage of {001} faces, have a higher solar light-to-electricity conversion efficiency, originating from larger current density, open-circuit voltage and solar absorption.^19–22 However, theoretical investigations of the dye sensitizer adsorption on the TiO₂ (001) surface are still scarce and urgently needed to further optimize the photovoltaic performance of DSSCs.

In this work, we have studied the adsorption behavior of dye sensitizer adsorption on the (001) surface, comparing with that of dye sensitizer adsorption on the (101) surface based on density functional theory (DFT) calculations. The N3 molecule, one of the most investigated ruthenium(II) polypyridyl complexes, was used as the sensitizer in our simulation. The N3 molecule is identified as a particularly efficient sensitizer with photo-conversion efficiency higher than 11%.²³ Moreover, it has a relatively simple but representative structure, with notable electronic accepter and donor groups and typical carboxylic anchoring groups. We have obtained both the energetically preferable structures and adsorbate-induced occupied gap levels in the system of N3 dye adsorption on the (001) surface. In addition, adsorption energies as well as energy levels alignment of the N3 molecule adsorption on (001) and (101) surfaces of TiO₂ are also calculated. These results are essential for photovoltaic applications and allow us to gain revealing insights into the detailed factors governing the efficiency of DSSCs.

2 Computational details

All calculations were performed using the Vienna ab initio simulation package (VASP) within the framework of DFT.^24–26 The projector augmented plane wave pseudopotentials were employed for the electron–ion interactions.²⁷ The local density approximation (LDA) exchange–correlation functional was used for structural optimization because it can reproduce the experimental crystal parameters of anatase TiO₂ with a deviation of 0.45% and 0.54% for a and c axes, respectively, compared with the 1.24% and 1.51% by using the generalized gradient approximation (GGA). On the other hand, the band gaps of bulk anatase TiO₂ are calculated to be 1.89 eV and 1.87 eV by GGA and LDA methods, respectively, which are consistent with previous results.^28,29 However, due to the self-interaction error,³⁰ both the LDA and GGA fail to reproduce the experimental band gap of bulk anatase TiO₂ (3.2 eV). Therefore, the electronic properties of the N3 molecule, TiO₂ surface and N3 molecule adsorption on the TiO₂ surface were calculated using a hybrid functional of PBE0, mixing 25% of HF exchange in a PBE scheme.³¹ All calculations were performed with a single k-point (the Γ point). The cutoff energy for the plane wave basis set was set to 500 eV. The periodically repeated unit cells measured 15.14 Å × 15.14 Å with 9 atomic layers and 16.37 Å × 15.14 Å with 12 atomic layers were adopted for (001) and (101) slabs, respectively. The vacuum distance larger than 15 Å was used in the calculation to remove the interaction between successive TiO₂ slabs. In structural optimization, the lowest three atomic layers were fixed to their bulk truncated positions allowing all others atoms to fully relax until the energy difference between two ionic steps was smaller than 2 × 10⁻⁵ eV.

3 Results and discussion

3.1 N3 adsorption on (001) surface

3.1.1 Adsorption structure and energy. The optimized structure of the TiO₂ (001) surface is depicted in Fig. 1a. In the bulk anatase TiO₂, each Ti atom is octahedrally coordinated to six O atoms, while each O atom is coordinated to three Ti atoms. At the TiO₂ surface, both the upmost Ti atoms and bridge O atoms have one coordination vacancy. The fivefold coordinated Ti atoms (Ti_5c), 3.78 Å apart in a square lattice, have been proven to be the most favorable anchoring sites for the carboxylic groups of ruthenium polypyridyl complexes.^32,33 In Fig. 1b, the optimized structure of the N3 dye molecule shows that the Ru atom is octahedrally coordinated to six N atoms which are provided by two bipyridyl ligands and two thiocyanate ligands. An approximate C₂ symmetry axis could be found oriented along the bisector of the ∠NRuN angle formed by the Ru atom and N atoms of the thiocyanate ligands. In each bipyridyl ligand, two H atoms in para positions are substituted by protonated carboxylic groups. Due to the non-coplanarity of these carboxylic groups, it is unlikely that all of them anchor on the TiO₂ surface simultaneously. It is thus that several binding configurations between the N3 dye and the TiO₂ surface should be taken into account, considering the types and numbers of anchoring carboxylic groups. In order to illustrate the anchoring patterns, we have numbered the O atoms of the carboxylic groups in Fig. 1b.

Fig. 1 The optimized structures of (a) TiO₂ (001) surface and (b) N3 dye molecule. Green, red, orange, yellow, gray, aquamarine and cyan spheres represent C, O, N, S, H, Ru and Ti atoms, respectively. The solid line in panel (b) represents the C₂ symmetry axis. Oxygen atoms of the dye molecule are numbered in order to clearly depict the adsorption pattern.

Several possible adsorption configurations of the sensitizer on the anatase (001) surface are shown in Fig. 2. It is noted that the N3 molecules are put on the surface initially in their fully protonated forms before relaxation. However, irrespective of the bonding types of carboxylic groups with Ti_5c, either monodentate or bidentate, the H atoms in the carboxylic groups can transfer to the bridge O atoms on the TiO₂ surface after relaxation. A similar phenomenon also occurs on the TiO₂ (001) surface with dissociative adsorption of water, methanol,³⁴ and formic acid.¹⁴ According to our calculation, the valence band maximum (VBM) of the TiO₂ (001) surface is raised by about 0.64 eV with respect to the VBM of the TiO₂ (101) surface. The VBM, which is partly contributed to by the p orbital of the bridge O_2c atom, denotes the high reactivity of surface O atoms and the possibility of capturing H atoms from carboxylic groups. The above result is in agreement with previous findings for formic acid and methanol adsorption on the TiO₂ surface.^2,4 The simplest and also the initial attached form of the dye molecule to the anatase surface is a single-bond type (not shown here). Then the rotational motion of the molecule leads to another O atom captured by the Ti_5c atom of the TiO₂ surface. Because of the approximate C₂ symmetry of the N3 molecule, there are only two non-equivalent carboxylic groups which belong to the same bipyridyl ligand. It is shown in Fig. 2 that, for structure M1 (M2), O1 and O2 (O5 and O6) atoms belonging to one carboxylic group form bonds with two Ti_5c atoms (Ti_5c–O bonds), respectively. In contrast, structure B1 appears with O2 and O5 atoms, belonging to different carboxylic groups, bonding with Ti_5c atoms. The average distances between molecular O and surface Ti atoms are about 1.96 Å, 1.96 Å, and 1.94 Å in structures M1, M2 and B1, respectively, indicating stronger bonding for two monodentate coordination than a bidentate bridging coordination.

Fig. 2 Different configurations of N3 dye adsorption on the anatase TiO₂ (001) surface. Configurations B4, B5 and T2 are the three most energetically preferable structures. Some oxygen atoms are numbered and referred to in Table 2. Green, red, orange, yellow, gray, aquamarine and cyan spheres represent C, O, N, S, H, Ru and Ti atoms, respectively.

After the second Ti_5c–O bond formation, the rotation of N3 molecules shown in structures M1, M2 and B1 is suppressed partly. There still exist rotation axes passing through the anchoring O atoms, along those the N3 molecules could rotate and more carboxylic groups could attach to the surface. The distance between O5 (O2) and O3 is 9.80 Å (9.95 Å) in an isolated N3 molecule, namely 2.59 (2.63) times the distance of two nearest surface Ti_5c atoms. Therefore, to form structures B2 and B3 (B4 and B5), different Ti_5c atoms along the [010] direction are bonded after rotation of structure M1 (M2). Similarly, if structure B1 tilts along its rotation axis (O2–O5), structure T1 with the third carboxylic group anchoring on the TiO₂ (001) surface with nondissociative adsorption (see Fig. S1 of ESI†) may appear. Considering the most preferable adsorption configuration of N3 on the TiO₂ (101) surface, which has been extensively studied,^33,35 structure T2 shown in Fig. 2 might also be possible.

The adsorption energy (E_b) of the N3 molecule is defined by the following expression, E_b = E_tot[slab] + E_tot[dye] − E_tot[slab + dye], where E_tot is the total energy of relevant parts.³⁶ The calculated adsorption energies of the N3 molecule in each structure using both LDA and PBE0 methods are shown in Table 1. The adsorption energies obtained by using the PBE0 method are about 1–3 eV less than those calculated by the LDA method for each structure. Whereas, structures B4, B5 and T2 are the three most energetically stable structures in both methods.

Table 1 Adsorption energies (eV) of N3 molecules in structures M1–T2 calculated by LDA and PBE0 methods, respectively

Structure	M1	M2	B1	B2	B3	B4	B5	T1	T2
LDA	3.69	3.88	3.94	5.10	5.14	6.07	6.12	4.28	6.37
PBE0	2.94	3.03	2.61	3.46	3.81	4.39	4.97	3.04	3.96

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Since we are concerned more about the energetically preferable structures, the Ti_5c–O bond lengths of structures B4, B5 and T2 are listed in Table 2. In structures B4 and B5, only bidentate modes of coordination are formed. The lengths of four Ti_5c–O bonds in structure B4 are almost identical, while they differ a lot in structure B5. This difference might be due to the influence of H atoms, which attach to the bridge O_2c atoms of the TiO₂ surface and come from the carboxylic groups. In structure B4, one of the two bridge O_2c atoms neighboring to each Ti_5c–O bond is attached by an H atom, while only the O_2c atoms close to the O1–Ti and O3–Ti bonds in structure B5 are saturated by H atoms. It is indicated that if an H atom attaches to the nearest surface O_2c atom of Ti_5c, the length of the Ti_5c–O bonds will decrease, resulting in stronger bonding between the surface Ti_5c atom and O atom of the N3 dye. In structure T2, among the four Ti_5c–O bonds, one bidentate and two monodentate modes of coordination are formed. It is clearly seen that, except for the O1–Ti bond, each of the other three Ti_5c–O bonds is close to a surface O_2c atom bonding with an H atom, resulting in the decrease in length of Ti_5c–O bonds. Moreover, the bond lengths of Ti_5c–O bonds in two monodentate modes, especially for O3–Ti, are even shorter than those of Ti_5c–O bonds in bidentate mode, consistent with the above discussion of stronger bonding for two monodentate coordination than a bidentate bridging coordination.

Table 2 Lengths (in Å) of interfacial Ti_5c–O bonds between O atom in N3 molecule and Ti atom on TiO₂ surface. The labeled oxygen atoms are shown in Fig. 2

Bond	O1–Ti	O2–Ti	O3–Ti	O4–Ti	O5–Ti
B4	2.04	2.02	2.05	2.01	—
B5	1.99	2.12	1.99	2.03	—
T2	2.04	1.95	1.89	—	1.95

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3.1.2 Influence of N3 adsorption patterns on electronic structure. In DSSCs, the conversion efficiency is mainly determined by the electronic structures of the dye molecule and semiconductor. To gain an efficient and stable solar cell, the dye molecule should be strongly bound to the underlying semiconductor material and absorb a large portion of solar radiation. Deducing from the large adsorption energy, we affirm that the N3 molecule forms strong chemisorption bonds with Ti_5c on the TiO₂ (001) surface. This strong interaction ensures the stability of DSSCs and results in a larger amount of molecular adsorption. On the other hand, the light adsorption performance of the N3 sensitizer with structure change is surely influenced. Fig. 3 shows the density of states (DOS) of the isolated N3 molecule and the total DOS of N3 molecules with the upmost three atomic layers of TiO₂ slabs of structures B4, B5, T2. It is noted that though N3 molecules are attached to the surface in different modes of coordination, their highest occupied molecular orbitals (HOMO) are all located in the band gap of TiO₂. In addition, the lowest unoccupied molecular orbital (LUMO) of the molecule falls in the conduction band (CB) of the TiO₂ surface for each structure.

Fig. 3 Density of states (DOS) of (a) isolated N3 molecule; N3 molecules with the upmost three atomic layers of TiO₂ slabs of structures (b) B4, (c) B5 and (d) T2, respectively. The Fermi level is represented by the dashed line and set as zero. The contribution of the N3 molecule to the DOS is represented by green filled curves.

Due to coupling between electronic states of the N3 molecule and the surface, broadening and shifting of both occupied and unoccupied states of the dye around the Fermi level can be clearly observed. The overall effect of shifting results in the narrowing of the HOMO–LUMO (pointed out by the black and red arrows in Fig. 3, respectively) gap of the N3 molecule and red shifted absorption spectrum of the sensitized TiO₂ surface. Moreover, the effect of gap narrowing increases in sequence of the three structures B4, B5 and T2. While the intensity of the LUMO state, which is critical to the light absorption in DSSCs, decreases in the same order. The orbital characteristics of the LUMO for different configurations of N3 adsorption on the TiO₂ surface are depicted in Fig. 4. For the isolated N3 molecule, the LUMO orbital is mainly delocalized on C and N atoms of two bipyridyl ligands,³⁷ indicating the important role of bipyridyl ligands in electron excitation and transfer. It has been demonstrated that the absorption bands in the visible region are assigned to electrons excited from the Ru–NCS t_2g-π* orbitals to bipyridyl-π* orbitals.³⁸ Due to the formation of chemical bonds between surface Ti_5c atoms and molecular O atoms, the LUMO of the N3 molecule is redistributed, but still delocalized on bipyridyl groups in structures B4 and B5. However, in structure T2, the original LUMO of the isolated N3 molecule splits into several orbitals. And the molecular parts of these newly produced orbitals tend to be more localized instead of the original delocalization of π* orbitals as shown in Fig. 4, thus might induce a negative effect on electron transfer in N3 molecules.

Fig. 4 Isodensity surface plot of (a) lowest unoccupied molecular orbital (LUMO) of isolated N3 molecule and (b–d) crystal orbitals of structures B4, B5 and T2 with the energy levels marked by red arrows in Fig. 3 (isodensity values: 0.025 for (a)–(c) and 0.015 for (d)).

It is intuitive that the N3 dye molecule undergoes larger distortion in structure T2 than in structures B4 and B5. In order to verify the above speculation, the distorted and deprotonated N3 molecules are extracted from structures B4, B5 and T2 for the evaluation of their energies (E_dis). Then each N3 molecule is fully relaxed to its ground state to obtain the energy (E_ref). The distortion energy is estimated by subtracting E_ref from E_dis. Comparing the distortion energies of N3 molecules in structures T2, B4 and B5, i.e., 0.43 eV, 0.25 eV and 0.16 eV by the LDA method (1.25 eV, 0.51 eV and 0.34 eV by the PBE0 method), the N3 molecule in structure T2 undergoes larger distortion indeed. It seems that structure T2 is easier to be observed in experiments than other structures deducing from the highest adsorption energy calculated by the LDA method. However, in actual DSSCs, the TiO₂ nanoparticles and N3 molecules are under solution conditions. In consideration of the adsorption of solvent molecules, structure B5 could be more preferable than structure T2 (discussion in the ESI†). Moreover, it is obvious that the larger distortion of the N3 molecule in structure T2 will increase the difficulty of the formation of structure T2. Combining the adsorption energy calculated by the PBE0 hybrid functional and the influence of solvent molecules, it is suggested that structure B5 might be the dominant structure in the N3/TiO₂ complex if (001) surfaces are exposed in DSSCs. So if not explicitly mentioned, structure B5 will be used for discussion in the following sections.

3.2 N3 adsorption on TiO₂ (101) surface

To make a comparison between N3 adsorption on different surfaces of TiO₂, the adsorption behavior of N3 on the TiO₂ (101) surface is also investigated (shown in Fig. S3 of ESI†). The (101) surface is the thermodynamically stable surface in TiO₂ nanocrystals, and has been extensively theoretically investigated before.^14,39–41 Unlike the (001) surface, O_2c atoms in the (101) surface tend to be more inert. It is found that the H atoms of carboxylic groups do not spontaneously transfer to the O_2c atom of the (101) surface after relaxation. Similar results have been observed in other adsorbates like H₂O, methanol,⁴² and formic acid.⁴³ However, experimental results show that the adsorbed N3 molecules contain both –CO₂⁻ groups and C=O bonds,³² indicating part of the carboxylic acid groups should be deprotonated. This discrepancy is ascribed to the solution conditions in experiments and zero temperature assumption in theoretical calculations. To mimic the experimental results, two H atoms from the N3 sensitizer are initially transferred to their nearest O_2c atoms for structural relaxation. Among several possible configurations, the most preferable one noted as E1 is shown in Fig. 5. In this structure, N3 anchors on the (101) surface dissociatively with a bidentate and two monodentate modes of coordination, indicating that the dye molecule is more likely to be adsorbed on the (101) surface in the form of partly deprotonated.^33,35

Fig. 5 The most preferable configuration of N3 adsorption on the TiO₂ (101) surface. Green, red, orange, yellow, gray, aquamarine and cyan spheres represent C, O, N, S, H, Ru, and Ti atoms, respectively.

3.3 Comparison of N3 adsorption on (001) and (101) surfaces

The bonding of N3 with the TiO₂ (101) surface, with adsorption energies of 3.84 eV calculated by the LDA method and 1.55 eV calculated by the PBE0 method, is considerably weaker than that of N3 with the TiO₂ (001) surface. In order to explain the difference in adsorption energy, projected density of states (PDOS) of Ti_5c atoms on (001) and (101) surfaces are shown in Fig. 6. It is noted that there are extra states in the energy range of −8.0 eV to −7.0 eV for the clean (001) surface, compared with those of the (101) surface. After the adsorption of N3 molecules, the intensity of states provided by Ti_5c in this energy range decreases sharply, due to the chemical bonding with carboxylic groups in the N3 molecule. The inset in Fig. 6a shows the contribution of 3d orbitals of Ti_5c on the clean (001) surface in this energy range. It is suggested a strong coupling of 3d orbitals of Ti_5c (mainly from d_xy and d_yz orbitals) with 2p orbitals of O atoms in the N3 molecule results in the downshift of 3d orbitals of Ti_5c atoms to a deeper energy level. However, for the (101) surface, the occupied states of Ti_5c atoms are mainly located inside the deeper energy range and contribute a little to the VBM of the (101) surface. It is thus that the shift in energy of the 3d states of Ti_5c atoms after bonding with the N3 molecule is relatively smaller. Moreover, the almost unchanged PDOS of Ti_5c near the Fermi level of the (101) surface indicates that the interaction of Ti_5c with N3 is relatively weaker than that of the (001) surface. Consequently, the adsorption energy of N3 on the (001) surface is much larger than that of N3 on the (101) surface.

Fig. 6 Projected density of states (PDOS) of surface Ti atoms on (a) (001) and (b) (101) surfaces. Red solid and black dashed lines represent PDOS of Ti atoms in clean and adsorbed surfaces, respectively. Dashed vertical lines correspond to Fermi levels of the clean surface. The inset in panel (a) shows DOS projected on the 3d orbitals of Ti_5c atoms on the clean (001) surface. Vaccum levels are used in energy levels alignment.

Total DOS and PDOS of N3 molecules adsorption on (001) and (101) surfaces are shown in Fig. 7 to make a comparison of DSSC-related performance between the two systems. In order to align their energy levels, the vacuum energy is set to zero in both systems. Despite the difference of broadening in the conduction and valence bands of the oxide, the states of N3, located in the band gap of the oxides, differ by little between the two systems. It is indicated that the electron donor groups are not strongly influenced by the TiO₂ surface. In addition, the LUMO–HOMO gap, 1.67 eV for both systems, shows that the absorption spectrum does not change much even when more {001} faces are exposed in TiO₂ nanoparticles. However, for N3 adsorption on the (001) surface, the shift-down of both occupied and unoccupied states of the dye around the Fermi level results in a decrease in the energy difference between the LUMO of N3 and the conduction band minimum (CBM) of TiO₂, changing from 0.9 eV for the (101) surface to 0.6 eV for the (001) surface. In addition, although the CBMs in both systems are provided by d orbitals of Ti atoms (shown in Fig. S4 of ESI†), the level position of the CBM of N3 adsorption on the (001) surface is slightly higher (about 60 meV) than that of N3 on the (101) surface, suggesting a higher power potential in DSSCs where photoanode materials are made by TiO₂ nanoparticles exposing more {001} faces.

Fig. 7 DOS of N3 adsorption on TiO₂ (a) (001) and (b) (101) surfaces. The contribution of the N3 molecule to the DOS is represented by green filled curves. Dashed vertical lines correspond to Fermi levels. Vacuum levels are used in energy levels alignment.

4 Conclusion

In summary, we have systematically investigated the adsorption behavior of N3 sensitizers on (001) surfaces of anatase TiO₂. Our results show that structure B5, where the N3 molecule anchors with its two carboxyl groups coordinated via bidentate coordination to the Ti_5c atoms of the TiO₂ surface, is believed to be the most easily formed structure. The adsorption energy of the N3 molecule on the TiO₂ (001) surface is large enough to enable the formation of dense dye molecular layers on anatase nanoparticles, not only resulting in a higher absorptivity of solar radiation, but also lowering the dark current produced by interaction between TiO₂ and a mediator in solution. Our study also reveals that the LUMO–HOMO gap of the N3 molecule decreases about 0.12 eV upon adsorption, suggesting an even larger range of the absorption spectrum than that of the isolated N3 molecule. In addition, the LUMO of N3 is still delocalized on bipyridyl groups and overlapped with some orbitals of TiO₂, providing paths for easy electron transfer from the N3 molecule to TiO₂. And the higher CBM of the TiO₂ (001) surface with N3 adsorption, compared with that of the (101) surface, indicates the higher open circuit potential. These results can provide practical guidance for the development of TiO₂ particles exposing more {001} faces as promising photoanode materials in DSSCs.

Acknowledgements

This work was supported by the Ministry of Science and Technology of China (Grant No. 2011CB606405), the National Nature Science Foundation of China (Grant No. 11104155, 51232005, and 51202121), Shenzhen Projects for Basic Research (Grant No. JC201105201119A, JCYJ20120831165730910, and KQCX20140521161756227), Guangdong Province Innovation R & D Team Plan for Energy and Environmental Materials (Grant No. 2009010025). Computational resources from the TIANHE-1 in the Tianjin Supercomputing Center are also acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra06743j

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