Simultaneous Interactions of Ru Dye with Iodide Ions and Nitrogen

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J. Phys. Chem. C 2010, 114, 11335–11341

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Simultaneous Interactions of Ru Dye with Iodide Ions and Nitrogen-Containing Heterocycles in Dye-Sensitized Solar Cells Hitoshi Kusama,* Hideki Sugihara, and Kazuhiro Sayama Energy Technology Research Institute, National Institute of AdVanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan ReceiVed: April 25, 2010; ReVised Manuscript ReceiVed: May 14, 2010

Iodide ions and nitrogen-containing heterocycles, including 4-t-butylpyridine, are fundamental in the electrolyte solution of dye-sensitized solar cells as a redox and a promotive additive, respectively. Although discrete interaction of iodide ions and of heterocycles with the sensitizing dye is known, their simultaneous interaction with the dye and its effect on dye-sensitized solar cell performance is still an open question. In this paper, we have studied simultaneous interactions of iodide ions and N-containing heterocycles with cationic Ru(2,2′bipyridine-4,4′-carboxylic acid)2(NCS)2 dye (N3) by means of density functional theory (DFT). The DFT results reveal that the dye interacted with both the iodide ions and the heterocycles at different sites simultaneously. The dye formed a S-I bond between the NCS ligand and I-, while concurrently forming two hydrogen bonds between the carboxyl group of its ligand and the heterocycles. However, the interaction of the heterocycles weakened the interaction of iodide ions, suppressing the regeneration of the oxidized dye, which was after electron injection to the TiO2 conduction band, by an I-/I3- redox couple, and thereby reducing the short-circuit photocurrent density of the dye-sensitized solar cell. Introduction Dye-sensitized solar cells (DSSCs) have received a lot of attention during the last twenty years due to their simple assembly and potential economic advantages compared to conventional silicon solar cells, starting when O’Regan and Gra¨tzel announced a high solar energy conversion efficiency of 7.9% with Air Mass 1.5.1 A standard DSSC consists of three fundamental components: (i) a sensitized photoanode, which is typically a Ru complex dye-sensitized nanocrystalline TiO2 film on a transparent conductive oxide (TCO) glass, (ii) an electrolyte solution containing I-/I3- as a redox couple, and (iii) a cathode, which is a platinized TCO glass. When the cell is illuminated with light, the ground-state dye absorbs a photon, and an electron is transferred to a higher-lying energy level, leading to its excited state. Next, electron injection from the photoexcited dye into the conduction band of the TiO2 occurs. The injected electron percolates through the porous TiO2 layer to the TCO glass and passes the external load to the cathode. Subsequently, the electron is transferred to I3- to yield I- at the cathode. Finally, the I- reduces the cationic dye to its original ground state. In this way, the device operates in a regenerative mode. One of the reasons for the significant advance in the solar energy conversion efficiency of DSSCs1 is the adoption by Gra¨tzel and co-workers of the Ru(H2dcbpy)2(NCS)2 sensitizer (N3), where H2dcbpy is 2,2′-bipyridine-4,4′-carboxylic acid, adsorbed to nanocrystalline TiO2 films having a large surface area.2 N3 dye consists of three parts: Ru, a polypyridyl ligand, and a NCS ligand. The photoexcited electron, which is localized on the polypyridyl ligand bonding to the TiO2 surface via its carboxyl group, can be efficiently injected into the TiO2 conduction band. After electron injection, the generated hole, which is localized on the S atom of the NCS ligand, can be efficiently filled with the electron from the iodide redox couple. * To whom correspondence [email protected].

should

be

addressed.

E-mail:

Great efforts have been made to understand operation mechanisms of the dye, such as electron injection into the TiO2 conduction band,3–6 as well as to improve dye performance, such as spectral response in the red and infrared regions,2,7–9 because the sensitizing dye is the most central component of a DSSC, determining the light-harvesting efficiency itself. Meanwhile, the light-to-electric energy conversion efficiency of DSSCs as a whole depends on not only the dye’s own property but also the other component’s performances, such as the I-/I3- redox couple to regenerate the oxidized dye. Although the redox couple plays an important role for the chemical stability of DSSCs as well as solar energy conversion efficiency,10 the dye regeneration mechanism has not been fully studied. The regeneration dynamics of N3 dye in I-/I3electrolyte was studied by Clifford and co-workers.11 They demonstrated that the regeneration reaction proceeded via a transient intermediate complex [dye+ · I-] formed by the reaction of a photogenerated dye cation with iodide ions:

dye+ + I- f [dye+ · I-]

(1)

[dye+ · I-] + I- f [dye · I2 ] f dye + I2

(2)

I2- then dismutates to yield iodide and triiodide: 2I2 f I + I3

(3)

The formation of the first intermediate (eq 1) is kinetically fast, whereas the subsequent reaction of the intermediate with a second iodide species (eq 2) is much slower and the ratedetermining step of the overall regeneration reaction.10,11 Earlier, Fitzmaurice and Frei proposed the formation of a dye · I2complex.12 Very recently, Privalov and co-workers confirmed

10.1021/jp103716r  2010 American Chemical Society Published on Web 05/28/2010

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that the formation of such complexes is energetically favorable by DFT calculations.10 The standard reduction potential of a redox couple is also a dominant factor determining DSSC performance because its open-circuit photovoltage (Voc) is defined as the absolute value of the difference between the standard reduction potential of the redox couple and the Fermi level of the TiO2 photoelectrode. The expected maximum Voc value of the cell consisting of a TiO2 photoelectrode and an I-/I3- redox system is 0.9 V13 but usually is not afforded because the sensitizing dye adsorption onto the TiO2 surface shifts its conduction band downward.14 To compensate for the TiO2 conduction band downshift, nitrogen-containing heterocycles, such as 4-t-butylpyridine (TBP), are added to the I-/I3- electrolyte solution.2,15–17 Generally, adding heterocycles enhances the Voc, the fill factor, and the solar energy conversion efficiency; however, it also reduces the Jsc of a DSSC. There have been few reports about the reduction mechanism of the Jsc induced by the heterocycles. In a previous paper,18 we presented a theoretical study on the interactions of Ncontaining heterocycles, such as TBP, with the neutral and oxidized Ru(II)-polypyridyl dye, using DFT. Our results showed that the heterocycles formed two hydrogen bonds with the dye: one via the N atom with a lone pair of the heterocycles and the H atom of the carboxyl group of the dye ligand that does not bind with the TiO2 surface14,19–21 and the other via the H atom adjacent to the N atom forming the other hydrogen bond and the O atom with a lone pair of the carboxyl groups. We also found that the positive atomic charge on the S atom of the NCS ligand in the oxidized state decreased via interaction with the heterocycles. Considering also the DFT results by Privalov and co-workers that the I- species interacts with cationic N3 via an NCS ligand, forming a S-I bond,10 we hypothesized that it was difficult for the oxidized dye to interact with I- via interaction with the heterocycles, which prevented regeneration of the dye and led to a decrease in the Jsc of the DSSC. Although the interactions of the Ru dye with the I-/I3- redox couple10 and with the N-containing heterocyclic additive18 were elucidated independently, the interactions of the dye with I-/ I3- and heterocycles simultaneously have never been studied. Herein, we focus on the simultaneous intermolecular interactions of the cationic N3 dye with iodide and the N-containing heterocycles, such as pyrazole, imidazole, pyridine, pyrimidine, pyrazine, and TBP. The main tools in this investigation are quantum chemical calculations at the DFT level, which are suitable for studies of large molecular systems, such as N3 dye. The results are compared to the Jsc in a DSSC containing the heterocycles as additives in an electrolyte solution in order to confirm the hypothesis that the heterocyclic additives retard the regeneration of oxidized dye by the I-/I3- redox couple and reduce the Jsc value. Computational Details DFT calculations were performed with the Gaussian 03 program at the Research Center for Computational Science, Okazaki, Japan, and with the Gaussian 03W using personal computers.22 The geometries were fully optimized in vacuo at hybrid DFT levels by B3LYP functions, which combine Becke’s three-parameter exchange function (B3)23,24 with the correlation function of Lee, Yang, and Parr (LYP).25 For all the systems, a LanL2DZ basis set, which corresponds to a Dunning/Huzinaga valence double-ζ basis (D95 V) for first-row elements26 and a Los Alamos ECP plus double-ζ basis for Na-La and Hf-Bi atoms,27–29 was used. The energies were corrected for the zero-

Kusama et al.

Figure 1. Optimized geometries of N3, N3 · I, and N3 · I2: white ) H, gray ) C, blue )N, red ) O, yellow ) S, teal ) Ru, and purple ) I atoms.

point vibrational energies (ZPE). The interaction energies were determined as the difference in energy between the complex and the sum of the isolated monomers. With this definition, a positive interaction energy corresponds to a strong interaction. Indeed, all of the complexes have nonimaginary frequency geometries. These findings confirm that the optimized structures correspond to real minima on the potential energy surface. To understand the nature and magnitude of the intermolecular interactions, natural bond orbital (NBO) analysis30,31 was conducted on optimized geometries with the NBO 3.1 program32 included in the Gaussian program package. The Mulliken population analysis was also performed on optimized structures. Results and Discussion Structures of Cationic N3 Dye and Its Complexation with Iodide Ions. The starting point of our study was the N3 dye in its ground doublet electronic spin state with a monopositive charge (1+) after the electron injection into the TiO2 conduction band, as illustrated in Figure 1 (N3). According to the literature,10 the structure of N3 interacting with I- via a S atom of the NCS ligand was optimized with a total charge of 0 and a multiplicity of 2 (N3 · I, Figure 1). Table 1 lists the main geometrical parameters of optimized structures. The intermolecular S · · · I distance of N3 · I is 3.234 Å, stronger than the net van der Waals radii of the binding atoms, 3.780 Å.33 The iodide interaction lengthened the Ru-N bonds of the Ru-NCS binding and C-S bonds of the NCS ligands but shortened the N-C bonds of the NCS ligands, corresponding

Interactions of Dye with I-1 and Heterocycles in DSSCs

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TABLE 1: Main Optimized Geometrical Parameters of N3 and N3-Iodide Complexesa parameter a

Ru-bpycis (Å) Ru-bpytrans (Å)a O-H (carboxyl group) (Å) Ru-NCS (Å) N-C(NCS) (Å) C-S (Å) S · · · I (Å) I-I (Å) N(bpytrans)-Ru-N(bpycis) (deg)a N(bpytrans)-Ru-N(bpytrans) (deg)a N(bpycis)-Ru-N(bpycis) (deg)a N(NCS)-Ru-N(NCS) (deg) Ru-N-C(NCS) (deg) N-C-S (deg) C-S · · · I (deg) S · · · I-I (deg) a

N3 · I

N3 2.087-2.087 2.098-2.098 0.985 1.996-1.996 1.201-1.201 1.658-1.658 78.7-78.7 89.6 177.1 94.8 175.0-175.0 178.9-178.9

2.070-2.074 2.066-2.056 0.984 2.059b-2.047 1.188b-1.197 1.692b-1.671 3.234 79.2-79.3 93.9 176.4 91.9 168.2b-176.6 176.2b-179.0 90.4

N3 · I2 2.075-2.071 2.055-2.039 0.983 2.075b-2.067 1.184b-1.195 1.707b-1.681 2.971 3.052 79.3-79.5 92.0 173.7 89.6 177.3b-176.3 179.3b-179.2 98.9 179.6

The subscripts cis and trans refer to the NCS ligands. b The NCS ligand interacts with I-.

SCHEME 1: N-Containing Heterocycles Studied in This Paper

with previous results.10 The small difference in the Ru-N distances of the Ru-bpy binding may be due to indirect trans influence of the iodide interaction with the NCS ligand.34 Interacting with I- results in a broadening of the N-Ru-N bond angle for the Ru-bpy in trans coordination to the NCS ligands but also in a narrowing of the N-Ru-N and Ru-N-C bond angles for the Ru-NCS binding as well as N-C-S for the NCS ligand interacting with iodide. The C-S · · · I bond is almost a right angle. The N3 · I species interacting with a second I-, which is represented by eq 2, was also optimized with a total charge of -1 and a multiplicity of 2 (N3 · I2, Figure 1). Compared with N3 · I, the Ru-N bonds of the Ru-NCS binding and C-S bonds of the NCS ligands interacting with iodide are longer, but the Ru-N bonds of the Ru-bpy binding in trans coordination to the NCS ligands are shorter. The intermolecular S · · · I distance for N3 · I2 is 0.3 Å closer than that for N3 · I. The bond length of I-I for N3 · I2 is shorter than that for isolated I2-, 3.456 Å. The bond angle of Ru-N-C for the NCS ligand interacting with iodide ions narrows by 9°, but the C-S · · · I bond angle widens over 8° due to the interaction with a second I-. The S · · · I-I bond angle is nearly linear. Interaction of N-Containing Heterocycles with Dye+ · I-. Scheme 1 represents the structures of the N-containing heterocycles adopted in this work. Even though cationic N3 dye interacts with I- via the S atom of the NCS ligand, the heterocycles seem to form two hydrogen bonds with the carboxyl group of the dye ligand: one via the N atom with a lone pair of the heterocycles and the H atom of the carboxyl group and the other via the H atom adjacent to the N atom forming the other hydrogen bond and the O atom with a lone

pair of carboxyl group.18 The hydrogen bonds exist because the dye does not bind with the TiO2 surface through all four carboxyl groups located on the bipyridine ligand.14,19–21 Figures S1 and S2 in the Supporting Information show optimized geometries of heterocycle-N3-I complexes with a total charge of 0 and a multiplicity of 2. Two carboxyl groups of the Ru-bpy ligand in cis coordination to the NCS ligands were considered as an interaction site with the heterocyclic molecule because others in trans coordination are involved in binding with the TiO2 surface.14 Thus, there are two conformers, denoted h (see Figure S1, Supporting Information) and v (see Figure S2, Supporting Information), whose NCS ligand interacting with I- is horizontal and vertical, referring to the heterocycles, respectively. Additionally, for pyrazole 1, imidazole 2, pyrimidine 4, and TBP 6 in Scheme 1, there are two conformers, denoted A and B. It should also be noted that there is a N-H · · · O hydrogen bond instead of a C-H · · · O, one in the case of 1A · N3 · I. Table S1 in the Supporting Information lists the main geometrical parameters of optimized structures for the heterocycle-N3-I complex. Irrespective of position, the interactions of N-containing heterocycles contribute little to the intermolecular geometries of N3 · I, such as the S · · · I bond distance and C-S · · · I bond angle, as well as the dye’s main features in Table 1. However, complexation with the heterocycles lengthens the O-H bond from 1.062 Å (1B · N3 · Ih) to 1.167 Å (6B · N3 · Iv), compared with the reference O-H bond length, 0.984 Å, calculated for N3 · I in Table 1. This finding indicates that the O-H bonds interacting with the heterocycles are weakened in the complex structures. For all the complexes, like the S · · · I bond, the intermolecular H · · · N and H · · · O distances are smaller than the net van der Waals radii of the binding atoms, 2.750 Å (H and N) and 2.720 Å (H and O),33 exhibiting that all the tested heterocycles form intermolecular hydrogen bonds with the carboxyl group. Therefore, DFT results reveal that the cationic N3 dye interacts with I- through the NCS ligand and with the N-containing heterocycles through the carboxyl group of the H2dcbpy ligand simultaneously. The bond elongation from 1.010 to 1.035 Å is also found at the N-H bond of pyrazole for 1A · N3 · Ih and 1A · N3 · Iv but is not observed in C-H bonds for the other heterocycles as well as 1B · N3 · I conformers, which suggests that the N-H · · · O bond is preferable to the C-H · · · O one. The longer the O-H, N-H, and C-H but the shorter the H · · · N and H · · · O, the more favorable the hydrogen bond is formed between the dye and

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TABLE 2: Intermolecular Interaction Energies (E) of Heterocycle-N3-I Complexes (in kcal · mol-1)

Kusama et al. TABLE 3: Interaction Energies (E) of Heterocycle-N3-I2 Complexes (in kcal · mol-1)

species

I-

heterocycles

species

second I-

I2-

heterocycles

N3 · I 1A · N3 · Ih 1B · N3 · Ih 2A · N3 · Ih 2B · N3 · Ih 3 · N3 · Ih 4A · N3 · Ih 4B · N3 · Ih 5 · N3 · Ih 6A · N3 · Ih 6B · N3 · Ih 1A · N3 · Iv 1B · N3 · Iv 2A · N3 · Iv 2B · N3 · Iv 3 · N3 · Iv 4A · N3 · Iv 4B · N3 · Iv 5 · N3 · Iv 6A · N3 · Iv 6B · N3 · Iv

89.61 84.10 83.97 82.41 81.94 82.91 84.34 84.39 84.97 82.14 82.14 84.63 84.30 83.11 82.51 83.41 84.59 84.78 85.23 82.82 82.81

25.26 18.17 23.49 22.35 21.40 17.57 18.43 17.85 22.98 23.01 25.79 18.50 24.20 22.91 21.90 17.82 18.81 18.11 23.66 23.68

N3 · I2 1A · N3 · I2h 1B · N3 · I2h 2A · N3 · I2h 2B · N3 · I2h 3 · N3 · I2h 4A · N3 · I2h 4B · N3 · I2h 5 · N3 · I2h 6A · N3 · I2h 6B · N3 · I2h 1A · N3 · I2v 1B · N3 · I2v 2A · N3 · I2v 2B · N3 · I2v 3 · N3 · I2v 4A · N3 · I2v 4B · N3 · I2v 5 · N3 · I2v 6A · N3 · I2v 6B · N3 · I2v

29.48 26.16 25.53 23.78 23.82 24.51 26.02 26.05 26.56 23.51 23.51 25.69 24.31 22.89 22.64 23.38 24.86 25.39 25.63 22.24 22.23

119.09 110.26 109.50 106.19 105.76 107.43 110.36 110.44 111.52 105.65 105.65 110.32 108.61 106.00 105.15 106.79 109.45 110.16 110.86 105.06 105.04

21.94 14.22 17.79 16.68 16.43 14.11 15.00 14.93 17.01 17.04 22.00 13.32 17.60 16.07 15.79 13.20 14.72 14.27 16.42 16.42

the heterocycles. Judging from the bond distances, O-H · · · N bonds are stronger than C-H · · · O ones. The O-H · · · N bond angles are close to linear except for 1A · N3 · Ih and 1A · N3 · Iv because, in these cases, the N-H · · · O is consistent with medium strength hydrogen bonding,35 unlike C-H · · · O. When the interacting I- positions are compared, h conformers indicate longer bond lengths of H · · · N, H · · · O, and C · · · O but a shorter one of O-H than v conformers. On the other hand, the bond lengths for intermolecular O · · · N and C-H of the heterocycles and the angles of O-H · · · N and C-H · · · O are not influenced by I- positions. Table 2 lists the intermolecular bond energy, E, of I- with N3-heterocycles and the E of heterocycles with N3-I. The E values of I- are over 4 kcal · mol-1 smaller than that of N3 · I, showing that all the tested heterocycle interactions reduce the stability of the N3-I complex. The more stable the interaction between N3 and N-containing heterocycles, the less stable the interaction between N3 and I-, as represented in Figure 2. Linear regression, except 1A · N3 · I, yields correlation coefficients of

Figure 2. Correlation between the E of I- and the E of heterocycles for the heterocycle-N3-I complexes. Open circles with a broken line and filled circles with a solid line denote the complexes that Iinteracts with horizontal and vertical NCS ligands referring to the heterocycles.

-0.96 for I- interaction with the horizontal NCS ligand and -0.93 for the vertical interaction. Interaction of N-Containing Heterocycles with Dye · I2-. To investigate the effect of N-containing heterocycles on the complete regeneration of oxidized dye by the I-/I3- redox couple, a second I- was considered. Figures S3 and S4 in the Supporting Information illustrate the optimized geometries of heterocycle-N3-I2 complexes with a total charge of -1 and a multiplicity of 2. Table S2 in the Supporting Information lists their geometric parameters. The lengths of N-C (1.184 Å) and C-S (1.707 Å) bonds for the NCS ligand interacting with I2 are virtually unchanged. S · · · I distances (2.971 Å) become very slightly closer, but I-I distances (3.052 Å) become subtly farther by the interaction with the heterocycles, regardless of the I2 position. The bond angles of Ru-N-C (177.3°) and C-S · · · I (98.9°) for N3 · I2 are widened by the heterocycle interactions, irrespective of iodide position. Compared to the reference length, 0.983 Å in Table 1, heterocycle complexation lengthens the O-H bond of the carboxyl group from 1.036 Å (1B · N3 · I2v) to 1.078 Å (6A · N3 · I2h and 6B · N3 · I2h), indicating that the O-H bonds are weakened in the complex structures. The intermolecular H · · · N distances are less than the net van der Waals radii of the binding atoms, 2.750 Å.33 The resulting H · · · O distances between the H atom of the heterocycles and the O atom of the N3 carbonyl group are also shorter than the net van der Waals radii of the binding atoms, 2.720 Å. These results exhibit that two intermolecular hydrogen bonds are also formed between the N3 dye and the heterocycles in the heterocycle-N3-I2 complexes. The O-H · · · N bond angles are close to linear and larger than the N-H · · · O for 1A · N3 · I2 and C-H · · · O. Table 3 lists the E values for a second I- with heterocycle-N3-I, for I2- with heterocycle-N3 and for heterocycles with N3 · I2. Comparing the configuration of iodide ions, the E values of horizontal conformers are about 1 kcal · mol-1 higher than those of vertical ones. This finding exhibits that the interactions via the S atom of the horizontal NCS ligand are preferable to via the vertical ligand for iodide ions. Similar to N3-I complexes, the interactions of iodide ions with the dye become unstable by heterocycle interactions with the dye, irrespective of the interacting position. The more stable the complexation between

Interactions of Dye with I-1 and Heterocycles in DSSCs

J. Phys. Chem. C, Vol. 114, No. 25, 2010 11339 stabilization energy E(2) associated with i f j delocalization is explicitly estimated by the following equation

E(2) ) ∆Eij ) qi

Figure 3. Correlation between the E of the iodide ion and the E of the heterocycles for the heterocycle-N3-I2 complexes.

N3 and N-containing heterocycles, the less stable the complexation between N3 · I and the second I- as well as between N3 and I2, as shown in Figure 3. Linear regression between the E of heterocycles and the E of the second I-, except 1A · N3 · I2, conformers in Figure 3 yields correlation coefficients of -0.96 for via the horizontal NCS ligand and -0.78 for via the vertical one. Linear regression between the E of the heterocycles and the E of I2- also yields correlation coefficients of -0.89 via the horizontal NCS ligand and -0.79 via the vertical one. To understand the nature and magnitude of the intermolecular interactions between the iodide ions and the NCS ligand of the dye for the heterocycle-N3-I2 complexes, NBO analysis was conducted. Each valence bonding NBO (σAB) must be paired with the corresponding valence antibonding NBO (σ*AB) to complete the span of the valence space in the NBO analysis31,32,34 * σAB ) cAhA - cBhB

(4)

where cA and cB are the polarization coefficients, and hA and hB are the natural hybrid orbitals on atoms A and B. Namely, the Lewis-type (donor) NBOs are complemented by the nonLewis-type (acceptor) NBOs that are formally empty in an ideal Lewis structure picture. The general transformation to NBOs leads to orbitals that are unoccupied in the formal Lewis structure. Consequently, the filled NBOs of the natural Lewis structure accurately describe the covalency effects in these molecules. Because the noncovalent delocalization effects are associated with σ f σ* interactions between the filled (donor) and unfilled (acceptor) orbitals, it is natural to describe them as “donor-acceptor”, charge transfer, or generalized “Lewis base-Lewis acid” type interactions. The antibonds represent the unused valence-shell capacity and spanning portions of the atomic valence space that are formally unsaturated by covalent bond formation. Weak occupancies of the valence antibonds indicate irreducible departures from an ideal localized Lewis picture, namely, true “delocalization effects”. Accordingly, the donor-acceptor (bond-antibond) interactions in the NBO analysis are considered by examining all possible interactions between the “filled” (donor) Lewis-type NBOs and the “empty” (acceptor) non-Lewis NBOs. Their energies are then estimated by second-order perturbation theory. These interactions (or energetic stabilizations) are referred to as “delocalization” corrections to the zeroth-order natural Lewis structure. For each donor NBO (i) and acceptor NBO (j), the

F2(i, j) εj - εi

(5)

where qi is the ith donor orbital occupancy, εi and εj are the diagonal elements (orbital energies), and F(i, j) is the offdiagonal element associated with the NBO Fock matrix. Hence, consideration of the valence antibond (σ*) leads to a far-reaching extension of the elementary Lewis structure concept and achieves delocalization corrections in simple NBO perturbative estimates using eq 4.36 The results of the NBO analysis in Table S3 in the Supporting Information indicate that the occupancies of the σ*(1)I-I antibond in the heterocycle-N3-I2 complexes via the horizontal NCS ligand are greater than the complexes via the vertical ligand. This behavior can be rationalized in terms of the chargetransfer interactions between orbitals. The third lone pair on the S atom, LP(3)S, participates as donor and the σ*(1)I-I antibond as acceptor in a strong intermolecular charge-transfer interaction, LP(3)S f σ*(1)I-I. This interaction can be considered as a measure of the relative stability of these complexes.37 The values of the charge-transfer energy, E(2), corresponding to this interaction in the vertical complexes are smaller than those in the horizontal complexes. Therefore, the σ*(1)I-I antibond occupancies in the vertical complexes diminish with respect to the values in the horizontal complexes. It is in line with the lengthening of the I-I bond in the horizontal complexes (see Table S2, Supporting Information). The sum of E(2) terms corresponding to delocalization of the S lone pair, LP(3)S, in the vertical complexes is also less than that in the horizontal complexes. Thus, it is expected that the LP(3)S occupancies in the vertical complexes are greater than those in the horizontal complexes (see Table S3, Supporting Information). The sums of the S lone pair occupancies in the horizontal complexes are generally smaller than those in the vertical complexes. Besides, the atomic charges on the S atom for the vertical complexes are more negative than those for the horizontal complexes, irrespective of analysis method. This finding, in agreement with the above results, exhibits that the flows of electron density from S to σ*(1)I-I in the horizontal complexes are greater than those in the vertical complexes. Eventually, NBO analysis also suggests that the horizontal conformers are more preferable than the vertical conformers. Implications on the DSSC Performance. We have reported in the previous study that the Jsc value of the DSSC decreases with the diminishing atomic charge on the S atom for the NCS ligand of the oxidized dye induced by its interaction with N-containing heterocycles as an additive. We have hypothesized that, as the positive atomic charge on the S atom of the NCS ligand diminishes via the interaction with the heterocycles, the interaction with I- becomes difficult for the oxidized dye, which prevents the oxidized dye from regenerating by the I-/I3- redox couple and leads to a lowering Jsc. As described above, we present here the theoretical evidence revealing the suppression of interaction between an oxidized dye and iodide ions by N-containing heterocycles. Figure 2 exhibits that the stronger the interaction between the oxidized dye and the heterocycles, the weaker the interaction between the oxidized dye and the first I- (eq 1). Moreover, the more stable the interaction between the dye and the heterocycles, the less stable the interactions between dye-I and the second Iand between dye and I2- (eq 2), as shown in Figure 3.

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Kusama et al. TABLE 4: Change in Atomic Charge on the N3 Molecule for the Complex Determined by Mulliken Population and NBO Analyses (in e) Mulliken

Figure 4. Correlation between the Jsc of the DSSC and the interaction energy (E) of I- with heterocycle · N3 in the heterocycle-N3-I complexes. Open circles with a broken line and filled circles with a solid line denote the complexes that I- interacts with horizontal and vertical NCS ligands referring to the heterocycles.

NBO

species

∆q(first)

∆q(second)

∆q(first)

∆q(second)

no heterocycles 1Ah 1Bh 2Ah 2Bh 3h 4Ah 4Bh 5h 6Ah 6Bh 1Av 1Bv 2Av 2Bv 3v 4Av 4Bv 5v 6Av 6Bv

-0.6695 -0.5030 -0.6195 -0.5086 -0.5270 -0.5048 -0.6039 -0.5957 -0.6030 -0.5066 -0.5072 -0.5044 -0.6193 -0.5083 -0.5263 -0.5060 -0.6052 -0.5948 -0.6042 -0.5122 -0.5133

-0.9442 -0.8881 -0.9127 -0.8894 -0.8948 -0.8857 -0.9088 -0.9056 -0.9045 -0.8675 -0.8666 -0.8779 -0.9144 -0.8867 -0.8975 -0.8859 -0.9086 -0.9054 -0.9068 -0.8622 -0.8611

-1.1294 -1.0508 -1.1009 -1.0676 -1.0813 -1.0590 -1.0916 -1.1077 -1.0699 -1.0617 -1.0615 -1.0352 -1.0996 -1.0711 -1.0578 -1.0398 -1.0983 -1.0996 -1.0971 -1.0595 -1.0634

-0.6762 -0.6308 -0.6589 -0.6295 -0.6343 -0.6577 -0.6690 -0.6409 -0.6851 -0.6376 -0.6414 -0.6476 -0.6476 -0.6693 -0.6267 -0.6548 -0.6782 -0.6587 -0.6536 -0.6614 -0.6414

the oxidized dye. Although the values differ by the method of analysis, the heterocycle interactions make the ∆q values less negative. Figure 6 depicts correlations between the Jsc of the DSSC and the ∆q on the dye molecule. The Jsc value decreases as the ∆q value becomes less negative, irrespective of its

Figure 5. Correlation between the Jsc of the DSSC and the interaction energy (E) of iodide ions for the heterocycle-N3-I2 complexes.

When the Jsc values of the DSSC in the previous study18 are compared with the theoretical results in this study, a correlation between the Jsc and the interaction energy (E) of I- with N3-heterocycles in the heterocycle-N3-I complexes, which is depicted in Figure 4, is found. Regardless of the I- interacting position with the NCS ligand, the larger the E of I-, the higher the Jsc value is. A correlation between the Jsc values of the DSSC and the E value of iodide for the heterocycle-N3-I2 complex is also observed in Figure 5. The Jsc is positively interrelated with the E value of the second I- with heterocycle-N3-I, regardless of their positions interacting with the NCS ligand. The Jsc value also increases with the E of I2- with the N3-heterocycle species. In fact, theoretical results demonstrate that the interaction of the heterocycles represses the regeneration of the oxidized dye. Table 4 lists the change in the atomic charge (∆q) on the dye molecule for the complex structure determined by Mulliken population and NBO analyses. The ∆q(first) was defined as the difference in atomic charge on the N3 molecule between the heterocycle-N3-I complex and the heterocycle-N3 complex. The ∆q(second) was also determined as the difference in atomic charge on the N3 molecule between the heterocycle-N3-I2 complex and the heterocycle-N3-I complex. With these definitions, a negative ∆q corresponds to more regeneration of

Figure 6. Correlation between the Jsc of the DSSC and (a) ∆q(first) or (b) ∆q(second).

Interactions of Dye with I-1 and Heterocycles in DSSCs position and analysis method. The correlations in Figure 6 reveal that the less the regeneration of oxidized dye occurs, the smaller the Jsc. Therefore, the hypothesis is confirmed. The N-containing heterocyclic additive in the electrolyte solution suppresses the regeneration of the oxidized dye by the I-/I3- redox couple, which is represented by eqs 1 and 2, lowering the Jsc of the DSSC. This suppression mechanism is supported by some experimental evidence. Greijer and co-workers reported that TBP suppressed the reaction of the NCS ligand of the dye with iodide ions by the measurement of resonance Raman scattering.38 Shi and co-workers also found the intensity of the in situ Raman line assigned to the interaction between the oxidized dye and the iodide ions was decreased by TBP addition to the electrolyte solution of an actual DSSC.39 Conclusions Simultaneous interactions of I- ions and six different Ncontaining heterocycles with cationic N3 dye at different sites were confirmed by a DFT method with a full geometric optimization. The first I- bonds to the S atom of the NCS ligand of the dye, while hydrogen bonds between the H atom of the carboxyl group for the N3 ligand and the N atom with a lone pair of the N-containing heterocycles and between the O atom with a lone pair of carboxyl groups of the N3 ligand and the H atom adjacent to the N atom involving the other hydrogen bond are formed. When the second I- is bonded to the first one, forming the I-S bond, the hydrogen bonds between the dye and the heterocycles are also observed. Interactions of I- via the S atom of the vertical NCS ligand, referring to N-containing heterocycles, are preferable than the horizontal one in the heterocycle-N3-I complexes. On the contrary, the horizontal configurations are more favorable for heterocycle-N3-I2 complexes than the vertical ones. The heterocycle interaction with the dye diminishes the iodide ions’ interactions with the dye. The more stable the interaction between the N3 and the N-containing heterocycles, the less stable the interaction between the N3 and the I- ions. The heterocycle interaction also makes the variation in the atomic charge on the dye molecule caused by reaction with iodide ions less negative, indicating that the heterocycles prevent the oxidized dye regenerating via iodide. When the results of the DFT analysis are compared to the experimentally measured dye-sensitized solar cell performance, in which the heterocycles were used as an additive to the electrolyte solution, the Jsc value of the cell increases with the negative change in the atomic charge on the N3 molecule as well as the interaction energy of iodide ions for the complex structures. The stronger the interaction of the oxidized dye with I- via the S atom of the NCS ligand, the easier the dye regeneration proceeds by the I-/I3- redox couple, leading to the higher Jsc of the dye-sensitized solar cell. Our results suggest that not only each component of the DSSC itself but also the interactions among them need to be considered as an important factor in improving DSSC performance. Acknowledgment. Theoretical calculations were partly performed using the Research Center for Computational Science, Okazaki, Japan. Supporting Information Available: Optimized geometries, selected geometrical parameters, and results of NBO and Mulliken population analyses of complexes. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737.

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