Theoretical Study on the Interactions between Black Dye and Iodide in

ARTICLE pubs.acs.org/JPCC

Theoretical Study on the Interactions between Black Dye and Iodide 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

bS Supporting Information ABSTRACT: Interactions between a carboxylated terpyridyl complex of tris-thiocyanato Ru(II), so-called “black dye”, and iodide ions were studied by using a density functional theory (DFT). All the oxidized linkage isomers [Ru(Htcterpy)(NCS)3] (1), [Ru(Htcterpy)(NCS)2(SCN)] (2 and 3), and [Ru(Htcterpy)(SCN)3] (4), where tcterpy is 4,40 ,400 -tricarboxy2,20 :60 ,200 -terpyridine, interacted with iodide ions forming a SI bond via the equatorial NCS ligand for 1 and 2, and the NI bond via the equatorial SCN for 3 and 4. For both monoiodide and diiodide ions, the interaction strength increased in the order of 3 < 4 < 2 < 1. A two-step interaction with two monoiodides via the equatorial NCS ligand occurred in only isomer 1 with a tetrabutylammonium (TBA), which formed hydrogen bonds with the S atom in one of the axial NCS ligands and with the O atom in the carboxyl group of the central pyridine in the terpydidine ligand. On the basis of the theoretical results, regeneration mechanisms for the oxidized black dye by the I/I3 redox couple after electron injection into the TiO2 conduction band in dye-sensitized solar cells, and the effects of the dye isomers and TBA counterion on DSSC performance were discussed.

’ INTRODUCTION During the last two decades, dye-sensitized solar cells (DSSCs) based on the concept of photosensitization of wide band gap oxide semiconductors have drawn a lot of attention. A basic DSSC, which was established by O’Regan and Gr€atzel,1 consists of three fundamental components: a sensitized photoanode, which is a Ru polypyridyl complex or an organic dyesensitized nanocrystalline TiO2 film on a transparent conductive oxide (TCO) glass, an electrolyte solution containing I/I3 as a redox couple, and a cathode, which is typically platinized TCO glass. Illuminating a cell with light causes the ground state of the dye to absorb a photon, and consequently, an electron is transferred to a higher energy level. This leads to an excited state. Next, an electron is injected from the photoexcited dye into the TiO2 conduction band. The injected electron percolates through the porous TiO2 layer into the TCO glass, passing the external load to the cathode. Subsequently, an electron is transferred to I3 to yield I at the cathode. Finally, I reduces the photo-oxidized dye molecule to its original ground state. In this way, a DSSC operates in a regenerative mode. At the heart of the DSSC function is electron injection (photo-oxidation) from the dye to TiO2 and regeneration (rereduction2) of the dye by an I/I3 redox.3 For successful sensitization, the LUMO level of the dye must be higher than the bottom of the TiO2 conduction band, while the redox energy must be higher than the HOMO level to allow the dye to be regenerated from its oxidized state. Additionally, the optimal dye for DSSC should be panchromatic, that is, adsorb visible light of all colors. Ideally, all photons below a threshold r 2011 American Chemical Society

wavelength of about 920 nm should be harvested and converted into electric current.4 Currently, one of the most efficient dyes for the conversion of light into electricity with TiO2 is black dye because the energy of the LUMO is located just above the TiO2 conduction band, and the absorption edge is 920 nm, which is in the near-infrared range.5 Although a cell with black dye has recorded an authorized maximum solar energy conversion efficiency (η) of 10.4% in 2005,6 the η value of DSSC has not increased in the last six years.7 Electron injection for black dye/TiO2 has been studied actively by means of transient absorption spectroscopy,811 but further improvements of η with black dye must incorporate knowledge of the other elemental process, namely the regeneration mechanism of oxidized dye by an I/I3 redox couple.12 Various mechanisms A, B, and C have been proposed for the regeneration reaction in DSSCs. Mechanism A: Sþ þ I f ½Sþ 3 I

ðA1Þ

½Sþ 3 I þ I f ½S 3 I2 f S0 þ I2

ðA2Þ

2I2 f I þ I3

ðA3Þ

Received: February 19, 2011 Revised: April 6, 2011 Published: April 18, 2011 9267

dx.doi.org/10.1021/jp201645y | J. Phys. Chem. C 2011, 115, 9267–9275

The Journal of Physical Chemistry C

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Clifford and co-workers have reported this two-step mechanism A for N3 dye, Ru(2,20 -bipyridine-4,40 -dicarboxylic acid)2(NCS)2,2 which is also one of the most efficient Ru dyes in DSSCs. After an electron is injected into TiO2, the process is initiated by binding I with the oxidized dye (Sþ) to form a transient intermediate complex [Sþ 3 I] (eq A1). This complex subsequently reacts with a second iodide ion to afford a neutral dye (S0) and I2 via [S 3 I2] (eq A2). Then I2 dissociates to yield iodide and triiodide ions (eq A3). The formation of the first intermediate (eq A1) is kinetically fast. However, the subsequent reaction of the intermediate with a second iodide species (eq A2) is much slower, and hence, the rate-determining step of the overall regeneration reaction. Privalov and co-workers have identified plausible pathways of the two-step regeneration mechanism via such complexes using DFT calculations.13,14 Mechanism B: Sþ þ I2 f ½Sþ 3 I2 f S0 þ I2

ðB1Þ

I2 þ I fI3

ðB2Þ

Schiffmann and co-workers have proposed the one-step mechanism B.15 The N3 dye cation is regenerated by I2 via a transient intermediate complex [Sþ 3 I2] (eq B1), and then I2 reacts with I to yield I3 (eq B2). In this regeneration mechanism, SI bond formation is central. Privalov and coworkers have also provided theoretical support for mechanism B using organic dye cations.14 Mechanism C: Sþ þ I f ½Sþ 3 I f S0 þ I

ðC1Þ

I þ I fI2

ðC2Þ

Recently, O’Regan and co-workers have suggested a third mechanism.3 Although similar to eq A1 of mechanism A, [Sþ 3 I] dissociate without the subsequent reaction of a second I (eq C1). It is important to realize that there is not a “one and only” mechanism for regeneration, as O’Regan and co-workers have noted.3 The regeneration mechanism of oxidized N3 dye has been investigated experimentally2 and theoretically.13,15 A theoretical study of regeneration has also been conducted on organic dyes such as 4-(diphenylamino)phenylcyanoacrylic acid.14 However, there has not been an experimental report on the regeneration of black dye, except the paper by Hagfeldt and co-workers.16 Although the electronic structure and spectroscopic property have been documented,1719 the regeneration mechanism of black dye has yet to be elucidated theoretically or experimentally. One reason improving DSSC performance is difficult may be that the synthesized samples of black dye contain four linkage isomers8 because isothiocyanate is a linear ambidentate ligand. Major isomer 1 is a complex with three N-bonded isothiocyanate (NCS) ligands, whereas isomers 2 and 3 possess two N-bonded NCS ligands and one S-bonded thiocyanate (SCN). Isomer 4 contains all S-bonded SCN ligands. The ratio between 1, sum of 2 and 3, and 4 in the synthesized product is 6:3:1.20 Although Nazeeruddin and co-workers discussed exclusively only the main isomer, which contains all N-bonded NCS ligands,4 the other isomers must also be investigated to enhance the DSSC performance because their ratio in the crude complex is considerable (40%). It has been reported that the isomers alter the electronic structures, such as HOMO, LUMO, and HOMOLUMO gap,

and the absorption spectra of black dye.17,20 Thus, the isomers also seem to affect the interaction between black dye and the iodide ions, and consequently, regeneration. The linkage isomers of N3 dye concerned with NCS ligands have been ruled out in the previous theoretical reports,13,15 but the interactions of iodide with all the black dye isomers, and not just the all N-coordinated one, need to be investigated theoretically to better understand the regeneration mechanism of oxidized dye with an I/I3 redox in DSSCs as well as to improve DSSC performance. Herein we focus on the intermolecular interactions of the four isomers in black dye with iodide ions. The main tools in this investigation are quantum chemical calculations at the DFT level, which are suitable for studies of large molecular systems like black dye. On the basis of the DFT results, we discuss the regeneration mechanisms for oxidized black dye by an I/I3 redox couple after electron injection into the TiO2 conduction band in DSSCs, and the influences of isomers.

’ COMPUTATIONAL DETAILS DFT calculations were performed with the Gaussian 09 program at the Research Center for Computational Science, Okazaki, Japan, and with the Gaussian 09W program on personal computers.21 The geometries were fully optimized in the gas phase at the hybrid DFT levels by B3LYP functions, which combine Becke’s three-parameter exchange function (B3)22,23 with the correlation function of Lee, Yang, and Parr (LYP).24 A LanL2DZ basis set, which corresponds to a Dunning/Huzinaga valence double-ζ basis (D95 V) for first-row elements25 and a Los Alamos effective core potential (ECP) plus a double-ζ basis for NaLa and HfBi atoms,2628 was used for all systems. The energies were corrected for the zero-point vibrational energies (ZPE), and the interaction energies were determined as the energy difference between the complex and the sum of the isolated monomers. Using this definition, a positive interaction energy corresponds to a strong interaction. All of the complexes had nonimaginary frequency geometries. These findings confirmed 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) analysis29,30 was conducted on the optimized geometries with the NBO 3.1 program31 included in the Gaussian program package. In NBO analysis, the stabilization energy E(2) associated with i f j delocalization is explicitly estimated by the following equation Eð2Þ ¼ ΔEij ¼ qi

F 2 ði, jÞ εj εi

ð1Þ

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. In addition, Mulliken population analysis was performed on the optimized structures.

’ RESULTS Structures of Oxidized Dye Isomers. According to the literature,17,20 four linkage isomers for N-coordinated NCS or S-coordinated SCN ligands are considered: 1 with three NCS ligands, 2 possessing one axial NCS, one equatorial NCS, and one axial SCN ligands, 3 with two axial NCS and one equatorial SCN ligands, and 4 containing three SCN ligands. Other linkage 9268

dx.doi.org/10.1021/jp201645y |J. Phys. Chem. C 2011, 115, 9267–9275


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Figure 1. Optimized geometries of [dyeI] species: white = H, gray = C, blue = N, red = O, purple = Na, yellow = S, teal = Ru, and violet = I atoms.

isomers with one NCS and two SCN ligands are shown in the Supporting Information. One protonated carboxylate (carboxyl) group is located on the central pyridine of the terpyridine ligand at position 3.4,20 For computational convenience, the two TBA counterions at the carboxylate groups attached to the peripheral pyridines of the terpyridine ligand are mimicked by Naþ.32,33 Our study began with the oxidized species in the doublet electronic spin state with a total charge of 0 because the total charge of the ground singlet state is 1. Figure S1 in the Supporting Information represents the optimized geometries at the B3LYP/LanL2DZ level, and Table S1 in the Supporting Information lists the main bond distances and angles of the optimized structures. Although the Htcterpy geometrical parameters are nearly the same among the four isomers, the bond angles of RuXC (X = N or S) for thiocyanates as well as RuX distances drastically vary with the isomer. The RuN bond distance for the equatorial NCS (RuN5) is about 0.05 Å larger than those for the axial ones (RuN6 and RuN7) in 10. A similar finding is obtained in 40 for the three RuS bonds. The RuNC angles for the NCS are almost linear, while the RuSC ones are around 105°, which are analogous to other Ru complexes with S-bonded SCN.3436 Structures of DyeI Interactions. Similar to N3 dye with two NCS ligands,13,15 the interaction of I with the oxidized black dye via the terminal atom of the NCS or SCN ligand seems plausible. In fact, other optimum geometries of the black dyeI dimer were not observed for any isomer by DFT. Figure 1 depicts the optimized geometries of the oxidized dyeI species with a total charge of 1 and multiplicity of 2. Although three NCS or SCN ligands can be involved in boding with I, only the equatorial ligands form stable SI bonds in 1I and 2I, and NI bonds in 3I and 4I. Table 1 lists the main bond distances and angles of the optimized structures. The intermolecular S11I14 distances for 1I and 2I are about 3.22 Å, which are stronger than the net van der Waals radii of the bonding atoms, 3.78 Å.37 The formed N11I14 bonds around 2.88 Å for 3I and 4I species

Table 1. Selected Bond Distances (Å), Bond Angles (deg), and Intermolecular Interaction Energies (E, kcal mol1) of I for the [DyeI] Species 1I

2I

3I

4I

RuN2

2.076

2.072

2.080

2.081

RuN3

1.940

1.948

1.939

1.950

RuN4

2.079

2.081

2.088

2.088

RuX5a

2.082

2.073

2.594

2.576

RuX6b RuX7c

2.047 2.047

2.553 2.042

2.042 2.051

2.552 2.535

X5C8a

1.187

1.189

1.710

1.712

X6C9b

1.193

1.737

1.195

1.737

X7C10c

1.193

1.194

1.194

1.737

C8Z11d

1.698

1.697

1.199

1.199

C9Z12e

1.683

1.193

1.681

1.193

C10Z13f

1.683

1.683

1.683

1.193

Z11I14d N2RuN4

3.214 160.8

3.217 160.5

2.865 160.7

2.893 160.3

N2RuX5a

101.4

101.3

96.4

96.0

N4RuX5a

97.8

98.2

102.8

103.7

N3RuX6b

91.1

94.1

92.0

94.0

N3RuX7c

91.1

91.4

90.9

94.7

RuX5C8a

173.3

173.5

109.6

111.6

RuX6C9b

175.6

103.5

170.6

103.3

RuX7C10c X5C8Z11a,d

175.6 178.4

175.3 178.3

175.0 177.3

103.3 177.2

X6C9Z12b,e

179.6

179.3

179.9

179.4

X7C10Z13c,f

179.6

179.8

180.0

179.4

C8Z11I14d

98.9

99.3

121.6

121.1

E

23.40

22.13

13.26

13.48

parameter

a

X5 = N5 for 1 and 2, and S5 for 3 and 4. b X6 = N6 for 1 and 3, and S6 for 2 and 4. c X7 = N7 for 1, 2, and 3, and S7 for 4. d Z11 = S11 for 1 and 2, and N11 for 3 and 4. e Z12 = S12 for 1 and 3, and N12 for 2 and 4. f Z13 = S13 for 1, 2, and 3, and N13 for 4. 9269



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Figure 2. Optimized geometries of [dyeI2] species: white = H, gray = C, blue = N, red = O, purple = Na, yellow = S, teal = Ru, and violet = I atoms.

are also closer than the net van der Waals radii, 3.53 Å. For the 1I, the C8S11 distance of the NCS ligand interacting with I is slightly longer than that for the free NCS. The C8N11I14 bond angles of 121° for 3I and 4I are larger than the C8S11I14 of 99° for 1I and 2I. For 2I, the increase in the RuN5 bond distance as well as the N3RuS6 angle is due to the interaction with I. Additionally, all the RuX bonds are elongated for NCS and SCN ligands in 3I and 4I. Furthermore, the interaction with I results in a 4° broadening of the N2RuS5, but a narrowing by 6° in the N4RuS5 bond angle for the 4I species. Moreover, Table 1 lists the intermolecular bond energy, E, of I with the oxidized black dye species. The E values are above 13 kcal mol1, and increase in the order of 3I < 4I < 2I < 1I, indicating the interaction stability between the oxidized dye and I. The higher the E value, the more stable the interaction between the oxidized black dye and iodide ion. Structures of the DyeI2 Interactions. Next, to confirm whether regeneration mechanism A in the Introduction applies to black dye, the [dyeI] species interacting with a second I was optimized with a total charge of 2. However, these attempts could not be optimized because an isomer where the second I stably interacts with the first one bonded to the NCS or SCN ligand was not identified. When the total charge is 1, stable dyeI2 species are found for all isomers (Figure 2). Compared to the [dyeI] species in Table 1, the intermolecular Z11I14 distances for [dyeI2] in Table 2 are closer and less than the net van der Waals radii of the bonding atoms. The distances of formed I14I15 bonds are around 3.04 Å, which is shorter than isolated I2 of 3.46 Å. The I14I15 bond distances for 1I2 and 2I2 are slightly longer than those for 3I2 and 4I2. The RuN3 bond distances become shorter upon I2 interaction. For 2I2, the RuN5 bond distance is elongated above 0.05 Å, and the angle of N3RuS6 increases over 4° compared to 20 in Table S1 in the Supporting Information. Additionally, the interaction of 30 with I2 increases the RuS5, RuN6, and RuN7 distances as

well as the N3RuN7 and RuS5C8 angles, but the N4RuS5 and RuN6C9 angles narrow (3I2 in Table 2). For 4I2, all of the RuS bond distances are about 0.08 Å longer than those of 40 species in Table S1 in the Supporting Information. Additionally, I2 interaction widens the N2RuS5 and RuS5C8 angles, but narrows the N4RuS5 and S5C8N11 angles. The E values of I2 with the oxidized dye in Table 2 range from 16 to 22 kcal mol1, and increase in the order of 3I2 < 4I2 < 2I2 < 1I2, which corresponds to the result of E of I with the oxidized dye in Table 1. To understand the nature and magnitude of the intermolecular interaction between the S or N atom of the dye ligand and iodide ions, we conducted NBO analysis on the [dyeI2] species. The N11 atoms interact with iodide for the 3I2 and 4I2 species with one valence lone pair, LP(1)N11, while the S11 atoms for the 1I2 and 2I2possess three valence lone pairs, LP(1)S11, LP(2)S11, and LP(3)S11 (Table 3). For 1I2 and 2I2 species, the LP(3)S11 occupancy is more stabilized than that for LP(1)S11. Moreover, the values of delocalization energy, E(2) for LP(3)S11 to the σ*I14I15 orbital, where LP(3)S11 participates as a donor and the σ*I14I15 antibond as an acceptor in a intermolecular charge transfer interaction, are 59.08 kcal mol1 for 1I2, and 58.94 kcal mol1 for 2I2. These values are larger than those for the LP(1)S11 to the σ*I14I15 orbital for 1I2 (3.54 kcal mol1) and 2I2 (3.59 kcal mol1). These findings indicate that 3 and 4 bind with iodide via their σ lone pair, but 1 and 2 prefer to bind via a π lone pair (LP(3)S11).38 The interaction of LPfσ*II can be considered a measure of the relative stability of dyeI2 complexes.39 The value of charge transfer energy E(2) corresponding to this interaction in the 2I2 species is smaller than that for the 1I2. The sum of the E(2) terms corresponding to the delocalization of LP(3)S11 in the 2I2 complex is 87.83 kcal mol1, which is less than that for 1I2 (88.12 kcal mol1). Thus, LP(3)S11 occupancy in 2I2 is greater than that in 1I2 (Table 3). Additionally, both NBO analysis and Mulliken population analysis indicate the atomic 9270



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Table 2. Selected Bond Distances (Å), Bond Angles (deg), and Intermolecular Interaction Energies (E of I2, kcal mol1) for the [DyeI2] Species 1I2

2I2

3I2

4I2

RuN2

2.077

2.072

2.081

2.081

RuN3

1.940

1.949

1.935

1.945

RuN4

2.080

2.082

2.080

2.083

RuX5a

2.089

2.079

2.621

2.611

RuX6b RuX7c

2.045 2.045

2.550 2.041

2.041 2.048

2.548 2.533

X5C8a

1.184

1.186

1.711

1.712

X6C9b

1.194

1.736

1.196

1.737

X7C10c

1.194

1.194

1.195

1.737

C8Z11d

1.708

1.708

1.188

1.188

C9Z12e

1.682

1.193

1.679

1.193

C10Z13f

1.682

1.682

1.682

1.193

Z11I14d I14I15

2.956 3.059

2.955 3.061

2.355 3.018

2.350 3.019

N2RuN4

160.7

160.4

160.9

160.5

N2RuX5a

100.3

99.9

97.7

96.8

N4RuX5a

98.9

99.7

101.3

102.8

N3RuX6b

91.4

94.1

91.4

94.4

N3RuX7c

91.3

91.6

92.1

94.6

RuX5C8a

177.7

178.5

108.9

111.0

RuX6C9b RuX7C10c

176.4 176.4

103.2 175.8

168.8 176.2

103.3 102.9

X5C8Z11a,d

179.2

178.7

175.9

176.0

X6C9Z12b,e

179.6

179.6

179.9

179.5

X7C10Z13c,f

179.6

179.8

180.0

179.7

C8Z11I14d

102.1

103.2

170.6

174.8

Z11I14I15d

178.2

177.6

177.9

178.6

E

21.58

20.39

16.61

16.84

parameter

a

X5 = N5 for 1 and 2, and S5 for 3 and 4. b X6 = N6 for 1 and 3, and S6 for 2 and 4. c X7 = N7 for 1, 2, and 3, and S7 for 4. d Z11 = S11 for 1 and 2, and N11 for 3 and 4. e Z12 = S12 for 1 and 3, and N12 for 2 and 4. f Z13 = S13 for 1, 2, and 3, and N13 for 4.

charges on the S11 atom for the 2I2 complex are more negative than for the 1I2 complex. Similar to the above results, this behavior demonstrates that the flow of electron density from S11 to σ*I14I15 in the 1I2 is greater than that for 2I2. Moreover, this observation is consistent with the larger value of the net charge transferred from iodide to dye, Δq for the 1I2 than the 2I2, regardless of the analysis method. Similar tendencies are observed upon comparing the 3I2 and 4I2 species. 4I2 has a lower LP(1)N11 occupancy, but higher σ*I14I15 antibonding occupancy and larger E(2) value of LP(1)N11fσ*I14I15 than 3I2, suggesting the I2 interaction for 4I2 is more stable than that with 3I2. Structures of the TBADyeIodide Interactions. As previously mentioned, black dye is an anion with a formal 1 charge in its ground singlet state. Navakhun and Ruangpornvisuti have reported that the self-assembly dimer of 3,4-dichloro-2,5-diamidopyrrole anion in the gas phase does not exist without the presence of two TBA molecules as counterions using DFT calculations.40 Yan and co-workers have also conducted geometric optimization of dipositive bis[4-(N,N0 -diphenylamino)phenyl2,20 :60 ,200 -terpyridine]ruthenium(II) with two counter cations,

2PF6 by DFT.41 Accordingly, we considered the coexistence of one TBA countercation based on the original form of black dye.4,20 The geometries of the oxidized black dye with a TBA were optimized with a total charge of þ1; however, except for 1, the isomers do not have a stable complex structure that includes TBA. Consequently, hereafter the iodide interactions with black dye considering the TBA counterion are investigated only with 1 species. Figure 3 represents the optimized structures of oxidized 1 with TBA, 1(TBA)þ. TBA binds with the S13 atom of one of the axial NCS ligands via its H atom in the butyl group. The intermolecular S13 3 3 3 H distance is 2.706 Å, which is smaller than the net van der Waals radii of the binding atoms, 3.00 Å,37 indicating the formation of an intermolecular hydrogen bond.42 As listed in Table 4, this bonding elongates the RuN7 bond, but narrows the RuN7C10 angle compared to 10 (Table S1 in the Supporting Information). Furthermore, the terminal H atom of the other butyl group interacts with the O atom of the carboxyl group on the central pyridine of the terpyridyl ligand. Moreover, its O 3 3 3 H distance of 2.700 Å suggests hydrogen bond formation because the net van der Waals radii of O and H atoms is 2.72 Å. The E value of TBA is 12.32 kcal mol1. With the TBA species, DFT calculations gave only the optimum structure of the SI bond via the S11 atom of equatorial NCS. For the TBA1I species with a total charge of 0, 1(TBA)I0 (Figure 3), the S11I14 distance is 3.211 Å, which is very similar to 1I (Table 1). The E value of I is 67.04 kcal mol1. Similar to the 1(TBA)þ species, intermolecular hydrogen bonds between 1 and TBA are formed. Additionally, the S13 atom of NCS interacts with two H atoms of a different butyl group. The distance of the O 3 3 3 H hydrogen bond for 1(TBA)I0 is 2.629 Å, which is closer than that of 1(TBA)þ. The E of TBA in 1(TBA)I0 is 55.96 kcal mol1, which is larger than that without I. These results indicate that the interaction of TBA with 1 in the 1(TBA)I0 species is stronger than that with 1(TBA)þ. The elongation of the RuN7 bond distance observed at 1(TBA)I0 (Table 4) due to the TBA is consistent with that of 1(TBA)þ. Unlike the complex without TBA, the geometry optimization of 1(TBA)I0 interacting with a second I occurred with a total charge of 1, as shown by 1(TBA)I2 in Figure 4. The distance of the formed S11I14 bond is 2.939 Å, which is less than the net van der Waals radii of the bonding atoms of 3.78 Å. Additionally, the I14I15 bond distance of 3.087 Å is shorter than the isolated I2 distance of 3.46 Å. The bond angle of S11I14I15 is nearly linear. The E values of the second I and of I2 are 9.93 and 76.97 kcal mol1, respectively. Although the bond distances vary, the three types of hydrogen bonds with TBA are retained. Furthermore, TBA induces a longer RuN7 bond and a narrower N3RuN7 angle compared to the free axial NCS ligand (Table 4). The structure of 1(TBA)þ interacting with I2 in 1(TBA)I20 in Figure 4 and Table 4 was optimized with a total charge of 0, which corresponds to 1I2 (Figure 2 and Table 2). The E value of I2 is 63.03 kcal mol1. Additionally, the observed intermolecular hydrogen bonds between 1 and TBA are analogous to 1(TBA)I0 in Figure 3. The E value of TBA is 53.77 kcal mol1,

’ DISCUSSION Regeneration Mechanisms for Black Dye. As described in the Introduction, various mechanisms A, B, and C have been proposed for the regeneration reaction in DSSCs. Do these three 9271



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Table 3. Selected Occupancy Data of NBOs (e), Second Order Perturbation Energy (E(2), kcal mol1), Atomic Charge on the Atom Interacting with Iodide (e), and Net Charge Transferred from Iodide to Dye (Δq, e) for the [DyeI2] Species 1I2

2I2

LP(1)S11a

1.9742

1.9739

LP(2)S11a LP(3)S11a

1.7961 1.4837

1.7966 1.4851

sumb

5.2540

5.2556

σ*I14I15a

0.4096

0.4126

LP(1)S11fσ*I14I15a

3.54

3.59

LP(3)S11fσ*I14I15a

59.08

58.94

LP(1)S11fσ*N5C8a LP(2)S11fπ*N5C8a

13.26 39.79

13.23 39.24

LP(3)S11fπ*N5C8a

29.04

28.89

sumc

88.12

87.83

NBO

0.1077

0.1102

Mullikend

0.0672

0.0680

parameter occupancy

LP(1)N11a

E(2)

LP(1)N11fσ*I14I15a

LP(1)N11fσ*S5C8a atomic charge of S11

3I2

4I2

1.7486

1.7445

1.7486

1.7445

0.2430

0.2450

55.50

56.94

9.13

9.05

64.63

65.99

atomic charge of N11

NBO

0.5382

0.5441

Δq

Mullikend NBO

0.5995

0.5963

0.1787 0.7986

0.1804 0.7970

Mullikend

0.6088

0.6051

0.7860

0.7845

a

Number in parentheses denotes the specific lone pair, LP. b Sum of occupancy for LP. c Sum of E(2) corresponding to the main delocalization of LP. d Determined by Mulliken population analysis.

Figure 3. Optimized geometries of 1(TBA)þ and 1(TBA)I0 species: white = H, gray = C, blue = N, red = O, purple = Na, yellow = S, teal = Ru, and violet = I atoms. Distances (normal letters) are given in angstroms and angles (italic letters) in degrees.

regeneration mechanisms apply to black dye? Our theoretical study aims to elucidate the interaction of iodide with black dye. Actually, we found that the oxidized black dye species (Figure S1 in the Supporting Information) interacts with I via the terminal S or N atom of NCS or the SCN ligand (Figure 1). These results reveal that mechanism C is applicable to black dye. Additionally, the oxidized black dye species in Figure S1 in the Supporting Information also interacts with I2 via NCS or SCN ligand, which is depicted in Figure 2. This finding provides theoretical evidence that black dye can be regenerated via mechanism B. As depicted in Figure 3, oxidized black dye with a TBA counterion interacts with a first I to form TBADyeI species. A second I then bonds to the first one, leading to TBADyeI2 species (Figure 4). Consistent with the findings of Hagfeldt and coworkers that the rapid formation of I2 derived from the dye regeneration in eq A2 occuers,16 these results demonstrate that the two-step regeneration mechanism A is applicable to black dye. Therefore, we theoretically confirmed black dye can be regenerated via three different mechanisms. It should be noted that 1 can be regenerated via mechanisms A, B, and C with (1(TBA)I0 in Figure 3 and 1(TBA)I2 and 1(TBA)I20 in Figure 4) or without TBA (1I in Figure 1 and 1I2 in Figure 2). The regeneration process of oxidized 1 with TBA, 1(TBA)þ can be initiated by binding I with the S atom of the equatorial NCS ligand to form a transient intermediate complex 1(TBA)I0 (eq A1 of mechanism A). This complex subsequently can react with a second iodide ion to afford a neutral dye and I2 via 1(TBA)I2 (eq A2 of mechanism A), or can dissociate without the subsequent reaction of a second I (eq C1 of mechanism C). The 1(TBA)þ as well as 10 also can be regenerated by I2 via a transient intermediate complex 9272



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Table 4. Selected Bond Distances (Å) and Bond Angles (deg) for the TBADyeIodide Species 1(TBA)þ

1(TBA)I0

1(TBA)I2

1(TBA)I20

RuN2

2.095

2.080

2.083

2.080

RuN3 RuN4

1.970 2.093

1.938 2.081

1.969 2.083

1.937 2.085

RuN5

2.027

2.073

2.087

2.082

RuN6

2.003

2.019

2.047

2.018

RuN7

2.046

2.075

2.083

2.074

N5C8

1.196

1.188

1.185

1.185

N6C9

1.196

1.195

1.192

1.195

N7C10

1.191

1.189

1.188

1.190

C8S11 C9S12

1.669 1.666

1.693 1.675

1.713 1.688

1.702 1.674

parameter

Figure 4. Optimized geometries of 1(TBA)I2 and 1(TBA)I20 species: white = H, gray = C, blue = N, red = O, purple = Na, yellow = S, teal = Ru, and violet = I atoms. Distances (normal letters) are given in angstroms and angles (italic letters) in degrees.

1(TBA)I20 as well as 1I2 (eq B1 of mechanism B). Similar to 10, the regeneration of 20 can be initiated by binding I or I2 with the S atom of the equatorial NCS ligand, but can proceed via only mechanism B or C. The regeneration of 30 and 40 also can proceed via mechanism B or C, but the initiation reaction may be I or I2 binding with the N atom of the equatorial SCN ligand. Judging from the interaction energies and population analyses, the dye regeneration proceeds easily in the order of 3 < 4 < 2 < 1. Implications on DSSC Performance. As explained in the Introduction, without employing a separation technique such as pH titration, synthesized black dye contains four linkage isomers, which seem to prevent the improvement of DSSC performance. In fact, our results indicate that the interaction strength with iodide drastically varies between isomers; isomer 1, which has three N-bonded NCS ligands, interacts the strongest with iodide via the S atom of NCS, whereas 3, which has two axial NCS and one equatorial SCN, shows the weakest interaction via the N atom of the SCN. The stronger the interaction of the oxidized dye with the iodide ions, the easier dye regeneration after electron injection into the TiO2 conduction band proceeds by an I/I3 redox couple, leading to a higher photocurrent in the DSSC.43,44 Thus, our study strongly suggests that oxidized black dye isomer 3 has a weaker interaction with iodide than isomer 1, and consequently less regeneration occurs, resulting in a lower DSSC performance. Actually, Kohle and co-workers have found that Ru(bmipy)(Hdcbpy)(NCS), where bmipy and dcbpy are 2,6-bis(1-methylbenzimidazol-2-yl)pyridine and 4,40 -dicarboxy-2,20 -bipyridine, respectively, containing 20%

C10S13

1.685

1.699

1.708

1.697

N2RuN4

159.5

160.8

159.3

160.7

N2RuN5

100.4

101.0

101.0

100.5

N4RuN5

99.9

98.2

99.6

98.8

N3RuN6

91.7

92.0

91.6

92.7

N3RuN7

89.9

90.6

88.8

90.2

RuN5C8 RuN6C9

178.5 177.2

173.1 176.7

178.0 176.1

174.6 176.9

RuN7C10

173.5

175.8

175.4

176.9

N5C8S11

179.7

178.4

178.6

179.3

N6C9S12

178.9

179.5

179.9

179.5

N7C10S13

179.2

179.5

179.7

179.7

S-bonded complex gives about 1020% lower cell performance than pure N-bonded complex.45 The TBA countercation also significantly influences the regeneration of black dye. The 10 species without TBA does not interact with the iodide ions via two-step mechanism A, implying that the lack of TBA diminishes the regeneration pathway of the oxidized black dye by I/I3 redox couple. Without TBA countercation, less regeneration occurs, leading to a lower DSSC performance. In fact, Nazeeruddin and coworkers have reported that the cell using black dye with two TBA shows a much lower DSSC performance compared to black dye with three TBA cations.4 In addition to increasing the solubility of the dye in organic solvents for dye adsorption on a TiO2 film due to its hydrophobicity,46 the TBA cation with black dye facilitates the regeneration reaction. Hence, our theoretical results suggest that the type of isomers and the number of TBA counterions for black dye must be considered to improve DSSC performance.

’ CONCLUSIONS A DFT method with full geometric optimization confirmed that I ions interact with the four linkage isomers in oxidized black dye. For [Ru(Htcterpy)(NCS)3] (1) and [Ru(Htcterpy)(NCS)2(SCN)] (2), I and I2 bind via the S atom of the equatorial NCS ligand. [Ru(Htcterpy)(NCS)2(SCN)] (3) and [Ru(Htcterpy)(SCN)3] (4) form NI bonds via the equatorial SCN ligand, but their interactions are much weaker than those of isomers 1 and 2. Axial NCS or SCN ligand binding with iodide was not found. The stronger the interaction of oxidized black dye with the iodide ions, the easier dye regeneration after electron injection into the TiO2 conduction 9273


The Journal of Physical Chemistry C band proceeds through one-step mechanisms B and C by an I/I3 redox couple. Judging from the interaction energies and population analyses, the interaction strengths with both I and I2 ions increase in the order of 3 < 4 < 2 < 1, but consecutive interactions with two I ions are not observed in any isomers. Considering the counterions, only isomer 1 interacts with a TBA, and forms two hydrogen bonds via the S atom in the one of axial NCS ligands and the O atom in the carboxyl group of the central pyridine for the terpyidine ligand, 1(TBA)þ. The 1(TBA)þ species exhibits a two-step interaction with two I ions as well as I2 via the S atom of the equatorial NCS ligand, forming hydrogen bonds with TBA. These results demonstrate that oxidized 1 with a TBA counterion can be regenerated through two-step mechanism A as well as one-step mechanisms B and C by an I/I3 redox couple. Therefore, a complex possessing three N-bonded NCS ligands with three TBA counterions is the most effective of the four isomers in black dye in terms of regeneration by an I/I3 redox couple in DSSCs. To enhance DSSC performance, the type of isomers and the number of counterions for sensitizing dye must both be considered.

’ ASSOCIATED CONTENT

bS

Supporting Information. DFT results of the oxidized black dye species and the isomers with one NCS and two SCN ligands. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (H.K.).

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Theoretical Study on the Interactions between Black Dye and Iodide in

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