Theoretical Study on the Intermolecular Interactions of Black Dye

Oct 24, 2012 - BC1 has a higher intermolecular interaction energy than BB1. On the basis of these theoretical results, the structure of black dye aggr...
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Theoretical Study on the Intermolecular Interactions of Black Dye Dimers and Black Dye−Deoxycholic Acid Complexes in DyeSensitized Solar Cells Hitoshi Kusama* and Kazuhiro Sayama National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan S Supporting Information *

ABSTRACT: Herein the intermolecular interactions in Ru(H3tcterpy)(NCS)3 (black dye) dimers, where tcterpy is 4,4′,4″-tricarboxy-2,2′:6′,2″-terpyridine, deoxycholic acid (3α,12α-dihydroxy-5β-cholan-24-oic acid, DCA) dimers, and black dye−DCA complexes in acetonitrile were investigated using density functional theory (DFT) and time-dependent DFT (TD-DFT). Among the five resulting black dye dimers, the most preferable species (BB1) forms intermolecular hydrogen bonds via the carboxyl groups and has a centrosymmetric structure similar to that reported for a black dye crystal. Theoretical calculations indicate six black dye− DCA complexes, and the most stable configuration (BC1) has three intermolecular hydrogen bonds between the two carboxyl groups of the dye ligand and one carboxyl and two hydroxyl groups of DCA. BC1 has a higher intermolecular interaction energy than BB1. On the basis of these theoretical results, the structure of black dye aggregation and the aggregation suppression mechanism by DCA during the immersion process to prepare for dye-sensitized solar cell (DSSC) are discussed.

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INTRODUCTION Dye-sensitized solar cells (DSSCs) based on the concept of photosensitization of wide band-gap oxide semiconductors have received much attention since O’Regan and Grätzel announced a high solar energy conversion efficiency (η) above 7% in 1991.1 Their basic DSSC consists of three fundamental components: a sensitized photoelectrode composed of a Ru polypyridyl complex dye-sensitized nanocrystalline n-type TiO2 semiconductor film on a transparent conductive oxide (TCO) glass, an electrolyte solution containing I−/I3− as a redox couple, and a counter electrode, which is typically platinized TCO glass. Illuminating a cell with light causes the ground state of the dye to absorb a photon, and an electron is consequently transferred to a higher energy level. This process leads to an excited state. Then 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 counter electrode. Subsequently, I3− is reduced to yield I− at the counter electrode. Finally, I− reduces a photo-oxidized dye molecule to its original ground state (regeneration). Thus, a DSSC operates in a regenerative mode. However along with these desired electron-transfer pathways, other loss reactions occur simultaneously [e.g., recombination of injected electrons in the TiO2 with acceptors in the electrolyte (I3− and/or I2)].2 The dye sensitizer, which is a crucial component of a DSSC, should fulfill the following characteristics.2,3 (i) It should have a © 2012 American Chemical Society

high molar extinction coefficient and absorption spectrum that spans the entire visible region and ideally the part of the nearinfrared (IR) region. (ii) Anchoring groups such as carboxyl groups should be present to strongly bind the dye onto the TiO2 surface. (iii) The excited state energy level (LUMO level) should be higher than the conduction band edge of TiO2 for an efficient electron-transfer process between the excited dye and conduction band of the TiO2. (iv) The oxidized state (HOMO level) should be more positive than the I−/I3− redox potential of the electrolyte for dye regeneration. (v) The structure should be optimized to avoid unfavorable dye aggregation on the TiO2 surface. (vi) The dye sensitizer should be photo, electrochemically, and thermally stable. Currently, black dye (Chart 1) is one of the most efficient dyes to convert light into electricity with TiO2 and I−/I3− because the energy level of its LUMO is located just above the TiO2 conduction band [characteristic (iii)] and the absorption edge on TiO2 is 920 nm [characteristic (i)], which is in the near-IR range.4,5 A cell using black dye has recorded an certified maximum η value of 11.4%.6,7 Unlike N719 dye, cis(NBu4)2[Ru(2,2′-bipyridine-4,4′-dicarboxylic acid)2(NCS)2],8 which is a very efficient Ru dye in DSSCs, the dye solution used in the immersion process usually contains both black dye Received: July 6, 2012 Revised: October 1, 2012 Published: October 24, 2012 23906

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Wenger and co-workers have pointed out that hydrogen bonding induces dye aggregation in solution.11 Black dye molecules in a crystal form hydrogen bonds between their carboxyl groups and become aggregated.13 However, the structure of black dye aggregation in a solvent remains unknown. Furthermore, to the best of our knowledge, the suppression mechanism of black dye aggregation by DCA has not been studied. Ikeda and co-workers have noted that dye-toadditive (such as DCA) association may effectively suppress dye aggregation.12 DCA molecules may form hydrogen bonds with black dye because DCA molecules have one terminal carboxyl group and two hydroxyl groups at C3 and C12 (Chart 1). Limmavarirat and co-workers have prepared a complex between DCA and salicylic acid (2-hydroxy-benzoic acid, SA) by grinding and coprecipitation methods. Their IR and X-ray powder diffraction (XRD) spectra have suggested that a hydrogen bond between the hydroxyl group of DCA and the carboxyl group of SA is formed in the crystal of the DCA−SA complex with a 1:1 stoichiometry.14 Herein, we focus on the intermolecular interactions of black dye−black dye, DCA−DCA dimers, and black dye−DCA complexes using quantum chemical calculations at the DFT level, which are suitable to investigate large molecular systems like black dye. On the basis of the DFT findings, we discuss the association and aggregation structures of black dye in solution. We also discuss the suppression mechanism of black dye aggregation upon adding DCA into the dye solution. Our theoretical results have implications on the design of additives for dye solutions and should improve DSSC performance.

Chart 1. Constitutional Formulas of Black Dye and DCA

and a cholanic acid derivative such as DCA.7 The presence of DCA enhances the short-circuit photocurrent density (Jsc), open-circuit photovoltage (Voc), and η of the black dyesensitized cell.9 Although some mechanisms have been suggested for the improved DSSC performance by DCA, the predominant one is that DCA suppresses black dye aggregation on the TiO2 surface [characteristic (v)],5,10 which prevents the loss of photogenerated electrons due to intermolecular electron transfer between the neighboring dye molecules.11 In a scanning tunneling microscopy (STM) study, Ikeda and coworkers have reported that adding DCA to a black dye solution causes the ratio of single dye molecules to aggregated dye molecules adsorbed on a rutile TiO2(110) surface to increase, but adsorbed DCA is not observed.12

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COMPUTATIONAL DETAILS DFT calculations were performed using the Gaussian 09 program at the Research Center for Computational Science, Okazaki, Japan and the Gaussian 09W program on personal computers.15 The geometries were fully optimized at the hybrid DFT level by mPW1PW91 functional, which combines

Figure 1. Optimized geometries of black dye and DCA monomers in acetonitrile. White, gray, blue, red, yellow, and teal represent H, C, N, O, S, and Ru atoms, respectively. 23907

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Figure 2. Optimized geometries of the black dye dimers in acetonitrile. White, gray, blue, red, yellow, and teal represent H, C, N, O, S, and Ru atoms, respectively. Broken lines denote intermolecular bonds.

TD-DFT31 calculations in acetonitrile were performed using a B3LYP exchange-correlations functional32 and a DGDZVP basis set: the all-electron, double-ζ valence polarized basis set optimized specifically for DFT methods.33,34 This manner has been shown to provide an accurate description of the optical properties in Ru isothiocyanate bipyridine35−37 and terpyridine38 complexes for DSSC sensitizer.

Perdew−Wang 1991 exchange functional as modified by Adamo and Barone (mPW1) with the Perdew and Wang’s 1991 gradient-corrected correlation functional (PW91).16 This combination of functional has been constructed with the main aim of improving the well-known deficiency in the long-range behavior of DFT functional, which is of particular importance for studying noncovalent intermolecular interactions.16−18 It has been also reported that the mPW1PW91 functional gives good results for black dye structures.19 A mixed basis set where 6-31G(d,p) basis functions20 were used on H, C, N, O, and S atoms and Los Alamos effective core potential (ECP) plus Hay−Wadt double-ζ basis set (LanL2DZ ECP)21−24 were used on Ru. This mixed basis set has been shown to provide an accurate description of the geometrical parameters in black dye.19,25,26 The solvent effects of acetonitrile were modeled using a conductor-like polarizable continuum model (CPCM)27 within the self-consistent reaction field (SCRF) theory. In the SCRF calculations, the dielectric constant of acetonitrile was 35.688. All of the species in acetonitrile had nonimaginary frequency geometries, confirming that the optimized structures correspond to real minima on the whole potential energy surface. The intermolecular interaction energies were determined as energy differences between the sum of the isolated monomers and the dimer or complex. To understand the nature and magnitude of the intermolecular interactions, natural bond orbital (NBO) analysis28,29 with the CPCM SCRF model was conducted on the optimized geometries with the NBO 3.1 program30 included in the Gaussian 09W program package. In addition, Mulliken population analysis was performed on the optimized structures.

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RESULTS Structures of Black Dye and DCA Monomers. Figure 1 depicts the optimized geometries of the isolated black dye and DCA molecule in acetonitrile. According to the literature,19,39 fully protonated black dye is considered: three protonated carboxylate (carboxyl) groups are located on the pyridines of the terpyridine ligand at position 3 (Chart 1). Geometry optimization of DCA indicates that the anti conformer with a torsion angle of 177.8° for the side chain at C17 is more stable by 0.00086 hartree than the gauche conformer with a torsion angle of 64.8°.14 Consequently, only the anti conformer of the DCA molecule is investigated hereafter. Structures of the Black Dye Dimers. Figure 2 illustrates the optimized geometries of the black dye dimers in acetonitrile, and Table S1 in the Supporting Information (SI) lists the main bond distances and angles of the optimized dimer structures as well as those for the monomer. Five stable configurations were found: BB1, BB2, BB3, BB4, and BB5. For BB1, the two terminal H atoms (H48 and H48′) of the carboxyl groups attached to the peripheral pyridine of the terpyridine ligand interact with the two carbonyl O atoms (O43′ and O43) of the carboxyl groups located on the central 23908

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Table 1. Distances and Angles of the Intermolecular Bonds, Relative Energies with Respect to the BB2 species (ΔE), and Intermolecular Interaction Energies (EHB) for the Black Dye Dimers BB1 distance (Å) H48′···O43 (1.711) H48···O43′ (1.711) H31···O44′ (2.210) H32···O44′ (2.260) H31′···O44 (2.210) H32′···O44 (2.260) Angle (deg) O43···H48′−O45′ (170.8) O45−H48···O43′ (170.7) C25−H31···O44′ (171.6) C26−H32···O44′ (171.9) O44···H31′−C25′ (171.6) O44···H32′−C26′ (172.0) parameter ΔE (hartree) EHB (kcal mol−1)

BB2 H47′···O43 H48···O44′ H31···O43′ H32···O43′ H31′···O44 H32′···O44

(1.712) (1.712) (2.205) (2.250) (2.218) (2.240)

O43···H47′−O42′ (170.7) O45−H48···O44′ (170.5) C25−H31···O43′ (172.6) C26−H32···O43′ (172.8) O44···H31′−C25′ (171.1) O44···H32′−C26′ (173.3) BB1 0.00002 −15.66

BB3

BB4

BB5

H47···O43′ (1.577) H47′···O43 (1.577)

H47···O41′ (1.581) H46′···O43 (1.579)

H46···O41′ (1.581) H46′···O41 (1.581)

O42−H47···O43′ (178.9) O43···H47′−O42′ (178.9)

O42−H47···O41′ (179.2) O43···H46′−O40′ (179.1)

O40−H46···O41′ (179.1) O41···H46′−O40′ (179.1)

BB2

BB3

BB4

BB5

0.00000 −15.67

0.00113 −14.96

0.00127 −14.87

0.00150 −14.73

black dye dimers may affect their excitation energies. Considering the order of the relative stability and structural resemblance to the experimental results,13 TD-DFT calculations in acetonitrile were performed on black dye monomer, BB1, and BB5. We must stress that our research focused on the relative peak shifts upon the intermolecular interaction of the black dye rather than reproducing the exact excitation energies and absorption spectra.42 The results for the black dye monomer in Table 2 are consistent with the recent theoretical results reported by

pyridine of the terpyridine ligand, forming a centrosymmetric structure. Both the intermolecular H···O distances are 1.711 Å (Table 1) and are smaller than the net van der Waals radii of the binding atoms (2.720 Å),40 indicating intermolecular hydrogen bonding. The intermolecular hydrogen bonds with around 2.240 Å bond distances are also observed between the O atom with a lone pair in the carboxyl group forming the other bond (O44 and O44′) and the H atom of the central and peripheral pyridines (H31′, H32′, H31, and H32). The bond angles of O−H···O and C−H···O are nearly linear. This configuration with hydrogen bonds closely resembles the crystal structure of black dye studied by Shklover and coworkers.13 Similar to BB1, there are two O−H···O hydrogen bonds via the H and O atoms for BB2; one is between the two central carboxyl groups (O43···H47′−O42′), while the other is between the two peripheral carboxyl groups (O45− H48···O44′). Additionally, four hydrogen bonds of C25− H31···O43′, C26−H32···O43′, O44···H31′−C25′, and O44···H32′−C26′ are found. For BB3, BB4, and BB5, one carboxyl group forms cyclic hydrogen bonds41 with the other carboxyl groups. Two central (BB3), one central and one peripheral (BB4), and two peripheral carboxyl groups (BB5) located on the terpyridine ligand are involved in cyclic hydrogen bonds. The intermolecular H···O distances are around 1.580 Å, which are closer than those observed in BB1 and BB2 in Table 1. The bond angles of O−H···O are very nearly linear. Table 1 also lists the relative energy with respect to the BB2 dimer (ΔE) and the intermolecular interaction energy (EHB). From the ΔE values, the most and the least stable black dye dimers are identified as BB2 and BB5, respectively. The EHB values exceed −14 kcal mol−1. The number of carboxyl groups involved in hydrogen bonding seems to influence EHB. The relative order of the EHB values among the five configurations is BB5 < BB4 < BB3 < BB1 ≈ BB2, which indicates the intermolecular interaction stability. Nazeeruddin and co-workers have reported that the electronic absorption spectra of black dye depend on the nature of the carboxyl groups at the terpyridine ligand.5 Hence, hydrogen bonds formed via the carboxyl groups observed in the

Table 2. Selected Excitation Energies (eV), Wavelengths (nm), Oscillator Strengths, and Major Contributions for the Black Dye Monomer, BB1, and BB5 Species species

excitation energy

wavelength

oscillator strength

monomer

1.641

755.4

0.0271

1.783 2.073

695.4 598.2

0.0451 0.0462

1.616

767.2

0.0489

1.793 2.106

691.6 588.8

0.1109 0.0939

1.631

760.3

0.0657

1.770 2.059

700.6 602.3

0.0863 0.1072

BB1

BB5

major contributiona H − 1→L (69.35) H→L (66.87) H→L + 1 (69.80) H − 1→L (98.14) H→L (49.44) H→L + 1 (98.48) H − 1→L (49.69) H→L (48.61) H→L + 1 (49.80)

a

H and L represent HOMO and LUMO, respectively. Number in parentheses is in %.

Sodeyama and co-workers.39 The excited state located at 2.073 eV (598.2 nm) is mainly controlled by the transition from the HOMO to the LUMO + 1. The peak at 1.783 eV (695.4 nm) is mainly contributed by the HOMO−LUMO transition. The peak with the lowest excitation energy of 1.641 eV (755.4 nm) is mainly controlled by the excitation from the HOMO−1 to the LUMO. Similar absorptions are observed in BB1, but their excitation energies and wavelengths change drastically. The 23909

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Figure 3. Optimized geometries of the black dye−DCA complexes in acetonitrile. White, gray, blue, red, yellow, and teal represent H, C, N, O, S, and Ru atoms, respectively. Broken lines denote intermolecular bonds.

Table 3. Distances and Angles of the Intermolecular Bonds, Relative Energies with Respect to the BC1 Species (ΔE), Intermolecular Interaction Energies (EHB), and Atomic Charge on the DCA Molecule for the Black Dye−DCA Complexes BC1 Distance (Å) H46···O031 (1.624) H122···O41 (2.106) H47···O241 (1.655) Angle (deg) O40−H46···O031 (164.6) O41···H122−O121 (146.7) O42−H47···O241 (175.5) parameter ΔE (hartree) EHB (kcal mol−1) natural charge (e) Mulliken charge (e)

BC2

BC3

BC4

BC5

BC6

H47···O241 (1.662) H122···O44 (2.010) H48···O031 (1.633)

H47···O031 (1.666) H122···O43 (2.050) H48···O241 (1.700)

H243···O41 (1.640) H46···O241 (1.538)

H243···O44 (1.639) H48···O241 (1.538)

H243···O43 (1.628) H47···O241 (1.525)

O42−H47···O241 (175.5) O44···H122−O121 (157.2) O45−H48···O031 (168.4) BC1 0.00000 −19.13 0.1211 0.1218

O42−H47···O031 (160.7) O43···H122−O121 (154.2) O45−H48···O241 (166.4) BC2 0.00009 −19.07 0.1048 0.0982

O41···H243−O242 (178.8) O40−H46···O241 (177.3)

O44···H243−O242 (178.8) O45−H48···O241 (177.3)

O43···H243−O242 (179.2) O42−H47···O241 (177.4)

BC3

BC4

BC5

BC6

0.00241 −17.61 0.0812 0.0909

0.00459 −16.25 0.0259 0.0232

0.00460 −16.24 0.0258 0.0231

0.00552 −15.67 0.0275 0.0244

lowest excited state of BB1 is red-shifted to 767.2 nm compared to the monomer (755.4 nm). On the other hand, the peak at 598.2 nm, which is mainly described by a HOMO→ LUMO + 1 transition, undergoes a blue-shift to 588.8 nm. The lowest exited state in BB5 is red-shifted by 4.9 nm. Compared to an 11.8-nm shift of lowest exited state for BB1, it reflects the weaker intermolecular interaction strength in BB5 (Table 1). The excited state at 2.073 eV does not shift at higher energy in BB5. Interaction of Black Dye with DCA. Figure 3 shows the optimized geometries of the black dye−DCA complexes in

acetonitrile. Table S2 in the SI lists the main bond distances and angles for the complexes as well as the monomers. There are six stable configurations: BC1, BC2, BC3, BC4, BC5, and BC6. For BC1 and BC2, a DCA molecule forms three bonds with black dye. One is via the O atom of the hydroxyl group at position 3 (O031) and the H atom of one of the peripheral carboxyl groups from the dye ligand (H46 for BC1 and H48 for BC2). Another is via the H atom of the hydroxyl group at position 12 (H122) and the O atom with a lone pair in the carboxyl group forming the other bond (O41 for BC1 and O44 23910

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monomer, the absorptions for the BC1 shift to shorter wavelengths, demonstrating that BC1 has a stronger intermolecular interaction than BC4 (Table 3). Structures of the DCA Dimers. For comparison to the black dye−DCA complexes, the DCA dimer structures in acetonitrile were optimized at the same level (Figure S1 and Table S3 in the SI). The DCA dimer has two stable configurations: CC1 and CC2. For CC1, two DCA molecules interact with each other via the H243 atoms of the carboxyl groups and the O121 atoms of hydroxyl groups at position 12. The H···O bond distances (1.666 Å, Table S3, SI) are shorter than the net van der Waals radii of the binding atoms (2.720 Å),40 indicating that hydrogen bonding occurs.41 For CC2, the DCA molecules interact with each other forming cyclic hydrogen bonds41 with the terminal carboxyl groups similar to the interactions in BB3, BB4, BB5, BC4, BC5, and BC6.43 The bond distances of H···O are 1.600 Å. The bond angles of O−H···O are nearly linear. The ΔE value of CC1 with respect to the CC2 is 0.00326 hartree and the EHB value of CC2 (−15.74 kcal mol−1) is larger than that of CC1 (−13.70 kcal mol−1), indicating that CC2 is the more favorable dimer structure. Similar to the monomer, TD-DFT calculations in acetonitrile indicate that the DCA dimers do not have excited states below 5.5 eV (225 nm), which is consistent with the observation that DCA does not work as a sensitizer.44

for BC2). The third is via the O atom with a lone pair in the carboxyl group at position 24 (O241) and the H atom of the central carboxyl group from the dye ligand (H47). Similar to BC1 and BC2, three bonds are observed in BC3; one is via the O031 atom of the hydroxyl group at position 3 and the H47 atom of the central carboxyl group from the dye ligand. The second is via the H122 atom of the hydroxyl group at position 12 and the O43 atom with a lone pair in the carboxyl group forming the other bond, and the third is via the O241 atom with a lone pair in the terminal carboxyl group and the H48 atom of the peripheral carboxyl group from the dye ligand. For BC1, BC2, and BC3, all of the intermolecular H···O distances (Table 3) are shorter than the net van der Waals radii of the binding atoms (2.720 Å),40 indicating intermolecular hydrogen bonding. The angles of the O−H···O bonds exceed 140°. For BC4, BC5, and BC6 (Figure 3), cyclic hydrogen bonds41 between the two carboxyl groups are formed in the same manner as black dye dimers BB3, BB4, and BB5. All of the distances for intermolecular H···O bonds are smaller than the net van der Waals radii of the binding atoms (2.720 Å, Table 3). The bond angles of O−H···O are nearly linear. Table 3 lists the EHB values for the intermolecular interactions as well as the relative energy with respect to the BC1 species (ΔE). Judging from the ΔE values, the most and the least stable black dye−DCA complexes are BC1 and BC6, respectively. The E values exceed −15 kcal mol−1, and increase in the order of BC6 < BC5 ≈ BC4 < BC3 < BC2 < BC1. This relative order indicates the interaction strength between black dye and DCA. Table 3 also lists the atomic charges on the DCA molecule determined by NBO and Mulliken population analyses. Regardless of the analysis method, intermolecular interactions positively change the atomic charge on the DCA molecule from 0. The relative orders of the atomic charge on the DCA molecule determined by both NBO (natural charge in Table 3) and Mulliken population analyses roughly agree with that for EHB value. The higher the EHB and the more positive the DCA atomic charge, the stronger the interaction between black dye and DCA. Table 4 lists the calculated absorptions for the BC1 and BC4 species in acetonitrile using the TD-DFT method. Both

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DISCUSSION Herein theoretical studies on the black dye dimer in solvent were conducted using a DFT method to identify the intermolecular interaction properties. Among the five stable configurations, BB1 shows the largest intermolecular interaction energy and has a centrosymmetric structure, where the two terminal H atoms of the carboxyl groups attached to the peripheral pyridine of the terpyridine ligand interact with the two carbonyl O atoms of the carboxyl groups located on the central pyridine of the terpyridine ligand. This configuration with hydrogen bonds closely resembles the crystal structure of black dye reported by Shklover et al.13 They consider the crystal to have a “ribbon” structure because it is onedimensional, although the “ribbons” have almost perfect coplanarity with the terpyridine planes in neighboring molecules via hydrogen bonds. They concluded that the formation of such hydrogen-bonded ribbons in solution might effectively prevent black dye from reaching the small pores on the TiO2 surface, decreasing the η value of DSSCs. Moreover, our TD-DFT results indicate that the excited state of BB1 near 600 nm is blue-shifted, but the lowest excited state around 760 nm is red-shifted compared to the black dye monomer. Ogomi and co-workers reported that the blue-shift in the absorption peak near 600 nm is due to the aggregation of black dye.10 Although not reported specifically for black dye, a red-shift of the lowest excited state due to dye aggregation has been reported for N71945 and metal-free indoline dyes such as D102 and D149.42 In particular, Dell’Orto et al. suggested that the aggregation of N719 dye occurs through hydrogen bonding. Therefore, we conclude that centrosymmetric BB1 with hydrogen bonds via the carboxyl groups is the preferred and probable dimer structure responsible for aggregation of black dye in solvent. Does DCA inhibit such black dye aggregation? If so, how does it occur? These questions led us investigate the structure of the black dye−DCA complex. The central and one of the peripheral carboxyl groups in the dye ligand form three

Table 4. Selected Excitation Energies (eV), Wavelengths (nm), Oscillator Strengths, and Major Contributions for the BC1 and BC4 Species species BC1

BC4

excitation energy

wavelength

oscillator strength

major contributiona

1.688 1.813 2.103 1.640 1.781 2.071

734.5 683.9 589.6 755.9 696.3 598.6

0.0320 0.0397 0.0501 0.0299 0.0441 0.0502

H − 1→L (69.23) H→L (64.66) H→L + 1 (69.68) H − 1→L (69.32) H→L (66.54) H→L + 1 (69.78)

a

H and L represent HOMO and LUMO, respectively. Number in parentheses is in %.

theoretical and experimental results43 indicate that the DCA monomer does not have excited states below 5.5 eV (225 nm). For BC4 in which the carboxyl group of DCA bonds to the one of the peripheral carboxyl groups of the dye ligand similar to BB5, the resulting excitation energies and major contributions to these energies agree with the black dye monomer (Table 2). Although the major contributions are similar to that of the 23911

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combination of black dye and D131 seems to generate a synergistic effect on the DSSC performance as well as an additive property. Aside from these reports, cosensitized DSSCs generally show improved light-harvesting, but a poorer overall efficiency compared to reference cells composed of the individual sensitizers. Clifford and co-workers have listed two possible reasons; first, there are only a finite number of anchoring sites on the TiO2 surface. Thus, any improvement in the IPCE in one part of the spectrum upon introducing a given sensitizer may be offset by a poorer performance in the IPCE in another part due to the removal of the other sensitizer dye(s), Second, the dye excited states become deactivated due to energy- or electron-transfer processes between the different sensitizers.3 The unfavorable electron-transfer processes between the different sensitizers must be induced by intermolecular interactions between the different sensitizers.11 Moreover, on the basis of our findings using TD-DFT calculations, the intermolecular interactions between the different dyes may also cancel the extended spectral response region of the sensitizer to the near-IR region [characteristic (i)] due to a bathochromic effect.50 Therefore, to avoid unfavorable aggregation and adverse effects on the light-absorption characteristics, the intermolecular interactions between dye molecules and between a dye molecule and an inhibitor such as DCA must be considered when selecting the combination of dyes and/or an inhibitor for either a single-dye sensitized or cosensitized solar cell.

hydrogen bonds via two hydroxyl groups and a terminal carboxyl group in DCA for the BC1 complex. The intermolecular interaction energy of BC1 (−19.13 kcal mol−1) is greater than those of BB1 (−15.66 kcal mol−1) and CC2 (−15.74 kcal mol−1) However, we are unsure if the 3.47 kcal mol−1 difference in the intermolecular interaction energy between BC1 and BB1 explains why the black dye monomer prefers interacting with the DCA monomer to form a black dye dimer when they coexist in solvent. On the basis of investigations using the BB1 and BC1 species, we suggest the following suppression mechanism for black dye aggregation by DCA during the coloration process of a TiO2 film. Initially, the DCA molecule interacts with a black dye molecule derived from the BB1 structure to form the BC1 structure with hydrogen bonds in solution. Subsequently, BC1 dissociates into the black dye and DCA molecules on the TiO2 surface. Finally, each black dye molecule adsorbs on the TiO2 without aggregation. That neither BB1 nor BC1 exists on the TiO2 surface explains why the absorption peak of black dye adsorbed on TiO2 using DCA additive was not shifted.9,10 STM results by Ikeda and co-workers demonstrated that the fraction of single dyes to the aggregated dyes adsorbed on a TiO2 surface is enhanced as the DCA concentration increases from 1 to 10 times the number of black dye molecules.12 According to the literature,7,38,46,47 the DCA concentration in the black dye solution used in the immersion process for DSSC preparation is usually 100 times greater than that of black dye. Wang and co-workers noted that the 0.2 mM black dye containing 20 mM DCA is the best condition for a high DSSC efficiency.46 In other words, to gain the desired effect, it is necessary to add a large excess of DCA into the black dye solution, which is consistent with our theoretical finding that the difference in the intermolecular interaction energy between black dye−DCA complex BC1 and black dye dimer BB1 is small. DCA effectively inhibits black dye aggregation during the immersion process of cell preparation, which leads to a decreased amount of dye on TiO2.9,46 This DCA inhibition of dye aggregation may promote electron injection from the photoexcited dye into the TiO2 conduction band48 and/or suppress an undesirable charge recombination of injected electrons in TiO2 with I3− and/or I2 in the electrolyte46 (see Introduction), consequently improving the Jsc, Voc, and η values.9,46 To increase the spectral response of a DSSC, sensitizers with different absorption spectra can be jointly adsorbed onto the TiO2 surface using a mixed dye solution for sensitization.2 Yella and co-workers announced that a cosensitized cell of Zn porphyrin YD2-o-C8 and organic Y123 dyes with a Co-based redox electrolyte exhibits an impressive panchromatic photocurrent response over the entire visible range, resulting in η of 12.3%.49 Additionally, Ogura and co-workers reported that a combination of black dye and organic D131 dye without DCA exhibits a remarkable η value of 11.0% using I−/I3− redox, which is higher than that of the reference cells made from the individual dyes alone.44 They hypothesized that D131 works as both a sensitizer and a dissociation reagent similar to DCA, and that black dye also inhibits aggregation of D131 and vice versa. Thus, they concluded that together both dyes inhibit aggregation and improve DSSC efficiency. It is noteworthy that the incident monochromatic photon-to-electron conversion efficiency (IPCE) values at wavelengths longer than their overlapping region of 300−720 nm increase. The

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CONCLUSIONS The intermolecular interactions of the black dye dimer in acetonitrile were investigated by a DFT method with a full geometry optimization. Five stable configurations with hydrogen bonds are found. For BB1 with a centrosymmetric dimer structure, the two terminal H atoms in the carboxyl group attached to the peripheral pyridine of the terpyridine ligand interact with the two carbonyl O atoms in the carboxyl group located on the central pyridine of the terpyridine ligand. The two O atoms with a lone pair in the carboxyl group forming the other bond interact with the two H atoms of the central and peripheral pyridines. Consequently, six hydrogen bonds are formed. Similarly, BB2 forms two kinds of hydrogen bonds via H atoms; one is between the two central and between the two peripheral carboxyl groups (O−H···O), while the other is between the pyridine ligand and carboxyl group (C−H···O). Cyclic hydrogen bonds form between two central carboxyl groups, between a central and peripheral carboxyl groups, and between two peripheral carboxyl groups in BB3, BB4, and BB5, respectively. The structure of BB1 closely resembles the previously reported crystal structure for black dye and is found to be the most favorable among the five configurations on the basis of the intermolecular interaction energies. However, the excited state of BB1 around 600 nm is blue-shifted, while the lowest excited state around 760 nm is red-shifted compared to the black dye monomer from the TD-DFT results. The black dye−DCA complexes form six stable configurations with intermolecular hydrogen bonds. For BC1, BC2, and BC3, the two hydroxyl groups and the terminal carboxyl group of DCA form three hydrogen bonds via a central and one of peripheral carboxyl groups in the dye ligand. For BC4, BC5, and BC6, cyclic hydrogen bonds between the carboxyl group of DCA and that of the black dye ligand are formed in the same manner as black dye dimers BB3, BB4, and BB5. 23912

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Intermolecular interaction energies and atomic charges on the DCA molecule determined by NBO and Mulliken population analyses indicate that BC1 has the strongest intermolecular interaction among the six black dye−DCA complexes. The difference in the intermolecular interaction energy between BC1 and BB1 suggests that DCA suppresses black dye aggregation during the coloration process of TiO2 film by forming stronger hydrogen bonds; it has been experimentally demonstrated that the concentration of DCA must greatly exceed that of black dye. Our theoretical results show that the intermolecular interactions between dye molecules and between dye and inhibitor molecules such as DCA must be considered to avoid undesirable dye aggregation and to prevent adverse effects on the light absorption characteristics when developing DSSC.

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ASSOCIATED CONTENT

S Supporting Information *

Main bond distances and angles of the optimized monomers, dimers, and complexes. Investigation of interaction energy correction. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*[email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Theoretical calculations were partly performed using the Research Center for Computational Science, Okazaki, Japan.

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REFERENCES

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