Charge and Energy Transfer in the Metal-free Indoline Dyes for Dye-sensitized Solar Cells

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1 CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 19, NUMBER 3 JUNE 27, 2006 ARTICLE Charge and Energy Transfer in the Metal-free Indoline Dyes for Dye-sensitized Solar Cells Li-ying Diao a, Wen-xiang Gu b, Yue-hui Chen a, Feng-cai Ma a a. Department of Physics, Liaoning University, Shenyang , China; b. Department of Applied Chemistry, South China Agricultural University, Guangzhou , China (Dated: Received on June 1, 2005; Accepted on October 14, 2005) Metal-free indoline dyes for dye-sensitized solar cells were studied by employing quantum chemistry methods. Comparative study of the properties of both ground and excited states of metal-free indoline dyes for dyesensitized solar cells revealed: (i) as the number of rhodanine rings increases, the energy difference between HOMO and LUMO decreases and there is a red shift in the absorption spectrum with the binding energy increased, and the transition dipole moment decreased; (ii) Based on an analysis of charge differential density, we observed that the charge and energy are transfered from the phenylethenyl to the indoline and rhodanine rings; (iii) The electron-hole coherences are mainly on the indoline and rhodanine rings, and the exciton sizes are 30 and 40 atoms for indoline dyes with one and two rhodanline rings, respectively. These results serve as a good example of computer-aided design in metal-free indoline dyes for dye-sensitized solar cells. Key words: Charge and energy transfer, Electron-hole coherence, Indoline dyes, Metal-free for dyesensitized solar cells I. INTRODUCTION Since the first report of dye-sensitized solar cells (Grätzel cells) [1], considerable scientific and industrial research has been devoted to them [1-4], as they offer high energy-conversion efficiencies at low cost. Because Ruthenium (the rare metal) dyes used in dyesensitized solar cells [5,6] are very expensive, scientists have long sought a metal-free organic dye which is inexpensive, environmentally friendly, and easily synthesized [7-12]. Recently, highly-efficient metal-free indoline dyes for dye-sensitized solar cells were reported [13,14]. The design of a novel metal-free organic dye requires insight into the connection between chemical structures and the properties of their excited states, e.g charge and energy transfer, electron-hole coherence and delocalization size, photoexcitation dynamics, and selftrap or relaxation dynamics at the excited states. To study the relationship between the chemical structure and its optelectronic property, several approaches have been developed, such as the excited-state molecular dynamics (ESMD) approach [15-17], a 2D real-space analysis method of density matrix studying electron-hole coherence and delocalization size [15-21], a 3D real-space analysis method of transition density (TD) and charge difference density [22-30] studying charge and energy transfer. The combination of 2D and 3D real-space analysis methods has been used to study the conugated molecule [25-30]. In this paper, the excited state Author to whom correspondence should be addressed. fcma@lnu.edu.cn properties of metal-free indoline dyes for dye-sensitized solar cells [13,14] (which can be seen from Fig.1) are studied with quantum chemistry methods; including: (i) the charge and energy transfer on the excited state are studied with 3D real-space analysis methods of transition density (TD) and charge difference density; (ii) the electron-hole coherence and delocalazation size are studied with 2D real-space analysis method of density matrix. FIG. 1 Chemical Structures of metal-free indoline dyes. 1, 2 and 3 stand for phenylethenyl, indoline ring and rhodanine ring, respectively. II. METHODS Geometry optimizations of the metal-free indoline dyes were preformed for the ground state by using density functional theory (DFT) [31] B3LYP with basis set 6-31G. The excited states of the metal-free indoline dyes were computed, using the time-dependent density functional theory (TD-DFT) [32,33] with B3LYP functional and basis set 6-31G, and keywords POP=FULL and IOP (9/40=2) [25], as it is implemented in the software package GAUSSIAN 03 [34]. ISSN /DOI: /ccp (3) c 2006 Chinese Physical Society

2 Chin. J. Chem. Phys., Vol. 19, No. 3 Charge and Energy Transfer in Indoline Dyes 239 TABLE I The calculated transition dipole moments of metal-free indoline dyes, where the optimized structure of the ground state, the Cartesian axes and the individual atoms in the numbered sequence are shown. A. 3D real-space analysis To visuaily inspect all molecular orbitals contributing to the corresponding excitation, the transition density and the charge-difference density [22-30] of the singlet excited states S µ were depicted with the cube representation. The singlet excited states can be written as S µ = C µai a + a a i S 0 (1) where S 0 and S µ are the singlet ground and excited states, a + a and a i are the creation and annihilation operators for electrons in the unoccupied Hartree-Fock molecular orbital ϕ a ( r), and the occupied Hartree-Fock molecular orbital ϕ i ( r) respectively, C µai represents the ith eigenvector of the Configuration-Interaction (CI) Hamiltonian based on the single-excitations from the occupied Hartree-Fock molecular orbital ϕ i ( r) to the unoccupied one ϕ a ( r). The transition density from the ground state to the excited state is given by ρ µ0 (r) = C µai ϕ a (r)ϕ i (r) (2) The transition density determines the transition dipole µ = rρ µ0 (r)d 3 r (3) giving the strength and the orientation for the interaction with the electromagnetic field. Similarly the charge-difference density is given by ρ µµ (r) = i, occ a,b unocc C µa C µai ϕ (r)ϕ i (r) C µbi C µai ϕ b (r)ϕ a (r) (4) It should be noted that the first and the second terms in Eq.(4) stand for the hole and electron in the transition whose charge difference densities are listed in Table I, respectively. Due to this change in charge distribution in the molecule after excitation, the nuclei will be driven out of the ground state potential minimum by forces F n (R n ) = e2 4πε 0 Z n r R n r R n 3 ρ µµ(r)d 3 r (5) We can qualitatively describe how the localization process acts based on the nuclear motion by Eqs.(4) and (5). B. 2D real-space analysis The transition density matrix in a site representation has been used to analyze the electron-hole coherence as well as excitation delocalization in conugated polymers [15-21]. Photoexcitation creates an electron-hole pair or an exciton by moving an electron from an occupied orbital to an unoccupied orbital [18]. Each element of the transition density reflects the dynamics of this exciton proected on a pair of atomic orbitals given by its indices [15]. In the 2D site representation, each data point (x, y) gives the probability Ψ(x, y) 2 of finding one charged particle at site x and the second one at site y. The probability amplitudes ψ(q, r) to have on charged particle in atomic orbital q at site x and the second in atomic orbital r at site y is given by [21] ψ(q, r) = 1 2 [ + C CI C CI Cq LCAO Cq LCAO (e )Cr LCAO (h + ) (h + )C LCAO ] r (e ) (6) where Cq LCAO (h + ) and Cr LCAO (e ) are the corresponding LCAO (linear combination of atomic orbitals) coefficients in the occupied and unoccupied molecular

3 240 Chin. J. Chem. Phys., Vol. 19, No. 3 Li-ying Diao et al. orbitals involved in the th configuration. The C CI are the associated CI (Configuration-Interaction) coefficient. The probability can be written as Ψ(x, y) 2 = q x ψ(q, r) 2 (7) r y TABLE II The calculated transition energies and the oscillator strengths. n Transition energy/cm 1 Oscillator Experimental Theoretical strength a, 540 b a, 541 b a The experimental results of indoline dye in tert-butyl alcohol/acetonitrile (1:1). b The experimental results of indoline dye on the TiO 2 films. As expected, with the increase of the number of the rhodanine rings, the energy level of HOMO increases and that of LUMO decreases, in addition the energy difference between HOMO and LUMO decreases (lowering the band gap). From the results of HOMO and LUMO, the ionization energy (HOMO energy level) and electron affinity (LUMO s) can be estimated [35], respectively. It should be noted that the energy difference (ε HL ) between the HOMO and LUMO at the ab initio level does not closely relate to excitation energy (i.e., band gap ε Exciton ) due to the absence of exciton binding energy (ε Binding ) of the electron-hole pairs and the lattice relaxation [35,36]. The band gap (the vertical transition to a free electron-hole pairs) is smaller than the energy difference (ε HL ) between the HOMO and LUMO. The calculated binding energy of the electron-hole pairs ε Binding =ε HL ε Exciton is 0.21 ev (n=0) and 0.26 ev (n=1). Therefore, as the number of rhodanine rings III. RESULTS AND DISCUSSION The calculated transition energies and oscillator strengths are listed in Table II. The energy differences between the experimental and theoretical results are due to the solvent effect in tert-butyl alcohol/acetonitrile (1:1) and the J-aggregate on the TiO 2 electrode, which are not considered in the calculation. Comparing the results, the interaction between the metal-free indoline dyes with one-unit rhodanine ring on the TiO 2 surface is stronger than the interaction between the metal-free indoline dyes with two-unit rhodanine rings on the TiO 2 surface. The calculated results of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) can be seen in Fig.2 (energy levels) and Table III (density). FIG. 2 The energy levels of the HOMO and LUMO of metalfree indoline dyes. FIG. 3 Contour plots of transition density matrices of metal-free indoline dyes. The axis labels represent the individual groups in the numbered sequence shown in Fig.1. The color bar is shown. For interpretation of the references for the color in this table legend, the reader is referred to the web version of this letter.

4 Chin. J. Chem. Phys., Vol. 19, No. 3 Charge and Energy Transfer in Indoline Dyes 241 TABLE III The HOMO, LUMO, transition and charge differential densities of metal-free indoline dyes. The green color represents the hole, the red electron density; the isovalues are (HOMO and LUMO) and (transition and charge difference densities) in atom units, respectively. For interpretation of the references for the color in this table legend, the reader is referred to the web version of this letter. increases, so does the binding energy. Though the difference of energy between the HOMO and LUMO decreases (the transition energy also red shifts with the increase of the number of the indoline ring), the binding energy also increases. So the design of the novel metal-free organic dyes must balance these two aspects. To study the charge and energy transfer, electronhole coherence and delocalization size at the excited state, the 2D and 3D real space analysis methods are employed (Fig.3). According to the Figures of the HOMOs and LUMOs in Table III, the densities of HOMOs are delocalized on the whole indoline dye, but the densities of LUMOs are localized on the indoline and rhodanine rings. Therefore, if the HOMO and LUMO stand for the ground and excited state properties, respectively [25,37], according to the charge differential density, the electrons transfer from the phenylethenyl to the indoline and rhodanine rings, which results in holes that are mainly localized on phenylethenyl, and the electrons are mainly localized on rhodanine rings. In addition, the indoline ring is the bridge for the electron transfer from phenylethenyl to rhodanine. The strength and orientation of dipole moment calculated with Eq.(3) were listed in Table I, where the cartesian axis of indoline dyes can be seen, which can be labeled in the transition density (listed in Table III). According to our calculations, when the number of rhodanine rings increases, the transition dipole moments decreases, this is due to

5 242 Chin. J. Chem. Phys., Vol. 19, No. 3 Li-ying Diao et al. the increase in binding energy. The charge difference densities show the direction and the result of the electron transfer, but one cannot distinguish which atom the electron comes from. To show (i) where the electron goes, (ii) the source atom of the excited electron, (iii) delocalized size of the exciton, the contour plots of the transition density matrices are employed. Their electron-hole coherences can be seen in Fig.3 (the individual atoms in the numbered sequence are shown in Table I), which supports the results of the 3D real-space analysis: i.e. the electron-hole coherence are mainly concentrated on the indoline and rhodanine rings, and exciton sizes are 30 and 40 atoms for indoline dyes with one and two rhodanline rings, respectively. IV. CONCLUSION The properties of both ground and excited states of the metal-free indoline dyes for dye-sensitized cells are studied by quantum chemistry methods (2D and 3D real-space analysis). With the increase of the indoline ring, the energy difference between HOMO and LUMO decreases, but the binding energy increases. The densities of HOMOs are delcocalized across entire indoline dyes at the ground state, but the densities of LUMOs are mainly localized on the indoline and rhodanine rings at the excited state, so the result of the transtion from the HOMOs to LUMOs is that the electrons mainly transfer from the phenylethenyl to the indoline and rhodanine rings, according to the charge difference density. Binding energy increases with the numbers of rhodanine rings and the transition dipole moment decreases. The electron-hole coherences are mainly on the indoline and rhdanine rings, and the excition sizes are 30 and 40 atoms for indoline dyes with one and two rhodanline rings, respectively. V. ACKNOWLEDGMENT This work was supported by the National Nature Science Foundation of China (No ). [1] B. O. Regan and M. Grätzel, Nature 353, 737 (1991). [2] M. Grätzel, Nature 414, 338 (2001). [3] M. Grätzel, J. Photochem. Photobiol C 4, 145 (2003). [4] M. Grätzel, J. Photochem. Photobiol A 164, 3 (2004). [5] M. K. Nazeeruddin, A. Kay, I. Rodicio, R. Humphry- Baker, E. Mrüller, P. Liska, N. Vlachopoulos and M. Grrätzel, J. Am. Chem. Soc. 115, 6382 (1993). [6] M. K. Nazeeruddin, S. M. Zakeeruddin, R. Humphry- Baker, M. Jirousek, P. Liska, N. Vlachopoulos, V. Shklover, C. H. Fischer and M. Grätzel, Inorg. Chem. 38, 6298 (1999). [7] S. Ferrere, A. Zaben and B. A. Gregg, J. Phys. Chem. B 101, 4490 (1997). [8] N. J. Cherepy, G. P. Smestad, M. Grätzel and J. Z. Zhang, J. Phys. Chem. B 101, 9342 (1997). [9] K. Hara, T. Horiguchi, T. Kinoshita, K. Sayama, H. Sugihara and H. Arakawa, Chem. Lett. 316 (2000). [10] A. C. Khazrai, S. Hotchandani, S. Das and P. V. Kamat, J. Phys. Chem. B 103, 4693 (1999). [11] K. Sayama, K. Hara, N. Mori, M. Satsuki, S. Suga, S. Tsukagoshi, Y. Abe, H. Sugihara and H. Arakawa, Chem. Commun (2000). [12] K. Hara, K. Sayama, Y. Ohga, A. Shinpo, S. Suga and H. Arakawa, Chem. Commun. 569 (2001). [13] T. Horiuchi, H. Miura and S. Uchida, Chem. Commun (2003). [14] T. Horiuchi, H. Miura, K. Sumioka and S. Uchida, J. Am. Chem. Soc. 126, (2004). [15] S. Tretiak, A. Saxena, R. L. Martin and A. R. Bishop, Phys. Rev. Lett. 89, (2002). [16] S. Tretiak, A. Saxena, R. L. Martin and A. R. Bishop, Proc. Natl. Acad. Sci. USA. 100, 2185 (2003). [17] M. T. Sun, Y. H. Chen, P. Song and F. C. Ma, Chem. Phys. Lett. 413, 110 (2005). [18] S. Mukamel, S. Tretiak, T. Wagersreiter and V. Chernyak, Science 277, 781 (1997). [19] S. Tretiak, V. Chernyak and S. Mukamel, J. Am. Chem. Soc. 119, (1997). [20] S. Tretiak and S. Mukamel, Chem. Rev. 102, 3171 (2002). [21] E. Zoer, P. Buchacher, F. Wudl, J. Cornil, J. Ph. Calbert, J. L. Bredas and G. Leising, J. Chem. Phys. 113, (2000). [22] W. J. D. Beenken and T. Pullerits, J. Phys. Chem. B 108, 6164 (2004). [23] W. J. D. Beenken and T. Pullerits, J. Chem. Phys. 120, 2490 (2004). [24] N. K. Persson, M. T. Sun, P. Kellberg, T. Pullerits and O. Inganäs, J. Chem. Phys. 123, (2005). [25] M. T. Sun, P. Kellberg, F. C. Ma and T. Pullerits, Chem. Phys. Lett. 401, 558 (2005). [26] M. T. Sun, J. Chem. Phys. 124, (2006). [27] M. T. Sun, P. Song, Y. H. Chen and F. C. Ma, Chem. Phys. Lett. 416, 94 (2005). [28] M. T. Sun, Y. Z. Li and F. C. Ma, Chem. Phys. Lett. 412, 425 (2005). [29] M. T. Sun, Int. J. Quantum. Chem. 106, 1020 (2006). [30] M. T. Sun, Chem. Phys. Lett. 408, 128 (2005). [31] M. R. Dreizler and E. K. U. Gross, Density Functional Theory. Heidelberg: Springer Verlag, (1990). [32] R. E. Stratmann, G. E. Scuseria and M. J. Frisch, J. Chem. Phys. 109, 8218 (1998). [33] M. E. Casida, C. Jamorski, K. C. Casida and D. R. Salahub, J. Chem. Phys. 108, 4439 (1998). [34] M. J. Frisch, et al. Gaussian 03, Revision A.1, Pittsburgh PA: Gaussian, Inc., (2003). [35] J. B. Foresman and A. Frisch, Exploring Chemistry with Electronic Structure Method, 2nd ed. Pittsburgh PA: Gaussian, Inc. (1996). [36] M. T. Sun, Chem. Phys. 320, 155 (2006). [37] J. L. Sun, G. H. Yang, G. Z. He and K. L. Han, Chin. J. Chem. Phys. 18, 325 (2005).