We constructed the model of dye-sensitized solar cells as follows. The ester bonding binds an Eosin Y molecule to the (001) surface of anatase type or the (110) surface of rutile type TiO2 semiconductor. At the semiconductor surface, the Ti dangling bonds terminate with hydroxyl groups. The acetonitrile solvents surround randomly the Eosin Y molecule. With two-dimensional periodic boundary condition and Ewald summation, QEq and QEq-CS methods determine the partial atomic charges of the model before and after the ET process. In the QEq-CS calculation for the ET process, the donor region is the xanthene group of Eosin Y molecule and the acceptor region is a hemisphere around the ester bonding in the TiO2 semiconductor with the origin at the Ti atom binding the dye molecule. The depth of solvents and semiconductor are about 30 A and 50 A, respectively, and the area of the system is about 30 A ( 30 A in this simulation. Table 1 summarizes the dependence of calculated energies on the size of acceptor region. Although the total energies have large difference between anatase type and rutile type, the difference between QEq and QEq-CS energies converge to about 0.6 eV for both types of the semiconductor. Because the excitation energy of the Eosin Y molecule is about 2.3 eV, this ET injection proceeds exothermically.
On the basis of our calculations, we discuss the importance of the ester bonding. The change of partial atomic charges indicates that the injected electron locates on some region beneath the xanthene group rather than around the Ti atom binding the dye molecule. This suggests that the ET process occurs through space from the dye molecule to the semiconductor surface. In order to confirm this idea, we disconnected and detached the Eosin Y molecule from the TiO2 surface, and did the same calculation. The results show that almost all the electron from the dye molecule transferred into the solvent molecules than rather than into the semiconductor. The large distance between the donor region and the acceptor region disturbs the ET injection into the semiconductor. The electron once injected to semiconductor leaks to the solvent molecules. These results explain that the key point of the ester bonding between the dye molecules and semiconductor surface is to keep the close distance between the donor dye molecule and acceptor semiconductor surface to achieve ultra fast ET injection.
Table 1 Calculated QEq and QEq-CS Energies
|Size of acceptor region(*)||Total electrostatic energy (eV)||Difference from QEq (eV)|
(*) We count number of atoms from the Ti atom binding the dye molecule.
Further, we will discuss the ET dependence on the temperature of the system. We have done this study under "COE project on Photoreaction Control and Photofunctional Materials" and "Promote Research Projects for High Performance Computing, Tsukuba Advanced Computing Center, Agency of Industrial Science and Technology". We thank Prof. William A. Goddard for giving O.K. an original QEq code, and Drs. Kozo Aoki for valuable comments.
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