## 3 Results and Discussion
### Absorption Spectra  
Based on the optimized molecular structures, we used the TD-DFT method to study the absorption spectra for dyes D35, D35-TiO\({}_{2}\), XY1, XY1-TiO\({}_{2}\), and cosensitized molecular system. Figure 3 shows that Dye D35 has a wide absorption range in the visible region with two prominent peaks, in which the strongest absorption peak is found in 453 nm that also contributed to HOMO-LUMO transition (see Table S2), and this state has a larger oscillator strength (f = 1.36). Because the HOMO electron cloud is concentrated on the whole molecular skeleton and LUMO resides in the bridge and acceptor units (see electron density distribution in Figure S1), the first excited state will result in efficient intramolecular CT.  
Figure 4 shows the Charge Different Density (CDD) for calculated excited states. For the S1 state, red electron is moved in a direction of the acceptor; the green hole resides in the donor unit, resulting in the electron transfer from donor to acceptor. For another excited state (S2) of D35, electron transition is composed of HOMO \(\rightarrow\) LUMO + 2, having a weight of 74%, which state is also an intramolecular CT from the triarylamine unit to cyanoacrylic acid. The above states exhibit a strong push-pull behavior characteristic. States S4 and S5 are also ICT states with the same characteristics as S1. Located excited state is found to be the S3 state that is an excitation of donor and bridge.  
Figure 3: Simulated spectra for the dye in acetonitrile solvent, adsorption on TiO\({}_{2}\) and cosensitization.  
Figure 2: Energy levels of the isolated dye in acetonitrile and its adsorption spectrum on TiO\({}_{2}\) as well as cosensitized molecular system.  
XY1 has a wide range of spectral response and strong absorption intensity at 529 nm, which come mainly from electronic transition (HOMO \(\rightarrow\) LUMO). Stronger absorption can make up for the deficiency of D35 in the range above 500. From absorption spectra in Figure 3, red-shifted movement for the first peak for dye-TiO\({}_{2}\) occurs compared with the isolated molecules, which can be attributed to the change of energy gap; moreover, the molar extinction coefficient has been improved to enhance the photoabsorption efficiency. For cosensitized molecular systems, XY1 and D35 have two absorption bands, and the first absorption is found at 530 that are close to the value of XY1 (see Table S2). There exists an influence of local electric field caused by the solar cell electrode, and some characteristics (such as absorption, dipole moment, and polarizability) should be changed by the local electric field (three fields (10, 20, 30) \(\times\) 10\({}^{-4}\) a.u.). Under an electric field condition of 10 \(\times\) 10\({}^{-4}\) a.u., absorption peak of XY1 and D35 has changed about 6 nm compared with the nonelectric field (see Table S3), and oscillator is reduced about 0.2; As the electric fields (20 \(\times\) 10\({}^{-4}\) a.u. and 30 \(\times\) 10\({}^{-4}\) a.u.) increase, the absorption spectra make obviously red-shifted, i.e., the maximum absorption wavelength is \(\sim\) 1000 nm.  
Figure 4: Intramolecular and intermolecular CT (charge transfer) for the dye/TiO\({}_{2}\) and the cosensitized systems.  
563.65 nm (f = 1.5047) and 611.14 nm (f = 1.3827), respectively. Therefore, the change of the local electric field should result in a red-shifted absorption, following the reduced oscillator strengths.