## 3 Results and Discussion
### Intramolecular and Intermolecular Charge Transfer (CT)  
Photoinduced CT and separation are important processes for generating currents in the external circuit. The possible CT channels include the CT process between the dye and semiconductor, and for desensitization systems international CT should be considered due to the electron transfer occurrence caused by the energy level discrepancy. 3D cube representation of CDD indicated that the first excited state of D35-TiO\({}_{2}\) is an ICT state, where the red electron was moved to the acceptor and surface of semiconductor, and the hole resided in the donor unit. Dynamic electron injection time can be estimated by the Newns-Anderson model [31; 32], which was defined as:  
\[\tau_{inj}(fs)=\frac{658}{\Delta(MeV)} \tag{1}\]  
\[\Delta=\sum_{p_{i}}\lvert\varepsilon_{i}-E_{LUMO}(ads)\rvert \tag{2}\]  
where \(\Delta\) and \(p_{i}\) stand for the energetic broadening and adsorbate portion of every molecular orbital, respectively; \(\varepsilon_{i}\) is orbital energy. When excited electrons were injected into the titanium dioxide, electron injection driving forces for D35 and XY1 are \(-\)1.71 eV and \(-\)1.54 eV (see Table S4); at the same time, the fast electron injection (fs) was calculated to be 9.51 fs (D35) and 9.12 fs (XY1), and the results indicated that fast electron injection is more likely to occur in the D35 system. It is hoped that the fast electron injection process is better than an intermolecular CT process during the intramolecular and intermolecular CT (D35 and XY1). It is worthwhile to note that the orbital energy difference should result in the international CT, which can be estimated with CDD and [PERSON] theory [30; 33]. From Figure 4, CDD revealed that all the electrons are localized on XY1 dye, and all the holes are situated on D35; the charge distribution on \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Dye** & **IP** & **EA** & \(\mathbf{h}\) & \(\mathbf{\omega}\) & \(\mathbf{\omega^{-}}\) & \(\mathbf{\omega^{+}}\) \\ \hline D35 & 4.649 & 3.042 & 0.804 & 9.203 & 11.226 & 7.380 \\ XY1 & 4.615 & 3.068 & 0.774 & 9.539 & 11.557 & 7.715 \\ \hline \end{tabular}
\end{table} 
Table 1: Chemical reactivity (in eV) of D35 and XY1 in acetonitrile solution; IP (Ionization Potential); EA (the Electron Affinity). electronic transition corresponding to the S\({}_{5}\) excited state that ICT state, where electrons transfer from D35 to unit XY1. The CT and recombination were calculated with the [PERSON] theory [30]. \[k=\sqrt{\frac{4\pi^{3}}{h^{2}\lambda k_{B}T}}|V_{DA}|^{2}\exp\left(-\frac{( \Delta G_{CT}+\lambda)^{2}}{4\lambda k_{B}T}\right) \tag{3}\]  
where \(K_{B}\) is the Boltzmann constant, h is [PERSON]'s constant, T is the temperature (\(T\) = 300 K), \(\lambda\) is the reorganization energy; and electronic coupling \(V_{DA}\) for CT is calculated with Generalized Mulliken-Hush (GMH) [35], which is calculated to be 135.5 cm\({}^{-1}\); \(\Delta G\) is the free energy change for CT process; \(\Delta G_{CT}=-\Delta G_{CR}-\Delta E_{0-0}\), where the \(E_{0-0}\) lowest excitation energy of donor (see Table S2), and \(\Delta G_{CT}=-0.54\) eV. Calculated CT rate is 4.895 \(\times\) 10\({}^{12}\) s\({}^{-1}\), which is smaller than the electron injection rate in the framework of fs. For the desensitization system, comparison between the electron injection from molecule to TiO\({}_{2}\) and intermolecular CT (D35 and XY1) demonstrated that fast electron injection could decrease the loss of intermolecular CT. In terms of the lifetime (\(t\)), a longer lifetime is hoped for keeping a stable state in the cationic state. According to the relationship: \(t\) = 1.499/(\(f\) E\({}^{2}\)), calculated lifetime (\(t\)) is listed in Table S4, which shows this order of D35 (2.27 ns) > XY1(1.92 ns). From the above results, it found that \(t\) for D35 is longer than that of XY1, meaning that improvement of CT will enhance the J\({}_{\text{sc}}\).