# The BCL Method for DSSC: Basis and Applications +
## 4 A Big Challenge: Understanding the Absorption Band of Ruthenium Dyes
### Results
#### 4.1.5 Triplet State  
The previous results represent the amount of electronic density concentrated on the anchor ligand that could be delivered to the semiconductor in accordance with the following photochemical process:  
\[S_{0}\ +\ hv\ \rightarrow\ S_{n}^{*} \tag{14}\]  
Figure 12: Comparison of absorbed energy (Ea) and the delivered energy (Ed) to the dicarboxybipiridine (B) and chromophoric (C) ligand for the four complexes. \[S_{n}^{*}+TiO_{2}\ \rightarrow\ S_{0}^{+}+TiO_{2}\ (e) \tag{15}\]  
Once the absorption process has been verified, the ruthenium complex is driven to a hot excited state where electronic injection occurs, previous to the non radiative decay. The electron transfer occurs through a possible transmitter-antenna mechanism, where the transmitter is located on the dicarboxibipyridine ligand and physically bonded to the surface of the semiconductor. However, an alternative scheme can be derived by considering that thermal deactivation occurs and that the excited complex decays to the lower singlet, and then, by intersystem crossing, it reaches a long lived thermally equilibrated excited state (thexi) with a triplet character. It is from this th  
\[S_{0}\ +\ hv\ \rightarrow\ S_{n}^{*} \tag{16}\]  
\[S_{n}^{*}\ \rightarrow\ S_{1}^{*} \tag{17}\]  
\[S_{1}^{*}\ \rightarrow\ T_{1}^{*} \tag{18}\]  
\[T_{1}^{*}+TiO_{2}\ \rightarrow\ S_{0}^{+}+TiO_{2}\ (e) \tag{19}\]  
In a second-row transition element, as in ruthenium, the triplet state can be populated from the singlet state given that the intersystem crossing yield; \(\phi_{isc}\) is non zero for metals belonging to this series. In order to include the triplet state in the present framework, it is necessary to make a geometrical optimization of the molecular structure of the complexes in the triplet-excited state configuration. The intersystem crossing constant can be related to the amount of participation of the bypiridine fragment in the SOMO orbital of the excited state configuration. \[\phi_{ISC}\ =\ \phi_{T}(B)=\ \varrho_{somo}(B) \tag{20}\]  
Furthermore, the available energy for electronic injection \(I_{T}\) can be defined by:  
\[I_{T}=E_{D}\phi_{T}(B) \tag{21}\]  
which can be understood as the fraction of the delivered energy to the \(B\) fragment in the triplet state. Table 2 contains calculated values for the optimized geometry. With the purpose to validate the triplet state optimized geometries, triplet energies were calculated and compared with the experimental emission wavelength. Calculated values reproduce the experimental tendency. The emission energy of Ru(bpy)3\({}^{2+}\) is overestimated, while it is underestimated for C1 and C2. Interestingly, predicted values for C3 and C4 are low respect to the other complexes and suggest that non-radiative decay could be a competitive process, being a possible explanation for the absence of emission in these complexes. The fourth column of Table 2 displays values show the participation of the dicarboxibypiridine ligand in the SOMO and LUMO. As it can be appreciated, the composition of the SOMO is rather different respect to the unoccupied LUMO. This difference is most  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Complex** & \begin{tabular}{c} **\(E_{\text{EM}}\)** \\ **(eV)** \\ \end{tabular}  & \begin{tabular}{c} **\(E_{T}\)** \\ **(eV)** \\ \end{tabular}  & \begin{tabular}{c} **\(\phi_{T}\)(B)** \\ **LUMO** \\ \end{tabular}  & \ \begin{tabular}{c} **SOMO** \\ \end{tabular}  & \begin{tabular}{c} **\(I_{T}.100\)** \\ \end{tabular}  \\ \hline Ru(bpy)3 & 2.07 & 2.30 & 1.00 & 1.00 & - \\ \hline C1 & 1.97 & 1.76 & 0.95 & 0.64 & 1.2 \\ \hline C2 & 1.87 & 1.54 & 0.94 & 0.43 & 0.4 \\ \hline C3 & - & 0.88 & 0.97 & 0.76 & 2.6 \\ \hline C4 & - & 1.04 & 0.94 & 0.55 & 1.1 \\ \hline \hline \end{evident for C2 and C4 complexes that exhibit low values 43% and 55%, respectively, while in the singlet state their participation is over 90%. The available energy for injection through the triplet state (\(I_{T}\)) is shown in the last column.