# The BCL Method for DSSC: Basis and Applications +
## 4 A Big Challenge: Understanding the Absorption Band of Ruthenium Dyes
### Results
#### 4.1.4 Analisys of MLCT Band  
Figure 10 displays the experimental absorption of the four compounds under study. It also shows the decomposition of the broad absorption band in terms of the described possible components of the excitation process, detailed in Equation (7). Accordingly, complex 1 shows the participation of a mixture of MLCT and IL electronic transitions. The MLCT excitations for this chromophoric complex can be separated in two types, one of them related to a charge transfer from the ruthenium center to the Chromophoric ligand (MC), while the other is directed to the dicarboxibipyridine group (MB). For the case of C1, MB transitions are observed, but then a second LH ligand is present like in the C2 complex, MC excitations are predominant. On the other hand, looking at the complexes that incorporate the amino substituted ligands, it can be seen that in complex C3 MLCT excitations are present, accompanied by ILCT and LL contributions. The abundance of ILCT transitions increase when moving  
Figure 10: Experimental absorption spectra and calculated electronic transitions(bar) showing the participation of basic electronic excitations, MC, MB, IL, ILCT and LL. to longer wavelengths. The same behavior is observed for the C4 complex, which shows falling-off in the contribution of MB excitations that is compensated by the presence of MC transitions. The above analysis shows that the different absorption bands are a mixture of different types of excitations. In C1 and C2, MLCT and IL are predominant, while for C3 and C4, intraligand charge transfer transitions outweigh. It also can be mentioned that MLCT are found within the range of 400-480 nm and ILCT appear at longer wavelength. As it was previously mentioned, each absorption is composed by a set of basic excitations, then the entire band can be described by a sum of them:  
\[\Gamma=\sum_{\lambda}f_{\lambda}\ \Gamma_{\lambda}=\sum_{\lambda}f_{\lambda} \left(\sum_{k}d_{k}\omega_{0}^{\alpha\beta}\right) \tag{10}\]  
Reorganizing and imposing the condition that \(\sum\limits_{k}d_{k}^{*}=1\), Equation (9) is obtained  
\[\Gamma=\sum_{k}d_{k}^{*}\omega_{k}^{\alpha\beta} \tag{11}\]  
showing the decomposition of the absorption band in terms of single basic processes, with their percental contribution measured by the \(d_{k}^{*}\) coefficients. Figure 11 symbolizes the calculated values of these coefficients for each of the complexes under study. The above figure reveals that for C1 the absorption band comprised in the range of 400 nm to 600 nm is a mixture of 56% IL + 32% MB + 10% MC + 2% LL excitations. The introduction of a second LH ligand modifies the previous composition by enhancing the number of MC (65%) excitations, with the associated diminishment of IL and MB excitations. The amino substituent introduced in the chromophoric ligand C3 shows that ILCT and MB excitation predominate. At the same time, an increase in the contribution of LL excitations prevail respect to MC excitations. Finally, in complex C4, the 64% of the absorbed energy is concentrated on ILCT excitation and 22% on MC excitations. In summary, employing the present framework, in combination with TDDFT calculations it is feasible to calculate the composition of the  
Figure 11: Participation of single basic excitations on the entire absorption band. visible bands and understand how its distribution changes by modifying the nature of the ligands. Focusing on the application of this methodology to the development of solar cells, it is interesting to calculate how much of the absorbed energy is deliveerd to the diferent fragments, and specifically to the B (carboxylate) fragments from where electronic injection to the semiconductor takes place. Therefore, a distribution function, \(f(\beta)\), containing the relative participation of the different fragments is build.