# The BCL Method for DSSC: Basis and Applications +
## 5 The \(\mathbf{I_{T}}\) Parameter: A Measure of the Electronic Density on the Anchor Group
### Results
#### 6.2.2 Theoretical Evaluation of Complexes as Sensitizers  
The idea behind this theoretical evaluation is to obtain a reliable parameter from ab initio calculations that could be employed to compare the suitability of different type of ruthenium complexes to act as sensitizers. The global efficiency index is built as the product of three independent parameters, which means that an increase in the value of one of them is not necessarily reflected in the other two. Accordingly, a champion dye is the result of a collaborative relationship between the three independent indexes which is reflected on the final whole value. Table 5 summarizes the values obtained for six different ruthenium dyes. The % of Global Efficiency Index is obtained by dividing the product F\({}_{1}\)F\({}_{2}\)F\({}_{3}\) by Esun (4.18 ev) which is the maximum energy emitted in the range of 400-700 nm. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**COMPLEX** & **EA** & **ED** & \(\mathbf{\Phi_{1}}\) & **F1** & \(\mathbf{\Delta\epsilon}\) & \(\mathbf{\Delta\
abla_{\text{DA}}}\) & **F2** & **F3** & **\%GEI** \\ \hline C1 & 0.92 & 0.38 & 0.06 & **0.02** & 1.03 & \(-\)0.26 & **0.09** & **5.87** & **0.27** \\ C2 (N3) & 0.91 & 0.59 & 0.12 & **0.07** & 1.26 & \(-\)0.31 & **0.12** & **3.06** & **0.64** \\ C3 & 0.93 & 0.28 & 0.11 & **0.03** & 1.54 & \(-\)0.31 & **0.16** & **1.99** & **0.23** \\ C4 & 1.57 & 0.35 & 0.03 & **0.01** & 1.21 & \(-\)0.26 & **0.11** & **4.66** & **0.13** \\ C6 & 3.74 & 0.42 & 0.07 & **0.03** & 1.32 & \(-\)0.28 & **0.12** & **3.77** & **0.33** \\ C5 (ppf2) & 1.58 & 0.45 & 0.10 & **0.05** & 1.33 & \(-\)0.30 & **0.13** & **2.77** & **0.44** \\ BD & 1.06 & 0.96 & 0.15 & **0.15** & 1.11 & \(-\)0.32 & **0.11** & **3.13** & **1.25** \\ \hline \end{tabular}
\end{table} 
Table 5: Calculated values for the Global Efficiency Index (GEI) has the product of F1, F2, and F3 parameters. Figure 27: Comparison of calculated properties for different types of Ligands. In Table 5, the calculated values obtained for the three factors F1, F2, and F3 are displayed along with their components: EA, ED, and \(\Phi\)t for F1, and the sum of the global hardness, \(\Delta\epsilon\), and \(\Delta\)V for F2. The last column of the table shows the Global Efficiency Index (GEI) obtained as the product of the three indexes, F1, F2, and F3. According to this index, the C2 complex displays the higher value followed by C6 and C1. The complex with one chromophoric ligand is the worst. The reason why C2 is successful lies in the higher value of F1: it possesses the higher efficiency for collecting and delivering energy to the anchor group (F1 = 0.07). The other two indexes do not show great difference with the other complexes. On the other hand, the cyclometalated complex is very inefficient for delivering energy (F1 = 0.03); however, it possesses the higher value for injecting energy (F2 = 0.16) due to the high value of the SOMO, but a very low efficiency of regeneration with iodide (F3 = 1.99). Figure 28 displays the values of the GEI in decreasing order for the four complexes which follow the same trend observed for the APCE. The previous comparison of calculated GEI values with APCE reveals and important correlation between them; however, it is more suitable to compare it with the Photo Conversion Efficiency (PCE) index, a parameter that measure the efficiency of a DSSC under standard condition of irradiance, air mass, and temperature. The reported values found in the literature of four different ruthenium dyes are compared with calculated GEI. The series start the reference complex C1, followed by the C5 complex which is the fluorinated version of C3. The two other dyes shown belong to the category of champion dyes and are the N3 dye and the back dye (BD), where the dcbpy is replaced by the tricarboxylated terpyridine(tcpy) ligand. From Figure 29, it can be concluded that the GEI correctly reproduces the increasing tendency of the PCE for these complexes and establishes that the BD is the most efficient among them.