# 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
#### 5.1.2 Analisys of Complexes
Figure 19b reveals an interesting relationship between the reduction potential, the energy of the LUMO and the electrophilicity of the anchor ligand: when the electrophilicity increases from 6 eV to 8 eV, the LUMO stabilizes (from \(-5.1\) eV to \(-5.7\) eV) and the reduction potential diminishes from \(-0.95\) V (R = OH) to \(-0.86\) V (R = CN). Evaluation of Complexes as Dye Sensitizers  
The evaluation of the ruthenium complexes as suitable candidates for a DSSC could be achieved by calculating a theoretical index using equations previously derived in Section 3.2. Figure 19: (**a**) Linear correlation between the oxidation potential and the HOMO energy. (**b**) Influence of the ligand electrophilicity on the reduction potential (line) and in the LUMO energy (dash). Figure 18: Molecular orbital scheme for [Ru(dmbpy)\({}_{2}\)R\({}_{2}\)ppl]\({}^{2+}\) complexes. For this purpose, the model that involves the participation of the anchor group in the triplet state throughout the parameter. It was chosen instead of the hot injection possibility (Section 3.1) where the absorbed energy was transmitted through the anchor ligand in a hot vibrational state. Figure 20 shows a basic description of how the different groups composing the ruthenium dye act in order to transfer the sunlight absorbed energy to the conduction band of the semiconductor. As mentioned before, in the present model it is assumed that the anchor ligand acts as a donating group, and that the charge concentrated in this anchor group is the charge available to be injected to the semiconductor. The amount of energy (\(I_{T}\)) that can be delivered to TiO\({}_{2}\) from the acceptor anchoring ligand (R\({}_{2}\)ppl) through the anchor group (\(R\)) in the electronic thermally equilibrated, thexi, state T\({}_{1}\), is calculated from Equation (22),  
\[I_{T}=E_{D}\phi_{T}(QR) \tag{22}\]  
where \(\phi_{T}\) is the intersystem crossing constant obtained from the composition of the SOMO on the triplet state configuration. \(E_{D}\) is the delivered energy,  
\[E_{D}=E_{A}f(BQR) \tag{23}\]  
that depends on the amount of absorbed energy, \(E_{A}\), that is deliverd to the anchor ligand. \[E_{A}=\sum_{\lambda}f_{\lambda}E_{\lambda} \tag{24}\]  
In the case of the hot injection mechanism, the crosslinking of systems does not occur, and all the absorbed energy is delivered to the anchor ligand and is available (\(I_{S}\)) to be injected through the singlet state. \[I_{S}=E_{D}\text{ when }\phi_{T}=0 \tag{25}\]  
Employing this set of equations with data provided by TDDFT, it becomes possible to determine the amount of energy from the sunlight spectra absorbed by the complex (\(E_{A}\)), which reaches the anchor ligand (\(E_{D}\)) from the triplet state (\(\phi_{T}\)), and that is available to be injected (\(I_{T}\)). In summary, the main objective of this chapter was to develop the theoretical \(I_{T}\) index that allows us to calculate the amount of energy absorbed from sunlight that is available to be injected. The values obtained through the calculations are shown in Table 4. For the  
Figure 20: Description of the energy flow on a ruthenium complex containing an anchor ligand composed by BQR fragments. purposes of comparative analysis, the It value for complex 5 is taken as a reference. The table shows that complex 5 absorbs 1.87 eV, delivering part of it, 0.77 eV, to the anchor ligand, where it concentrates on the anchor group with an efficiency of 83%. With all this information, the It parameter, representing the energy available to be injected, can be calculated, corresponding to 0.64 eV. The presence of ppl(COOH)\({}_{2}\) instead of dcbpy, complex 3, generates a complex with similar absorbed energy, 1.89 eV, but the delivered energy drops to 0.44 eV and only 31% is received by the anchor group. The value of It = 0.14 clearly indicates that there is a great difference between both ligands in terms of transmitting the absorbed energy. Within the R2 ppl series, complexes with R = COOMe and R = CN possess lower It values than the carboxy substituent.