## 3 Results and Discussions
### Photovoltaic Properties
#### 3.3.2 Electron Injection Efficiency (\(\Delta G^{injact}\))  
Electron injection efficiency in a DSSC is the proportion of photoexcited electrons in the dye that are successfully transported to the semiconductor's conduction band. When light is absorbed by the dye in the DSSC, a photoexcited electron is generated in the molecule's HOMO. This photoexcited electron needs to be moved to the semiconductor's conduction band so it may take part in charge transport, allowing the DSSC to generate an electrical current. This phenomenon is referred to as electron injection [39].  
The efficiency of electron injection depends on the electrical coupling between the dye and the semiconductor, the energy levels of the dye's HOMO and LUMO, the conduction and valence bands of the semiconductor, and the kinetics of the electron transfer process. Experimentally, the short-circuit current density of a DSSC in both light and dark settings is often compared to assess electron injection efficiency. The ratio of the photocurrent to the intensity of the incident light acts as a barometer for the efficiency of the electron injection process. The photocurrent is represented by the difference in current density between these two states.  
Two methods may be employed to examine the \(\Delta G^{injact}\): the relaxed and unrelaxed routes. A relaxed route is used by an electron to inject the molecule from its ground state into the semiconductor's conduction band. The unrelaxed route is employed when an electron is introduced from the excited state of the dye into the semiconductor conduction band. Equations (2) and (3) are used to compute \(\Delta G^{injact}\).  
\[\Delta G^{injact}=E^{dye^{*}}+E_{CB} \tag{2}\]  
where:  
\(\Delta G^{injact}=\mathrm{Electron}\) injection efficiency  
\(E^{dye^{*}}=\mathrm{Oxidation}\) potential energy in the excited state  
\(E_{CB}=\mathrm{the}\) semiconductor's reduction potential (4.0 eV).  
\[E^{dye^{*}}=E^{dye}-E_{00} \tag{3}\]  
where:  
\(E^{dye}=\mathrm{Oxidation}\) potential energy in the ground state  
\(E_{00}=\mathrm{Vertical}\) electronic transition energy.  
The findings, as shown in Table 3, reveal the sequence of decreasing \(\Delta G^{injact}\) values for the natural dyes in both the gas and solvent phases. In the gas phase, it was observed that \(\Delta G^{injact}\) decreased in the following order: \(\mathrm{peonidin}>\mathrm{cyanidin}>\mathrm{pleargonidin}>\mathrm{petunidin}> \mathrm{deplinidin}\), while for the solvent phase, the order is \(\mathrm{peonidin}>\mathrm{cyanidin}>\mathrm{pleargonidin}>\mathrm{deplinidin}> \mathrm{petunidin}\). In a DSSC, the term \"\(\Delta G^{injact}\)\" describes the energy difference necessary for the injection of electrons from the excited dye molecule into the semiconductor's conduction band [40]. A higher \(\Delta G^{injact}\) value indicate an improved performance of the device, denoting a more favorable energy environment for electron injection.  
and convert it into an excited state, whereas \(\Delta G^{singlet}\) indicates the energy required for electron injection. To achieve the maximum \(J_{SC}\), a high LHE and a substantial \(\Delta G^{singlet}\) are preferable. Penoidin is recommended as a promising candidate dye for DSSC applications due to its higher \(\Delta G^{singlet}\) value [41], and it has a potential to improve overall charge transfer efficiency and increase J\({}_{\text{SC}}\) in DSSCs.