## 3 Results and Discussions
### Photovoltaic Properties
#### 3.3.6 Electronic Coupling Constant (\(\mid V_{RP}\mid\))  
In a DSSC, the electronic coupling constant measures how strongly the dye molecule interacts with the semiconductor surface. It calculates the amount of electron transfer between the electronic states of the dye and the semiconductor, which is an important step in the conversion of light energy into electrical energy. The electronic coupling constant, which is expressed in electron volts (eV), may be calculated using the DFT, a popular quantum mechanical method. A larger coupling constant, which indicates a stronger bond between the dye and the semiconductor and a faster rate of electron transfer, may lead to improved DSSC performance [46].  
The packing and orientation of the dye molecule and the semiconductor surface, as well as the properties of the electrolyte in the vicinity, all have an effect on the electronic coupling constant. Enhancing the electronic coupling between the dye and the semiconductor is a current area of research that aims to improve the performance of DSSCs. The generalized Mulliken-Hush (GMH) model presupposed the following method for calculating coupling constants from Equations (7) and (8).  
\[\mid V_{RP}\mid=\Delta E_{RP}/2 \tag{7}\]  
\[\Delta E_{RP}=[E^{dye}{}_{LUMO}+2\;E^{dye}{}_{HOMO}]-[E^{dye}{}_{LUMO}+E^{ dye}{}_{HOMO}+E_{CB}] \tag{8}\]  
where:  
\(\mid V_{RP}\mid=\) Electronic coupling constant.  
As shown in Table 3, the order of the energy gaps of the natural dyes in the gas phase is pelargonidin > delphinidin > cyanidin > petunidin > peonidin. However, in the solvent phase, the sequence changes to pelargonidin > petunidin > delphinidin > cyanidin > peonidin. The energy gap plays a significant role in a dye's ability to absorb light and participate in electronic transitions. Pelargonidin reportedly possesses the smallest energy gap among other studied dyes for both the gas and solvent phases [47]. For successful light harvesting in optoelectronic devices like DSSCs, a lower energy gap is preferred, since it enhances the likelihood of collecting light in the visible spectrum. This also indicates that pelargonidin has a stronger inclination for coupling, referring to the electrical coupling between an excited dye molecule and a semiconductor's conduction band. This indicates that pelargonidin is more likely to facilitate the fast transfer of electrons from the dye molecule to the semiconductor's conduction band. Effective electron transport is crucial for DSSCs because it enables the conversion of absorbed light energy into electrical energy. The final column in Table 3 presents the reported experimental efficiencies of DSSCs sensitized with dyes extracted in ethanol solvent, providing a comprehensive overview of their performance.  
These findings support the notion that pelargonidin, among the studied natural dyes, is the most favorable sensitizer due to its small energy gap and strong electron coupling. These characteristics suggest that pelargonidin is likely to have increased light absorption and quick electron injection into the semiconductor material's conduction band, enhancing the overall effectiveness of the DSSCs.  
It is imperative to recognize several inherent limitations to this study. Firstly, the adoption of a 6-31 G basis set, while conventionally considered large, may be perceived as outdated in the current computational landscape. Additionally, the omission of dispersion correction introduces the possibility of results deviating more significantly from actual outcomes. Nevertheless, this decision aligns with the methodology employed in a prior investigation conducted by [PERSON] et al. [9].  
In future studies related to this research, we aim to address these limitations by exploring the adoption of a more advanced basis set and incorporating dispersion correction. This strategic enhancement will not only enable more accurate comparisons with the current study but also has the potential to broaden the scope of our investigation.