## 3 Results and Discussions  
### Electronic Parameters  
The efficiency of DSSCs is notably influenced by a dye's electrical characteristics, including factors such as bandgap energy and HOMO and LUMO energy levels. Frontier molecular orbitals (FMOs), also known as HOMO and LUMO contributions, must be taken into account in order to determine the dye sensitizers' charge-separated states. The FMO dispersion of the sensitizers has a major impact on the electrical charge transfer characteristics of dyes [23; 24]. As shown in Figures 2 and 3, the contour plots of HOMO and LUMO orbitals were calculated using DFT/B3 LYP/6-31G levels for the selected anthocyanin dyes in both gas and ethanol solvent phases.  
HOMO and LUMO energies are crucial factors in solar cell analysis that determine the likelihood of charge transfer. The HOMO energy levels of cyanidin, delphinidin, pelargonidin, peonidin, and petunidin are \(-6.0238\), \(-6.0360\), \(-6.1068\), \(-5.9536\), \(-6.0216\) and \(-6.0551\), \(-6.1062\), \(-6.1261\), \(-5.9890\), \(-6.1228\) eV for vacuum (gas) and ethanol solvent phases, respectively. The absolute energies of LUMOs in the same dyes are \(-3.7274\), \(-3.2090\), \(-4.3125\), \(-3.6050\), \(-3.1968\) and \(-3.6929\), \(-3.3225\), \(-4.2801\), \(-4.1489\), \(-3.3252\) eV for vacuum (gas) and ethanol solvent phases, respectively. The HOMO and LUMO levels are tailored for DSSC use, aligning with the TiO\({}_{2}\) conductive edge energy level and the electrolyte redox potential. This ensures effective charge separation and a reliable dye recovery procedure. The HOMO level of the dye must be sufficiently lower than the redox potential, while the LUMO level must be sufficiently higher than the conduction band edge (\(E_{CB}\)) of TiO\({}_{2}\) for effective electron injection from the excited dye to the conduction band [25].  
Upon comparing the LUMOs depicted in Figures 2 and 3, a notable observation emerges, indicating a higher degree of localization in the LUMO compared to the HOMO. Conventionally, optimal orbital overlap is achieved when both the HOMO and LUMO are delocalized, fostering robust interactions and favorable reactions. However, in the context of our DFT DSSC investigation, a localized LUMO presents potential advantages. The localized nature of the LUMO, as revealed in our findings, leads to favorable outcomes regarding the specific locations of reactions and provides insights into charge transfer dynamics. This observation aligns with the findings of [PERSON] et al. [26] and [PERSON] et al. [27], underscoring the utility of a localized LUMO in DFT DSSC studies. Furthermore, prior research has indicated that similar LUMO behavior can be influenced by factors such as molecular structural symmetry and interactions with solvents [9; 28].  
The results indicate that the LUMO energies of cyanidin, delphinidin, and petunidin are higher than the conduction band edge of the TiO\({}_{2}\) electrode (\(-4.0\) eV) in both phases. Consequently, these dyes are capable of injecting electrons into the semiconductor's conduction band. However, pelargonidin has an inability to do so, given its lower LUMO values compared to TiO\({}_{2}\) in each phase, as shown in Figure 4.  
Figure 2: The contour plots of HOMO and LUMO orbitals for the selected anthocyanin dyes in the gas phase.  
Figure 3: The contour plots of HOMO and LUMO orbitals for the selected anthocyanin dyes in the ethanol solvent phase.  
In both the gas and solvent phases, the computed energy gaps of the model compounds under study decrease in the following sequence: delphinidin > petunidin > peonidin > cyanidin > pelargonidin and petunidin > delphinidin > cyanidin > pelargonidin > peonidin. The findings emphasize that pelargonidin exhibits lower energy levels in both phases, indicating its inefficiency in electron transition from LUMO to the conduction band. However, as a result, it is suggested that cyanidin, with its optimum energy gap in both phases, is expected to be more stable and stands out as a promising candidate for DSSCs.