## 3 Results and Discussions
### Absorption Properties  
Oscillator strengths (f), which dictate the amount of light absorbed by molecules, serve as absorption characteristics connected to the maximum absorption wavelength and the vertical transition energy of the dye from the ground state to an excited state [29]. Tables 1 and 2 list the oscillator strengths, excitation energies, and absorption wavelengths of the dye molecules in both gas and ethanol solvent phases. The energy levels and oscillator strengths of the natural dyes in both the gas and solvent phases exhibit significant patterns. In the gas phase, the energy levels decrease in the following order: petunidin > delphinidin > pelargonidin > cyanidin > peonidin. This order demonstrates how the dye molecules' energy levels are positioned relative to one another, with lower energy levels being more advantageous for electron injection and transfer into a semiconductor's conduction band in DSSCs. In the solvent phase (ethanol),  
Figure 4: HOMO and LUMO energy levels of the selected anthocyanin dyes in the (**a**) vacuum phase and (**b**) ethanol solvent phase. the decreasing order is delphinidin > petunidin > pelargonidin > cyanidin > peenoidin. The oscillator strengths in the gas phase follow the decreasing order of petunidin = delphinidin > pelargonidin > cyanidin = peenoidin, reflecting the interplay between electronic transitions and incoming light. Similarly, in the solvent phase, the order is petunidin = delphinidin > pelargonidin > cyanidin = peenoidin. Additionally, the oscillator strength values in the gas phase undergo alterations when an ethanol solution is introduced to the dye molecules. This implies that the polarity of the solvent, ethanol in this case, can influence the electronic transitions and optical characteristics of the dyes. According to the data, petunidin and delphinidin exhibit stronger oscillators than the other dyes. This indicates that petunidin and delphinidin interact more strongly with light and are more likely to effectively absorb light in the studied system. A higher absorption wavelength in DSSCs implies that the dyes may absorb light with longer wavelengths, which equates to lower energy photons. This is crucial because the typical operation of a DSSC involves absorbing light from the visible and near-infrared range, utilizing the absorbed energy to create electron-hole pairs in the dye molecule. Achieving a higher total light-to-energy conversion efficiency in the DSSC may result from using a larger fraction of the solar spectrum due to a higher absorption wavelength [30]. The optical absorption spectra of five naturally occurring dyes: cyanidin, delphinidin, pelargonidin, and petunidin are provided for both the gas and solvent phases. These absorption spectra values reflect the wavelengths at which the dyes exhibit the highest light absorption. In the gas phase, the wavelengths of cyanidin, delphinidin, pelargonidin, and petunidin are given as 1382.88, 564.34, 879.92, 1401.18, and 563.29 nm, respectively. The wavelengths for the same dyes in the solvent phase are 1430.93, 565.12, 857.00, 1447.05, and 565.83 nm. That redshift, or a shift towards longer wavelengths, is a phenomenon exhibited by molecules when their absorption spectra show a displacement towards longer wavelengths. A redshift in the absorption spectra can have an impact on the DSSC's photo-to-current conversion efficiency. According to the results of Tables 1 and 2, cyanidin and peenidin exhibit greater absorption wavelengths compared to other dyes. Despite their longer wavelengths, these dye derivatives face limitations in electron injection into the semiconductor's conduction band due to their lower LUMO energy levels. The energy level of the LUMO is a critical factor for effective electron injection in DSSCs. In contrast, petunidin and delphinidin exhibit longer absorption wavelengths. This implies that, in comparison to the other dyes, they are capable of absorbing light at substantially higher levels of energy.