## 1 Introduction  
The crucial quest for sustainable and renewable energy sources has become increasingly paramount in addressing the world's escalating energy needs while concurrently mitigating the environmental impacts associated with conventional energy generation methods [1]. Within the domain of solar energy technologies, dye-sensitized solar cells (DSSCs) have attracted significant attention owing to their potential cost-effectiveness and efficiency [2]. The function of DSSCs is based on the principle of converting solar energy into electricity through the utilization of light-absorbing molecules, or dyes, which play a key role in initiating charge separation and transfer processes [3]. The careful selection of these dye molecules is crucial in determining the performance and efficiency of DSSCs. Several factors contribute to the prominence of DSSCs, including their facile fabrication process, utilization of low-cost materials, and the ability to capture a broad spectrum of light [4]. In light of the increasing emphasis on sustainability and reduced environmental impact, DSSCs emerge as a promising avenue for the future of solar energy [5]. Additionally, the application of eco-friendly natural dyes as sensitizers for DSSCs has garnered growing interest, driven by the aim to enhance the sustainability and environmental friendliness of these photovoltaic devices [6]. To explore the potential of natural dyes in DSSCs, researchers employ density functional theory (DFT), a powerful computational tool widely adopted in the field of materials science [7]. DFT provides a theoretical framework for investigating the optoelectronic properties of materials, allowing researchers to predict and comprehend their behavior with a high degree of accuracy [8]. This approach proves particularly valuable in studying complex systems, such as the interactions between dye molecules and semiconductor surfaces in DSSCs. [PERSON] et al. explored the correlation between intramolecular charge transfer (ICT) and the wavelength of light absorbed by a molecule. Their findings documented that increased ICT leads to the absorption of longer wavelengths of light, causing the molecule's bandgap to narrow with the rise in the wavelength of light absorption. These findings suggest that dyes exhibiting strong ICT and narrower bandgaps are good candidates for applications in DSSCs [9]. [PERSON] et al. provided insights into the characteristics of a typical dye used in the application of DSSCs. Their study aimed to establish correlations between the electrical structure, spectroscopic features, and the attainment of desirable properties in optoelectronic materials by using computational methodology. The equilibrium geometries and electronic structure of the examined dyes were optimized using a variety of DFT functionals. Natural bond order (NBO) analysis was carried out, and the topological and local features of the charge density distributions were estimated [10]. [PERSON] et al. investigated the influence of substitutions of donors and electron acceptors incorporated in linkers on the optoelectronic properties of D-A dye-sensitized solar cells in their DFT/TD-DFT study. They employed computational techniques, specifically, time-dependent density functional theory (TD-DFT) and DFT, to design effective sensitizer dyes for DSSCs. The investigation extended to several metal-free organic dyes featuring the D-p-A-A arrangement, examining the impact of donor and acceptor groups on their structural, photochemical, and electrochemical properties. Their findings revealed that the donor group and the electron-accepting substitutions added to p-linkers become a critical factor in the fine-tuning of the optoelectronic characteristics of selected dyes and provide valuable insights into the design of cost-effective sensitizers with high efficiency for DSSCs [11]. [PERSON] et al. reported the optoelectronic properties of triphenylamine-based dyes for solar cell applications, focusing on the designing and creation of organic sensitizers for DSSCs.