Due to the role of dyes in dye-sensitized solar cells (DSSCs), designing novel dye sensitizers is an effective strategy to improve the power conversion efficiency. To this end, the fundamental issue is understanding the sensitizer's trilateral relationship among its molecular structure, optoelectronic properties, and photovoltaic performance. Considering the good performance of N-annulated perlyene dye sensitizers, the geometries, electronic structures, and excitations of the selected representative organic dye sensitizers C276, C277, and C278 as well as dyes adsorbed on TiO2 clusters were calculated in order to investigate the relationship between molecular structures and properties. It was found that fusing thienyl to N-annulated perlyene can elevate the highest occupied molecular orbital (HOMO) energy, reduce the orbital energy gap, increase the density of states, expand the HOMO to the benzothiadiazole moiety, enhance the charge transfer excitation, elongate the fluorescence lifetime, amplify the light harvesting efficiency, and induce a red-shift of the absorption spectra. The transition configurations and molecular orbitals of the dye-adsorbed systems support that the electron injection in DSSCs based on these dyes is a fast mode. Based on extensive analysis of the electronic structures and excitation properties of these dye sensitizers and the dye-adsorbed systems, we present new quantities as open-circuit voltage and short-circuit current density descriptors that celebrate the quantitative bridge between the photovoltaic parameters and the electronic structure-related properties in order to expose the relationship between properties and performance. The results of this work are critical for the design of novel dye sensitizers for solar cells.