Triphenylamine and 9-phenylcarbazole are the most common electron donor groups, now based on the two groups, eight D-π-A dyes are designed as sensitizers for dye-sensitized solar cells (DSSCs).The eight dyes use the same π-conjugated bridge (thiophene moiety and carbon-carbon double bond) and acceptor fragment (cyanoacrylic acid), and the donor group is added with additional electron-D groups to the original triphenylamine and 9-phenylcarbazole (C4H9 alkyl chain, C4F9 perfluoroalkyl chain, and methoxy), and comparing the properties of several donor groups and terminal branched chains while ensuring that the π-bridges and acceptors are identical. The photophysical properties, electronically excited states, and chemical reactivity affecting the performed dyes have been determined with DFT and TD-DFT calculations of bond lengths and dihedral angles between fragments, frontier molecular orbitals, density of states, isosurface molecular electrostatic potential, charge density differences, fragment transition density matrix, UV-Vis absorption spectra, quantum chemical, and photovoltaic parameters. Comparisons have been made between the dyes under study's photophysical characteristics, electrically excited states, and chemical reactivity. Among all the different donor dyes designed, SH-3 and ZD-3 are poorly molecularly planar compared to the same series of molecules with parameters such as large HOMO-LUMO energy gaps (2.78 eV, 3.28 eV), maximum excited energies (2.93 eV, 3.13 eV), and the shortest absorption peaks (422.76 nm, 396.48 nm), which are considered to be the worst material for photovoltaic applications. Whereas, SH-4 and ZD-4 have the smallest energy gap values (2.35 eV, 2.74 eV) and vertical excitation energies (2.66 eV, 3.04 eV) as well as having the longest absorption peaks (465.34 nm, 408.42 nm), the largest open circuit voltages (1.42 eV, 1.34 eV), which are the best designs among the two groups of molecules. The rest of the designed organic dyes have suitable photophysical properties and all of them are highly recommended for DSSCs.