Novel derivatives of OD1 with D–A2–π–A1 configuration have been designed. The calculated geometrical parameters and optoelectronic properties are compared with those of the parent triphenylamine-based dye molecule (OD1) comprising a triphenylamine terminal electron-rich group (D), 3,4-ethylene dioxythiophene π-spacer, fluorophenyl electron-withdrawing group (A1), and cyanoacrylic acid anchor group. The designed derivatives differ from OD1 with D–π–A1 configuration in the incorporation of an electron-acceptor group (A2) between the donor group and π-spacer unit, namely benzotriazole (BTZ), benzothiadiazole (BTDZ), or phthalimide (PHI), denoted as ND2-BTZ, ND3-BTDZ, and ND4-PHI, respectively. The effects of the incorporation of each electron-deficient unit on the geometry, absorption spectra, and electrochemical properties are investigated by using density functional theory (DFT) and time-dependent (TD)DFT methods. Additionally, the preferred dye adsorption process on model Ti(OH)4 is investigated. The results for the binding energy, selected bond distances, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels and their distribution, energy gaps, and total density of states (TDOS) plots are discussed and analyzed. The intermolecular interaction between two monomers of each dye and iodine is also investigated, and the complexation energy [corrected for the basis set superposition error (BSSE)] is calculated and analyzed. The results reveal that the introduction of the BTDZ and PHI functional groups is more promising for formation of organic dyes with D–A2–π–A1 configuration.