The molecular structure, UV-Visible spectra, and optical properties of D-π-A conjugated organic dye molecules (Disperse Red 1 (DR1) and Disperse Red 73 (DR73)) were analyzed using Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT) and compared with Azobenzene molecule to study the effect of Donor and Acceptor substituents on the molecular properties. The performance of DFT functionals is investigated using B3LYP hybrid functional and three long-range corrected functionals (CAM-B3LYP, LC-ωPBE, and ωB97XD) in conjunction with 6-31G(d,p) basis set. Using TD-DFT, we calculate the vertical excitation energies and transition dipole moment values for 100 excited states. These values were further utilized to calculate frequency dependent polarizability under Sum-Over-States (SOS) formalism and refractive index of these molecular systems. We observe that B3LYP and CAM-B3LYP perform well in estimating molecular structures while CAM-B3LYP models the UV-Visible spectra of molecules with the least error compared to experimental results. Therefore, CAM-B3LYP is reported to be the most suitable candidate for modelling disperse dye molecules. Large polarizability response is also observed for these molecules (DR1 and DR73) in comparison to parent Azobenzene structure due to charge transfer between donor and acceptor groups. For DR1 and DR73 molecules, α xx component of polarizability dominates in contrast to azobenzene where α zz dominates. The HOMO → LUMO transition during excitation contributes to the peak molecular response in simulated UV-Visible spectra. The high polarizability response of selected D-π-A conjugated molecules in comparison to parent molecule suggests that these molecules are promising candidates for tailor-made photonic and optoelectronic device development.