Density functional theory (DFT) calculations are performed on the newly developed and designed photosensitizers having [D-D-triad-A]- and [D-π-π-A]-type structural models for near-infrared absorption dye-sensitized solar cells (DSSCs). For this purpose, three novel molecules are designed, which are named as follows: [naphthalene-anthracene-thiophene-furan-benzonitrile] as dye S1, [coronene-anthracene-thiophene-furan-benzonitrile] as dye S2, and [fluorene-thiophene-furan-benzonitrile] as dye S3. In all three systems, benzonitrile is the acceptor moiety, while thiophene and furan are bridging moieties. Naphthalene and anthracene are donor moieties in S1, whereas coronene and anthracene are donor moieties in S2, and fluorene is the only single donor moiety used for designing the dye complex S3. All three dye complexes are optimized under the DFT framework by using the B3LYP hybrid functional with 6-31G(d,p) basis set on Gaussian 16W software. The absorption spectra are calculated utilizing time-dependent density functional theory (TD-DFT) with the CAM-B3LYP/6-31G(d,p) basis set. The calculated absorption maxima of S1 and S2 are 749.45 and 750.04 nm, respectively, while for S3, it is reported to be at 337.35 nm, which suggests that the designed molecular structure having a double-donor moiety is suitable for high absorption wavelength. Further, the analysis of frontier molecular orbital energy gap suggests that the molecular systems S1, S2, and S3 have values 2.17, 2.13, and 3.618 eV, respectively, which lie in the semiconducting region. The other parameters calculated for the photovoltaic performance are exciton binding energy, change in free energy of charge regeneration, change in free energy of charge injection, oscillator strength, light harvesting efficiency, and open-circuit voltage.