In this work, the molecular engineering approach was applied to the organic dyes of AE, AQ, TE, and TQ having the donor-acceptor (D-A) configuration to investigate the solar cell efficiency. In these structures, dimethylaniline and triphenylamine were used as the electron donors and 1,1,4,4-tetracyanobuta-1,3-dienes (originating from TCNE) and 2-(4-(4,4-dicyanobut-3-en-2-ylidene)cyclohexa-2,5-dien-1-ylidene)malononitrile (originating from TCNQ) as the electron acceptors. The incorporation of tetracyanoethylene (TCNE) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) due to the strong electron-withdrawing ability enhance the performance of the dye-sensitized solar cell (DSSC). The results reveal that a change in the electron donor and acceptor moieties affects the photovoltaic processes. Also, the dyes having 2-(4-(4,4-dicyanobut-3-en-2-ylidene)cyclohexa-2,5-dien-1-ylidene)malononitrile electron acceptor (AQ and TQ) have better charge transfer indices such as longer charge transfer distance (DCT) and lower overlap of electron-hole distribution (S) in comparison with the dyes having 1,1,4,4-tetracyanobuta-1,3-dienes as an electron acceptor (AE and TE). Moreover, the properties of the absorption spectra indicate that TCNQ-adduct dyes (AQ and TQ) illustrate a red-shift compared with TCNE-adduct dyes (AE and TE) due to the higher ability of the electron-withdrawing. Finally, AQ and TQ dyes are the preferred candidates to improve the efficiency of the studied DSSCs because of higher charge transfer, electron transfer rate constant, and lower chemical hardness.