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Dye-sensitized solar cells (DSSCs) based on triphenylamine (TPA) as a donor group linked with the acceptor cyanoacrylic acid electron acceptor by 2,2'-bithiophene as π-bridged (D-π-A) has been investigated by Density Functional Theory (DFT) at the B3LYP/6-311G(d,p) level of theory, to establish the conformational orientation of cyanoacrylic acid group as well as evaluate the effect of planarizing the 2,2'-bithiophene unit in position 3 and 3' by electron withdrawing or donor groups on the electronic structure properties of ground and doping(n,p) states. Also, the Time Dependent Density Functional Theory (TD-DFT) at the CPCM-TD-CAM-B3LYP//CAM-B3LYP/6-311G(d,p) level of theory were selected to modulate the electronic absorption spectra and charge-transfer capabilities of the molecules analyzed in the present work. The results indicate that adding an auxiliary donor or withdrawing group to the 2,2'-bithiophene in the (D-π-A) arrangement allow to modify the LUMO's energy of the dyes, while the HOMO´s energy is slightly affected.