In the present work we perform a computational study of the properties of a push-pull organic dye with a quinoidal thiophene unit as the conjugated linker between the electron donor and acceptor groups. We investigate the photophysical properties of the dye related to its potential use as a molecular sensitizer in dye-sensitized solar cells. We rationalize the solvation effects on the absorption band of the dye in protic and aprotic solvents, identifying the interaction of alcohol solvents with the amine in the donor group as the source for the blue shift of the absorption band with respect to aprotic solvents.