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A thorough density functional theory study is performed for the three carboxyl-based derivatives of the exTTF-TCF chromophore, where the π-extended tetrathiafulvalene (exTTF) electron-donor is linked to the tricyanofuran (TCF) electron-acceptor through an ethylene bridge, as dyes for dye-sensitized solar cells. Calculations predict that the carboxyl group in the acceptor moiety adopts an adequate orientation for an efficient anchoring on the semiconductor TiO₂ surface. The carboxylic acid group holds a negative charge twice larger than the cyano moiety that favors the electron injection to the semiconductor. Time-dependent calculations allow for the assignment of the absorption bands in the UV-vis spectrum of exTTF-TCF and confirm the presence of two low-lying charge-transfer electronic transitions that account for the moderately-intense absorption in the 450-800 nm range. The striking optical absorption properties of exTTF-TCF are preserved for the carboxylic analogues. Finally, periodic calculations show relevant topological differences between the carboxylic derivatives anchored on the TiO₂ surface, which would notably influence in the power conversion efficiency of a dye-sensitized solar cell.