Following a previous paper [J. Phys. Chem. C, 2011, 115, 4297–4306], we reinvestigate the interface between a dye and a semiconductor surface as found in dye-sensitized solar cells. In order to elucidate the influence of the dye binding mode on cell performances, three possible adsorption modes of N3 on TiO₂ anatase (101) are considered: mixed monodentate/bidentate, mixed monodentate/bidentate with additional NCS interaction, and double bidentate. The corresponding interfaces were studied at the density functional theory (DFT) and time-dependent DFT (TD-DFT) levels, using a hybrid exchange-correlation functional and both periodic and non-periodic approaches. Although computed electronic structures are in line with an electron injection from the dye to the semiconductor in all cases, the dye's binding mode noticeably influences computed data, especially concerning injection times as well as simulated UV-visible spectra. This further outlines that the high flexibility of this model system in the binding mode might also be responsible for the excellent efficiency observed, still barely beaten by other systems at the experimental level. It also pinpoints the role of modeling for these systems, which allows investigation of a specific binding mode, even when it is difficult to tackle experimentally.