Linear absorption spectra of dye-semiconductor systems (perylene attached to nanostructured TiO2) are studied theoretically and experimentally. The systems show ultrafast photoinduced heterogeneous electron transfer (HET). By applying a time-dependent formulation of the absorbance, the theoretical analysis of the measured data is carried out. The respective electron-vibrational wave packet propagation fully accounts for the electronic coupling to the conduction band continuum of TiO2 and is based on a single-reaction-coordinate model (corresponding to a perylene in-plane C-C stretching vibration with a quantum energy of 1370 cm(-1)). By the insertion of different bridge-anchor groups, the electronic coupling responsible for HET is varied. The dye absorbance in a solvent and the trends in the line broadening of the vibrational progression due to the coupling to the conduction band continuum are reproduced for all investigated types of bridge-anchor groups. HET rates deduced from the calculations on the absorbance displaying line broadenings follow the qualitative trend obtained from transient absorption spectra.