Optimizing the photovoltaic efficiency of dye-sensitized solar cells (DSSC) based on staggered gap heterojunctions requires a detailed understanding of sub-band gap transitions in the visible from the dye directly to the substrates conduction band (CB) (type-II DSSCs). Here, we calculate the optical absorption spectra and spatial distribution of bright excitons in the visible region for a prototypical DSSC, catechol on rutile TiO$_2$(110), as a function of coverage and deprotonation of the OH anchoring groups. This is accomplished by solving the Bethe-Salpeter equation (BSE) based on hybrid range-separated exchange and correlation functional (HSE06) density functional theory (DFT) calculations. Such a treatment is necessary to accurately describe the interfacial level alignment and the weakly bound charge transfer transitions that are the dominant absorption mechanism in type-II DSSCs. Our HSE06 BSE spectra agree semi-quantitatively with spectra measured for catechol on anatase TiO$_2$ nanoparticles. Our results suggest deprotonation of catechols OH anchoring groups, while being nearly isoenergetic at high coverages, shifts the onset of the absorption spectra to lower energies, with a concomitant increase in photovoltaic efficiency. Further, the most relevant bright excitons in the visible region are rather intense charge transfer transitions with the electron and hole spatially separated in both the [110] and [001] directions. Such detailed information on the absorption spectra and excitons is only accessible via periodic models of the combined dye-substrate interface.
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