  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
substrate's 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
catechol's 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.
