  We investigate by first-principles simulations the resonant electron-transfer
lifetime from the excited state of an organic adsorbate to a semiconductor
surface, namely isonicotinic acid on rutile TiO$_2$(110). The
molecule-substrate interaction is described using density functional theory,
while the effect of a truly semi-infinite substrate is taken into account by
Green's function techniques. Excitonic effects due to the presence of
core-excited atoms in the molecule are shown to be instrumental to understand
the electron-transfer times measured using the so-called core-hole-clock
technique. In particular, for the isonicotinic acid on TiO$_2$(110), we find
that the charge injection from the LUMO is quenched since this state lies
within the substrate band gap. We compute the resonant charge-transfer times
from LUMO+1 and LUMO+2, and systematically investigate the dependence of the
elastic lifetimes of these states on the alignment among adsorbate and
substrate states.
