  The full monolayer of pentacene adsorbed on rutile TiO$_2$(110) provides an
intriguing model to study charge-transfer excitations where the optically
excited electrons and holes reside on different sides of the internal interface
between the pentacene monolayer and the TiO$_2$ surface. In this work we
investigate the electronic properties of this system with density functional
theory, and compute its excitonic and optical properties making use of \emph{ab
initio} matrix elements. The pentacene molecules are found to lie flat on the
surface, head to tail, and slightly tilted towards the troughs of the oxygen
rows of the surface --- in agreement with experiment. Molecular states appear
in the band gap of the clean TiO$_2$ surface which enable charge transfer
excitations directly from the molecular HOMO to the TiO$_2$ conduction band.
The calculated optical spectrum shows a strong polarization dependence and
displays excitonic resonances corresponding to the charge-transfer states. We
characterize the computed excitons by their symmetry and location in k-space
and use this information to explain the polarization dependence of the optical
spectrum.
