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.
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