  We study within the many-body Green's function $GW$ and Bethe-Salpeter
formalisms the excitation energies of several coumarin dyes proposed as an
efficient alternative to ruthenium complexes for dye-sensitized solar cells.
Due to their internal donor-acceptor structure, these chromophores present
low-lying excitations showing a strong intramolecular charge-transfer
character. We show that combining $GW$ and Bethe-Salpeter calculations leads to
charge-transfer excitation energies and oscillator strengths in excellent
agreement with reference range-separated functional studies or coupled-cluster
calculations. The present results confirm the ability of this family of
approaches to describe accurately Frenkel and charge-transfer photo-excitations
in both extended and finite size systems without any system-dependent
adjustable parameter, paving the way to the study of dye-sensitized
semiconducting surfaces.
