  We report a resonant inelastic x-ray scattering study of electronic
excitations in Li_2CuO_2, an insulating compound comprised of ribbons of
edge-sharing copper-oxygen chains. Three excitations, which show little
dependence on momentum transfer, are observed in our measurements. The lowest
energy excitation at ~2.1 eV is dispersionless and is attributed to a localized
d-d orbital excitation. We also observe two excitations at ~5.4 eV and ~7.6 eV
which we assign to charge-transfer excitations. These high-energy excitations
are also dispersionless along the copper-oxygen chain direction. However, in
each case we observe a small energy dispersion along the direction
perpendicular to the copper-oxygen ribbons, suggesting a significant interchain
coupling in this system. We also discuss the possible implications of
ferromagnetic nearest-neighbor intrachain coupling on the charge excitation
spectra.
