[en] We investigate the excitation spectrum of a singly charged LiF surface using an embedded cluster approach. The spectrum is determined by multiconfiguration self-consistent field calculations. We find stable trionic states, i.e., quasimolecular states of a three-quasiparticle complex consisting of two holes and one electron interacting through the Coulomb potential. The excitation energy of the lowest trionic state is approximately 12.1 eV. The mean hole-hole spacing is about 7.6 a.u. (or 4 A). Our results confirm the interpretation of experiments [P. Roncin , Phys. Rev. Lett. 89, 043201 (2002)] where trion excitation was suggested as effective energy-loss channel during the neutralization of Ne(+) ions at an LiF surface.