The theoretical approach proposed by Borisov et al. [Phys. Rev. Lett. 77, 1893 (1996)] to treat negative-ion conversion of neutral atoms at ionic crystal surfaces is described in detail. Due to the localization of the valence-band electrons at the anionic sites of the crystal, the conversion process is viewed as a result of successive binary collisions between the projectile and the negatively charged sites at the surface. Parameter free calculations of F- formation in grazing scattering from LiF(100) and KI(100) are performed using a model in which all sites of the crystal lattice but one, the active site, are represented by eventually polarizable point charges. Parallel velocity thresholds for negative-ion formation, relative efficiency of the negative-ion formation for LiF and KI crystals, and dependences of this efficiency on the scattering angle correspond well to the experimental results. [S0163-1829(97)08635-9].