We study the influence of antiprotons and protons traveling through LiF on the band structure of the insulator using the embedded-cluster method. The crystal is represented by F m − Li n + clusters with up to 19 fluorine ions embedded in a lattice of point charges representing the remainder of the crystal. The minimum excitation energy of LiF perturbed by the ͑anti͒proton impurity is calculated employing the multiconfiguration self-consistent field method. The repulsive potential of the antiproton causes a dramatic local perturbation of the LiF band structure. We find a strong suppression of the excitation energy by more than an order of magnitude compared to that of the unperturbed crystal. The present results provide a simple explanation of recent stopping-power experiments for antiprotons in LiF which, surprisingly, found a "metal-like" behavior of the wide-band-gap insulator LiF. Our results also agree with recent experimental data indicating a deviation from metallic behavior of the stopping power of proton projectiles.