Novel phases of LinI (n = 2, 3, 4, 5) compounds are predicted to form under high pressure using first-principles density functional theory and an unbiased crystal structure search algorithm. All of the phases identified are thermodynamically stable with respect to decomposition into elemental Li and the binary LiI at a relatively low pressure (approximate to 20 GPa). Increasing the pressure to 100 GPa yields the formation of a high pressure electride where electrons occupy interstitial quasiatom (ISQ) orbitals. Under these extreme pressures, the calculated charge on iodine suggests the oxidation state goes beyond the conventional and expected -1 charge for the halogens. This strange oxidative behavior stems from an electron transfer going from the ISQ to I- and Li+ ions as high pressure collapses the void space. The resulting interplay between chemical bonding and the quantum chemical nature of enclosed interstitial space allows this first report of a halogen anion beyond a -1 oxidation state.