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Motivated by the recent report of superconductivity above 200 K inultra-dense hydrogen sulfide, we search for high-\tc\ conventionalsuperconductivity in the phase diagram of the binary Li-S system, using {\emab-initio} methods for crystal structure prediction and linear responsecalculations for the electron-phonon coupling. We find that at pressures higherthan 20 GPa, several new compositions, besides the known Li$_2$S, arestabilized; many exhibit electride-like {\em interstitial} charge localizationobserved in other alkali metal compounds. Of all predicted phases, only Li$_3$Sat P > 640 GPa displays a sizable \tc, in contrast to what is observed insulfur and phosphorus hydrides, where several stoichiometries lead to high \tc.We attribute this difference to 2$s$-2$p$ hybridization and avoided coreoverlap, and predict similar behavior for other alkali metal compounds.

Search for high-Tc conventional superconductivity at megabar pressures in the lithium-sulfur system