For a given chemical system we present a systematic approach to predict structures, which may exist at high pressure, by investigating the global enthalpy landscape. We combine global optimizations, based on empirical potential energy functions, and local optimizations (volume, cell shape, and atomic positions) on both Hartree-Fock and density functional theory level. We predict the existence of high-pressure phases for the alkali metal sulfides of the composition M2S (M=Li, Na, K, Rb, Cs), together with the transition pressures among these phases. (C) 2004 American Institute of Physics.