Periodic density functional calculations have been carried out on a series of tetrahedral frameworks, which includeknown and hypothetical zeolite topologies. For each framework both SiO2 and SiS2 compositions were considered. We demonstrate that the energy landscape of tetrahedral sulfides is dramatically different from that of silica and that hypothetical frameworks are too distorted for silica, for example, supertetrahedral frameworks such as RWY are significantly stabilized as sulfides. We discuss this change in terms of the increased tolerance of sulfides for tetrahedral distortion and a more general increase in the material's flexibility. The latter is shown clearly from a comparison between the pseudofrequencies (the frequencies calculated with all atomic masses set to one for comparison) of the two compositions, being noticeably lower in the case of SiS2.