Solid-state molybdenum sulfide clusters with an octahedral metal framework, the Chevrel phases, are applied to the catalytic cracking of methyl tert-butyl ether (MTBE) to yield isobutene. The copper salt of the nonstoichiometric sulfur-deficient cluster, Cu (x) Mo6S8-delta (x = 2.94 and delta a parts per thousand 0.3), after storing in air, is thermally activated in a hydrogen stream, followed by the reaction with MTBE. Two kinds of catalytically active sites develop depending on the activation temperature: one developed at 100-200 A degrees C is a Bronsted-acidic hydroxo ligand on the copper cation while the other developed at 350-400 A degrees C is a Lewis-acidic coordinatively unsaturated molybdenum atom with a sulfur-deficient site. A nonstoichiometric sulfur-deficient neutral cluster Mo6S8-delta (delta a parts per thousand 0.4) also catalyzes the cracking reaction when activated at 400 A degrees C.