Catalyzes the conversion of (2E,6E)-farnesyl diphosphate (FPP) to yield the bicyclic sesquiterpene guaia-6,10(14)-diene via a 1,10-cyclization, which requires the abstraction of the pyrophosphate from FPP to yield the (E,E)-germacradienyl cation. The only accepted substrate is farnesyl diphosphate (FPP). (2E,6E)-farnesyl diphosphate = (1R,4R,5S)-(-)-guaia-6,10(14)-diene + diphosphate Binds 3 Mg(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Asp (DDXXD) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.