Catalyzes the conversion of (2E,6E)-farnesyl diphosphate (FPP) to yield the bicyclic sesquiterpene (2S,10R)-(-)-(E)-beta-caryophyllene via a probable 1,10-cyclization, which could involve the abstraction of the pyrophosphate from FPP to yield a (E,E)-germacradienyl cation. (2E,6E)-farnesyl diphosphate = (-)-(E)-beta-caryophyllene + 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.