Catalyzes the conversion of (2E,6E)-farnesyl diphosphate (FPP) to yield the bicyclic sesquiterpene (1R,6S,7S)-(-)-alpha-amorphene via a probable 1,6-cyclization, which could involve the abstraction of the pyrophosphate from FPP to yield a (R)-bisabolyl cation (PubMed:23307484, PubMed:27666571, PubMed:27829890). The only accepted substrate is (2E,6E)-farnesyl diphosphate (FPP) (PubMed:27829890). (2E,6E)-farnesyl diphosphate = (-)-alpha-amorphene + diphosphate Binds 3 Mg(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Glu (DDXXE) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.