Involved in sesquiterpene (C15) biosynthesis. The major product is alpha-farnesene. (2E,6E)-farnesyl diphosphate = (3E,6E)-alpha-farnesene + diphosphate Binds 3 Mn(2+) ions per subunit. Terpene metabolism; oleoresin biosynthesis. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family. Tpsd subfamily.