Catalyzes the formation of (R)-(+)-limonene, terpinolene, (1R,5S)-(+)-camphene, (1R,5R)-(+)-alpha-pinene, beta-myrcene and traces of alpha-phellandrene. (2E)-geranyl diphosphate = (4R)-limonene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. kcat is 0.012 sec(-1) with geranyl diphosphate as substrate. Optimum pH is 7.0. Belongs to the terpene synthase family.