Catalyzes the conversion of geranyl diphosphate to (+)-(4R)-limonene (PubMed:28272875, PubMed:28272876). Produces exclusively the (+)-enantiomer (PubMed:28272875). Can use neryl diphosphate as substrate (PubMed:28272876). Has no activity with farnesyl diphosphate (PubMed:28272875). (2E)-geranyl diphosphate = (4R)-limonene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit (PubMed:28272876). The best cofactor is Mn(2+) (PubMed:28272875). No effect with monovalent cations (PubMed:28272875). Inhibited by 2-fluorogeranyl diphosphate (FGPP) and 2-fluoroneryl diphosphate (FNPP). kcat is 0.186 sec(-1) for geranyl diphosphate in presence of manganese. kcat is 0.118 sec(-1) for geranyl diphosphate in presence of magnesium. kcat is 0.43 sec(-1) for neryl diphosphate. 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.