  The isostructural {\alpha}-{\gamma} phase transition in cerium is analyzed
using density-functional theory with different exchange-correlation
functionals, in particular the PBE0 hybrid functional and the exact- exchange
plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach.
We show that the Hartree-Fock exchange part of the hybrid functional actuates
two distinct solutions at zero temperature that can be associated with the
{\alpha} and {\gamma} phases of cerium. However, despite the relatively good
structural and magnetic properties, PBE0 predicts the {\gamma} phase to be the
stable phase at ambient pressure and zero temperature, in contradiction with
low temperature experiments. EX+cRPA reverses the energetic ordering, which
emphasizes the importance of correlation for rare- earth systems.
