  Simple cubic (SC) phase has been long experimentally determined as the
high-pressure phase III of elemental calcium (Ca) since 1984. However, recent
density functional calculations within semi-local approximation showed that
this SC phase is structurally unstable by exhibiting severely imaginary
phonons, and is energetically unstable with respect to a theoretical
body-centered tetragonal I41/amd structure over the pressure range of phase
III. These calculations generated extensive debates on the validity of SC
phase. Here we have re-examined the SC structure by performing more precise
density functional calculations within hybrid functionals of
Heyd-Scuseria-Erhzerhof (HSE) and PBE0. Our calculations were able to
rationalize fundamentally the phase stability of SC structure over all other
known phases by evidence of its actual energetic stability above 33 GPa and its
intrinsically dynamical stability without showing any imaginary phonons in the
entire pressure range studied. We further established that the long-thought
theoretical I41/amd structure remains stable in a narrow pressure range before
entering SC phase and is actually the structure of experimental Ca-III'
synthesized recently at low temperature 14 K as supported by the excellent
agreement between our simulated X-ray diffraction patterns and the experimental
data. Our results shed strong light on the crucial role played by the precise
electron exchange energy in a proper description of the potential energy of Ca.
