  Hydrogen-rich compounds hold promise as high-temperature superconductors
under high pressures. Recent theoretical hydride structures on achieving
high-pressure superconductivity are composed mainly of H2 fragments. Through a
systematic investigation of Ca hydrides with different hydrogen contents using
particle-swam optimization structural search, we show that in the stoichiometry
CaH6 a body-centred cubic structure with hydrogen that forms unusual "sodalite"
cages containing enclathrated Ca stabilizes above pressure 150 GPa. The
stability of this structure is derived from the acceptance by two H2 of
electrons donated by Ca forming a "H4" unit as the building block in the
construction of the 3-dimensional sodalite cage. This unique structure has a
partial occupation of the degenerated orbitals at the zone centre. The
resultant dynamic Jahn-Teller effect helps to enhance electron-phonon coupling
and leads to superconductivity of CaH6. A superconducting critical temperature
(Tc) of 220-235 K at 150 GPa obtained from the solution of the Eliashberg
equations is the highest among all hydrides studied thus far.
