First principles study and reconsideration of the mechanical and dynamic stability of hydrogen-rich compound cI14-CaH6 high critical temperature superconductor under pressure

•Reconsideration in the stability cI14-CaH6 high Tc superconductor using DFT calculations.•Study of mechanical and vibrational properties of cI14-CaH6 under pressure.•Study of the superconductivity and some critical parameters. In this paper, we used the density functional theory based on GGA-PBE approximation, to reconsider the stability of CaH6 in phase cI14, which corresponds to the superconducting state according to some theoretical study. Our motivation for reconsidering is the conflict between an experimental and theoretical result about the stability of CaH6 in the superconducting phase under high stress. The obtained results of the elastic constants at a wide range of pressures indicated the mechanical instability of CaH6 in the cI14 prototype. The phonon spectrum showed positive frequencies at pressures higher than 150 GPa, which correspond to dynamic stability.