Lattice stability and superconductivity of the metallic hydrogen at high pressure

Ab initio calculations of metallic hydrogen are presented. Investigation of the lattice stability of metallic monoatomic phases confirms the main part of conclusions obtained previously by Kaganʹs group in the framework of the perturbation approach to fourth order in the electron–phonon interaction. The results of the ab initio calculation of the critical temperature Tc of the superconducting transition is also presented. It is shown that Tc can reach very high values about 600 K near the lattice instability in respect to shear deformations.