Characterization of the energy of hydrogen under pressure in pure metals

In this work we study the total energy of hydrogen under pressure in a metallic medium. We use the effective jellium model to characterize the electronic density, which, based upon the density-functional formalism, determines, in principle, all the physical properties of the system. Although this formalism is not valid for systems under pressure, we will use some approximations obtained from the model of molecular hydrogen in a dense system confined by a penetrable barrier. In this model, the energy of the ground state of the molecular hydrogen ion and its associated pressure are obtained for different barrier heights and nuclear radii. With these results, we recover the system at zero pressure, but with a given initial density, able to treat with the jellium model. This analysis is very useful and quite exact for the treatment of such complex systems as hydrogen under pressure.