With the aid of a second-order perturbation scheme, the energy of metallic hydrogen is calculated for pressures ranging from 0 to 110 Mbar. The zero-point energy is taken into account by evaluating the density of states resulting from the phonon spectra. For pressures higher than 3 Mbar the compressibilities as derived from the total energy and from the elastic constants agree within 10%. In this view and from the calculated band structure, there is no apparent evidence for the use of higher-order correction terms in this pressure region, where also the equation of state is rather insensitive to the treatment of the electron correlations. For lower pressures, however, the perturbation scheme seems to break down and the results depend strongly on the treatment of the electronic correlations. © 1974 Società Italiana di Fisica.