  Internal energies, enthalpies, phonon dispersion curves, and
superconductivity of atomic metallic hydrogen are calculated. The (standard)
use pseudopotentials in density-functional theory are compared with full
(Coulomb)-potential all-electron linear muffin-tin orbital calculations.
Quantitatively similar results are found as far as internal energies are
concerned. Larger differences are found for phase-transition pressures;
significant enough to affect the phase diagram. Electron--phonon spectral
functions $\alpha^2 F(\omega)$ also show significant differences. Against
expectation, the estimated superconducting critical temperature T$_{c}$ of the
first atomic metallic phase I4$_{1}$/amd (Cs-IV) at $500$ GPa is actually
higher.
