  We propose a means for constructing highly accurate equations of state (EOS)
for elemental solids and liquids essentially from first principles, based upon
a particular decomposition of the underlying condensed matter Hamiltonian for
the nuclei and electrons. We also point out that at low pressures the neglect
of anharmonic and electron-phonon terms, both contained in this formalism,
results in errors of less than 5% in the thermal parts of the thermodynamic
functions. Then we explicitly display the forms of the remaining terms in the
EOS, commenting on the use of experiment and electronic structure theory to
evaluate them. We also construct an EOS for Aluminum and compare the resulting
Hugoniot with data up to 5 Mbar, both to illustrate our method and to see
whether the approximation of neglecting anharmonicity et al. remains viable to
such high pressures. We find a level of agreement with experiment that is
consistent with the low-pressure results.
