Test of a theoretical equation of state for elemental solids and liquids

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 curve with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity etc. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.