We construct a multiphase equation of state (EoS) of hydrogen in the range 0.2 to 5 g/cc and up to 10 eV based on ab initio electronic structure calculations. In the molecular solid, cold curve and phonon spectra calculations are performed for various structures, proposed in the literature, to cover the stability field up to 500 GPa. A weak structural dependence is observed, and the solid EoS is averaged over these data. In the dissociating molecular fluid and in the dense plasma, calculations are made to complete the abundant data set in the literature. Two physical models are used to fit these calculations: a double-Debye model for the solid phase and a one-component plasma model with a mass action law for dissociation to implicitly access the molecular phase in the fluid state. The output of the calculations; energy, pressure, temperature, and density are perfectly reproduced with thermodynamical consistency. This model also allows us to access to the total free energy. The ionic quantum zero-point contribution is taken into account. The present hydrogen EoS is shown to reproduce most of the existing experimental data very well: the solid compression curve, the Hugoniot curve, the sound velocity in the molecular fluid, and the melting curve. The usefulness of this EoS is illustrated by the computation of an interesting isotopic shift on the melting curve and of an isentropic compression path reaching temperatures lower than 1000 K in the terapascal range.

• Received 10 September 2010

DOI:https://doi.org/10.1103/PhysRevB.83.094101