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We present and discuss a wide-range hydrogen equation of state model based ona consistent set of ab initio simulations including quantum protons andelectrons. Both the process of constructing this model and its predictions arediscussed in detail. The cornerstones of this work are the specification ofsimple physically motivated free energy models, a generalmultiparameter/multiderivative fitting method, and the use of the most accuratesimulation methods to date. The resulting equation of state aims for a globalrange of validity ($T = 1-10^9 K$ and $V_m = 10^{-9}-1 m^3/mol$), as the modelsare specifically constructed to reproduce exact thermodynamic and mechanicallimits. Our model is for the most part analytic or semianalytic and isthermodynamically consistent by construction; the problem of interpolatingbetween distinctly different models -often a cause for thermodynamicinconsistencies and spurious discontinuities- is avoided entirely.

A first-principles global multiphase equation of state for hydrogen