Equation of State, Ionization, and Metallization of Helium in Wide Density-Temperature Ranges by Density Functional Theory Calculations

Helium is the second most abundant element in the universe and plays a critical role across a wide range of scientific domains. We present a comprehensive analysis of helium by Single-Atom-in-Box (SAIB) Density Functional Thoery (DFT) across a broad range of densities (0.1 - 100 g/cm³) and temperatures (500 - 16,000,000 K). Strong agreement at high temperatures of the equation of state, Hugoniot, and thermodynamic properties (specific heat, Grüneisen parameter, thermal expansion coefficient, and bulk sound velocity) is shown with a more accurate (but computationally more expensive) first-principles equation of state (FPEOS) model that is based on DFT Molecular Dynamics (DFT-MD) and path integral Monte Carlo (PIMC) calculations. Recent discussion of the continuum lowering and ionization potential’s evolution at degenerate and non-degenerate conditions motivated analysis of the Fermi, 1s state, and continuum energies through the density of states. Additionally, the density of states provides a strong basis for the band gap closing and continuum lowering with increasing compression, which is most apparent with increasing temperatures. A close examination of the occupied and unoccupied eigenstates at each k-point suggests helium has an indirect gap that closes with increasing compression, which agrees with a previous work that utilized a similar method (but with a tighter density-temperature range considered), while the direct or Γ-point gaps widen with increasing compression.