Consistent wide-range equation of state of silicon by a unified first-principles method

Using a unified method of the extended first-principles molecular dynamics, we report a wide-range (density $\ensuremath{\rho}=2.329--18.632$ $\mathrm{g}/{\mathrm{cm}}³$, temperature $T=1.00\ifmmode\times\else\texttimes\fi{}{10}⁴--1.29\ifmmode\times\else\texttimes\fi{}{10}⁸$ K) equation of state (EOS) and principal Hugoniot of silicon, which agree well with experimental results, and then evaluate the precision of the results of first-principles calculations and a universal database. Moreover, we investigate the effects of finite-temperature exchange-correlation functionals and emphasize their importance and necessity in the warm dense matter regime, although it vanishes in the nondegenerate and fully degenerate limits. Finally, we show the ionic radial distribution function and density of electronic states to study the evolution of warm dense Si towards the classic plasma limit along its principal Hugoniot. The established standard theoretical EOS table of Si provides a benchmark for the development of high-precision first-principles methods and may improve radiation-hydrodynamics simulations of inertial confinement fusion and deepen the understanding of high-energy-density physics.