All-Electron Path Integral Simulations of Warm, Dense Matter: Application to Water and Carbon*

We develop an all-electron path integral Monte Carlo (PIMC) method for warm dense matter and apply it to study water and carbon. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at lower temperatures and enable the construction of a coherent equation of state over a density-temperature range of 3--12 g/cm$^3$ and 10$^2$--10$^9$ K. PIMC results converge to the Debye-Huckel limiting law at high-temperatures and illuminate the breakdown of DFT pseudopotentials due to core excitations.