All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of $(2.5–7.5)\times {10}^5\mathrm{K}$, and both methods together form a coherent equation of state over a density-temperature range of $3–12\mathrm{g}/{\mathrm{cm}}^3$ and ${10}^4–{10}^9\mathrm{K}$.

Figure 1

Comparison of excess pressure relative to the ideal Fermi gas plotted as a function of temperature for water.

Figure 2

Comparison of excess pressures relative to the ideal Fermi gas plotted as a function of temperature for carbon.

Figure 3

Comparison of excess internal energies relative to the ideal Fermi gas plotted as a function of temperature for (a) carbon and (b) water. The lower density data have been shifted by a constant, $-2$, in both cases.

Figure 4

Nuclear pair-correlation functions for (a) carbon and (b) water.