Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter ($2.3–18.6\mathrm{g}{\mathrm{cm}}^{-3}$, $5.0\times 10^5-1.3\times 10^8\mathrm{K}$). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

Figure 1

Internal energy and pressure vs temperature for a single silicon atom in periodic cell of 5.0 Bohr.

Figure 2

The top two panels compare the nuclear pair correlation functions from PIMC calculations and DFT-MD at various temperatures. The middle panel shows the integrated nucleus-electron pair correlation function, $N(r)$, computed with PIMC calculations. Results are compared with an isolated ion in order to estimate the ionization state of the plasma. The two lowest panels display the electron-electron pair correlation functions for pairs with parallel and opposite spins. All results are for fourfold compression.

Figure 3

Pressure-density conditions of our PIMC and DFT-MD simulations. The blue line shows the shock Hugoniot curve.

Figure 4

Internal energy and pressure for a silicon plasma at a density of $9.316\mathrm{g}{\mathrm{cm}}^{-3}$ are shown vs temperature. We plot the excess quantities relative to a fully ionized noninteracting plasma.