Fast and Accurate Quantum Molecular Dynamics of Dense Plasmas Across Temperature Regimes

We develop and implement a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory. The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) density functional theory and path integral Monte Carlo calculations for microscopic features such as the electron density as well as the equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in the Kohn-Sham method and lower temperatures than is accessible by path integral Monte Carlo calculations, while being significantly less computationally expensive than either of those two methods.

Figure 1

Time for a single electron density optimization for 128 hydrogen atoms in a given random arrangement at $2\mathrm{g}/{\mathrm{cm}}^3$. The Kohn-Sham temperature scaling is clearly shown as a prohibitive factor in extending across temperature regimes, while our functional shows no such issue.

Figure 2

Top: The ion-electron pair correlation function $g_{ie}(r)$ is plotted for a random distribution of hydrogen atoms at density $2\mathrm{g}/\mathrm{cc}$ and temperature of 5 eV. Bottom: The same but for aluminum at $2.8\mathrm{g}/\mathrm{cc}$ and temperature $100\mathrm{K}=0.008617\mathrm{eV}$. $r_{\mathrm{ws}}$ is the ion Wigner-Seitz radius. Both systems show excellent agreement for the electron densities between our functional and Kohn-Sham, where the same pseudopotential is used.

Figure 3

Pressure results for simple-cubic hydrogen at $2\mathrm{g}/\mathrm{cc}$ (top) and for fcc aluminum at $100\mathrm{K}=0.008617\mathrm{eV}$ (bottom). Both results show our functional closely reproducing Kohn-Sham results.

Figure 4

Pressure results for deuterium at $4.04819\mathrm{g}/\mathrm{cc}$. Our functional is in good agreement with Kohn-Sham and PIMC calculations and spans the entire temperature range. The bottom panel shows the relative pressure with Kohn-Sham and PIMC calculations in their respective ranges.

Figure 5

Pair distribution function $g_{ii}(r)$ for Al at experimental density $2.349\mathrm{g}/\mathrm{cc}$ and temperature $1023\mathrm{K}=0.08815\mathrm{eV}$ (lower curves) and warm dense conditions $2.7\mathrm{g}/\mathrm{cc}$ and 5 eV (upper curves, shifted by 2). Excellent agreement is shown between the Kohn-Sham and our functional.