Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

Figure 1

The principal deuterium Hugoniot compared to previous theoretical and experimental studies. Holst [47] and Caillabet [48] are DFT-PBE simulations, Militzer [49] is a PIMC simulation. The PBE* results are generated by solving the Hugoniot equation using the CEIMC-VMC configurations but computing energy and pressure with DFT-PBE. Knudson [22] and Boriskov [14] are experimental results. The initial density for the Boriskov experiment was ${\rho }_0=0.171\mathrm{g}/{\mathrm{cm}}^3$, slightly higher than for the other Hugoniots. The value ${\rho }_0=0.167\mathrm{g}/{\mathrm{cm}}^3$ has been used in computing the upper relative compression scale.

Figure 2

Pressure vs temperature along the deuterium Hugoniot compared to previous theoretical studies.

Figure 3

Ion-ion radial distribution function $g_{dd}(r)$, near the Hugoniot line. The large peak for $1<r<2$ signals the presence of bonded atoms and indicates the majority of the atoms are bound into molecules at 4000 K. This peak nearly disappears as the system becomes a monatomic liquid at 8000 K, although a small feature remains. The ion-ion distribution function at $T=10000\mathrm{K}$ overlaps almost entirely with the $T=15000\mathrm{K}$ curve. Inset: The Hugoniot function plotted at 8000 K, for CEIMC-RQMC and DFT-PBE.