Path integral Monte Carlo simulations of warm dense aluminum.

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

First-principles simulations of warm dense lithium fluoride.

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of LiF. Our simulations cover a wide density-temperature range of 2.08-15.70gcm^{-3} and 10^{4}-10^{9} K. Since PIMC and DFT-MD accurately treat effects of atomic shell structure, we find a pronounced compression maximum and a shoulder on the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, LEOS, and models. In addition, we compute pair-correlation functions that reveal an evolving plasma structure and ionization process that is driven by thermal and pressure ionization. Finally, we compute electronic density of states of liquid LiF from DFT-MD simulations and find that the electronic gap can remain open with increasing density and temperature to at least 15.7 gcm^{-3}.

First-principles equation of state and electronic properties of warm dense oxygen.

We perform all-electron path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of oxygen. Our simulations cover a wide density-temperature range of 1-100 g cm(-3) and 10(4)-10(9) K. By combining results from PIMC and DFT-MD, we are able to compute pressures and internal energies from first-principles at all temperatures and provide a coherent equation of state. We compare our first-principles calculations with analytic equations of state, which tend to agree for temperatures above 8 × 10(6) K. Pair-correlation functions and the electronic density of states reveal an evolving plasma structure and ionization process that is driven by temperature and density. As we increase the density at constant temperature, we find that the ionization fraction of the 1s state decreases while the other electronic states move towards the continuum. Finally, the computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.

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)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.

Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica.

Silica (SiO(2)) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger's equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense alpha-PbO(2) structure above the core-insulating D" layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.