Session A13: Focus Session: Simulations of Matter at Extreme Conditions I: Hydrogen Helium, and Planetary Materials

Quantum Monte Carlo Simulations of Warm Dense Hydrogen

Quantum Monte Carlo methods are the most accurate and general methods for computing total electronic energies. However, in general, they have been limited to high temperatures or to zero temperature. In recent years, we and others have been working on methods [1] that utilize the Born Oppenheimer approximation to allow simulations coupling the correlated quantum systems and a system of ions. Using quantum Monte Carlo, one estimates the Born-Oppenheimer energy change for a movement of the ions which is then used in a Monte Carlo simulation of the ionic degrees of freedom. The quantum effects of the ionic degrees of freedom and the boundary conditions on the phase of the wavefunction can be integrated over. We have performed simulations of dense hydrogen down to temperatures of 300K. We have used this method to determine the equation of state of warm dense hydrogen, to study the cross-over from the molecular liquid to the atomic liquid [2] and for the melting temperature of solid atomic hydrogen [3]. \newline [1] C. Pierleoni and D. M. Ceperley, ChemPhysChem 6, 1 (2005); physics/0501013. \newline [2] K. Delaney, C. Pierleoni and D. M. Ceperley, Phys. Rev. Letts. 97, 235702 (2006). \newline [3] C. Pierleoni, D. M. Ceperley and M. Holzmann, Phys Rev. Letts. 93, 146402 (2004).   

Electrical conductivity of liquid Hydrogen

DC electrical conductivity of liquid Hydrogen under high pressure has been measured by shock-wave experiments a long time ago [Phys. Rev. Lett. 76, 1860 (1996)], however, an accurate theoretical calculation of electrical conductivity is still unavailable. Ab-initio DFT calculations seem to overestimate the DC conductivity value by about 6 times. On the other hand, coupled electron-ion Monte Carlo (CEIMC) simulation [Phys. Rev. Lett. 97, 235702 (2006)] has predicted different high-pressure Hydrogen molecular-atomic transition than the DFT calculation. In this talk I will report our preliminary electrical conductivity results from CEIMC simulations using the Kubo formula with energies and current-current matrix elements computed with correlated quantum Monte Carlo methods.   

Properties of Hydrogen-Helium Mixtures at High Pressure and Temperature

Most of the over 200 recently discovered extrasolar planets are giant gas planets that consist primarily of dense, hot hydrogen and helium. Using density functional molecular dynamics (DFT-MD) simulations, we study these fluids at the extreme conditions found in planet interiors. We characterize the interaction of hydrogen and helium, analyze the electronic properties, and report on structural changes in the fluid as a function of density and temperature. We further study the influence of helium concentrations on the stability of hydrogen molecules.   

Ultra-High-Pressure Water

We present the first all-electron QMD simulations of water in the ultra-high-pressure regime up to conditions typical for the deep interior of Jupiter and Saturn. We calculate the equation of state and the Hugoniot curve and study the structural properties via pair correlation functions and self-diffusion coefficients. In the ultra-dense superionic phase, we find a continuous transition in the protonic structure. Water at conditions of Jupiter's core (i.e. 20000 K, 50 Mbar, 11 g/cm$^3$) forms a fluid dense plasma. Supported by the DFG within SFB 652. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Ab initio Molecular Dynamics Simulations of Water Under Shock Compression: Chemistry Behind Shock Fronts

We report herein first principles simulations of water under shock loading of velocities from 5 - 11 km/s. Accurate description of the plateau in the ionic conductivity at high pressures and temperatures is of particular importance to models of the planetary dynamo mechanism in Neptune and Uranus. We attribute this plateau to the exceedingly short- lived molecular and ionic states that occur in water under these extreme conditions. In particular, at the intersection of the shock hugoniot and Neptune isentrope we observe transient metallization that we attribute to the formation of short-lived negatively charged species that contribute electronic states at or around the band gap.   

Molecular structures of CO$_{2}$ and N$_{2}$O under pressure

Carbon dioxide and nitrous oxide are investigated at pressures up to 50 GPa and 1000 K using \textit{ab initio} methods. In this pressure-temperature range, both materials have a number of stable molecular structures. We demonstrate that the constituent molecules in these structures do not undergo significant changes and that the proposed phases are consistent with experimental data. The differences found between the CO$_{2}$ and N$_{2}$O phase diagrams can be understood in terms of the polarity of the N$_{2}$O molecules.   

Quantum Monte Carlo Computations for Equations of State, Phase Transitions, and Elasticity of Silica

We have performed Quantum Monte Carlo (QMC) computations for silica in the quartz, stishovite, and $\alpha$-PbO$_2$ structures as functions of compression. In spite of the great success of DFT there is still need for improvement. The local density approximation (LDA) gives excellent results for individual silica phases, but LDA predicts stishovite to be the stable ground state rather than quartz. The Generalized Gradient Approximation (GGA) does give correct energy differences, but other properties, such as the bulk moduli, are worse with the GGA than the LDA. We included thermal contributions using density functional perturbation theory with the code ABINIT. We have also computed the shear elastic constant c$_{11}$-c$_{12}$ in stishovite, which is associated with the phase transition to the CaCl$_2$ structure, with QMC. We find excellent agreement with experiments. We find that the main differences between QMC and DFT are crystalline phase dependent energy and pressure shifts. This work is supported by NSF grants EAR-0530282, EAR-0310139, and by DOE contract DE-FG02-99ER45795 to John Wilkins. Computations were performed on blueice at NCAR under a BTS grant, and on Tungsten and Abe at NCSA, and at the Carnegie Institution of Washington.   

The effect of temperature and anisotropic pressure on the phase transitions in $\alpha$-cristobalite

The role of temperature and anisotropy of the pressure tensor in the pressure--induced transformations of $\alpha$-cristobalite is investigated by means of first principle molecular dynamics combined with an improved version of the metadynamics algorithm for the study of solid-solid phase transitions\footnote{R.~Marto\v{n}\'{a}k, D. Donadio, A. R. Oganov and M. Parrinello, Nat. Mat. \textbf{5}, 623 (2006).} We reproduce for the first time the transition to $\alpha-$PbO$_2$ as found in experiments\footnote{L.~S. Dubrovinsky {\it et al.} Chem. Phys. Lett. \textbf{333}, 264 (2001).} and we observe that the transition paths are qualitatively different and yield different products whether the applied pressure is hydrostatic or not. While in hydrostatic conditions $\alpha-$PbO$_2$ or stishovite is obtained depending on the temperature and initial conditions, more complicated pathways with several metastable structures are followed upon non-hydrostatic compression and post-stishovite phases are obtained. Based of our simulations, we predict the metastability of a new class of high pressure polymorphs of silica obtained by non-hydrostatic compression.   

The Melting Line of Molecular Hydrogen at High Pressure

We have measured the melting line of molecular hydrogen to pressure P=82 GPa in a diamond anvil cell (DAC) using pulsed laser heating and found a peak at P=64.5$\pm$4 GPa and T=1055$\pm$20 K. Previous attempts to measure the melting temperature of hydrogen in a DAC by CW ohmic heating methods were limited by the diffusion of hydrogen at elevated temperatures. We have developed a technique of temperature determination in a pulsed laser heated DAC and succeeded to achieve much higher pressures and temperatures. In the pulsed laser method hydrogen diffusion is suppressed allowing access to high temperatures at elevated pressures.   

Post-perovskite MgCO$_3$ phase at pressures up to 800 GPa

The high-pressure phases of magnesite (MgCO$_3$) are investigated by variable cell first-principles molecular dynamics simulations. At pressures compatible to lower mantle conditions ($\sim$120 GPa), the carbon atoms are surrounded by 4 oxygen atoms, which is consistent with the work of Skorodumova et al. (2005). Perovskite phase is observed at pressures greater than 300 GPa, but its stability is still subject to further studies. Stable post-perovskite structure is observed at pressures up to 800 GPa, and is found to be more stable than the perovskite phase. The results may bring important implications to interior models of giant planets, which may lead to a better understanding in giant planets physics.   

First-Principles Studies of Anisotropic Constitutive Relationships in Nitromethane and RDX

One of the goals of energetic materials (EMs) research is to obtain accurate equations of state (EOS). These EOS establish fundamental relationships between thermodynamic variables and provide necessary input for the description of materials at the mesoscopic and continuum levels. Ultimately, these EOS are governed by interactions at the atomic scale, and the investigation of these relationships provides an opportunity to connect the shock sensitivity of EMs with underlying atomic-scale structure. In order to investigate this fundamental structure-property relationship, we performed first-principles density functional theory studies of hydrostatic and uniaxial compressions in several crystallographic directions of nitromethane and RDX. Equilibrium properties, including lattice parameters and elastic constants, as well as the hydrostatic equation of state obtained from our calculations are compared with experiment. The shear stresses upon uniaxial compression will be examined, and the possibility of a correlation of their behavior with shock sensitivity will be discussed.