| In this dissertation, a study of hydrogen and helium at high pressure is presented using state-of-the-art first-principles simulations using Quantum Monte Carlo (QMC) and Density Functional Theory (DFT). The Coupled Electron Ion Monte Carlo method, a novel QMC-based first-principles simulation method, is extensively used in order to produce the most accurate study of hydrogen at high pressure to date. The main motivation for this work comes from the study of giant planets, like Jupiter and Saturn. These planets are mainly composed of mixture of hydrogen and helium and the thermodynamic properties of the mixture is a basic ingredient to models of their evolution and interior structure. One of the main goals of our work is to produce an accurate parametrization of the free energy of hydrogen and helium from first principles simulations that can replace the Saumon-Chabrier-Van Horn model equations of state.;We present a detail study of molecular dissociation in liquid hydrogen. We observe clear evidence of the plasma phase transition at low temperatures, through regions of (∂P/∂p)=0 and from discontinuities in the electronic conductivity. Both QMC-based and DFT-based simulation methods agree in the reported transition, although Monte Carlo methods predict higher transition pressures. Using the size of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures slightly below 2000 K. We calculate the melting curve of solid molecular hydrogen up to pressures of 200 GPa using free energy integrations in the liquid and solid phases, and determine its intersection with the plasma phase transition.;We also study the equation of state of hydrogen, helium and hydrogen-helium mixtures at pressures beyond 200 GPa. We find very good agreement between both simulation methodologies for pressures beyond 600 GPa. From the equation of state calculations, an analysis of the miscibility properties of the mixture is performed. We find that the temperatures for the dcmixing of helium and metallic hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures around 5 Mbar. Helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter. These results are directly relevant to models of the interior structure and evolution of Jovian planets. |
