Quantum Monte Carlo for minerals at high pressure: Phase stability, equations of state, and elasticity of silica

Silica is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. As the simplest silicates, understanding pure silica is a prerequisite to understanding the rocky part of the Earth, its majority. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates. 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 Schrodinger's equation. Using ground state QMC plus phonons within the quasiharmonic approximation from 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 most well-constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the most dense alpha-PbO2 structure above the core-insulating D" layer, suggesting the absence of significant free silica in the bulk lower mantle, which has been assumed but never proven. We also find an accurate shear elastic constant and its geophysically important softening with pressure.