Quantum Monte Carlo is among the most precise simulation techniques to study realistic materials in physics and chemistry and provides a significant gain in precision compared with traditional density functional theory. One significant limitation of today?s QMC methods is the high computational demand. Since a substantial part of the QMC computation is spent in on forming and evaluating Slater determinants, the team plans to develop different localization transformations in order to obtain sparse determinants. The sparsity can be exploited in multilevel preconditioners, incomplete decomposition preconditioners, and iterative solvers to reach linear scaling with system size. The newly developed QMC methods will enable the team to obtain accurate equations of state, phase transitions, and elasticity of solid materials that are of high interest in geophysics. The spin state of iron in solid solutions magnesiowustite, perovskite and post-perovskite (Mg,Fe)SiO3 as well as the properties of water-carbon dioxide mixtures will be determined using QMC.
Our understanding of the interior of the Earth comes from seismic observations and from the characterization of geological materials at high pressure. This characterization is not only obtained with high-pressure laboratory experiments but also with computer simulations because the properties of materials depend on the interactions between the atoms and those can be determined with computer simulations from the fundamental laws of physics. This project focuses on making those simulation methods much more accurate by developing new mathematical techniques to improve the quantum Monte Carlo method. These newly developed methods will enable the team to characterize different metal oxides, silicates, and mixtures of fluid water and carbon dioxide at high pressure.
The equations of state of MgSiO3 perovskite (Pv) and post-perovskite (PPv) phases as well as the phase transition pressures between them under Earth’s lower mantle temperature conditions were predicted using quantum Monte Carlo (QMC) simulations and density functional perturbation theory (DFPT) calculations. These QMC predictions are consistent with experimental results not only for the equations of state but also for the Pv-PPv phase transition pressure, which is better than previous density functional theory (DFT) predictions within local density approximation (LDA) or general gradient approximation (GGA). LDA well described the thermal equations of state of Pv and PPv phases but underestimated the Pv-PPv phase transition pressure. On the contrary, GGA gave an accurate Pv-PPv phase transition pressure but over estimated the unit cell volume for both phases. This is the first time that QMC was successfully applied to major complex mantle mineral phases. In QMC simulations, Mg and Si atoms are relatively heavy elements that have more than 10 electrons outside their cores. We therefore use pseudopotentials that reduce the number of electrons needed in QMC simulations. We generated our own pseudopotentials for Mg, Si and O atoms with the OPIUM code using the WC exchange correlation functional. These pseudopotentials were tested by calculating the bond lengths of MgO, O2 and SiO with QMC. The bond lengths obtained were in good agreement with experimental results (the difference being smaller than 0.1%). The consistency of bond lengths between QMC and experiment indicated that our pseudopotentials and methodology are accurate. In each QMC computation we use a simulation cell subject to periodic boundary conditions. Finite-size errors arise from one-body effects due to discrete k-point sampling of the Brillouin zone and two-body effects from spurious electron correlation in the periodic cells. We minimize the one-body errors by using twist-averaged boundary conditions. We average over eight twists, allowing us to improve our sampling of the Brillouin zone. The two-body errors are minimized by using the Model Periodic Coulomb (MPC) interaction, which corrects the potential energy for the spurious correlation effects. We then use the scheme of Chiesa et al. to correct the kinetic energy two-body effects. While applying these techniques, we then perform our calculations in three different supercell sizes of 40, 80, and 120 atoms and fit an extrapolation to infinite cell size. These corrections and extrapolations helped us obtain good Pv-PPv phase transition pressures. Pure FeSiO3 is another end of (Fe,Mg)SiO3. A post-perovskite II (PPv-II) phase of FeSiO3 was found to have higher enthalpy than Pv and PPv phases but lower enthalpy than some other structures after DFT+U calculations for several thousands of configurations at 100 GPa. The X-ray diffraction (XRD) pattern of FeSiO3 PPv-II was calculated. The intensities and positions of two main X-ray diffraction peaks of PPv-II FeSiO3 compare well with experimental results of the recently reported "H-phase" of (Fe,Mg)SiO3.
