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 goal of proposal was to study the two most abundant minerals that exist in the Earth'slower mantle by applying and developing atomistic computer simulation techniques. Wespecifically focused on the feasibility of using the benchmark-level, ab initio, many-bodymethod, quantum Monte Carlo (QMC). While the extreme temperature-pressure conditions (3,000K and 1.2 million atmospheres) near the core-mantle boundary are challenging to probeexperimentally, they are readily accessible with first-principles simulations, such as QMC,that characterize the properties of matter by simulating the motion of electrons and ions onparallel supercomputers. These simulations enabled us to accurately determine the structuraland chemical behavior of MgO, (Mg,Fe)O, and MgSiO3 systems in the lower mantle. Thisinformation is critical for determining structural and dynamical properties of the lowermantle that influence large scale geophysical processes. MgO is a prototypical lower mantle mineral with a high pressure structural phase transitionfrom B1 (NaCl-structure) to B2 (CsCl-structure) around 500 GPa at low temperature. QMCcomputed highly accurate equations of state for the B1 and B2 phases, providing a newbenchmark for phase transition pressure and bulk modulus of each phase. In the (Mg,Fe)O system, the Fe undergoes an electronic, pressure-induced high-spin tolow-spin transition in the lower mantle. The transition plays a number of important roles indetermining the chemical and physical properties of the lower mantle, such as ironpartitioning and changes in elastic and structural behavior. QMC computed equations of statefor of both spin states, providing a new benchmark for phase transition pressure and bulkmodulus of each phase. The MgSiO3 mineral undergoes a structural phase transition from perovskite topost-perovskite in the so called D'' region of the core-mantle boundary. This phasetransition is believe to be responsible for the anomalous seismic discontinuities observedat the core-mantle boundary. QMC computed highly accurate equations of state for theperovskite and post-perovskite phases, providing a benchmark data for the phase transitionand bulk moduli.
