THEORY OF MINERALS AT HIGH PRESSURES BEYOND BAND THEORY

Density functional theory has proved itself a generally reliable method for predicting and understanding properties of minerals, but it sometimes fails. In some cases the failure is due to many-body effects or strong local intra-atomic Coulomb interactions, and in other cases there is no obvious reason for the problems. For example, the local density approximation (LDA) predicts good properties for SiO₂ quartz and stishovite, but incorrectly gives stishovite as the ground state. The generalized gradient approximation (GGA) fixes this problem, but is less accurate for elastic properties. We have applied quantum Monte Carlo (QMC) combined with phonons computed using density functional perturbation theory (DFPT) to silica, and obtain experimental accuracy in the thermal equation of state and phase transtions. For Feo we are using correlated methods based on LDA, such as LDA+U and DMFT, as well as QMC. DMFT has the advantage of giving the spectral density (electronic structure) as well as the total energy, but still contains approximations. QMC is an exact computation under the constraint of the many-body nodes which comes from a trial wave function. This work is suported by NSF.