Theoretical methods will be used to study properties of mantle phases to better understand the physical properties of the Earths mantle and to guide experimental studies. Important problems that will be addressed include study of the behavior of transition metal ions such as ferrous and ferric iron and minor elements such as Co, Ni, and Mn in lower mantle minerals such as magnesiowustite and perovskite; design and interpretation of x-ray spectroscopic experiments on high pressure minerals to understand their electronic properties at high pressures in the Earth's mantle; diffusion and rheology of perovskite and magnesiowustite at high pressures and temperatures; high-pressure high-temperature elasticity of perovskite and magnesiowustite; high pressure melting; and solubility of rare gases in oxide melts and solids at high pressures. This work will give important predictions for geophysics and geochemistry that will aid understanding of the evolution and dynamics of the Earth and terrestrial planets. It will give predictions of mineral properties in the experimentally difficult regime of the high pressures and temperatures of the deep Earth and will increase our understanding of experimental observations of mineral behavior.