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Recent progress in theoretical mineral physics based on the ab initio quantum mechanical computation method has been dramatic in conjunction with the rapid advancement of computer technologies. It is now possible to predict stability, elasticity, and transport properties of complex minerals quantitatively with uncertainties that are comparable to or even smaller than those attached in experimental data. These calculations under in situ high-pressure (P) and high-temperature conditions are of particular interest because they allow us to construct a priori mineralogical models of the deep Earth. In this article, we briefly review recent progress in studying high-P phase relations, elasticity, thermal conductivity, and rheological properties of lower mantle minerals including silicates, oxides, and some hydrous phases. Our analyses indicate that the pyrolitic composition can describe Earth's properties quite well in terms of density and P- and S-wave velocity. Computations also suggest some new hydrous compounds that could persist up to the deepest mantle and that the postperovskite phase boundary is the boundary of not only the mineralogy but also the thermal conductivity.
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