First principles study of liquid MgSiO$_3$ at conditions of the Earth's deep mantle

Constant-pressure {\it ab initio} molecular dynamic simulations at high temperatures have been used to study MgSiO$_3$, the major constituent of the Earth's lower Mantle. In this work, we focus the properties of molten MgSiO$_3$, where its existence in the core-mantle boundary is still in debate. By using liquid configuration, we have performed variable-cell {\it ab initio} molecular dynamic simulations at relevant thermodynamic conditions across one of the measured melting curve. The calculated equilibrium volumes and densities are compared with the simulations using orthorhombic perovskite configuration under the same conditions. For molten MgSiO$_3$, we have determined the diffusion coefficients and shear viscosities at different thermodynamic conditions. Our results provide the evidences of the existence of molten MgSiO$_3$ near the core-mantle boundary.