Critical point, liquid-vapor coexistence, and melting of Mg$_{2}$SiO$_{4}$ from ab-initio simulations*

We report density functional theory-based molecular dynamics calculations (DFT-MD) of Mg$_{2}$SiO$_{4}$ liquid and vapor across the liquid-vapor coexistence boundary that spanned 0.22-3.22 g/cc in density and 5000-10000 K in temperature. The critical point was estimated through a bootstrap analysis of a collection of DFT-MD isotherms above and below the critical point. Additionally, we describe the structure and composition of the liquid and vapor around the critical point. Finally, we discuss melting behavior at $P$=1 bar.