“…In this work, the initial states are estimated by starting from DFT calculations at the desired densities (2.20, 2.65, and 4.29 g/cm 3 for fused silica, α-quartz, and stishovite, respectively) 49 , then we consider each isotherm with temperature T and fit the pressure and energy data along the isotherm as functions of density by using cubic splines 50 , and the density ρ at which the energy term [E − E i ] equals the pressure term [(P + P i )(V i − V )/2] defines the Hugoniot, which has definitive values in T, ρ, P and E. We also calculate the shock velocity u s and particle velocity u p , relevant to shock experiments, by u 2 s = ξ/η and u 2 p = ξη, where ξ = (P −P i )/ρ i and η = 1−ρ i /ρ. This approach has been used previously for calculating the Hugoniot of several other materials [51][52][53][54][55][56][57] , and was found to produce consistent Hugoniots with other computational methods, such as progressive determination by running a large number of EOS calculations around the Hugoniot curve 58,59 In order to cross check the validity of the Hugoniot results based on the relatively sparse temperature-density grid, we have recalculated the Hugoniot of α-quartz by performing 2D interpolation of the pressure and energy data as functions of (T, ρ) and then determined the conditions at which the function H(ρ, T ) = E − E i + (P + P i )(V − V i )/2 equals zero. We have also made tests by using a partial set of our EOS data (by excluding the 6.62 g/cm 3 isochore).…”