Density-functional calculation of multiple-shock Hugoniots of liquid nitrogen

We have performed molecular dynamics simulations at fixed density and temperature points to obtain the internal energy and pressure of shock-compressed fluid nitrogen. Our calculations were performed using the generalized gradient approximation in density functional theory. While the single-shock Hugoniot derived from this equation of state agrees well with gas-gun experiments, in contrast, the second-shock Hugoniots show discrepancies with the experimental measurements. This is particularly the case in the region where negative Gr\"uneisen parameters were deduced experimentally and where shock cooling was measured.