Path Integral Monte Carlo Calculation of the Deuterium Hugoniot
  Restricted path integral Monte Carlo simulations have been used to calculate the equilibrium properties of deuterium for two densities: 0.674 and 0.838 gcm^-3 (rs = 2.00 and 1.86) in the temperature range of 10000 < T < 1000000 K. Using the calculated internal energies and pressures we estimate the shock hugoniot and compare with recent Laser shock wave experiments. We study finite size effects and the dependence on the time step of the path integral. Further, we compare the results obtained with a free particle nodal restriction with those from a self-consistent variational principle, which includes interactions and bound states. 
B. Militzer, D.M. Ceperley