  Accurately modeling dense plasmas over wide ranging conditions of pressure
and temperature is a grand challenge critically important to our understanding
of stellar and planetary physics as well as inertial confinement fusion. In
this work, we employ Kohn-Sham density functional theory (DFT) molecular
dynamics (MD) to compute the properties of carbon at warm and hot dense matter
conditions in the vicinity of the principal Hugoniot. In particular, we
calculate the equation of state (EOS), Hugoniot, pair distribution functions,
and diffusion coefficients for carbon at densities spanning 8 g/cm$^3$ to 16
g/cm$^3$ and temperatures ranging from 100 kK to 10 MK using the Spectral
Quadrature (SQ) method. We find that the computed EOS and Hugoniot are in good
agreement with path integral Monte Carlo results and the SESAME database.
Additionally, we calculate the ion-ion structure factor and viscosity for
selected points. All results presented are at the level of full Kohn-Sham DFT
MD, free of empirical parameters, average-atom, and orbital-free approximations
employed previously at such conditions.
