  We perform all-electron path integral Monte Carlo (PIMC) and density
functional theory molecular dynamics (DFT-MD) calculations to explore warm
dense matter states of oxygen. Our simulations cover a wide density-temperature
range of $1-100$~g$\,$cm$^{-3}$ and $10^4-10^9$~K. By combining results from
PIMC and DFT-MD, we are able to compute pressures and internal energies from
first-principles at all temperatures and provide a coherent equation of state.
We compare our first-principles calculations with analytic equations of state,
which tend to agree for temperatures above 8$\times$10$^6$~K. Pair-correlation
functions and the electronic density of states reveal an evolving plasma
structure and ionization process that is driven by temperature and density. As
we increase the density at constant temperature, we find that the ionization
fraction of the 1s state decreases while the other electronic states move
towards the continuum. Finally, the computed shock Hugoniot curves show an
increase in compression as the first and second shells are ionized.
