We calculate the hydrogen Hugoniot using ab initio path integral Monte Carlo. We introduce an efficient finite-temperature fixed-node approximation for handling fermions, which includes an optimized mixture of free particle states and atomic orbitals
. The calculated Hugoniot confirms previous fixed-node path integral calculations at temperatures around T=30,000 K and above, while approaching smoothly the low temperature gas gun results. The ability to optimize the free energy within the path integral opens many new possibilities for developing nodal density matrices for path integral simulations of other chemical systems.
