  We put together a first-principles equation of state (FPEOS) database for
matter at extreme conditions by combining results from path integral Monte
Carlo and density functional molecular dynamics simulations of the elements H,
He, B, C, N, O, Ne, Na, Mg, Al and Si as well as the compounds LiF, B4C, BN,
CH4, CH2, C2H3, CH, C2H, MgO, and MgSiO3. For all these materials, we provide
the pressure and internal energy over a density-temperature range from ~0.5 to
50 g/cc and from ~10^4 to 10^9 K, which are based on ~5000 different
first-principles simulations. We compute isobars, adiabats and shock Hugoniot
curves in the regime of L and K shell ionization. Invoking the linear mixing
approximation, we study the properties of mixtures at high density and
temperature. We derive the Hugoniot curves for water and alumina as well as for
carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal
shock compression ratios of H2O, H2O2, Al2O3, CO, and CO2 to be 4.61, 4.64,
4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to
determine the points of maximum shock compression for all available binary
mixtures. We identify mixtures that reach higher shock compression ratios than
their endmembers. We discuss trends common to all mixtures in
pressure-temperature and particle-shock velocity spaces. In the supplementary
material, we provide all FPEOS tables as well as computer codes for
interpolation, Hugoniot calculations, and plots of various thermodynamic
functions.
