  We report first principle results for nuclear structure and optical responses
of high pressure liquid hydrogen along two isotherms in the region of molecular
dissociation. We employ Density Functional Theory with the vdW-DF approximation
(vdW) and we benchmark the results against existing predictions from Coupling
Electron-Ion Monte Carlo (CEIMC). At fixed density and temperature, we find
that pressure from vdW is higher than pressure from CEIMC by about 10 GPa in
the molecular insulating phase and about 20 GPa in the dissociated metallic
phase. Molecules are found to be overstabilized using vdW, with a slightly
shorter bond length, and with a stronger resistance to compression. As a
consequence, pressure dissociation along isotherms using vdW is more
progressive than computed with CEIMC. Below the critical point, the
liquid-liquid phase transition is observed with both theories in the same
density region but the one predicted by vdW has a smaller density
discontinuity, i.e. a smaller first order character. The optical conductivity
computed using Kubo-Greenwood is rather similar for the two systems and
reflects the slightly more pronounced molecular character of vdW.
