Benchmarking vdW-DF first-principles predictions against Coupled Electron–Ion Monte Carlo for high-pressure liquid hydrogen

We report first-principles results for the 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 benchmark the results against existing predictions from Coupled Electron–Ion Monte Carlo (CEIMC). At fixed density and temperature, we find that the pressure obtained from vdW is higher than that 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 over-stabilized 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 that 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 formulation is rather similar for the two systems and reflects the slightly more pronounced molecular character of vdW.