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

## TL;DR

This study compares first-principles predictions of high-pressure liquid hydrogen's properties using vdW-DF density functional theory against Coupling Electron-Ion Monte Carlo, revealing systematic differences in pressure and molecular stability.

## Contribution

It benchmarks vdW-DF against CEIMC for high-pressure liquid hydrogen, highlighting differences in pressure, molecular stability, and phase transition characteristics.

## Key findings

- vdW predicts higher pressures than CEIMC by 10-20 GPa.
- vdW overestimates molecular stability and resistance to compression.
- Both methods observe a liquid-liquid phase transition with similar density regions.

## Abstract

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.