[xanmas]

(Disclaimer, I'm working on FCIQMC right now)

One of the reasons that FCIQMC doesn't have nuclear motion is that the gradients from FCIQMC, and actually most QMC techniques, are really computationally intensive, so this means that creating the ab-initio surface for the nuclei to roll over is really hard. Perhaps you were considering some sort of FCIQMC approximation to the path integral, but it's not entirely obvious to me how this would work.

As for how DFT would work for this... It should work quite well for qualitative predictions. Actually, DFT does remarkably well for metals and functionals like asymptotically corrected PBE0 are providing remarkable physical insight. While I wouldn't trust the numbers that come from any DFT simulation to three decimal points, I'd certainly trust the physics that's captured.

That being said, metallic hydrogen should be a strongly multireference system, so I'd be interested in seeing how a green's function approach based in many-body perturbation theory (see GF2 from Zgid at U Michigan) would do, as it doesn't struggle with issues of references while still giving you coupled cluster level accuracy.

[Xcelerate]

Very interesting. I hadn't heard of GF2 before; I'll have to look it up.

As a side note, I find it interesting how I'm always running into people working in such specialized fields on HN. I wouldn't have imagined I'd find someone working on FCIQMC posting on here, but I'm always surprised. Sounds like fun research.