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Comment by Xcelerate | Hacker News Reader

> but that'd be the gold standard if you can also afford to include quantum nuclear motion

Yeah, which I haven't seen for FCIQMC. (Alavi's group really seems to be the only ones actually using the method so far. I imagine it's still too new for someone else to want to code up unless he distributes the code.)

Also, I was perusing your post history (hope you don't mind), and noticed you do DFT calculations. You probably know much more about that than me; I'm primarily MD but keep up with the quantum chemical methods more as a side research project.

What are your thoughts using DFT for metallic hydrogen? Is there an exchange-correlation functional that could be good enough?

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(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.

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.

Yep. Personally, I trust DFT about as far as I can throw it, and think that spending time worrying about functionals is fairly pointless and likely to end up over-fitting data, especially if they aren't incorporating new physics :)

That last paper does say, however:

> We used the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation density functional, which is well suited for very high-pressure studies, as the charge density is more uniform than at low densities, and it obeys the uniform limit and gives a good account of the linear response of the electron gas to an external potential

but also

> DFT studies of high-pressure phases of hydrogen have been performed using several approximate density functionals, and a significant dependence of the results on the functional has been noted. The enthalpy differences between phases are so small that changes of only a few meV per proton can make a noticeable difference to the phase diagram

so that's some physics. They seem to end up using DMC for the static lattice and DFT for the vibrational corrections on top of that.

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