Multi-geminal wave functions

[Pablo_Lopez_Rios]

Hi Vladimir,

Thanks very much for your fixes. Clearly there are several codepaths in the geminals module that were in desperate need of testing (and there will likely be more).

If you let me have your email address (by email via the forum, for example) I can put you in as the commit author to properly attribute the changes.

Thanks,
Pablo

[Vladimir_Konjkov]

Following the geminal work earlier in this thread, a friendly challenge for anyone who enjoys squeezing trial wave functions.

The task: get the lowest fixed-node DMC energy for the all-electron Ne atom, using

- any single-determinant input wave function — HF, DFT, OO-MP2 natural orbitals, or anything else, in a Gaussian or Slater basis (gwfn.data / stowfn.data); no multideterminant expansions;
- plus anything CASINO can put on top of it: Jastrow + backflow + geminals (MAGP, psi_s : geminal).

Why Ne: the correlation is purely dynamical — no near-degeneracies, so no cheap multideterminant fix; a Jastrow–Slater–backflow wave function already leaves only a few mHa of fixed-node error. Whatever you gain here, you gain by genuinely improving the nodes.

The bar to beat is the orbital-dependent backflow (OBF) result of Holzmann & Moroni, Phys. Rev. B 99, 085121 (2019) [arXiv:1910.07167], Table I:

VMC = -128.91956(21) DMC = -128.93129(28)

Whoever posts a DMC energy below the OBF number (with a sensible time step and an honest error bar in CASINO outputs) wins.

Best regards,
Vladimir.