Hi Chris,
OK, so you know that to do a diffusion Monte Carlo calculation you need to have a trial wave function produced by a preliminary HF/DFT run. For the DMC to give the right answer the nodal surface of the trial many-body wave function needs to be approximately correct (so that the 'fixed-node error' is small); in practice this means that you would like the HF/DFT calculation to give approximately the right charge density, and the DMC propagation in imaginary time can then be thought of as 'improving' the many-body wave function by effectively correcting the pair-correlation function so that (at least) the total energy comes out right.
So in your case if the DFT calculation is not giving the correct orbitally-ordered state, then the density is not right and your trial wave function probably won't be good enough. You therefore need to find a way to convince the DFT code to do this. If I was doing this -- and I'm aware that my answer will be unpopular with physicists because it uses the hated Gaussian basis sets -- I would use the CRYSTAL code (
http://www.crystal.unito.it). This is a commercial code but as a UK academic you can have it for free. It has excellent links with CASINO for all versions from 1995 to 2009 (though they just released a new 2014 version a week or so ago; I'm working with the developers to add CASINO support for this - should be finished within a week to ten days).
CRYSTAL has excellent tools for encouraging the SCF to converge into different local minima (which work precisely because Gaussian basis sets have appropriate angular momentum dependence) and is very good for getting orbitally-ordered states. If you look at my paper "
Oxygen stripes in La0.5Ca0.5MnO3 from ab initio calculations" Phys. Rev. Lett.
91, 227202 (2003) you'll see I was able to drive manganites into states with different orbital-ordering, spin-ordering, and charge-ordering (i.e. different charge states arranged into 'stripes'), which at the time I thought was very cool indeed. There's also my paper "
Magnetic interactions and the co-operative Jahn-Teller effect in KCuF3" M. D. Towler, R. Dovesi and V.R. Saunders Phys. Rev. B
52, 10150 (1995) where - even though it's approximately cubic, the orbital ordering on the copper ions means the thing is a one-dimensional antiferromagnet. It also shows how to understand 'superexchange' in terms of the spin-polarization of the intervening F ions. I thought that was cool as well.
As for the 'strong correlation' problem, this is an issue caused by approximate XC functionals such as LDA/GGA not giving the correct orbital-dependent potential (one of the cases where the fact that the DFT eigenvalues strictly speaking have no meaning becomes important - influencing the SCF to give the wrong density). Perversely, because of course it does not account for 'correlation', the unrestricted Hartree-Fock method - which CRYSTAL can do - is ideal for this. In that case the exact exchange cancels out the self-interaction exactly and introduces the correct orbital dependence i.e. it distinguishes between 'different orbital exchange' ('J') and 'same orbital exchange = same-orbital Coulomb interaction' (approximately 'U') so there's no need to introduce U artificially as in the LDA+U method. See my paper "
Ab initio study of NiO and MnO" M.D. Towler, N.L. Allan, N.M. Harrison, V.R. Saunders, W.C. Mackrodt and E. Aprà Phys. Rev. B
50, 5041 (1994). You may also have some success with exact-exchange or hybrid DFT methods, though I have less experience with this.
To be fair, I have no experience with making plane-wave DFT codes produce orbitally-ordered states. Clearly it's possible in some cases but you'll have to ask an expert.
It's interesting to note that a considerable number of many-body theorists have convinced themselves that first principles electronic structure methods can't do strongly-correlated materials like NiO because we use 'naive band theory' (this was the official position of the Cambridge University solid-state physics course at one point; it probably still is). They often imagine the U term in the Hubbard model or whatever is some magic thing that we cannot include except artificially - even though U is just an on-site Coulomb interaction and therefore part of the basic Hartree electron-electron term (strong correlation isn't 'correlation' in the sense of what is left out of HF theory or as in the phrase 'exchange-correlation functional' in DFT).. Almost all such statements turn out - incredibly - to be based on the assumption that we can't do spin-polarized band theory i.e. Mott's argument about a linear chain of H atoms always being a metal no matter what the lattice constant is only true if you force up and down spin orbitals to have the same energy, which of course no-one sane would actually do. If you do an unrestricted HF calculation of a linear hydrogen chain you can very easily see the metal-insulator transition at a lattice constant a little over 2 Angstrom and everything comes out perfectly (you can even calculate U almost exactly - with Hartree-Fock!).
Note finally that almost no-one has done DMC calculations of such things, and that you're likely to need a big computer to do so (QMC has a poor scaling with atomic number and calculations for heavier atoms are difficult; you will of course need to use pseudopotentials). That said, Lucas Wagner showed some very interesting QMC calculations of superconducting cuprates this summer at the annual QMC conference at my place in Tuscany (you can find his talk online on our website talk archive:
http://vallico.net/casinoqmc/talk-archive/ )
Hope this helps, and sorry for the slight delay in responding (busy week).
Cheers,
Mike
Of the CRYSTAL authors Mauro Causa of Napoli University - who has posted on these forums - is an honourable exception and I know he likes playing with CASINO. Perhaps he can help me with fixing the interface..?