[Wien] basis set size for oxygen crystal

[Stefaan Cottenier]

> What you find is about consistent with my observations. I would say
> that for an RMT of 0.5 a fairly good calculation is roughly an RKMAX
> of 3.5, and for an RMT of 2.0 an RKMAX of 8.

It depends of course on what you're looking at, but these look to be 
rather conservative values. The default RKMAX in wien2k is 7.0 (for a 
typical RMT of 2.0), and that's not without a reason.

That's why the tests in my table started only at the equivalent of 
RKMAX=8.6. I did not expect anything dramatic would happen from there on.

> As a rough guide this
> corresponds to (linear approximation)
>
> RKMAX = 3.5 + 3*(RMT_min-0.5)
>
> This is a crude estimate, to be used with extreme caution.

That would correspond to RKMAX=5.1 for this oxygen case (RMT=1.02), 
using a 'crude estimate' that is rather conservative. In spite of that, 
5.1 lies only at the onset of convergence (see table), a safer choice 
would be RKMAX=5.6. That is the reason of my surprise.

> In terms of the physics, my thoughts (Peter probably knows better).
> With small RMTs Wien2k can have problems because at the muffin tin
> boundary the density is large which can lead to a large discontinuity
> of the density in APW+lo. As RKMAX increases the discontinuity
> decreases. At least in part this is probably because the smaller the
> RMT, the more rapid is the variation in density around the muffin tin
> and a larger PW basis set is needed to better match the density
> changes within the muffin tin..

So you say that what makes small-RMT-oxygen different from 
large-RMT-oxygen or from any other large-RMT element, is the larger and 
more rapidly varying density near RMT, which requires a correspondingly 
larger basis set than it would if the density were smaller or were 
varying less rapidly.

This would imply that simply rescaling the RKMAX ("RKMAX=8.0 for RMT=2.0 
corresponds to RKMAX=4.0 for RMT=1.0") yields a calculation that is 
effectively *less* accurate.

> There are also subtle issues with the
> O linearization energies as the automatic search often fails to find
> the optimum energy when the density is not well confined within the
> muffin tin, although this is not that critical (I think, fingers
> crossed).

We tried several ways to chose the linearization energies in this case, 
and they make no essential difference.

> N.B., I assume you have taken care of other issues, for instance
> running spin-polarized as this is needed for O2, using a larger GMAX
> or oversampling which I think is also better for the Coulomb potential
> with small RMTs (similar to H)

Yes, spinpolarized (antiferromagnetic coupling between ferromagnetic 
O2-molecules), and GMAX=26.

> N.N.B., If you are doing this calculations for thermodynamics, of
> course PBE/LDA/WC are pretty bad for O2.

PBE was used, but the purpose was a numerical check rather than a 
faithful description of the crystal as it appears in experiment.

Stefaan