[Wien] basis set size for oxygen crystal

Wed Jun 19 20:29:47 CEST 2013

Dear all,

Perhaps it is worthwhile to reiterate the basic reason APW based methods typically use RKmax to determine sufficient planewave convergence rather than Kmax (for the less experienced users, at least): for a given atom, the wavefunctions become more rapidly oscillatory, in both angular and radial directions, as one approaches the nucleus. Hence, a fixed RKmax naturally increases(decreases) planewave resolution (Kmax) at Rmt as Rmt is decreased(increased), as needed to accommodate the more(less) rapid oscillations in the wavefunctions at Rmt. Are the oscillations exactly twice as rapid at 1/2 the Rmt? Certainly not. So the scaling is not perfect. But it provides a far better indicator of convergence, as a single number, for a range of sphere sizes, than Kmax alone.

John

-------------------------------------------------------
John E. Pask
Physicist
Condensed Matter and Materials Division
Lawrence Livermore National Laboratory
P.O. Box 808, L-045
Livermore, CA 94551 USA
Phone: +1 925-422-8392

On Jun 19, 2013, at 8:15 AM, Peter Blaha wrote:

> Well, at http://www.wien2k.at/reg_user/faq/rkmax.html it even says you need  RKmax=6.5 for O.
> 
> On the other hand I do not understand the following:
> 
> 
> >> The table lists the RKMax value, the matrix size, the corresponding
> >> RKMax if the muffin tin radius would be 2.0 (that gives a better feeling
> >> of the large size of this basis set) and the volume of the unit cell
> >> determined from an equation of state fit:
> >>
> >> 6.00 1426 11.8  505.0
> 
> Why do you say, RKmax with (R=1.02) of 6  "corresponds" to RKmax=11.8 (when the spheres would be 2)  ??
> This statement implies that you use a "constant Kmax", and this is exactly, what we don't need to do. Instead one could still use RKmax=6, which would reduce the "Kmax" to 3 and lead to a much smaller matrix size.
> 
> I admit, that the scaling for different R-mts with "RKmax" is not always "perfect", but it is not that bad either.
> 
> 
> 
> On 06/19/2013 03:46 PM, Laurence Marks wrote:
>> 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. 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.
>> 
>> 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.. 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).
>> 
>> 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)
>> N.N.B., If you are doing this calculations for thermodynamics, of
>> course PBE/LDA/WC are pretty bad for O2.
>> 
>> On Wed, Jun 19, 2013 at 8:07 AM, Stefaan Cottenier
>> <Stefaan.Cottenier at ugent.be> wrote:
>>> 
>>> Dear wien2k community,
>>> 
>>> I'm puzzled by the following observation about convergence tests for a
>>> molecular crystal built entirely from O2-molecules (two O2-molecules per
>>> unit cell): the basis set needs to be particularly large before even the
>>> the volume of the unit cell can be reliably determined.
>>> 
>>> Does anybody knows what is the mathematical/physical reason for this?
>>> 
>>> More details:
>>> 
>>> The RMT for oxygen is 1.02, dictated by the bond length in the O2
>>> molecule. The number of k-points was safely converged. For any basis set
>>> reported in the table hereafter, the E(V)-curves were nice and smooth --
>>> only the position of the minimum and the curvature (bulk modulus) keep
>>> changing.
>>> 
>>> The table lists the RKMax value, the matrix size, the corresponding
>>> RKMax if the muffin tin radius would be 2.0 (that gives a better feeling
>>> of the large size of this basis set) and the volume of the unit cell
>>> determined from an equation of state fit:
>>> 
>>> 4.38  574  8.6  487.7
>>> 4.78  750  9.4  506.4
>>> 5.20  945 10.2  502.4
>>> 5.60 1182 11.0  503.7
>>> 6.00 1426 11.8  505.0
>>> 
>>> There might be a numerical scatter of about 1-2 in the volumes given in
>>> the right-most column. This means that the difference between the last
>>> three volumes is probably negligible, and something as 504 au^3 is the
>>> converged volume. But the jumps from 487 to 506, and from 506 to 502 are
>>> definitely not due to numerical noise.
>>> 
>>> Why does this case require such a large basis set?
>>> 
>>> Thanks,
>>> Stefaan
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>> 
>> 
>> 
> 
> -- 
> 
>                                      P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
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