[Wien] basis set size for oxygen crystal

[Peter Blaha]

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
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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Email: blaha at theochem.tuwien.ac.at    WWW: 
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