[Wien] lapw1 runs too slow for H2 molecule

[Stefaan Cottenier]

> And as I said before, NEVER compare two calculations with different
> RMTs/RKMAX against each other unless you normalize somehow to the same
> reference.

Some time ago I was pondering a situation where this was hard to  
avoid. It might be the right occasion to raise issue this here:

It is about the calculation of the formation energy interstitial  
impurities (e.g. Al on the tetrahedral site in Si). To this end, one  
should calculate:

* A=:ENE for a supercell with (for instance) 32 Si atoms and 1 Al atom
* B=:ENE for a supercell with 32 Si atoms with the equilibrium volume  
per atom -- just bulk Si
* C=:ENE for a supercell for fcc Al, with the equilibrium volume per  
atom and supercell volume roughly similar to the one of the Si supercell

[The reason of taking supercells also for bulk Si and bulk Al is that  
the effective matrix size in :RKM changes abruptly with volume for  
small unit cells, and I don't dare to trust that by using simply the  
same RKM one has effectively the same matrix size as in the supercell  
for the impurity. But that's another issue, not the topic of this post.]

Call C' the value of C divided by the number of atoms in the Al supercell.

The formation energy for the tetrahedral Al impurity is then:

B+C'-A

So far, so good. In the case of Al and Si, one can take the same RMT's  
for both elements. And then one uses the same RKM for all three  
calculations, no problems appear. But what if the impurity is very  
different from Si, and it is needed to take a different RMT? For case  
A, the basis set size is determined by RKM/RMT_min (RMT_min is the  
smaller of the two RMT's). For case B, it is determined by RKM/RMT_Si,  
and for case C by RKM/RMT_imp : the effective basis set sizes will be  
different, is it then allowed to use these 3 energies in the same  
equation? I doubt so.

One could adjust RKM, such that in all 3 cases the same Kmax is used.  
But that introduces variations in the energies that are of the same  
order of magnitude than the formation energies that are searched.  
Looks like a dangerous game.

The solution I can imagine, is to use very large RKM values (e.g. 9).  
The dependence of :ENE on the basis set size will then be small, such  
that the effect described here does not matter very much.

Has anybody another strategy?
Or do I see problems where there actually aren't?

Stefaan

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