[Wien] Electron density at the nucleus (Electron capture nuclear decay rate work)

[Peter Blaha]

There is no physics involved in constraining the 1s wavefuction to zero at
an arbitrary radius RMT. It is anyway constrained to be zero at r=infinity
and only this is meaningful.

It seems pretty clear that the results are as they are, whether you like it or not.

If you want to cheat the results, you could do a "frozen core", i.e.
after init_lapw you do:

x lapw0    --> creates a potential from superposed atomic densities
x lcore    --> create the core density
rm case.inc --> remove the input file to prevent recalculation of core states

run_lapw

Of course, for consistency you should never change sphere sized when you compare
densities.

Amlan Ray schrieb:
> Dear Prof. Marks,
> I am writing in reply to your suggestion dated April 19, 2010 on the 
> above subject. The RMT(Be) was always larger than RMT(O). I used 
> RMT(Be)=1.45 BU and RMT(O)=1.23 BU. Later on, I used up to RMT(Be)=1.58 
> BU and RMT(O)= 1.1 BU. As RMT(Be) is increased from 1.45 to 1.58 for 
> BeO(Normal case), the 1s electron density at Be nucleus increases very 
> slightly by 0.0158% and the total electron density at the Be nucleus 
> increases by 0.014%. However when the calculation is repeated for the 
> compressed BeO, keeping RMT(Be)=1.58 or less, the 1s electron density at 
> the Be nucleus always decreases and 2s electron density at Be nucleus 
> always increases, the net result is about 0.1% increase of the total 
> electron density at the nucleus due to about 9% volume compression of 
> BeO lattice, against the experimental number of 0.6%.
>  
> My problem is regarding the reduction of 1s electron density at Be 
> nucleus due to the compression. As per your suggestion, I have checked 
> out the leakage of 1s electron charge from the Be muffintin sphere. I 
> subtracted out the total 2s valence charge in Be sphere (CHA001) from 
> the total charge (CTO001) in Be sphere to obtain the 1s charge in Be 
> sphere. So CTO001-CHA001 = 1s charge in Be sphere.
> I kept RMT(Be)=1.45 BU fixed for both the uncompressed and compressed 
> cases and studied the 1s charge leakage from Be sphere. I find
> 1) for 9% volume compression of BeO, leakage of 1s charge from Be sphere 
> = 0.01%; reduction of 1s electron density at Be nucleus due to 
> compression = 0.148%.
> 2) for 16.6% volume compression of BeO, leakage of 1s charge from Be 
> sphere=0.018%; reduction of 1s electron density at Be nucleus due to 
> compression = 0.265%.
> 3) for 28.4% volume compression of BeO, leakage of 1s charge from Be 
> sphere = 0.033%; reduction of 1s electron density at Be nucleus due to 
> compression = 0.466%.
>  
> If I fix RMT(Be)=1.58 BU for all the calculations, then
> 1) for 9% volume compression of BeO, leakage of 1s charge from Be sphere 
> = 0.004%; reduction of 1s electron density at Be nucleus due to 
> compression = 0.15%.
> 2) for 16.6% volume compression of BeO, 1s charge leakage from Be sphere 
> =0.011%; reduction of 1s electron density at Be nucleus due to 
> compression = 0.265%.
>  
> So as the compression on BeO lattice is increased, Hartree potential 
> increases and the character of the 1s electron wave function of Be 
> changes. The 1s wave function becomes more defused and spread out and so 
> the leakage from the Be sphere increases with the compression. Since the 
> free atom 1s wave function becomes more defused and spread out due to 
> the compression, the 1s electron density at Be nucleus decreases. Now if 
> a boundary condition such as 1s wave function must be zero at RMT(Be) is 
> put on, then the compression will not cause the spread out of the wave 
> function. WIEN2K suggests that we should use a smaller value of RMT(Be) 
> when BeO lattice is compressed. This should increase the 1s electron 
> density at the nucleus, if the wave function is constrained to be zero 
> at RMT(Be). The absolute percentage of the 1s charge leakage from Be 
> sphere might be small, but it tends to increase very quickly with the 
> compression. I think if the 1s wave function is constrained to be zero 
> at RMT=1.45 or 1.58, then that can influence the change of 1s electron 
> density at Be nucleus under compression by the fraction of a percent.
>  
> In the case of 2s valence electrons of Be, I find that when RMT(Be) is 
> kept fixed at 1.45 BU, then 2s valence charge in Be sphere increases 
> from 0.1943 to 0.2213 for 16.6% volume compression of BeO. The 2s 
> electron density at Be nucleus also increases due to the compression. 2s 
> electron wave function satisfies an appropriate boundary condition at 
> RMT and that may be the part of the reason for the increase of 2s 
> electron density under compression.
>  
> So my suggestion is to kindly consider putting a boundary condition such 
> as 1s Be wave function = 0 at RMT(Be). Such a boundary condition should 
> affect the character of the wave function and hence the change of 1s 
> electron density at the nucleus due to the compression.
>  
> With best regards
>                                                                                          
> Amlan Ray
> Address
> Variable Energy Cyclotron Center
> 1/AF, Bidhan Nagar
> Kolkata - 700064
> India
> 
> 
> 
> ------------------------------------------------------------------------
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-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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