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

Wed Apr 21 15:11:33 CEST 2010

A few comments, and perhaps a clarification on what Peter said.

Remember that while Wien2k is more accurate than most other DFT codes,
it still has approximations with the form of the exchange-correllation
potential and in how the core wavefunctions are calculated. Hacking by
applying unphysical constraints so it will match experiments is wrong.
(Remember the story of the graduate student who matched all properties
of silicon by tuning the parameters of the DFT calculation for each
one so it was "right".)

I would instead suggest that you look at better functionals for the
core wavefunctions, see Novak et al, Phys. Rev. B 67, 140403(R) (2003)
as well as the papers that cite it and the earlier paper by U. Lundin
and O. Eriksson, Int. J. Quantum Chem. 81, 247 (2001) and papers that
cite this. If you ask Peter or Pavel really nicely they may be able to
provide the code that uses this functional but you will almost
certainly have to do some coding work. This might not explain your
experimental results, and if it does not either the experiments are
wrong or we just don't have good enough theory yet for what you are
measuring, probably the latter.

On Wed, Apr 21, 2010 at 6:48 AM, Peter Blaha
<pblaha at theochem.tuwien.ac.at> wrote:
> 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
> --------------------------------------------------------------------------
> 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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-- 
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
Web: www.numis.northwestern.edu
Chair, Commission on Electron Crystallography of IUCR
www.numis.northwestern.edu/
Electron crystallography is the branch of science that uses electron
scattering and imaging to study the structure of matter.