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

[Peter Blaha]

The construction of atomic spheres with a certain RMT is only a mathematical
trick to obtain nicely represented wave functions and potentials in a
convenient way. Of course there is a weak dependency of results on RMT, because
series expansions converge better or worse with different RMTs, but there's
no physics in it.

> RMT(Be). As I understand, in this model, 1s electrons are seeing 
> scf-potential of the crystal only within the Be sphere. Outside the Be 
> sphere, it should see the potential of the interstitial region. Since 
> there is an abrupt change of potential at the muffintin radius RMT(Be), 
> so the wave function inside and outside the Be sphere should be 
> different and there should be a matching boundary condition at RMT(Be). 

No, the 1s electron sees the (spherical) potential not only inside RMT, but
the potential is continued outside with a 1/r tail. (There is only ONE
1s wavefunction on a radial grid reaching to "infinity".)
Of course one can discuss this approximation, but as you have shown
yourself, treating the 1s state as "valence", where it sees the accurate
non-spherical potential everywhere, does NOT change anything qualitatively
(there is a limited basis set for the Be-s functions when you include 1s,
but that does not matter for this purpose).


 > However  my main point is that the core wave function
> inside and outside the Be sphere should be different and there should be 
> boundary conditions at RMT(Be).

 From the above it should be clear, that there is only ONE 1s function.

For a core state, however, we make the approximation that the core-density outside
the sphere is added as a constant smeared out over the whole interstitial. Also this
is an approximation (and the code gives WARNINGS if the "core leakage" is too large),
but again, your test with 1s as valence (where this is not done) proves that there is
no real problem.
PS: In the next release it will be possible to Fourieranalyze the leaking core density
and get a correct charge distribution even with sizable core-leakage.


-- 
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
-----------------------------------------