[Pw_forum] spilling parameter in Lowdin - how to assign the charge that went into Nirvana ?

Andrea Ferretti ferretti.andrea at unimore.it
Tue Mar 20 11:31:48 CET 2007

Hi Kostya, Hi all,

>  I am encountering an issue where the charge that is missing from the
> total Lowdin charge sum due to the non-zero spilling parameter is very
> important for me. For example, 1% of missing charge may not sound that
> bad, unfortunately, these missing charges will mostly come from the
> negative ions which happen to be diffuse.
>  Is there any way to assign it back ? For example, by entirely
> projecting the remaining charge onto overlapping diffuse Gaussians that
> would be roughly proportional to the atomic radii? Or, perhaps, there
> is some other solution out there?

I came into the same problem, but I have not much to add in order to find 
a solution starting from Lowding orbitals...

moreover, sometime ago I went through the coefficients expressing the 
Lowding orbitals (LO's) in terms of the atomic orbitals (basically atomic 
orbitals are orthogonalized in order to setup projectors)...
I found that in some cases the resulting LO's were so much 
different from the starting atomic ones (for example I saw large 
projections of the same LO onto atomic orbitals (s-states) 
from different atoms, which was somehow counterintuitive to me)..

basically, I think that when spilling parameter becomes large the physical 
information one would like to obtain from lowding projections is hardly 

One possible alternative approach which does not suffer the same 
problem is to use Wannier functions (especially the Marzari-Vanderbilt 
"maximally localized" WF)...
For insulators and semiconductors an exact (no spilling factor) 
partition of the total charge into localized orbitals can be obtained...   
in the same line, WF projected DOS can be obtained as well

again, this is just one possible choice (others are there for sure) and 
most of the game is played by the final localization reached by the 
Wannier functions (is this localization enough to my purposes ? ans so 

any other suggestion ??
am I missing something ??

hope it helps


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