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

Andrea Ferretti ferretti.andrea at unimore.it
Sat Mar 24 15:54:59 CET 2007

Hi Kostya,

> > 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
>  I think the issue with WF is that they are hard to assign back to the
> atoms, since now these are just electron pairs somewhere in the middle.

this is the case when a covalent bond exists... but this is also the 
reason of the increasing of the spilling parameter when using Lowding 
orbitals... in a sense, electronic charge is physically in between atoms 
for covalent bonding and this is why WFs sit there
(of course, WFs does not always sit on bonds, it is equally 
standard they sit on atoms, like eg in the case of lone pairs, d-orbitals in Transition 
metals etc etc)

>  For Lowdin projection the 1995 paper (link below) claimed that the
> atomic basis could be optimized, I wonder if QE does that, and whether
> it is done for each atom, or just for all atoms of the same type at
> once.
> http://dx.doi.org/10.1016/0038-1098(95)00341-X

Lowding orbitals in Quantum-Espresso (at least as far as I know) are 
computed from the atomic reference states from pseudopotential data
according to:

S_ij = < i | j >      are the overlaps of atomic orbitals i and j

lowding orbitals are then obtained as
| low_i > =  R_ij  | j >

where  R = S^{-1/2} 

so I think there is no optimization (in the sense of the paper above)
but maybe I am missing something

all the best

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