[Pw_forum] Projected density of states

Gerardo Ballabio g.ballabio at cineca.it
Thu Mar 31 12:35:24 CEST 2005

On 03/31/05 19:14:40, Pingo Mutombo wrote:
> How can I compute the projected density of states for selected  
> atoms of a given supercell? I can calculate the total DOS for a   
> Si(111)-7x7 surface. However  I am unable to calculate the   
> projected density of states  probably because of the big size of  
> the unit cell(249 atoms). At least I would like to calculate  the  
> projected density  of states for selected Si atoms (adatom and rest  
> atoms).

Hi Pingo,
"density of states for selected atoms" isn't a well defined concept  
in density-functional theory. Indeed, wavefunctions computed by PWscf  
(or any other DFT code) are "collective" and can't be associated with  
any particular atom.

You may project the wavefunctions onto atomic states:

   |psi> = (sum over atomic states) <atomic state|psi> |atomic state>

where "atomic state" is s, px, py, pz... for a particular atom; this  
gives you the "fraction" of wavefunction localized on that atom. Keep  
in mind however that this is an approximation, because atomic states  
of different atoms aren't orthogonal in general, thus they don't form  
an orthonormal set. As a result, the sum of such "fractions" over all  
atoms may not be exactly 1, and the sum of all "atomic" DOS may not  
equal the total DOS.


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