[Pw_forum] Projection of plane wave functions into atomic orbitals

[Cyrille Barreteau]

Dear Francesco and Stefano,

Thank you very much for your clear answer, it is extremely helpful.
By the way I wanted to congratulate all the pwscf developpers for the
impressive work you have done. It is really a very good code.

      Cyrille

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 >> I have a question concerning the problem of projection of PW wave
 >> function
 >> on atomic orbitals.
 >> example 8 shows the case of bulk Ni with LDA pseudo pot NiUS.RRKJ3.UPF
 >> which uses two wave functions s and d (see below)
 >>
 >>     2    6             Number of Wavefunctions, Number of Projectors
 >>  Wavefunctions         nl  l   occ
 >>                        4S  0  1.00
 >>                        3D  2  9.00
 >>
 >> The result of the projection with projwfc.x gives the following
 >> decomposition:
 >>
 >>  Atom #   1: total charge =   9.8849, s, p, d, f =   0.9347  0.0000
 >> 8.9501
 >>      Spilling Parameter:   0.0115
 >>
 >> My question is the following: where have the p electrons gone?


In your pseudo the p channel is the local channel, i.e. you have no
projectors for the p because it has no nonlocal part at all for the p
pseudo.
This mean that the projecting proceudure cannot find the p-like charge.
It is better to use a directly separated pseudo as the vanderbilt pseudo
to overcome this problem.
Francesco



Stefano de Gironcoli wrote:
> 
>> I have a question concerning the problem of projection of PW wave 
>> function
>> on atomic orbitals.
>> example 8 shows the case of bulk Ni with LDA pseudo pot NiUS.RRKJ3.UPF
>> which uses two wave functions s and d (see below)
>>
>>     2    6             Number of Wavefunctions, Number of Projectors
>>  Wavefunctions         nl  l   occ
>>                        4S  0  1.00
>>                        3D  2  9.00
>>
>> The result of the projection with projwfc.x gives the following 
>> decomposition:
>>
>>  Atom #   1: total charge =   9.8849, s, p, d, f =   0.9347  0.0000  
>> 8.9501
>>      Spilling Parameter:   0.0115
>>
>> My question is the following: where have the p electrons gone?
> 
> 
> 
> The code projects the calculated wavefunctions on the atomic 
> wavefunctions that are present in the pseudopotential file. In this case 
> the 4s and 3d.
> There is no 4p wavefunction in the pseudopontential and there will not 
> be any 4p projected density of states in the projected DOS.
> 
> The fact that the spilling parameter is not that bad indicates that 
> these wavefuntions are not really needed in order to describe the 
> occupied manyfold.
> If some important atomic wavefunction were missing the spilling 
> parameter would be much worse.
> 
> It is possible that if the 4p wavefunctions were present in the 
> pseudopotential somewhat different  projected densities of states would 
> result... (together with  a smaller spilling parameter).
> This is because the 4p states of an atom are NOT ORTHOGONAL to the 4s/3d 
> states of neighboring atoms so that part of the DOS that would be 
> interpreted as 4p when this state is present are interpreted as 4s of 3d 
> if it is absent...
> This would imply that some redundancy (overcompleteness) is present in 
> the atomic-wavefunction basis-set and the choice operated by the code 
> (orthogonalizing the atomic wavefunctions before making the projection 
> ro get the so called Lowdin projections) is only one of the infinite 
> (all arbitrary) ways this redundancy is removed.
> 
> Stefano de Gironcoli
> 
> 
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