# [Pw_forum] Calculational equation of PDOS

Stefano de Gironcoli degironc at sissa.it
Fri Apr 1 23:01:25 CEST 2011

In all pseudopotentials there are a number of angular momenta for which
the non local part mimic the orthogonality condition with respect to the
removed core electrons.. and there is a local part that is applied to
all angular momenta and can be determined inverting the pseudo KS eqs
for some angular momentum or just obtained smoothing the AE potential...

Silicon has s and p core states.. does not have d core states; so s and
p non locality only should be necessary.
In the BHS paper the local part of the potential is computed from the
nodeless 3d orbital.
In Si.pbe-rrkj.UPF the local part is probably obtained smoothing the AE
local potential or anyway there is no projector associated with it...

The pdos is another story. Which angular momenta are available in pdos
depends on which atomic wavefunctions are defined... In the case of Si,
3s and 3p only... so no d pdos.

pdos have (limited) meaning only when the wavefunctions on which one is
projecting are rather localized .. otherwise results are rather random..
I think that adding a rather delocalized 3d orbital to the
pseudopotential would not produce very meaningful pdos.

hope this helps

stefano

On 04/01/2011 04:11 PM, xirainbow wrote:
> Dear Professor Gabriele Sclauzero:
> After reading your thesis, I examine the Si.pbe-rrkj.UPF and find that there
> is not d orbital for Si.
>
> This the date in Si.pbe-rrkj.UPF:
> ______________________________________________________
>      2    3             Number of Wavefunctions, Number of Projectors
>   Wavefunctions         nl  l   occ
>                         3S  0  2.00
>                         3P  1  2.00
> <PP_BETA>
>      1    0             Beta    L
>      2    0             Beta    L
>      3    1             Beta    L
> —————————————————————————————
>
> However, in the table II of Phys. Rev. B 26, 4199 (1982,Pseudopotentials
> that work From H to Pu), the configurations used to derive pseudopotential
> always have d orbital for all kinds of atoms, including H.
>
> Does this sugguest that there is no pseudopotential for d orbital in
> Si.pbe-rrkj.UPF?
> Does this sugguest that the pdos of d orbital is always zero based on
> Si.pbe-rrkj.UPF?
> I am a little confused:(
>
> On Fri, Apr 1, 2011 at 4:04 PM, Gabriele Sclauzero<sclauzer at sissa.it>wrote:
>
>> Il giorno 01/apr/2011, alle ore 07.09, xirainbow ha scritto:
>>
>> Dear Professor
>>
>>
>> Thanks for upgrading my position :D
>>
>> Gabriele Sclauzero:
>> Thank you for your prompt help.
>>
>>
>> I'm glad of that, at least all the efforts I put in writing it could be
>> useful to someone (thanks also to those who corrected the manuscript...)
>>
>>
>> Cheers,
>>
>>
>> GS
>>
>> Thanks again:P
>>
>>
>> On Thu, Mar 31, 2011 at 7:58 PM, Gabriele Sclauzero<sclauzer at sissa.it>wrote:
>>
>>> Dear Wang,
>>>
>>>      I remember that I put down a formula for that in my PhD thesis (
>>> http://www.sissa.it/cm/thesis/2010/SclauzeroG_PhDthesis.pdf), if this may
>>> help you (see eq. 2.74 at page 58). I'm sure you could find it in many other
>>> places, though.
>>>
>>>     I believe there's no such thing as the Rcut you write in your formula
>>> below. As you say, the atomic wavefunctions are built from the radial part
>>> R_nl(r), which is taken from the pseudopotential file, and the spherical
>>> harmonics. However you should not forget that there is also structure factor
>>> which comes from the translation of the nucleus from the origin.
>>> The integral is done in reciprocal space for each k-point, hence a
>>> k-dependence is added to the atomic wavefunction when transforming it to the
>>> G-basis (have a look in PW/atomic_wfc.f90).
>>>
>>> The following paper might also be useful to you:
>>>
>>> Solid State Communications, Vol. 95, No. 10, pp. 685-690, 1995
>>>
>>>
>>>
>>>
>>> HTH
>>>
>>> GS
>>>
>>> Il giorno 31/mar/2011, alle ore 12.27, xirainbow ha scritto:
>>>
>>> Dear all:
>>>            I want to know the calculational equation of partial density of
>>> state(PDOS) in QE.
>>>            I could not find the equation on any paper. I think it may be:
>>> \int_0^{Rcut}  \Psi(\vec r)*R_n(r)*Y_{lm}(\theta,\phi)*r^2 dr d\theta
>>> d\phi.
>>> where the Psi(\vec r) is the KS wave function of solid.
>>> Y_{lm}(\theta,\phi) is the spherical harmonics. R_n(r) is the the radial
>>> wave function of a isolated atom.
>>>      If I was right, what is the formation of R_n(r)?
>>>
>>>
>>> --
>>> ____________________________________
>>> Hui Wang
>>> School of physics, Fudan University, Shanghai, China
>>> _______________________________________________
>>> Pw_forum mailing list
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>>>
>>>
>>>
>>> § Gabriele Sclauzero, EPFL SB ITP CSEA
>>> *   PH H2 462, Station 3, CH-1015 Lausanne*
>>>
>>>
>>> _______________________________________________
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>>>
>>
>> --
>> ____________________________________
>> Hui Wang
>> School of physics, Fudan University, Shanghai, China
>>   _______________________________________________
>> Pw_forum mailing list
>> Pw_forum at pwscf.org
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>>
>>
>>
>> § Gabriele Sclauzero, EPFL SB ITP CSEA
>> *   PH H2 462, Station 3, CH-1015 Lausanne*
>>
>>
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>>
>
>
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