[DFTB-Plus-User] R: Format of the Slater-Koster files

Alessandro Pecchia alessandro.pecchia at cnr.it
Sun Sep 29 19:07:43 CEST 2019

Dear Roozbeh,


the internal order of the p orbitals is not |px>, |py>, |pz> but |py> |pz> |px>. 

This follows more naturally from the  order of angular momentum eigenstates |-1>, |0>, |1>  transformed into Tesseral wavefunctions. I think Ben can comment more on this, probably.


Hence, the SK rotations agree with 1954 paper. 

For hh(1,1) use ll**2+mm**2+nn**2=1, 


hh(1,1) = Eyy = mm**2*sk(1) + (1 - mm**2)*sk(2)

hh(2,2) = Ezz  = nn**2*sk(1) + (1 - nn**2)*sk(2)

hh(3,3) = Exx  = ll**2*sk(1) + (1 - ll**2)*sk(2)

hh(2,1) = Eyz = mm*nn* (sk(1)-sk(2))

hh(3,1) = Exy = mm*ll* (sk(1)-sk(2))

hh(3,2) = Exz = nn*ll* (sk(1)-sk(2))


Also d-orbitals follow a similar ordering starting from |-2>, |-1>, |0>, |1>, |2>, 

hence |dxy>, |dyz>, |dz^2-r^2>, |dxz>, |dx^2-y^2>    




Da: DFTB-Plus-User [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto di Roozbeh Anvari
Inviato: domenica 29 settembre 2019 02:03
A: User list for DFTB+ related questions
Oggetto: Re: [DFTB-Plus-User] Format of the Slater-Koster files




   I was wondering about how DFTB+ rotates H and S,  for example for a p-p interaction : ( reference:: DFTB+%SK.F90%subroutine pp(hh, ll, mm, nn, sk) ) : 


    hh(1,1) = (1.0_dp-nn**2-ll**2)*sk(1)+(nn**2+ll**2)*sk(2)
    hh(2,1) = nn*mm*sk(1)-nn*mm*sk(2)
    hh(3,1) = ll*mm*sk(1)-ll*mm*sk(2)
    hh(2,2) = nn**2*sk(1)+(1.0_dp-nn**2)*sk(2)
    hh(3,2) = nn*ll*sk(1)-nn*ll*sk(2)
    hh(3,3) = ll**2*sk(1)+(1.0_dp-ll**2)*sk(2)


   while, (Slater, J. C., & Koster, G. F. (1954) . Physical Review, 94(6), 1498.) :  

      Exx = ll**2 *(pp_sigma) - (1-ll**2) *(pp_pi)   

      Exy = ll*mm *(pp_sigma) - ll*mm *(pp_pi)

      Exz = ll*nn *(pp_sigma) - ll*nn *(pp_pi)


here, could you please confirm the relative directions of the directional cosines and also sampled energy integrals in the .SKf files ?  i.e. ( (ll , mm , nn) == (dx, dy , dz ) &  (hh(1,1) , hh(1,2),  hh(1,3) == (Ex,x,Ex,y Ex,z)  ? ) 



how accurate would be the calculated band structure without taking into account the potential shift  in H = H0 + shift ?  the E-K I have calculated using just H0/S from .SKF looks very similar to 

    that given by dftb+ and dft, but band widths are significantly narrower, 


Best regards 








On Thu, Sep 19, 2019 at 2:02 PM Roozbeh Anvari <roozbeh.anvari at gmail.com> wrote:

Dear Balint, 


thank you for your help,


Best regards,






On Thu, Sep 19, 2019 at 5:08 AM Bálint Aradi <aradi at uni-bremen.de> wrote:

Dear Roozbeh,

> I wonder why the overlap values are so large, are not the RAW values
> normalised ? 

The first few lines are only placeholders (historical heritage...).
Aftert that, the overlap integrals are less than one. For homonuclear
cases, identical orbitals (e.g. H-H  Sss0) give values close to 1 (makes
sense), while different orbitals or heteronuclear cases yield values one
order of magnitude lower.

> To check this, I am searching where skHamCont and skOverCont  are read
> from  .SKF but have not found it yet, 

The reading of skf and construction of the containers happens in
multiple steps at multiple places:




I hope this helps.

  Best regards,


Dr. Bálint Aradi
Bremen Center for Computational Materials Science, University of Bremen

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