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

Roozbeh Anvari roozbeh.anvari at gmail.com
Mon Sep 30 01:24:11 CEST 2019

```Dear Alessandro,

Thank you for your help,
Cheers
Roozbeh

On Sun, Sep 29, 2019 at 1:07 PM Alessandro Pecchia <
alessandro.pecchia at cnr.it> wrote:

> 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>
>
>
>
> Alessandro
>
>
>
> *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
>
>
>
>    Hi,
>
>
>
>    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)  ? )
>
>
>
> 2.
>
> 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
>
> Roozbeh
>
>
>
>
>
>
>
>
>
>
>
>
>
> 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,
>
> Roozbeh
>
>
>
>
>
>
>
>
>
> 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:
>
>
> https://github.com/dftbplus/dftbplus/blob/master/prog/dftb+/lib_type/oldskdata.F90
>
>
>
>
> https://github.com/dftbplus/dftbplus/blob/master/prog/dftb+/lib_dftb/slakocont.F90
>
>
> I hope this helps.
>
>   Best regards,
>
>   Bálint
>
>
> --
> Dr. Bálint Aradi
> Bremen Center for Computational Materials Science, University of Bremen
>
>
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