[DFTB-Plus-User] d orbital order {hh(4, 1) element for "subroutine dd" in lib_dftb/sk.F90}

Bálint Aradi aradi at uni-bremen.de
Wed Sep 28 08:48:32 CEST 2016

Dear Sharma,

> Sorry for raising the issue again. Based on your two earlier emails and
> the paper, the equation 29 should correspond to hh(2,1) or hh(1,2),
> right? However, it is matching closely with hh(4,1).

Actually, since due to an extension in development we will change to a
more generalised rotation scheme soon, I have rederived the
transformations a few month ago again. To be on the safe side, I have
compared them yesterday once more to the programmed ones in sk.F90, and
they match, provided the order of the real tessarals is -l,...,l.

> Eqn 29 is:
> Exy,yz = <2,− 2,0|H|2,− 1,R> = 3LM^2 N(ddsigma) + LN(1−4M^2)*(ddpi) +
> LN(M^2 − 1)(ddsigma)
> As xy, yz, z2, xz, x2-y2 = -2 -1 0 1 2 = 1 2 3 4 5 
> ==>   Exy,yz = hh(1,2) 
>     hh(2,1) = -3.0_dp*ll*(-1.0_dp+nn**2+ll**2)*nn*sk(1)&
>         &+(4.0_dp*nn**2+4.0_dp*ll**2-3.0_dp)*nn*ll*sk(2)&
>         &-ll*(nn**2+ll**2)*nn*sk(3)

But they do match, don't they? Using l^2 + m^2 + n^2 = 1, you have
exactly the same expressions as far as I can see. (Apart of the typo in
Eqn 29, as the last integral should be (dddelta).

  Best regards,


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

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