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

Sharma SRK Chaitanya Yamijala sharmajncasr at gmail.com
Wed Sep 28 15:36:57 CEST 2016

```Dear Balint,

Thank you for helping me. Maybe I am missing some simple point (which I
don't know what it is). I couldn't see the one-to-one correspondence
between the expression in the paper and in the current code (for dd case).
But, as you have already checked with your new version also, I believe that
my understanding is wrong somewhere and I will try to find my mistake.

Sincerely,
Sharma.

--------------------------------------------------------------------
Sharma
http://www.chem.rochester.edu/groups/huo/people/

On Wed, Sep 28, 2016 at 2:48 AM, Bálint Aradi <aradi at uni-bremen.de> wrote:

> 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,
>
>   Bálint
>
>
> --
> Bremen Center for Computational Materials Science, University of Bremen
>
>
>
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