[Wien] Electric Field Gradient in case.scf_mini

[saeid jalali]

In order (to try) to explain both the written expression in the usersguide, "The EFG tensor is given in both, the ``local-rotation-matrix'' coordinate system, and then diagonalized. The resulting eigenvectors of this rotation are given by columns.", which is in brief taking into account the columns and the programmed expression in the efg.f given by Peter,  
"anorm=sqrt(eivec(1,1)**2+eivec(1,2)**2+eivec(1,3)**2)
winkel=acos(eivec(1,1)/anorm) * 180.d0 / acos(-1.d0)
WRITE(6,1355) ((eivec(i,j),j=1,3),i=1,3),jatom,winkel"
which is in brief taking into account the rows instead of columns are correct, let us back to the  active and passive transformations.
We know that in an active transformation the coordinate system is fixed and this is the vector that rotates applying the rotation matrix.
However, in a passive transformation the vector is fixed and this is the coordinate system that rotates.
Now one can interpret the passive transformation as an active transformation taking transpose of the matrix into account which is identical to exchanging the columns and rows.

 
So it looks that nothing is wrong with both the usresguied and the program efg.f.
 
Obviously taking x = (1,0,0) and   x' = (1.0000 0.2760 -0.3709) and then calculating winkel = arccos(x . x'/|x|*|x'|)* 180.d0 / acos(-1.d0) gives the expected 24.8 result. 
 
I will be thankful to anyone telling us if something is wrong here.
Your,
Saeid Jalali.

Peter Blaha <pblaha at zeus.theochem.tuwien.ac.at> wrote:
I'm sorry, at the moment I cannot clarify what is ok and what is wrong:

The UG says it is a column vector; however, in the code (efg.f) the
angle is calculated from a "row":

anorm=sqrt(eivec(1,1)**2+eivec(1,2)**2+eivec(1,3)**2)
winkel=acos(eivec(1,1)/anorm) * 180.d0 / acos(-1.d0)
WRITE(6,1355) ((eivec(i,j),j=1,3),i=1,3),jatom,winkel

It could well be that "winkel" was programmed for a case where the EFG was
fixed along z and only x,y could rotate (in this case column or row does
not matter).

Please check it! (Take part of efg.f ; initialize mat with "hand" selected 
values and diagonalize with eigen3 and check the eigenvectors/angles.

I'd be gratefull if you could confirm which is right and which is wrong.

Regards
> 
> Dear Wien2k users,
> 
> I'm trying to calculate EFG and have some questions 
> concerning information about EFG in the case.scf_mini file. 
> A typical entry looks like below:
> 
> MAIN DIRECTIONS OF THE EFG 1.0000 0.2760 -0.3709 
> 0.4072 -0.5385 1.0000 
> -0.0567 1.0000 0.6408 
> :ANG014: ANGLE WITH OLD X-AXIS = 24.8 
> 
> :ETA014: ASYMM. ETA = 0.56833
> 
> 
> I found in the usersguide that, this gives the eigenvectors of 
> EFG (in colums). If I'm not wrong this the axes of the "EFG cordinate 
> system".
> Thats why if the first column will be the x' axis (x axis in the 
> EFG system) the angle with the old x axis could be calculated as 
> follows:
> alpha = arccos(x . x'/|x|*|x'|). However when I take 
> x = (1,0,0) and x' = (1.000, 0.4072, -0.0567)
> I get alpha = 22.3 instead of 24.8. 
> 
> I've checked this for several results and I have never get
> exact angle shown in *.scf_mini. 
> 
> I will be appreciated if somebody could explain me how the angle 
> between the axes is calculated, or if there is an error in 
> my impretation.
> 
> Greetings
> Daniel Kmiec
> 
> -- 
> ______________________________________________________________________
> Mag. Daniel Kmiec http://www.ap.univie.ac.at/users/kmiec/
> 
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
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> 


P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671 FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at WWW: http://info.tuwien.ac.at/theochem/
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