[Wien] Question on EFG and eigenvectors and sugestion for the output

[Stefaan Cottenier]

> I have a small question (may be a stupid one) but I have difficulties to
> find an answer ...

After lots of struggles with tensors of rank 2, I came to the  
conclusion there are not too many stupid questions in this respect ;-)

> Concerning the calculation of the EFG in WIEN2k, we have access to the
> eigenvalues of the EFG tensor and to the eigenvectors.
> The EFG is a trace less tensor and, using the convention |Vzz| >= |Vyy|
>  >= |Vxx|, we can obtain the quadrupolar parameter Cq = eQVzz/h
> with the sign of Cq.
> (I hope for the moment I am right ).

Yes, right.

> Now what about the eigenvectors or principle axis of the tensor.
> Is the direction of the  principle axis defined without ambiguity ?
> For instance, if I have an atom on a site with a local symmetry -1. I
> was assuming that the principle axis of the EFG tensor can be either in
> one direction or the opposite ?
> Am I true ?
> If not, why ?

You can change the direction of the axis, yes. The problem of finding  
the principle axis system for an EFG is mathematically equivalent to  
finding the principle axes of a 3D ellipsoid. Obviously you can have  
the freedom there as well to invert your axes.

You can convince yourself about this by plotting a 1/r potential in  
one dimension, as well as the corresponding field (=the first  
derivative) and the gradient of the field (the second derivative of  
the potential). The latter will turn out to be symmetrical with  
respect to an inversion of the direction of your axis.

> Suggestion for the output of lapw0.
> Can we add in the output0 and scf0 the calculation of Cq.
> I suggest to add those two lines in efg.f

Do you really think this is useful? It's a multiplication by  
fundamental constants only (e/h), and the quantity that really  
determines the value is Q, which you have to specify for any  
individual case anyway...?

Stefaan



>
>>             WRITE(6,1340)
>> jatom,VZZ
>>             WRITE(6,1341)   V20,V20SRF
>>             WRITE(6,1342)   V22,V22SRF
>>             WRITE(6,1343)   V22M,V22MSR
>>             WRITE(6,1344)   V21,V21SRF
>>             WRITE(6,1345)   V21M,V21MSR
>>             WRITE(6,1350)   qmat(1,1),qmat(1,2),qmat(1,3),TENS(1),0.,0.
>>             WRITE(6,1350)   qmat(2,1),qmat(2,2),qmat(2,3),0.,TENS(2),0.
>>             WRITE(6,1350)   qmat(3,1),qmat(3,2),qmat(3,3),0.,0.,TENS(3)
>>             WRITE(6,1355)   ((eivec(i,j),j=1,3),i=1,3),jatom,winkel
>>             WRITE(6,1356)   jatom,VZZ*24.177d0
>> <-----
>>             WRITE(6,1360)
>> jatom,ETA
>>  1355 FORMAT(/,9X,'MAIN DIRECTIONS OF THE EFG ',3F8.4,/,36X,3F8.4,/ &
>>       ,36X,3F8.4,/, &
>>       ':ANG',i3.3,':',1X,'ANGLE WITH OLD X-AXIS =    ',f8.1)
>>  1356 FORMAT(/,':CQ_',i3.3,':',1X, 'QUADRUPOLAR PARAMETER =',F12.5,'
>> MHz IF Q IS EQUAL TO 1b (10-28m^2)')   <-----
>>  1360 FORMAT(/,':ETA',i3.3,':',24X,'ASYMM. ETA =',F12.5,//)
> and also in lapw0.F
>
>>         IF(logefg(jatom)) THEN
>>            WRITE(21,1340)  jatom,efgb(jatom)%vzz
>>            WRITE(21,1341)  efgb(jatom)%V20,efgb(jatom)%V20SRF
>>            WRITE(21,1342)  efgb(jatom)%V22,efgb(jatom)%V22SRF
>>            WRITE(21,1343)  efgb(jatom)%V22M,efgb(jatom)%V22MSR
>>            WRITE(21,1344)  efgb(jatom)%V21,efgb(jatom)%V21SRF
>>            WRITE(21,1345)  efgb(jatom)%V21M,efgb(jatom)%V21MSR
>>            WRITE(21,1350)  efgb(jatom)%qmat(1,1),efgb(jatom)%qmat(1,2), &
>>                 efgb(jatom)%qmat(1,3),efgb(jatom)%TENS(1),0.,0.
>>            WRITE(21,1350)   efgb(jatom)%qmat(2,1),efgb(jatom)%qmat(2,2), &
>>                 efgb(jatom)%qmat(2,3),0.,efgb(jatom)%TENS(2),0.
>>            WRITE(21,1350)   efgb(jatom)%qmat(3,1),efgb(jatom)%qmat(3,2), &
>>                 efgb(jatom)%qmat(3,3),0.,0.,efgb(jatom)%TENS(3)
>>            WRITE(21,1355)   ((efgb(jatom)%eivec(i,j),j=1,3),i=1,3), &
>>                 jatom,efgb(jatom)%winkel
>>            WRITE(21,1356)  jatom,efgb(jatom)%vzz*24.177d0
>>                               <----
>>            WRITE(21,1360)  jatom,efgb(jatom)%eta
>>         ENDIF
>
>> 1355 FORMAT(/,9X,'MAIN DIRECTIONS OF THE EFG
>> ',3F8.4,/,36X,3F8.4,/,36X,3F8.4,/,&
>>  & ':ANG',i3.3,':',2X,'ANGLE WITH OLD X-AXIS =    ',f8.1)
>> 1356 FORMAT(/,':CQ_',i3.3,':',2X, 'QUADRUPOLAR PARAMETER =',F12.5,'
>> MHz IF Q IS EQUAL TO 1b (10-28m^2)')    <----
>> 1360 FORMAT(/,':ETA',i3.3,':',25X,'ASYMM. ETA =',F12.5,/,/)
>
> Regards
> Florent
>
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-- 
Stefaan Cottenier
Instituut voor Kern- en Stralingsfysica
K.U.Leuven
Celestijnenlaan 200 D
B-3001 Leuven (Belgium)

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