Symmetry

[Clara]

I will admit that I always have trouble with visualising this (I remember from a course on solid state physics that I succeeded best at finding the symmetry axis when I had a small model of the molecule in my hands). But this is my trial at an answer.

I take the yellow arrow as the z-direction.

Fe-I:
4-fold rotation axis in z-direction.
2-fold rotation axes in the other directions.
=> 3 perpendicular 2-or-more-fold rotation axes, which determine the axes of the principle component axis system. For the direction of the 4-fold rotation axis there is axial symmetry around it for the electric field gradient tensor.

Fe-II
4-fold rotation axes in all 3 directions.
=> These axes determine the principle component axis system, and there is axial symmetry about all axes.

[Clara]

Reading an answer from a fellow student, I see that I indeed also forgot about the 2nd theorem.
In the case of Fe-II I say there are 3 f-fold rotation axes which results, by this 2nd theorem, in the eletric field gradient tensor being zero.

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