This work is aimed at clearing out the nature of the axial Fe 42 center detected by electron-paramagnetic resonance in iron-doped for which two different models have been put forward. While some authors ascribe such a center to a impurity at a site, although suffering an off-center motion along directions, other groups propose that the Fe 42 center involves a ion at a site, which later also undergoes an off-center shift along a principal direction of the lattice. Seeking to clarify this puzzling situation, the possible off-center shift of both and impurities in is explored in this work by means of density functional calculations. As a salient feature it is shown that there is a huge barrier that prevents the motion of against one of the closest anions. The case of at a site is more complex as the energy difference (10Dq) between the lower-lying (,) and (,,) levels is found to be equal to only , and thus several states as a function of the displacement coordinate have to be explored in order to determine what is the actual ground state and the associated equilibrium coordinate . The ground state is found to correspond to the configuration with spin and , thus involving a significant off-center motion from the site, which is found to be accompanied by a small ligand relaxation. As a salient feature this ground state is different from that derived constraining at the site. The present calculations also reproduce the experimental feature observed for the Fe 42 center. An analysis of first-excited states at equilibrium allows one to understand this fingerprint in a simple way.