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To perform a local orbital analysis of electronic and magnetic interactions,we construct the Wannier functions (WFs) of the Fe $3d$ orbitals in the parentcompound of the recently discovered iron pnictide superconductors, LaFeAsO, anda comparison material LaFePO. Comparing the WFs for the stripeantiferromagnetic order with those for no magnetic order, the difference is asignificant spreading (``{\it de}localization'') of specifically the $d_{xy}$and $d_{xz}$ (but not $d_{yz}$) WFs, where parallel Fe spins lie along the $x$direction. The WF basis gives a tight-binding representation of the firstprinciples, density functional based Fe-derived bands. Comparing hoppingparameters, it is found that changes due to stripe antiferromagnetism, even ifit is weak, enables more isotropic hopping involving spin-majority electrons inthe Fe $3d_{xz}$ (but not the $3d_{yz}$) orbital. This change,counterintuitively, actually reinforces electronic anisotropy. Further insightis gained by comparing the WFs of LaFeAsO and LaFePO, identifying how thedifference in WFs is related to the difference in hopping integrals and showinghow the pnictide atom is influential in forming the stripe antiferromagnetism.Kinetic energy considerations suggest that orbital fluctuation, in addition tospin fluctuation, may contribute to the decrease in observed ordered momentcompared to the calculated values.

Crystal Symmetry and Magnetic Order in Iron Pnictides: a Tight Binding Wannier Function Analysis