  By expanding the wave function in plane waves, we use the pseudopotential
method of density functional theory within the generalized gradient
approximation to calculate the effective magnetic coupling energies of the
S=5/2 spins in the Fe2 dimer, approximated as Fe$_2$O$_2$H$_2$. Setting the
Fe-O bond length at the value corresponding to the minimum total energy, we
find the difference in antiferromagnetic and ferromagnetic exchange energies as
a function of the Fe-O-Fe bond angle $\theta$. The effective interaction is
antiferromagnetic for 63$^{\circ}<\theta<105^{\circ}$, and is ferromagnetic
otherwise. Full potential augmented plane wave calculations were also performed
at $\theta=100,105^{\circ}$, confirming these results, and providing
information relevant to the local anisotropy of the spin interactions.
