Using a methodology based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 2013, 138, 174115] we calculate the magnetic exchange coupling parameters in a recently synthesized set of Fe7III disklike clusters [Inorg. Chem. 2011, 50, 3849-3851] to explain the unusually high ground-state spin found in the experiments. We show that the calculated exchange interactions for the new series of Fe7III disks present strikingly different trends compared to prior Fe7 III disks. These differences are attributed to variations in the bridging ligands and the consequent structural changes in the complexes. The impact of these differences on the experimental ground-state spin of these complexes is rationalized using a simple classical spin model system and the calculated magnetic exchange couplings.