where E AP is the AP-corrected LS energy and Ŝ2 LS is the ideal spin-squared expectation value of the pure LS state. In the weak coupling regime, when the broken symmetry solution exhibits a large degree of spin polarization, AP reduces to SP (Eq. ( )). In the strong coupling regime, S 2 B approaches S 2 LS and AP reduces to NP. To quantify the extent of geometric relaxation resulting from these optimization calculations, the root mean square difference (RMSD) at maximum overlap values for the crystal structure, HS, and broken-symmetry LS minimum energy geometries were computed relative to corresponding optimized AP geometries. These RMSD values are shown in Table . As one might expect, meaningful geometric relaxation is observed when optimizing structures in the gas phase from initial crystal structures. The average RMSD of the crystal structures relative to the AP geometries was 0.48Å. The largest internal coordinate displacements of bond lengths, angles, and dihedrals involving a metal center averaged over the set of nine compounds were 0.09Å, 12.6 • , and 34.2 • , measured between crystal and AP geometries.