We computed spin-state energies for the various X-ray structures reported for different temperatures by Goeta et al. We examined only the singlet, triplet, and quintet spin states, as preliminary calculations (see Section S1.2 and S1.3 of the SI) indicated that the septet and nonet states are very high in energy and do not contribute to the magnetism of the dimer at temperatures below 290 K. We also omitted the XRD geometries at temperatures between 150 K and 270 K, as the magnetic susceptibility does not vary significantly over this temperature range. The magnetic moment at high temperature clearly derives from the four singly occupied orbitals, two formed from alternative linear combinations of the two metal dz 2 orbitals, and the other two being in-phase combinations of the metal dxy and dx 2 -y 2 orbitals, respectively, with very small contributions from s orbitals of the P5 ring. The out-of-phase combinations of the metal dxy and dx 2 -y 2 orbitals (which belong to the E2 irrep in D5 symmetry) overlap strongly with the E2 orbitals of the P5 ring, placing these orbitals deeper in the bonding manifold. A similar pattern is observed for combinations of the metal dxz and dyz orbitals, where out-of-phase and in-phase combinations mix with p orbitals and s orbitals of the P5 ring, respectively, with the former comprising the RAS1 space and the latter the RAS3 space. The population of the correlating antibonding orbitals in all four cases is no less than 0.06 at all temperatures, which is indicative of strong electronic correlation associated with these orbitals.