Magnetic Properties of Coordination Compounds

Whether a coordination compound behaves as paramagnetic (weakly attracted into an external magnetic field, because it contains one or more unpaired electrons) or diamagnetic (weakly repelled, because every electron is paired) is decided entirely by how the metal's d-electrons are actually distributed among the split d-orbitals — which, in turn, depends on the field strength of the surrounding ligands (Section 5.3) exactly as it does for colour.

For metal ions with $d^1$, $d^2$, or $d^3$ configurations, the electrons simply fill the three lower-energy $t_{2g}$ orbitals singly (following Hund's rule) regardless of whether the ligand field is weak or strong, since there are enough empty orbitals in the $t_{2g}$ set to avoid pairing entirely — so these configurations always give the same, unambiguous number of unpaired electrons (1, 2, or 3 respectively) no matter what ligand is present. The same is true at the other extreme, for $d^8$, $d^9$, and $d^{10}$: there is no genuine choice available in how the electrons distribute, so the number of unpaired electrons (2, 1, and 0 respectively) is again fixed regardless of ligand.

The interesting, ligand-dependent cases are $d^4$ through $d^7$, where a genuine choice exists between two different ways of filling the orbitals. Take $\text{Co}^{3+}$, a $d^6$ ion, as the standard teaching example. With a weak-field ligand like $\text{F}^-$, as in $[\text{CoF}_6]^{3-}$, the crystal field splitting $\Delta_o$ is too small to make electron pairing worthwhile, so the six d-electrons spread out as far as possible: all five orbitals are singly occupied first, and only the sixth electron is forced to pair up, in one of the three $t_{2g}$ orbitals. This gives the configuration $t_{2g}^4 e_g^2$ (one $t_{2g}$ orbital paired, the other two $t_{2g}$ and both $e_g$ orbitals singly occupied) — a total of 4 unpaired electrons, so $[\text{CoF}_6]^{3-}$ is strongly paramagnetic. This is called the high-spin configuration. …