Magnetism of Coordination Compounds

Core Idea

The magnetic behavior of coordination compounds is determined by the number of unpaired electrons, which depends on the d-electron configuration and the crystal field splitting. Paramagnetic complexes (with unpaired electrons) are attracted to magnetic fields; diamagnetic complexes (all electrons paired) are weakly repelled. The spin-only magnetic moment formula μ = √(n(n+2)) BM, where n is the number of unpaired electrons, provides a first approximation that connects magnetic measurements directly to electronic structure.

Explainer

Magnetic measurements are among the simplest and most informative experiments in coordination chemistry. Placing a sample between the poles of a magnet and measuring its response immediately tells you whether it has unpaired electrons: paramagnetic substances are drawn into the field, while diamagnetic substances are weakly repelled. A quantitative measurement of the magnetic susceptibility yields the magnetic moment, from which you can determine the number of unpaired electrons — and from that, the electronic configuration and spin state.

The spin-only magnetic moment formula μ = √(n(n+2)) Bohr magnetons (BM) connects the measured moment directly to the electron count. For n = 1, μ = 1.73 BM; for n = 5, μ = 5.92 BM. This formula assumes that the magnetic moment comes entirely from electron spin with no contribution from orbital angular momentum. This approximation works well for most first-row transition metal complexes because the crystal field quenches the orbital contribution by lifting the orbital degeneracy. For second- and third-row metals, and for lanthanides, spin-orbit coupling contributes significantly and more sophisticated treatments are needed.

The practical power of magnetic measurements lies in distinguishing high-spin from low-spin configurations. Consider Fe²⁺ (d⁶): a high-spin octahedral complex has four unpaired electrons (μ ≈ 4.9 BM), while a low-spin complex has zero (μ = 0, diamagnetic). A simple measurement with a Gouy balance or SQUID magnetometer instantly identifies the spin state, which in turn reveals whether the ligand field is weak or strong. This is one of the primary experimental tools for probing electronic structure, complementing the spectroscopic information from UV-Vis spectra.

Spin-crossover phenomena extend magnetic measurements into the realm of smart materials. When Δ is approximately equal to the pairing energy P, the complex sits at the boundary between high-spin and low-spin states. Temperature changes can push the equilibrium: cooling favors the low-spin state (lower energy), while heating favors the high-spin state (higher entropy from unpaired electrons and the longer, softer metal-ligand bonds). In the solid state, cooperative interactions between molecules can make this transition abrupt with hysteresis — the complex remembers whether it was last heated or cooled. These bistable spin-crossover compounds are actively researched for molecular memory devices and display technologies.