Magnetism of Coordination Compounds

Introduction

Magnetic measurements reveal something about a complex's electronic structure. Unpaired electrons usually make a complex paramagnetic; all-paired electron configurations are diamagnetic in the basic model. Crystal field splitting and pairing energy therefore connect ligand identity and geometry to magnetic response. A quantitative moment, however, needs more care than a simple arrow count.

Core explanation

Start with the metal oxidation state and d-electron count. Fe²⁺ is d⁶. In a weak octahedral field, its ideal high-spin arrangement t₂g⁴e g² has four unpaired electrons and is paramagnetic. In a strong octahedral field, t₂g⁶e g⁰ has no unpaired electrons and is diamagnetic in the simple model. The same metal oxidation state can therefore give different magnetic behaviour when ligand field changes. Merely reading “iron(II)” from a formula is insufficient.

For Co³⁺, the ionic count is d⁶ as well, but higher oxidation state often strengthens ligand splitting. A particular cobalt(III) ammine complex may be low spin; one should still identify its actual ligand sphere and geometry before assigning a real magnetic state. For Mn²⁺ d⁵ in a weak octahedral field, five unpaired electrons are expected. For Zn²⁺ d¹⁰, all d electrons pair, so the isolated-ion d contribution is diamagnetic. These anchor cases make orbital-box reasoning concrete.

The qualitative rule is not an exact force law. Every material has a diamagnetic response from paired electrons, but unpaired-electron paramagnetism often dominates when present. Interactions between neighbouring centers in solids can lead to ferro-, antiferro- or other collective magnetic behaviour. A metal complex may also have orbital contributions to its moment and temperature-dependent response. The basic para/di classroom classification assumes isolated or weakly interacting centers in an appropriate setting.

The spin-only formula μ ≈ √[n(n + 2)] Bohr magnetons uses n unpaired electrons. It gives a useful rough estimate for some first-row transition-metal complexes when orbital angular momentum is substantially quenched. For n = 4, μ ≈ √24 ≈ 4.90 BM. This is not an exact measured moment for every d complex, and it is especially unreliable as a universal formula for lanthanide f ions, where spin–orbit and orbital contributions often matter strongly.

Geometry matters. Four-coordinate d⁸ Ni²⁺ can be tetrahedral with unpaired electrons or square planar with a paired lower-orbital arrangement. A measured diamagnetic response can support square-planar assignment when combined with other evidence. It does not by itself prove the structure; diamagnetism could also arise through other electronic arrangements or interactions in a complicated material.

To solve a problem, sketch orbitals. For octahedral d⁵, high spin gives five single arrows across t₂g and e g, whereas low spin gives t₂g⁵ with one single arrow. Both are paramagnetic, but their approximate moments differ. The label “low spin” does not mean diamagnetic. Count electrons and arrows rather than relying on the label alone.

Magnetism can also help test colour explanations. A d⁰ ion has no metal d unpaired electrons and cannot exhibit d–d absorption from an occupied d orbital in the ordinary model, yet a charge-transfer band may still make its compound colourful. These observations constrain different aspects of the electronic structure.

Step-by-step reasoning

1. Determine the metal oxidation state and d count. 2. Identify geometry and ligand-field strength. 3. Fill a split-orbital diagram, stating any high/low-spin assumption. 4. Count unpaired electrons for a qualitative para/di prediction. 5. Use spin-only numbers only as an approximation when appropriate.

Visual explanation

Draw two Fe²⁺ d⁶ diagrams: t₂g⁴e g² with four unmatched arrows and t₂g⁶e g⁰ with three pairs. Place a magnet symbol by the first and a small opposing arrow by the second.

Real-world analogy

Unpaired dance partners have an unmatched movement that stands out, while fully paired partners cancel in a simplified tally. Electron spin is quantum-mechanical rather than dancing, but the analogy helps remember why unpaired counts affect magnetic response.

Real-world example

Magnetic susceptibility measurements can distinguish spin states of coordination complexes and help validate a proposed ligand-field diagram. Chemists combine the result with spectroscopy and structure instead of inferring everything from one magnetic number.

Why?

Why may a stronger ligand field reduce the magnetic response of octahedral d⁶? A larger splitting favours pairing all six electrons in lower t₂g orbitals, removing the four unpaired electrons of the high-spin arrangement.

Common misconception

“Low spin always means diamagnetic.” Low-spin octahedral d⁵ has one unpaired electron and remains paramagnetic. Count the actual orbital occupancy.

Worked example

An octahedral d⁶ complex is specified as high spin. Fill t₂g⁴e g²: one t₂g orbital has a pair, the other two t₂g orbitals each have one electron, and both e g orbitals have one. Four electrons are unpaired. The spin-only estimate is √[4(4 + 2)] = √24 ≈ 4.90 BM, while a measured value may differ because the approximation omits other effects.

Quick check

1. Is ideal low-spin octahedral d⁵ diamagnetic? Answer: No. It has one unpaired electron and is paramagnetic.

Exam focus

Show d count, geometry, splitting and arrows before assigning magnetism. Label spin-only moment as an estimate, and do not apply it indiscriminately to f-block ions.

Advanced insight

Temperature-dependent magnetic susceptibility can reveal spin crossover or coupling between metal centers. A simple room-temperature para/di label may hide these changes, so advanced interpretation uses a measured susceptibility curve.

Summary

Unpaired electrons generally produce paramagnetism, while fully paired configurations are diamagnetic in the basic model. Ligand field can alter spin state and unpaired count for the same metal ion. Exact moments require attention to orbital and collective effects.

Practice questions

1. How many unpaired electrons occur in high-spin octahedral d⁶? Answer: Four. 2. How many occur in low-spin octahedral d⁶? Answer: Zero. 3. Is Zn²⁺ d¹⁰ expected to have an unpaired d electron? Answer: No. Its d subshell is filled. 4. What does the spin-only formula omit? Answer: Orbital angular momentum, spin–orbit coupling and collective magnetic interactions, among other effects.