Magnetic Behaviour of d-Block Ions

Introduction

Magnetic response gives evidence about electron pairing. A d-block ion with unpaired electrons is generally paramagnetic; one with all electrons paired is diamagnetic in the elementary treatment. But a metal's formal d count is only the first step. Ligand-field splitting, geometry and pairing energy decide how electrons occupy the available d levels.

Core explanation

For a free-ion-like d¹ species, one d electron is unpaired, so paramagnetism is expected. A d⁰ species has no d electrons and no d-electron spin contribution; a d¹⁰ ion has a filled set with paired electrons. These endpoints commonly show diamagnetism from the metal d shell. Yet a complete compound's magnetism can include ligand radicals or other electronic effects, so the statement must refer to a specified species.

In an octahedral ligand field, five d orbitals split into lower t₂g and upper e g sets. Electron filling depends on the gap Δ oct relative to electron-pairing energy P. For d⁶ Fe²⁺ with a weak-field ligand such as water, Δ oct can be smaller than the cost of pairing in lower orbitals. The high-spin arrangement t₂g⁴e g² has four unpaired electrons in the standard model. With strong-field cyanide, low-spin d⁶ can fill t₂g⁶e g⁰ with all electrons paired. The same formal oxidation state and d count can therefore yield different magnetic behaviour.

For d⁵ Fe³⁺, a weak-field high-spin arrangement can have five unpaired electrons, while a sufficiently strong octahedral field can lead to a low-spin arrangement with one unpaired electron. Stating “Fe³⁺ has five unpaired electrons” without specifying its complex can be wrong. Tetrahedral splitting is usually smaller than comparable octahedral splitting for many complexes and often leads to high-spin arrangements, though exact behaviour should be checked for the specific metal and ligands.

Magnetic classification can be tested experimentally by susceptibility measurements. A paramagnetic material is attracted by a magnetic field; diamagnetic substances show a weaker opposing response. In a coordination compound, magnetic measurements can help discriminate candidate geometries or spin states, but a measured moment may differ from a simple spin-only estimate because orbital contributions, spin–orbit coupling or interactions between metal centres matter. One cannot always count unpaired electrons from an approximate mass-susceptibility observation without a model.

O₂ provides a reminder outside transition-metal chemistry: it is paramagnetic because MO theory predicts two unpaired electrons, despite not containing a d-block metal. Conversely, Zn²⁺ is d¹⁰ and typically diamagnetic in simple complexes. Magnetism is about actual spin occupancy, not the periodic-table region.

For complex ions, calculate formal dⁿ first. In [Fe(CN)₆]⁴⁻, six CN⁻ ligands total −6 and the complex charge is −4, so Fe is +2 and d⁶. The strong field makes low spin plausible, giving paired electrons. In [Fe(H₂O)₆]²⁺, water is neutral, Fe is still +2 and d⁶, but the weaker field favours high spin. Thus ligand identity changes the conclusion after the same charge calculation.

Step-by-step reasoning

1. Assign metal oxidation state from ligand charges. 2. Determine formal d electron count. 3. Identify geometry and the relevant d-level splitting. 4. Compare field strength with pairing tendency and fill orbitals. 5. Count unpaired electrons and state the magnetic classification.

Visual explanation

Draw two octahedral d⁶ diagrams. In the small-gap high-spin case, place four unpaired arrows across t₂g and e g; in the large-gap low-spin case, pair six electrons within t₂g. Write “same d⁶, different spin” under them.

Real-world analogy

Workers may spread out across rooms when moving between rooms is easy, but pair up in lower-floor rooms when climbing is costly. Electron occupation similarly balances pairing energy against the gap to upper d orbitals.

Real-world example

Magnetic measurements of iron coordination compounds can help distinguish high-spin and low-spin Fe²⁺, which may also differ in colour and reactivity. The metal name alone does not supply these properties.

Why?

Why can cyanide make a d⁶ Fe²⁺ complex diamagnetic while water gives a paramagnetic one? Cyanide often produces a larger octahedral splitting, favouring electron pairing in lower t₂g orbitals rather than promotion into e g.

Common misconception

“All compounds of an element have the same number of unpaired electrons.” Oxidation state and ligand environment change d occupancy and splitting, so each complex needs its own count.

Worked example

Compare [Fe(H₂O)₆]²⁺ and [Fe(CN)₆]⁴⁻. Both formally contain Fe²⁺ d⁶. Weak-field water commonly gives t₂g⁴e g² high spin, with four unpaired electrons and paramagnetism. Strong-field cyanide can give t₂g⁶, zero unpaired electrons and diamagnetism. The contrast tests ligand-field effects rather than changing iron's formal oxidation state.

Quick check

1. What feature of an electron configuration chiefly produces ordinary paramagnetism in a simple complex? Answer: One or more unpaired electrons.

Exam focus

Show oxidation-state and d-count arithmetic before filling split orbitals. Do not assign a universal spin state from Fe²⁺ or Fe³⁺ alone. State ligand and geometry assumptions.

Advanced insight

OpenStax Chemistry 2e presents the high-spin aqua versus low-spin cyanide Fe²⁺ comparison at https://openstax.org/books/chemistry-2e/pages/19-3-spectroscopic-and-magnetic-properties-of-coordination-compounds. Spin-only estimates can need correction for orbital and spin–orbit contributions.

Summary

Unpaired electrons make a simple ion or complex paramagnetic; paired electrons give diamagnetism in the elementary account. Ligand-field splitting can change spin state for the same d count, so magnetism belongs to the actual species, not the element name.

Practice questions

1. Is a simple d⁰ metal ion expected to have unpaired d electrons? Answer: No. 2. How many unpaired electrons are in low-spin octahedral d⁶ t₂g⁶? Answer: Zero. 3. How many unpaired electrons are in high-spin octahedral d⁶ t₂g⁴e g²? Answer: Four. 4. Is O₂ paramagnetism evidence that oxygen is a transition metal? Answer: No. O₂'s unpaired electrons arise from its molecular-orbital occupancy.