Magnetism and Electron Configuration

Introduction

The same d-electron count can give different numbers of unpaired electrons when ligands change the energy gap between d levels. Magnetic behaviour provides evidence about that electronic arrangement. A high-spin complex leaves more electrons unpaired; a low-spin complex pairs them in lower levels when the splitting is large enough. Geometry and oxidation state must be known before a magnetic prediction is made.

Core explanation

Paramagnetic species have one or more unpaired electrons and are attracted to a magnetic field. Diamagnetic species have all electrons paired and respond weakly in the opposite direction. For a transition-metal complex, first determine the metal oxidation state and its d-electron count. Neutral Fe is often written [Ar]3d⁶4s²; Fe²⁺ loses the two 4s electrons in the usual ion-counting convention, giving d⁶. Fe³⁺ is d⁵. Do not count ligand electrons as though they were all metal d electrons.

In an octahedral field, three t₂g orbitals are lower and two e g orbitals higher. The energy gap Δ oct competes with the cost of pairing two electrons in one orbital. If Δ oct is relatively small, an electron may occupy a higher e g orbital before pairing lower down: high spin . If Δ oct is large, pairing in lower t₂g orbitals may be favoured: low spin . This choice matters especially for d⁴ through d⁷ octahedral configurations; d⁰, d¹, d², d³, d⁸, d⁹ and d¹⁰ do not show the same simple high/low-spin alternative in a basic octahedral filling diagram.

For octahedral d⁶ Fe²⁺, a high-spin distribution can be written t₂g⁴e g² and has four unpaired electrons. A low-spin distribution t₂g⁶e g⁰ has zero unpaired electrons. Both contain six d electrons, so electron count alone does not specify magnetism. Strong-field ligands tend to give larger splitting and can favour low spin; weaker-field ligands can favour high spin. Metal oxidation state also affects splitting. A particular compound should be assigned from its known ligand field or measured magnetism, not a generic claim that all Fe²⁺ salts behave identically.

Tetrahedral complexes usually have a smaller splitting in the standard comparison and are commonly high spin, but that is a tendency, not a theorem for every metal and ligand. Square-planar d⁸ complexes can be diamagnetic despite having metal d electrons because their orbital ordering differs greatly from an octahedral diagram. VSEPR geometry cannot replace ligand-field geometry for these cases.

Magnetic moment measurements can estimate the number of unpaired electrons, though orbital contributions and coupling complicate exact values. A simple spin-only relation is μ ≈ √[n(n+2)] Bohr magnetons for n unpaired electrons; it is an approximation. OpenStax Chemistry 2e explains crystal-field splitting, high/low spin and magnetic properties at https://openstax.org/books/chemistry/pages/19-3-spectroscopic-and-magnetic-properties-of-coordination-compounds.

Step-by-step reasoning

1. Determine metal oxidation state from ligand charges and complex charge. 2. Convert the metal ion to a d-electron count. 3. Identify coordination geometry and draw the proper splitting pattern. 4. Compare splitting with pairing cost to decide high or low spin if applicable. 5. Count unpaired electrons and predict para- or diamagnetism.

Visual explanation

Draw octahedral d⁶ diagrams side by side. For high spin, place four electrons in t₂g and two in e g with four arrows unpaired. For low spin, fill all three t₂g boxes with pairs and leave e g empty. Put a small Δ arrow for high spin and a larger one for low spin.

Real-world analogy

Workers choose between sharing a crowded lower-floor room and taking an empty upper-floor room. If climbing costs little, more occupy separate rooms; if climbing is expensive, they pair downstairs. Electrons compare orbital splitting with pairing energy, although their behaviour follows quantum rules rather than human preference.

Real-world example

Magnetic measurements help chemists infer whether a coordination compound has high- or low-spin electrons when optical colour alone is ambiguous. The combination of spectroscopy and magnetism can narrow its electronic structure and sometimes its geometry.

Why?

Why can changing ligands change magnetism without changing Fe²⁺ to another element or oxidation state? Ligands alter Δ oct. The same six d electrons can redistribute between t₂g and e g levels, changing how many remain unpaired.

Common misconception

“Any transition-metal ion is paramagnetic” is false. Some metal ions are d⁰ or d¹⁰, and low-spin or square-planar complexes can have all electrons paired. Count the actual electrons in the actual geometry.

Worked example

An octahedral Fe²⁺ complex is known to have a strong ligand field. Fe²⁺ is d⁶. If Δ oct exceeds the relevant pairing cost, its electrons fill t₂g⁶e g⁰, leaving none unpaired. The idealized complex is diamagnetic. A weak-field Fe²⁺ analogue may instead be t₂g⁴e g² with four unpaired electrons and be paramagnetic.

Quick check

1. How many unpaired electrons occur in an ideal low-spin octahedral d⁶ configuration? Answer: Zero; the six electrons pair within the three lower t₂g orbitals.

Exam focus

Show oxidation state, d count, geometry, orbital diagram and unpaired count in that order. Do not label “high spin” merely because an ion is coloured. If calculating a spin-only moment, state its approximation and the number n used.

Advanced insight

The spin-only formula neglects orbital angular momentum and magnetic coupling between centres. Experimental moments can therefore differ from the simple prediction, especially for heavy metals or exchange-coupled solids. The qualitative paired-versus-unpaired inference remains a useful first model.

Summary

Magnetism depends on unpaired electrons, not just metal identity. Octahedral splitting and pairing energy decide high- versus low-spin filling for relevant d counts. A d⁶ Fe²⁺ example can range from four unpaired electrons to none when ligand field changes.

Practice questions

1. What d count does Fe³⁺ have in the usual ionic convention? Answer: d⁵, after removing two 4s and one 3d electron from neutral iron's valence configuration. 2. Is high-spin octahedral d⁶ paramagnetic? Answer: Yes; the simple t₂g⁴e g² filling has four unpaired electrons. 3. Why is Zn²⁺ commonly diamagnetic? Answer: It is d¹⁰, with its d electrons paired in the usual configuration.