High-Spin and Low-Spin Complexes

Introduction

When a d electron can either pair in a lower orbital or occupy a higher one, two energy costs compete. Pairing costs energy because electrons repel, while moving upward costs the crystal-field gap. If the gap is small, keeping more electrons unpaired can win; if the gap is large, pairing below can win. These are the high-spin and low-spin possibilities.

Core explanation

In an octahedral field, lower t₂g orbitals and upper e g orbitals are separated by Δ oct. Let P denote an approximate pairing energy. For d⁶, after three electrons singly occupy the three t₂g orbitals, subsequent placement involves choices. A weak field with Δ oct smaller relative to P favours occupation of e g before all lower electrons pair. The ideal high-spin d⁶ arrangement is t₂g⁴e g², containing four unpaired electrons. A strong field with a sufficiently large Δ oct favours t₂g⁶e g⁰, with all six electrons paired and zero unpaired electrons.

The d count alone does not specify spin state for such cases. Fe²⁺ is d⁶, but its high- or low-spin behaviour depends on ligands, geometry, metal–ligand distance and other electronic factors. [Fe(H₂O)₆]²⁺ is generally a weak-field high-spin example, while sufficiently strong-field ligands such as CN⁻ can support low-spin Fe²⁺ complexes. One should verify exact species when assigning a real compound rather than assuming every cyanide-containing metal behaves identically.

Not every d count has a high/low choice in a simple octahedral diagram. d¹, d² and d³ fill separate lower orbitals identically regardless of whether Δ oct is relatively small or large. d⁸, d⁹ and d¹⁰ also have no ordinary alternative high/low occupancy of the octahedral sets in the same sense. The classic octahedral high/low comparisons concern d⁴ through d⁷. A question asking whether d³ is “high spin” may be imprecise because there is no competing low-spin electron arrangement within the simple two-level picture.

Tetrahedral Δ tet is normally smaller than pairing energy, so tetrahedral complexes are usually high spin. Square-planar d⁸ complexes can have a large separation that favours paired lower orbitals. The words high and low spin should always be tied to a geometry and electron count. Comparing a tetrahedral and square-planar ion solely by an octahedral Δ oct value would misuse the model.

Magnetic measurements provide evidence about unpaired electrons. A high-spin d⁶ ion with four unpaired electrons is paramagnetic, while ideal low-spin d⁶ with none is diamagnetic in the basic spin picture. Measured moments can include orbital contributions and interactions, so a numerical moment is not always an exact unpaired-count meter. Qualitative differences are often sufficient to test a proposed spin state.

The energy comparison is a model. P is not always one fixed number independent of the electronic configuration, and covalent bonding affects Δ. Detailed electronic structure can be more complicated, especially for 4d/5d metals or distorted geometries. Yet the central rule—compare the cost of upper-level occupation with the cost of pairing—remains the right conceptual starting point.

Step-by-step reasoning

1. Calculate the metal's oxidation state and d-electron count. 2. Confirm geometry and draw the appropriate split-orbital diagram. 3. Identify where pairing versus upper-level occupation becomes a choice. 4. Compare Δ with pairing energy under the given ligand field. 5. Fill boxes and count unpaired electrons for the predicted spin state.

Visual explanation

Draw two octahedral d⁶ diagrams side by side. In the left, show t₂g⁴e g² with four single arrows and label small Δ. In the right, show t₂g⁶e g⁰ with three pairs and label large Δ.

Real-world analogy

Students can share a crowded lower-floor room or pay the cost of climbing to an empty upper room. If climbing is cheap, they spread out; if climbing is expensive, they share lower rooms. The analogy captures competing costs, not literal electron choices.

Real-world example

Changing an Fe²⁺ coordination environment can change its magnetic response through a spin-state change. This is useful when interpreting magnetic data for metal complexes and some switchable materials.

Why?

Why does a stronger octahedral field tend to favour low spin for d⁶? It raises the upper e g orbitals farther above t₂g, making lower-level pairing comparatively less costly than promoting electrons across the larger gap.

Common misconception

“Low spin means no unpaired electrons in every case.” Low-spin d⁵ still has one unpaired electron in the basic octahedral diagram; “low” is relative to the high-spin alternative.

Worked example

For octahedral d⁵, a weak field gives t₂g³e g², one electron in each of five orbitals and five unpaired electrons. A strong field gives t₂g⁵e g⁰: the three lower orbitals hold two pairs and one single electron, so one remains unpaired. Both are paramagnetic, but to different extents under a simple model.

Quick check

1. How many unpaired electrons occur in ideal low-spin octahedral d⁶? Answer: Zero.

Exam focus

Show an orbital-box diagram when comparing spin states. State both d count and geometry, and avoid calling every small-unpaired count diamagnetic.

Advanced insight

Spin-crossover compounds can switch between high- and low-spin states when temperature, pressure or light changes the relative free energies. That behavior illustrates how close the competing electronic states can be.

Summary

High versus low spin reflects competition between crystal-field splitting and electron-pairing cost. In octahedral d⁴–d⁷ cases, ligand field can change unpaired count. Spin-state prediction requires more than an oxidation-state label.

Practice questions

1. Which ideal octahedral d⁶ arrangement has four unpaired electrons? Answer: High-spin t₂g⁴e g². 2. Which has zero unpaired electrons? Answer: Low-spin t₂g⁶e g⁰. 3. Does d³ have a distinct high/low octahedral occupancy choice in the simple model? Answer: No. Its three electrons occupy the three lower t₂g orbitals singly. 4. Why are tetrahedral complexes usually high spin? Answer: Their splitting is generally small compared with pairing energy.