High-Spin vs Low-Spin Complexes: How to Tell Them Apart

[Fe(H₂O)₆]²⁺ and [Fe(CN)₆]⁴⁻ both contain iron(II), a d⁶ ion, in an octahedral complex. Yet the first is strongly attracted into a magnetic field and the second is not attracted at all. The six d electrons are arranged differently. In the aqua complex they spread out, leaving four unpaired; in the cyanido complex they pack together in pairs, leaving none. The first is a high-spin complex, the second a low-spin complex, and the difference comes down to a contest between two energies.

This comparison assumes you know how ligands split d orbitals into t₂g and eg sets. If not, read crystal field theory first.

The contest: Δo versus pairing energy

In an octahedral complex, the first three d electrons go singly into the three t₂g orbitals, following Hund’s rule. The fourth electron then faces a choice:

• Go up into an empty eg orbital, costing the splitting energy Δo, but keeping its spin unpaired.
• Pair up in a t₂g orbital, avoiding Δo, but paying the pairing energy, P: the extra repulsion of two electrons sharing one orbital, plus the loss of exchange stabilisation from parallel spins.

The rule is simple:

• If Δo < P, electrons go up before pairing → high-spin (maximum unpaired electrons).
• If Δo > P, electrons pair before going up → low-spin (minimum unpaired electrons).

Pairing energy does not change much for a given metal ion. Δo changes a lot with the ligand. So in practice the ligand usually decides: weak-field ligands (I⁻, Br⁻, Cl⁻, F⁻, H₂O) tend to give high-spin complexes, and strong-field ligands (CN⁻, CO, bipy, phen) give low-spin complexes. Ammonia and en sit in between, and the outcome depends on the metal.

Side-by-side comparison

Feature	High-spin	Low-spin
Energy condition	Δo < P	Δo > P
Typical ligands	weak field: halides, H₂O, OH⁻, oxalate	strong field: CN⁻, CO, NO₂⁻, bipy, phen
Electron arrangement	electrons spread over t₂g and eg	t₂g fills first
Unpaired electrons	maximum possible	minimum possible
Magnetism	strongly paramagnetic	weakly paramagnetic or diamagnetic
Metal–ligand distance	longer (electrons in antibonding eg)	shorter
Ionic radius of metal	larger	smaller
Usual metals	3d metals in low oxidation states	4d and 5d metals; 3d metals in higher oxidation states
Geometry	tetrahedral complexes nearly always high-spin	almost always octahedral or square planar
Ligand substitution	often faster	often slower (e.g. low-spin d⁶ is inert)

Which d counts can show a difference?

Only certain electron counts give two possible arrangements. For d¹, d², d³ there’s only one way to fill (all in t₂g, unpaired). For d⁸, d⁹, d¹⁰ the t₂g set is full either way. The choice exists only for d⁴, d⁵, d⁶ and d⁷ in octahedral complexes:

d count	High-spin configuration	Unpaired	Low-spin configuration	Unpaired
d⁴	t₂g³ eg¹	4	t₂g⁴	2
d⁵	t₂g³ eg²	5	t₂g⁵	1
d⁶	t₂g⁴ eg²	4	t₂g⁶	0
d⁷	t₂g⁵ eg²	3	t₂g⁶ eg¹	1

A quick way to find the d count: take the group number of the metal and subtract its oxidation state. Fe is in group 8, so Fe²⁺ is d⁶ and Fe³⁺ is d⁵ (see transition metal electron configurations).

Worked comparison: d⁶ in numbers

Using CFSE values (t₂g = −0.4 Δo, eg = +0.6 Δo per electron):

• High-spin d⁶ (t₂g⁴ eg²): 4(−0.4) + 2(+0.6) = −0.4 Δo, with one pair of electrons.
• Low-spin d⁶ (t₂g⁶): 6(−0.4) = −2.4 Δo, with three pairs.

Low-spin gains an extra 2.0 Δo of stabilisation but must pay for two extra pairs, 2P. It wins when 2Δo > 2P, in other words when Δo > P. That is the rule from the start, now derived rather than stated.

This large CFSE also explains why low-spin d⁶ complexes, such as [Co(NH₃)₆]³⁺, are famously slow to swap ligands. Chemists call them inert.

Real examples

Complex	Metal ion	d count	Spin state	Unpaired electrons
[Cr(H₂O)₆]²⁺	Cr²⁺	d⁴	high	4
[Mn(H₂O)₆]²⁺	Mn²⁺	d⁵	high	5
[Fe(H₂O)₆]³⁺	Fe³⁺	d⁵	high	5
[Fe(CN)₆]³⁻	Fe³⁺	d⁵	low	1
[Fe(H₂O)₆]²⁺	Fe²⁺	d⁶	high	4
[Fe(CN)₆]⁴⁻	Fe²⁺	d⁶	low	0
[CoF₆]³⁻	Co³⁺	d⁶	high	4
[Co(NH₃)₆]³⁺	Co³⁺	d⁶	low	0

The cobalt pair is worth studying. Co³⁺ has a large charge, so its Δo is large; even ammonia pushes it past P, giving a diamagnetic complex. Only a very weak-field ligand, fluoride, keeps Co³⁺ high-spin. The iron pairs show the ligand effect directly: same metal, same charge, different ligand, different spin state.

How to tell them apart experimentally

1. Magnetic measurements

This is the most direct test. The spin-only formula estimates the magnetic moment from the number of unpaired electrons, n:

μ = √(n(n + 2)) μB

where μB is the Bohr magneton.

n	Spin-only μ / μB
0	0
1	1.73
2	2.83
3	3.87
4	4.90
5	5.92

A measured moment near 4.9 μB for an Fe²⁺ complex signals high-spin; a diamagnetic sample signals low-spin. Real values can differ a little from spin-only because of orbital contributions, but they’re usually close enough to count electrons. See paramagnetic vs diamagnetic for how these measurements work.

2. Bond lengths and ionic radii

In high-spin complexes, electrons occupy eg orbitals that point straight at the ligands. Those electrons push the ligands away, so metal–ligand bonds are longer. Low-spin complexes keep eg emptier and have shorter bonds. X-ray crystallography can therefore reveal the spin state.

3. Colour and spectra

Because low-spin complexes have larger Δo, they usually absorb at shorter wavelengths. The difference can be striking: high-spin d⁵ ions such as [Mn(H₂O)₆]²⁺ are very pale, because every d–d transition would need an electron to reverse its spin, which is “spin-forbidden” and weak.

When each applies

• First-row (3d) metals in the +2 state with water or halides: expect high-spin.
• Any metal with CN⁻, CO or bipy/phen: expect low-spin.
• First-row +3 ions with N-donor ligands (NH₃, en): often low-spin, especially Co³⁺.
• Second- and third-row (4d, 5d) metals: almost always low-spin, because their larger orbitals give bigger Δo and their pairing energies are lower.
• Tetrahedral complexes: almost always high-spin, because Δt is only about 4/9 of Δo.
• d⁸ with strong-field ligands: tends to adopt square planar geometry instead, which is effectively the low-spin option for d⁸ (e.g. diamagnetic [Ni(CN)₄]²⁻).

Spin states in action

Haemoglobin. In deoxyhaemoglobin, the iron(II) is high-spin and slightly too large to sit in the plane of the porphyrin ring. When O₂ binds, the iron centre becomes low-spin and diamagnetic overall, and the smaller iron moves into the ring plane. That small movement pulls on the protein and helps explain why haemoglobin picks up oxygen cooperatively (see haemoglobin).

Spin crossover. Some iron(II) complexes with nitrogen-donor ligands have Δo very close to P. Changing the temperature or pressure, or shining light on them, can switch them between high-spin and low-spin, changing their colour and magnetism. Researchers study these materials for sensors and molecular memory devices.

Common mistakes

• Applying high/low-spin to d¹–d³ or d⁸–d¹⁰ octahedral ions. There’s only one arrangement for these.
• Saying “strong-field ligands give more unpaired electrons”. It’s the opposite: strong field → low-spin → fewer unpaired electrons.
• Forgetting the metal’s role. Ammonia gives high-spin [Co(NH₃)₆]²⁺ but low-spin [Co(NH₃)₆]³⁺: the higher charge raises Δo.
• Using 4s electrons in the d count. Transition metal ions lose their 4s electrons first, so Fe²⁺ is [Ar] 3d⁶, not 3d⁴4s².
• Expecting tetrahedral low-spin complexes. They are extremely rare.

Key takeaways

• The spin state depends on Δo versus pairing energy P: Δo < P gives high-spin, Δo > P gives low-spin.
• Only d⁴–d⁷ octahedral complexes have a genuine choice.
• Weak-field ligands and 3d M²⁺ ions favour high-spin; strong-field ligands, M³⁺ ions and 4d/5d metals favour low-spin.
• Magnetic moments (μ = √(n(n + 2)) μB) are the clearest way to count unpaired electrons and identify the spin state.
• High-spin complexes have longer bonds and larger metal ions; low-spin complexes are more compact and, for d⁶, very inert.