Maximum number of unpaired electrons

Question

What is the maximum number of unpaired electrons possible in an octahedral complex?

Answer 1

Five — achieved by a high-spin d⁵ complex.

Why 5 is the ceiling

An octahedral field splits the five d orbitals into two sets:

• t_2g — three orbitals, lower energy
• e_g — two orbitals, higher energy

Three plus two is five orbitals, and by the Pauli principle each holds at most one unpaired electron. So five is a hard structural limit — adding a sixth d electron has nowhere to go but into an already-occupied orbital, where it must pair up and cancel a spin.

Why d⁵ high-spin reaches it

When the splitting energy Δ_o is smaller than the pairing energy — a weak-field ligand — electrons prefer climbing into the higher e_g set over doubling up. By Hund's rule they occupy all five orbitals singly with parallel spins:

t_2g: ↑ ↑ ↑   e_g: ↑ ↑  → 5 unpaired

Real examples: [Mn(H₂O)₆]²⁺ and [FeF₆]³⁻, both d⁵ with weak-field ligands.

Everything else falls short

d⁴ high-spin: 4 unpaired — not enough electrons.
d⁶ high-spin: 4 unpaired — the sixth electron must pair into t_2g, cancelling one.
d⁵ low-spin: only 1 unpaired (t_2g⁵), because a strong-field ligand like CN⁻ makes Δ_o large enough that pairing costs less than promotion. [Fe(CN)₆]³⁻ is the classic case.

So d⁵ is the peak of the curve, and it only delivers 5 in the high-spin case. Same electron count, same geometry, completely different magnetism — the ligand decides.

How this is measured

Unpaired electrons make a complex paramagnetic, and the magnetic moment follows μ = √(n(n+2)) Bohr magnetons. For n = 5 that is √35 = 5.92 BM, the largest value any octahedral d-block complex can show. Measuring μ is how chemists distinguish high-spin from low-spin experimentally.

One footnote in case your course covers it: this ceiling of 5 applies to d-block complexes. Lanthanides and actinides use f orbitals — seven of them — so an f⁷ ion such as Gd³⁺ carries 7 unpaired electrons. But for a standard octahedral transition-metal complex, the answer is 5.