TM electrons

d-electron count definition

Number of electrons in the metal d orbitals after accounting for oxidation state

How to find d-electron count

Determine oxidation state, then subtract electrons from neutral metal configuration (remove 4s before 3d)

Example: Cr3+ d-electron count

Cr = [Ar] 3d5 4s1 → Cr3+ = d3

Does d-electron count equal number of unpaired electrons?

No, it only gives total d electrons, not their arrangement

What determines number of unpaired electrons?

d-electron count, geometry, and ligand field strength

What is ligand field strength?

Ability of ligands to cause electron pairing (strong-field vs weak-field)

High spin definition

Electrons occupy orbitals singly before pairing → more unpaired electrons

Low spin definition

Electrons pair in lower orbitals first → fewer unpaired electrons

d1 configuration unpaired electrons

1 (always)

d2 configuration unpaired electrons

2 (always) HS

d3 configuration unpaired electrons

3 (always, octahedral) HS

d4 high spin unpaired electrons

4

d4 low spin unpaired electrons

2

d5 high spin unpaired electrons

5

d5 low spin unpaired electrons

1

d6 high spin unpaired electrons

4

d6 low spin unpaired electrons

0

d7 high spin unpaired electrons

3

d7 low spin unpaired electrons

1

d8 typical unpaired electrons

Usually 0 (square planar) or 2 (octahedral)

d9 unpaired electrons

1

d10 unpaired electrons

0

Why d1–d3 are simple

No pairing needed → number of unpaired electrons equals d count

Why d4–d7 are complex

Electrons can pair or stay unpaired depending on ligand strength

Relationship between unpaired electrons and magnetism

Unpaired electrons → paramagnetic; none → diamagnetic

Spin-only magnetic moment formula

μ = √(n(n+2)) where n = number of unpaired electrons

Common mistake in d-electron counting

Forgetting to remove 4s electrons before 3d

Example: Fe2+ d-electron count

Fe = [Ar] 3d6 4s2 → Fe2+ = d6

Example: Co3+ d-electron count

Co = [Ar] 3d7 4s2 → Co3+ = d6

One-line rule for d-electron count

d count tells total electrons; unpaired depends on their arrangement