d-electron count
/ written d-n, e.g. d6 is 'd six' /
When chemists describe a transition-metal complex, they constantly say things like 'iron(III) is d5' or 'this is a d8 metal.' Behind that shorthand is a simple count: how many electrons remain in the metal's d orbitals after it has become the ion it is in the complex. Almost everything about a transition-metal complex's color, magnetism, geometry, and stability tracks this one number.
To find it, start from the neutral metal's group and subtract the oxidation state. A cleaner way: for a first-row transition metal, the d-electron count equals the group number (the metal's total valence electrons) minus the oxidation state. Iron is in group 8, so iron(III) is 8 - 3 = d5, and iron(II) is 8 - 2 = d6. Manganese (group 7) as Mn(II) is d5; copper (group 11) as Cu(II) is d9; titanium(IV) is d0. A point that trips beginners: when a transition metal ionizes, it loses its outer s electrons first, before any d electrons, so a configuration like 4s2 3d6 for neutral iron becomes simply 3d6 for Fe2+ — there is no leftover 4s electron to worry about in the ion.
The d-electron count is the gateway to the bonding part of the subject. In a given geometry the d orbitals split into sets, and how the dn electrons fill those sets — whether they spread out (high-spin) or pair up (low-spin), how much crystal-field stabilization they gain, whether the d8 metal prefers square planar — all follow from the count together with the ligand field. It also underlies the 18-electron rule, since the d electrons plus the electrons donated by the ligands are what that rule tallies.
Iron sits in group 8. In Fe2+ it has lost two electrons, leaving 3d6 (a d6 ion); in Fe3+ it has lost three, leaving 3d5 (a d5 ion). Notice the 4s electrons go first, so you never write 4s for the ion — the count is purely in the d orbitals.
Subtract the oxidation state from the group number; the outer s electrons are lost before any d electrons.
A frequent slip is keeping the 4s electrons in the ion. For transition-metal cations the 4s empties before the 3d, so Fe2+ is 3d6, not 4s2 3d4. Count d electrons as group number minus oxidation state and you avoid the trap.