Electron-configuration exceptions

Prediction versus measured ground state

The common Aufbau diagram would place two electrons in 4s before continuing to fill 3d. That prediction works often, but Cr and Cu show that the true rule is simpler: the ground state is the arrangement with the lowest total energy.

The “half-filled shell” explanation needs nuance

It is useful to notice that Cr has 3d⁵ and Cu has 3d¹⁰, but saying “half-filled and filled subshells are magically stable” is incomplete. The energy balance includes 3d–4s spacing, electron–electron repulsion, exchange and orbital relaxation.

Moving one electron can reduce the total energy even if one-electron filling rules would predict otherwise.

Heavier transition elements

Exceptions become less amenable to one mnemonic in the 4d and 5d series. Nb, Mo, Ru, Rh, Pd, Pt and Au all illustrate that ns and (n−1)d occupancies can reorganize.

For heavy atoms such as gold, relativistic effects shift orbital energies significantly. This is one reason a universal “promote one electron to make d⁵ or d¹⁰” story fails.

Neutral atoms and ions are separate questions

A neutral-atom exception should not be copied mechanically to its ions. When transition metals ionize, ns electrons are usually removed before (n−1)d electrons because the relative orbital energies change after d occupation.

Cu is [Ar]3d¹⁰4s¹, but Cu⁺ is [Ar]3d¹⁰. Fe is [Ar]3d⁶4s², while Fe²⁺ is [Ar]3d⁶.

Experimental evidence behind configurations

Electron configurations are inferred from spectroscopy, ionization energies, magnetic behavior and quantum calculations. They are not assigned only by a classroom arrow diagram.

Photoelectron spectroscopy is particularly informative because electron binding energies reveal subshell structure and can expose deviations from a naive filling order.

A practical rule for problem solving

Selected ground-state exceptions

The table is not a new mnemonic to memorize blindly. It demonstrates that several near-degenerate configurations compete and the winner changes across the d block.

Palladium shows the danger of one simple story

Pd is especially instructive because its ground state is commonly written [Kr]4d¹⁰5s⁰. It does not fit the “move exactly one s electron to obtain d⁵ or d¹⁰” slogan used for Cr and Cu.

The result follows from the detailed 4d–5s energy balance. Once again, the physical principle is total energy, not a special exception rule patched onto Aufbau.

Configurations can depend on what is being described

Free atoms, ions, atoms in molecules and atoms in solids do not all have the same orbital-energy landscape. A configuration quoted for an isolated neutral atom is therefore not a universal label that survives unchanged in every chemical environment.

In coordination chemistry, d-electron count is usually referenced after assigning an oxidation state. Ligand fields then split the metal d orbitals and determine magnetic and spectroscopic behavior.

This is why electron configuration is best treated as a model tied to a specified species and state, not as an immutable address for every electron.

Magnetic evidence constrains electron arrangements

An electron configuration predicts the number of unpaired electrons and therefore whether an isolated atom or ion is paramagnetic. Comparing predicted magnetic behavior with experiment is one way to test electronic assignments.

Hund’s rule and exchange effects matter because arrangements with different numbers and couplings of unpaired electrons can have different energies even when they occupy the same nominal subshells.

For complex atoms, the measured spectrum contains many closely spaced terms associated with different angular-momentum couplings. A shorthand configuration such as 3d⁵4s¹ summarizes occupancy but does not specify the complete quantum state.

Relativistic effects become chemically visible

In heavy atoms, inner electrons move fast enough that relativistic corrections alter orbital contraction and expansion. The 6s orbital of gold is stabilized and contracted, while 5d energies are shifted in the opposite direction.

These effects contribute both to gold’s unusual 5d¹⁰6s¹ configuration and to broader chemical properties such as its characteristic color and relativistic bonding behavior. Heavy-element exceptions are therefore not merely enlarged versions of the chromium story.

Exercises

Chromium

State the observed ground-state configuration beyond [Ar].

Copper ion

Starting from Cu = [Ar]3d¹⁰4s¹, give Cu²⁺.

Concept

What principle outranks the simple Aufbau arrow diagram?