Hund's rule

Equal-energy orbitals first

A p subshell contains three degenerate orbitals in an isolated atom; a d subshell contains five. If two electrons are placed into 2p, the ground-state pattern is ↑, ↑, empty rather than ↑↓, empty, empty. The electrons spread across different orbitals before being forced to share one spatial state.

The rule is not “electrons dislike pairs” in a vague sense. Separate occupancy reduces some electron–electron repulsion and, for parallel-spin electrons, quantum-mechanical exchange lowers the energy. The balance favors the maximum number of unpaired electrons within the degenerate set.

Hund, Pauli and Aufbau do different jobs

For nitrogen, 1s²2s²2p³, Hund gives one electron in each 2p orbital. For oxygen, 2p⁴, the fourth p electron must pair in one of those orbitals because all three are already singly occupied.

Magnetism is the experimental consequence

An atom or ion with one or more unpaired electrons has a net paramagnetic response. If every electron is paired, the species is diamagnetic in the simple atomic picture.

Thus carbon has two unpaired 2p electrons in its isolated ground-state atom, nitrogen has three, oxygen has two, fluorine has one and neon has none. This sequence follows directly from Hund filling.

In molecules and coordination complexes, orbital energies can split so strongly that the simple free-atom Hund picture must be modified. High-spin and low-spin transition-metal complexes are an important example: ligand-field splitting competes with electron pairing energy.

Spin projections and the arrow notation

The arrows ↑ and ↓ are shorthand for spin projections mₛ = +1/2 and −1/2 along a chosen axis. They should not be imagined as tiny electrons literally rotating clockwise or counterclockwise.

Hund’s rule is most reliable when the orbitals being compared are genuinely degenerate or nearly degenerate and the rest of the electronic environment does not split them strongly. It is a ground-state rule, not a prohibition against paired electrons or excited configurations.

The deeper statement is energetic: among allowed configurations of a given degenerate subshell, the state with maximum spin multiplicity often lies lowest.

Exchange energy is quantum mechanical

The lower energy of parallel-spin occupancy is often loosely described as electrons “staying apart.” Spatial separation can reduce Coulomb repulsion, but Hund’s rule also contains an intrinsically quantum effect called exchange. For identical fermions, the spin symmetry and spatial symmetry of the many-electron wavefunction are linked.

Parallel-spin electrons in different orbitals are described by a spatial wavefunction that reduces the probability of finding the two electrons in the same region. The resulting exchange stabilization has no classical analogue. This is why Hund’s rule should not be reduced to a picture of tiny magnets simply aligning.

From unpaired electrons to spin multiplicity

If the total electron spin is S, the spin multiplicity is 2S + 1. Three parallel unpaired electrons in a p³ subshell can combine to S = 3/2, giving multiplicity 4—a quartet. This language becomes useful in atomic spectroscopy and transition-metal chemistry.

Hund’s first rule says that, for a given electron configuration, the term with maximum spin multiplicity usually lies lowest. Additional Hund rules help order states with the same spin but different total orbital angular momentum.

When orbital splitting competes with Hund

In a free atom, p or d orbitals within one subshell are degenerate before smaller interactions are considered. In a coordination complex, ligands can split the five d orbitals into groups separated by a ligand-field energy. If that splitting exceeds the pairing cost, electrons may pair in lower orbitals rather than occupy every higher orbital singly.

This produces the familiar distinction between high-spin and low-spin complexes. The underlying principle is still energy minimization: Hund favors unpaired occupation when the orbitals are close enough in energy.

Carbon, nitrogen and oxygen form a useful sequence

Across C, N and O the 2p population changes from p² to p³ to p⁴. Carbon has two unpaired electrons, nitrogen reaches three, and oxygen falls back to two because the fourth electron must begin pairing. This gives a direct experimental prediction: the isolated atoms do not all have the same magnetic response even though they sit next to one another in the periodic table.

The sequence also shows why “more electrons means more unpaired electrons” is false. Unpaired count rises only until the degenerate subshell is half filled, then decreases as pairing completes the subshell.

Exercises

Carbon

Draw the three 2p boxes for carbon, 2p².

Oxygen

How many unpaired electrons are in isolated ground-state O, 2p⁴?

Magnetism

Which isolated atom is diamagnetic: N (2p³) or Ne (2p⁶)?