Hund’s rule explains why electrons occupy separate orbitals of the same energy before pairing up. When electrons fill an atom’s orbitals, they do not simply crowd into the first available spaces. Instead, they tend to spread out among equal-energy orbitals, with their spins aligned, before two electrons share an orbital.
This behavior helps determine the electron configurations of atoms, influences the magnetic properties of elements, and contributes to the patterns that appear across the periodic table. Understanding Hund’s rule makes it easier to predict how electrons are arranged and why atoms of different elements behave differently.
What is Hund’s rule?
Hund’s rule, also called Hund’s rule of maximum multiplicity, states that when electrons occupy orbitals of equal energy, they fill those orbitals individually with parallel spins before pairing in any one orbital.
An orbital is a region of an atom where an electron is likely to be found. Orbitals have different shapes and energies, depending on their type and the atom’s electronic structure. Each orbital can hold a maximum of two electrons, and those two electrons must have opposite spins.
When several orbitals have the same energy, however, electrons generally occupy them one at a time before sharing. For example, the three orbitals in a p subshell have equal energy in an isolated atom without external fields that distinguish their orientations. If three electrons occupy this subshell, each orbital receives one electron rather than one orbital receiving two while another remains empty.
The key idea is that electrons spread out across equal-energy orbitals before pairing. This arrangement usually produces a lower-energy, more stable electronic state than an arrangement in which electrons pair prematurely.
Hund’s rule is one of three fundamental principles commonly used to determine electron configurations. The other two are the Aufbau principle, which describes how electrons generally occupy lower-energy orbitals first, and the Pauli exclusion principle, which limits each orbital to two electrons with opposite spins.
How electrons occupy atomic orbitals
To understand Hund’s rule, it helps to distinguish three related concepts: shells, subshells, and orbitals.
An electron shell is a broad energy level associated with an atom’s electrons. Shells contain subshells, which are identified by letters: s, p, d, and f. Each subshell contains a particular number of orbitals.
An s subshell contains one orbital, a p subshell contains three, a d subshell contains five, and an f subshell contains seven. Because each orbital can hold two electrons, these subshells can accommodate two, six, ten, and fourteen electrons, respectively.
The orbitals within a given subshell generally have the same energy in an isolated atom without an external field that breaks their equivalence. These are called degenerate orbitals. Hund’s rule governs how electrons distribute themselves among these equal-energy orbitals.
Consider the p subshell. Its three orbitals can hold six electrons altogether, but the electrons do not ordinarily pair in the first orbital before occupying the others. Instead, the first three electrons occupy three separate orbitals. Only when additional electrons arrive does pairing begin.
This pattern is not a matter of electrons deliberately avoiding one another. It emerges from the quantum-mechanical properties of electrons and the energies of the possible arrangements.
Why electrons occupy separate orbitals before pairing
The reason behind Hund’s rule lies in quantum mechanics, which describes how particles behave at atomic scales.
Electrons have a property called spin, an intrinsic form of angular momentum. Spin is not literally a tiny sphere rotating like a planet, but it has measurable quantum properties. For an electron, the spin projection along a chosen direction can take one of two values, conventionally represented as spin up or spin down.
Electrons are also identical fermions, meaning their combined quantum state must obey the Pauli exclusion principle. This requirement influences how the electrons can be arranged within an atom.
When electrons occupy different orbitals of equal energy with parallel spins, their combined quantum state can have a lower energy than some competing arrangements. In many atoms, this is associated with exchange effects arising from the antisymmetric quantum state of identical electrons. The exchange interaction is a quantum-mechanical effect, not a classical force that simply pushes electrons into separate spaces.
Electron–electron repulsion also matters. Electrons all carry negative electric charge, so their electrostatic interaction affects the total energy of an atom. Distributing electrons among different orbitals can change the balance of this repulsion and the exchange contribution to the energy.
The most stable arrangement is the one with the lowest total energy, taking all relevant interactions into account. For partially filled sets of equal-energy orbitals, this often favors placing electrons in separate orbitals with parallel spins before pairing them.
Hund’s rule is therefore a useful general principle based on the energy ordering of atomic states. It is not an absolute statement that electrons always spread out whenever possible. The rule applies most directly to orbitals of equal energy, and the detailed electron configuration ultimately depends on the atom’s quantum-mechanical energy levels.
Hund’s rule in action: The three p orbitals
The p subshell provides a straightforward way to see how Hund’s rule works.
A p subshell contains three orbitals, often labeled pₓ, pᵧ, and p𝓏 to indicate their different spatial orientations. In an ordinary isolated atom, these orbitals have equal energy. Each can hold two electrons with opposite spins.
Orbital diagrams represent these orbitals as boxes or lines and electrons as arrows. An upward arrow and a downward arrow indicate opposite spin projections.
The following examples show how electrons fill a p subshell:
| Number of p electrons | Orbital arrangement | What happens |
|---|---|---|
| 1 | ↑ _ _ | The first electron occupies one orbital. |
| 2 | ↑ ↑ _ | The second electron enters an empty orbital with parallel spin. |
| 3 | ↑ ↑ ↑ | Each orbital contains one electron. |
| 4 | ↑↓ ↑ ↑ | The fourth electron pairs in one orbital. |
| 5 | ↑↓ ↑↓ ↑ | A second orbital becomes paired. |
| 6 | ↑↓ ↑↓ ↑↓ | All three orbitals are filled. |
The precise choice of which orbital receives the first electron is arbitrary when the orbitals are equivalent. What matters is the pattern: the first three electrons occupy separate orbitals, and each has the same spin orientation in the diagram. The fourth electron begins pairing.
This example captures the central rule. If electrons were to pair in one p orbital while leaving another equal-energy p orbital empty, the arrangement would generally not be the lowest-energy state for that electron count.
Examples of Hund’s rule in real atoms
Hund’s rule helps explain the electron configurations of many elements, particularly those with partially filled p, d, and f subshells.
Carbon has six electrons. Its ground-state electron configuration is 1s² 2s² 2p². The first two shells’ occupied s orbitals each contain a pair, while the two 2p electrons occupy separate p orbitals with parallel spins.
Nitrogen has seven electrons, with the configuration 1s² 2s² 2p³. Its three 2p electrons occupy all three p orbitals individually. This gives nitrogen three unpaired electrons in its ground state.
Oxygen has eight electrons, with the configuration 1s² 2s² 2p⁴. Three electrons initially occupy separate 2p orbitals. The fourth then pairs with one of them, leaving two unpaired electrons.
These examples illustrate why counting electrons alone is not enough to determine an orbital arrangement. The number of orbitals available in a subshell and their relative energies also matter.
The same principle applies to d subshells, which contain five orbitals. Transition metals often have partially filled d subshells, so Hund’s rule is especially useful when describing their electron configurations and magnetic behavior. The details can be more complicated than in the p subshell because the energies of the subshells and the interactions among electrons can compete.
How Hund’s rule relates to the Aufbau principle and the Pauli exclusion principle
Hund’s rule is easiest to apply when considered alongside two other principles of electron configuration.
The Aufbau principle states that electrons generally occupy available orbitals in order of increasing energy. In a simple introductory model, this means filling orbitals such as 1s before 2s, and 2s before 2p. For larger atoms, the energy ordering becomes more complicated, and some subshells can lie close in energy or change their relative ordering depending on the atom.
The Pauli exclusion principle states that no two electrons in an atom can have the same complete set of four quantum numbers. One consequence is that a single orbital can hold no more than two electrons, and those electrons must have opposite spin projections.
Hund’s rule addresses a different question: when several orbitals have equal energy, how should electrons be distributed among them? It predicts that they generally occupy the orbitals singly with parallel spins before pairing.
Together, these principles provide a practical method for writing many ground-state electron configurations. First, identify the relevant orbitals and their energies. Next, fill the lower-energy orbitals before higher-energy ones. Finally, when electrons enter a group of equal-energy orbitals, place one electron in each orbital with parallel spins before adding pairs.
These rules work well for many atoms, but they do not eliminate every complication. Some elements have electron configurations that differ from simple predictions because the competing subshell energies and electron interactions make another arrangement lower in energy.
Why Hund’s rule matters for magnetism
One important consequence of Hund’s rule is that it helps determine how many unpaired electrons an atom has. Unpaired electrons often play a major role in an element’s magnetic properties.
Electrons possess magnetic moments associated with their spin and orbital motion. In an atom, these contributions combine according to quantum-mechanical rules. When electrons are paired in the same orbital with opposite spins, their spin magnetic moments tend to cancel. Unpaired electrons can leave a net magnetic moment.
Materials containing atoms or ions with unpaired electrons can be paramagnetic, meaning they are attracted to an applied magnetic field. The attraction arises because the magnetic moments tend to align with the external field, although thermal motion opposes this alignment.
By contrast, substances whose electrons are all paired are often diamagnetic, meaning they are weakly repelled by a magnetic field. This distinction is useful but not sufficient to predict every material’s behavior. Molecular structure, bonding, interactions between atoms, and the collective behavior of electrons in solids can all affect magnetism.
Hund’s rule is particularly relevant to many transition-metal atoms and ions because their d subshells can contain several unpaired electrons. The number and arrangement of those electrons help explain why certain metal ions exhibit magnetic behavior and why their magnetic properties can change when they form compounds.
How Hund’s rule influences chemical behavior
Electron configurations affect how atoms form chemical bonds, and Hund’s rule helps determine those configurations. By predicting the distribution of electrons among orbitals, it contributes to our understanding of bonding, reactivity, and the properties of elements.
For example, nitrogen’s three unpaired 2p electrons help explain why it can form three covalent bonds in many common compounds. A covalent bond forms when atoms share electron density. However, the number of unpaired electrons in an isolated atom does not by itself determine the number of bonds it will form. Bonding changes the electronic structure, and the electrons in a molecule occupy molecular orbitals rather than simply retaining their original atomic arrangements.
Transition metals provide another important example. Their partially filled d subshells allow a variety of electron arrangements, oxidation states, and bonding patterns. Hund’s rule helps describe the starting point for understanding these properties, while the surrounding chemical environment determines the actual energies and occupancies of the relevant orbitals.
The rule also contributes to explanations of the periodic table. As electrons are added across a period, they fill subshells in patterns that influence atomic size, ionization energy, magnetic properties, and chemical behavior. Hund’s rule is one part of this larger picture, working alongside orbital energy ordering and electron interactions.
When Hund’s rule has limits
Although Hund’s rule is a powerful guide, it is not a universal instruction to maximize the number of unpaired electrons in every circumstance.
Its simplest form applies to electrons occupying orbitals of equal energy within a subshell. If the orbitals have different energies, electrons may favor the lower-energy orbital even when that means pairing before occupying a higher-energy one.
External magnetic or electric fields can also change the relative energies of orbitals. In molecules and solids, interactions with neighboring atoms, chemical bonding, and the surrounding environment can alter the electronic structure. The simple orbital-filling picture may then need to be replaced by a more detailed quantum-mechanical treatment.
Even among isolated atoms, electron configurations are determined by the total energy of the entire system, including electron–electron interactions. The Aufbau principle, the Pauli exclusion principle, and Hund’s rule provide a useful framework, but accurate predictions for more complicated atoms can require calculations that account for these interactions.
Hund’s rule remains valuable because it captures a common and important pattern in atomic structure: when electrons have several equivalent orbitals available, they generally occupy them separately with parallel spins before pairing. That pattern connects the quantum behavior of individual electrons to observable properties such as magnetism and chemical reactivity.
