Hund’s Rule

What is Hund’s Rule?

Hund’s Rule of Maximum Multiplicity, most commonly referred to as Hund’s Rule, states that every atomic orbital within a sublevel is singly occupied before it is doubly occupied and that all singly occupied orbitals possess electrons with the same spin. Electrons will always occupy their own suborbital before they pair up with another electron in the same orbital.

This rule is useful when constructing both electron configurations and molecular orbital diagrams.

Hund’s Rule in Action

Correct Usage

The most common mistake made when using Hund’s Rule is doubly pairing electrons before it is necessary. When filling out p orbitals, electrons should not be paired until each suborbital has one electron. Once all orbitals have a single electron, pair them with electrons of opposite spin, again starting from the left. When all electrons are accounted for, the configuration is complete!

Electron Configurations Example: Nitrogen

Let’s look at an example of the Box Electron Diagram for nitrogen:

Nitrogen has 7 electrons, and we know its electron configuration is 1s2 2s2 2p3. The 1s box must fill up before the 2s, and the 2s must fill up before the 2p. After filling up both the 1s and 2s, we have used 4 of our 7 available electrons, with 3 remaining for the 2p orbital.

Now we must apply Hund’s Rule! Electrons will always occupy their own suborbital before they pair up with another electron in the same orbital. Therefore, each electron in the 2p orbital gets its own box, and there is no need for spin pairing. They will also all spin in the same direction.

Electron Configuration Example: Oxygen

Now let’s take a look at the electron box diagram for oxygen. Oxygen’s electron configuration is 1s2 2s2 2p4.

We know it has 8 total electrons, and 6 in its outermost shell. Just as with nitrogen, the 1s and 2s orbitals will be filled, but we need to use Hund’s Rule to fill the 2p orbital correctly. Electrons will always occupy their own suborbital before they pair up with another electron in the same orbital. Therefore, each electron in the 2p orbital gets its own box before any two electrons pair up. However, this time we have four 2p electrons and only three boxes, so we start pairing from the left, leaving the last two orbitals with one electron each.

Electron Configuration example: Chlorine

Now we will put Hund’s Rule to the test on an element with a few more electrons than nitrogen or oxygen.

Once again, we see that the boxes have been filled out according to Hund’s Rule, where each valence electron box receives one electron before any box receives two. As you can see, chlorine needs just one more electron to fill the n=3 shell, making it highly reactive. It wants to steal just one more electron, which it does for example from sodium to form table salt.

Electron Configuration example: Manganese

Mn 1s 2s 2p 3s 4s 3d

Hund’s Rule holds, even for many transition metals such as manganese for which we must access the 3d orbital to construct a box diagram.

In other transition metal compounds, a phenomenon called crystal field splitting causes the d orbitals to have different energies, despite being in the same subshell! This is not usually discussed in depth in general chemistry curriculum, but plays a major role in some physical chemistry and inorganic chemistry courses. In these cases, due to the lower energy of some of d orbitals, it is actually more favorable for them to be completely filled with an electron pair while the other d orbitals still have no electrons. The simple schematic below shows the difference in energy Δ₀ and the unusual filling pattern that results.

File:CFT-Low Spin Splitting Diagram-Vector.svg — Molecular orbital diagram. This low spin configuration appears to defy Hund’s Rule, because of a difference in energy (Δ₀) between the orbitals within the 3d subshell. (Public Domain image from Wikimedia Commons)

Why Does Hund’s Rule Hold?

All electrons have a negative charge, and like charges repel each other. Electrons seek to minimize this repulsion, so they will always want to occupy their orbital where there is no other electron to repel it rather than share an orbital with another electron.

The reason why all unpaired spins must align in the same direction stems from the nature of spin. Spins interact with each other such that two parallel spins have lower energy than two opposite spins. This means that if you put two electrons in neighboring orbitals and orient one up and the other down, this will be higher in energy, and therefore not the ground state of the atom.

Discovering the Rule

German physicist Friedrich Hund formulated this rule in 1927. At the time, Hund was a lecturer at the University of Rostock. Around this time he also discovered the foundations of Molecular Orbital Theory and the phenomenon of quantum tunneling.

Importance for Understanding Elements and Materials

During most reactions between atoms, the first interactions occur between the valence electrons of the given atoms. The most stable atoms have complete electron shells, such as noble gases. In a box diagram, they will have every box doubly filled. The most reactive atoms have incomplete valence shells. It is these unpaired valence electrons that determine the chemistry and reactivity of the atom. Some properties are also determined by the completeness of the valence electron shell, such as the color of light given off by the element when an electron is excited to a higher energy level and then returns to its normal (ground state) energy level.

Magnetism

One of the most important consequences of Hund’s rule is the existence of magnetic elements. We call an element with unpaired electrons “paramagnetic” because the unpaired electrons’ spin can interact and align with a magnetic field. Elements with only paired electrons, on the other hand, have no net spin, because all the electron spins cancel each other out. These elements will not interact with a magnetic field, and they are called “diamagnetic.”

These examples make it clear that Hund’s Rule is crucial to understanding the chemical and physical properties of elements!