physics

Hund's rule of maximum multiplicity

Hund's rule of maximum multiplicity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hund's rule of maximum multiplicity rather than just read about it. In short: Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that in a subshell of an atom, electrons are first singly filled with same spin before they are filled doubly.

Key takeaways

Hund's rule of maximum multiplicity belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hund's rule of maximum multiplicity to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hund's rule of maximum multiplicity from memory before moving on to harder problems.

Reference excerpt

Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that in a subshell of an atom, electrons are first singly filled with same spin before they are filled doubly. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.

Atoms The multiplicity of a state is defined as 2S + 1, where S is the total electronic spin. A high multiplicity state is therefore the same as a high-spin state. The lowest-energy state with maximum multiplicity usually has unpaired electrons all with parallel spin. Since the spin of each electron is 1/2, the total spin is one-half the number of unpaired electrons, and the multiplicity is the number of unpaired electrons + 1. For example, the nitrogen atom ground state has three unpaired electrons of parallel spin, so that the total spin is 3/2 and the multiplicity is 4. The lower energy and increased stability of the atom arise because the high-spin state has unpaired electrons of parallel spin, which must reside in different spatial orbitals according to the Pauli exclusion principle. An early but incorrect explanation of the lower energy of high multiplicity states was that the different occupied spatial orbitals create a larger average distance between electrons, reducing electron-electron repulsion energy. However, quantum-mechanical calculations with accurate wave functions since the 1970s have shown that the actual physical reason for the increased stability is a decrease in the screening of electron-nuclear attractions, so that the unpaired electrons can approach the nucleus more closely and the electron-nuclear attraction is increased. As a result of Hund's rule, constraints are placed on the way atomic orbitals are filled in the ground state using the Aufbau principle. Before any two electrons occupy an orbital in a subshell, other orbitals in the same subshell must first each contain one electron. Also, the electrons filling a subshell will have parallel spin before the shell starts filling up with the opposite spin electrons (after the first orbital gains a second electron). As a result, when filling up atomic orbitals, the maximum number of unpaired electrons (and hence maximum total spin state) is assured. For example, in the oxygen atom, the 2p4 subshell arranges its electrons as [↑↓] [↑] [↑] rather than [↑↓] [↑] [↓] or [↑↓] [↑↓][ ]. The manganese (Mn) atom has a 3d5 electron configuration with five unpaired electrons all of parallel spin, corresponding to a 6S ground state. The superscript 6 is the value of the multiplicity, corresponding to five unpaired electrons with parallel spin in accordance with Hund's rule. An atom can have a ground state with two incompletely filled subshells which are close in energy. The lightest example is the chromium (Cr) atom with a 3d54s electron configuration. Here there are six unpaired electrons all of parallel spin for a 7S ground state.

Molecules Although most stable molecules have closed electron shells, a few have unpaired electrons for which Hund's rule is applicable. The most important example is the dioxygen molecule, O2, which has two degenerate pi antibonding molecular orbitals (π*) occupied by only two electrons. In accordance with Hund's rule, the ground state is triplet oxygen with two unpaired electrons in singly occupied orbitals. The singlet oxygen state with one doubly occupied and one empty π* is an excited state with different chemical properties and greater reactivity than the ground state.

Exceptions In 2004, researchers reported the synthesis of 5-dehydro-m-xylylene (DMX), the first organic molecule known to violate Hund's rule. Local non-Hund configurations have been assigned to 4d and 5d metals participating in metal-metal bonding that overcomes the local exchange interaction, such as in the FeMo-cofactor of nitrogenase and synthetic models thereof.

See also Hund's rules (includes this plus 2 other rules) High spin metal complexes

References

External links A glossary entry hosted on the web site of the Chemistry Department of Purdue University

Worked examples

Example 1 — a first encounter with Hund's rule of maximum multiplicity

Start with the simplest possible case. Write down what Hund's rule of maximum multiplicity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hund's rule of maximum multiplicity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hund's rule of maximum multiplicity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hund's rule of maximum multiplicity

In research: Hund's rule of maximum multiplicity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hund's rule of maximum multiplicity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hund's rule of maximum multiplicity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum chemistry, Rules, so understanding it makes those chapters shorter.
In everyday life: Look for Hund's rule of maximum multiplicity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hund's rule of maximum multiplicity in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hund's rule of maximum multiplicity means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hund's rule of maximum multiplicity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hund's rule of maximum multiplicity in simple terms?

Why does Hund's rule of maximum multiplicity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hund's rule of maximum multiplicity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hund's rule of maximum multiplicity.