physics

HOMO and LUMO

HOMO and LUMO 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 HOMO and LUMO rather than just read about it. In short: In chemistry, HOMO and LUMO are types of molecular orbitals described at absolute zero. The acronyms stand for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively.

Key takeaways

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

Reference excerpt

In chemistry, HOMO and LUMO are types of molecular orbitals described at absolute zero. The acronyms stand for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. HOMO and LUMO are sometimes collectively called the frontier orbitals, such as in the frontier molecular orbital theory.

Gap The energy difference between the HOMO and LUMO is the HOMO–LUMO gap. Its size can be used to predict the strength and stability of transition metal complexes, as well as the colors they produce in solution. As a rule of thumb, the smaller a compound's HOMO–LUMO gap, the less stable the compound.

Semiconductors The HOMO level is to organic semiconductors roughly what the maximum valence band is to inorganic semiconductors and quantum dots. The same analogy can be made between the LUMO level and the conduction band minimum.

Organometallic chemistry In organometallic chemistry, the size of the LUMO lobe can help predict where addition to pi ligands will occur.

SOMO A SOMO is a singly occupied molecular orbital such as half-filled HOMO of a radical. This abbreviation may also be extended to semi occupied molecular orbital.

Subadjacent orbitals: NHOMO and SLUMO If existent, the molecular orbitals at one energy level below the HOMO and one energy level above the LUMO are also found to play a role in frontier molecular orbital theory. They are named NHOMO for next-to-highest occupied molecular orbital and SLUMO for second lowest unoccupied molecular orbital. These are also commonly referred to as HOMO−1 and LUMO+1 respectively.

See also Diels–Alder reaction Electron configuration Klopman–Salem equation Koopmans' theorem Ligand Woodward–Hoffmann rules Band gap

References

Further reading Fleming, Ian (2010). Molecular Orbitals and Organic Chemical Reactions. doi:10.1002/9780470689493. ISBN 978-0-470-74658-5.

External links OrbiMol Molecular orbital database

Illustrations

Worked examples

Example 1 — a first encounter with HOMO and LUMO

Start with the simplest possible case. Write down what HOMO and LUMO 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 HOMO and LUMO 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 HOMO and LUMO 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 HOMO and LUMO

In research: HOMO and LUMO 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 HOMO and LUMO 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: HOMO and LUMO is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum chemistry, Quantum chemistry stubs, so understanding it makes those chapters shorter.
In everyday life: Look for HOMO and LUMO 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 HOMO and LUMO in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what HOMO and LUMO 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 HOMO and LUMO out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is HOMO and LUMO in simple terms?

Why does HOMO and LUMO 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 HOMO and LUMO?

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 HOMO and LUMO.