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Triangulene

Triangulene is a science 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 Triangulene rather than just read about it. In short: Triangulene (also known as Clar's hydrocarbon) is the smallest triplet-ground-state polybenzenoid. It exists as a biradical with the chemical formula C22H12.

Triangulene — main illustration
Triangulene — illustration

Key takeaways

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

Reference excerpt

Triangulene (also known as Clar's hydrocarbon) is the smallest triplet-ground-state polybenzenoid. It exists as a biradical with the chemical formula C22H12. It was first hypothesized by Czech chemist Erich Clar in 1953. Its first confirmed synthesis was published in a February 2017 issue of Nature Nanotechnology, in a project led by researchers David Fox and Anish Mistry at the University of Warwick in collaboration with IBM. Other attempts by Japanese researchers including Yasushi Morita and Takeji Takui have been successful only in making substituted triangulene derivatives. A six-step synthesis yielded two isomers of dihydrotriangulene which were then deposited on xenon or copper base. The researchers used a combined scanning tunneling and atomic force microscope (STM/AFM) to remove individual hydrogen atoms. The synthesized molecule of triangulene remained stable at high-vacuum low-temperature conditions for four days, giving the scientists plenty of time to characterize it (also using STM/AFM).

[n]Triangulenes Triangulene, as defined here, is a member of a wider class of [n]triangulenes, where n is the number of hexagons along an edge of the molecule. Thus, triangulene may also be referred to as [3]triangulene.

Theory A tight-binding description of the molecular orbitals of [n]triangulenes predicts that [n]triangulenes have (n − 1) unpaired electrons, which are associated to (n − 1) non-bonding states. When electron–electron interactions are included, theory predicts that the ground state total spin quantum number S of [n]triangulenes is S = ⁠n − 1/2⁠. Thus, [3]triangulenes are predicted to have an S = 1 ground state. The intramolecular exchange interaction in triangulene, which determines the energy difference between the S = 1 ground state and the S = 0 excited state, is predicted to be the largest among all polycyclic aromatic hydrocarbon (PAH) diradicals, due to maximum overlap of the wave function of the unpaired electrons. The ground state spin of [n]triangulenes can be rationalized in terms of a theorem by Elliot H. Lieb, which relates, for a bipartite lattice, the ground state spin of the Hubbard model at half filling to the sublattice imbalance.

Experiments So far, the ultra-high vacuum on-surface syntheses of [n]triangulenes with n = 3, 4, 5 and 7 (the hitherto largest triangulene homologue) have been reported. In addition, the on-surface synthesis of [3]triangulene dimers has also been reported, where inelastic electron tunneling spectroscopy provides a direct evidence of a strong antiferromagnetic coupling between the triangulenes. In 2021, an international team of researchers reported the fabrication of [3]triangulene-based quantum spin chains on a gold surface, where signatures of both spin fractionalization and Haldane gap were observed.

References

Illustrations

Triangulene illustration

Worked examples

Example 1 — a first encounter with Triangulene

Start with the simplest possible case. Write down what Triangulene claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Triangulene 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 Triangulene 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 Triangulene

In research
Triangulene appears in science 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 Triangulene 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
Triangulene is common in secondary-school and first-year university syllabi. It links to neighbouring topics Free radicals, Polycyclic aromatic hydrocarbons, Substances discovered in the 2010s, so understanding it makes those chapters shorter.
In everyday life
Look for Triangulene 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 Triangulene in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Triangulene means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Triangulene out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Triangulene in simple terms?

Triangulene (also known as Clar's hydrocarbon) is the smallest triplet-ground-state polybenzenoid. It exists as a biradical with the chemical formula C22H12.

Why does Triangulene matter?

Because it connects several science 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 Triangulene?

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 Triangulene.

Tags

  • Free radicals
  • Polycyclic aromatic hydrocarbons
  • Substances discovered in the 2010s

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