Related Experiment Video
Updated: May 19, 2026

08:03
Advanced Self-Healing Asphalt Reinforced by Graphene Structures: An Atomistic Insight
Published on: May 31, 2022
From aromaticity to self-organized criticality in graphene
Dmitry Yu Zubarev1, Michael Frenklach, William A Lester
1Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720-1460, USA.
Physical Chemistry Chemical Physics : PCCP
|August 9, 2012
Summary
Graphene
Area of Science:
- Condensed matter physics
- Materials science
- Quantum chemistry
Background:
- Graphene's unique properties stem from its electronic structure, particularly electron delocalization.
- Traditional models of aromatic bonding may not fully capture graphene's delocalization.
- Understanding delocalization is key to controlling graphene's observable properties.
Purpose of the Study:
- To expand the understanding of electron delocalization in graphene.
- To investigate the relationship between electronic structure modifications and physical responses.
- To identify novel bonding mechanisms in finite-size graphene systems.
Main Methods:
- Computational modeling of graphene's π-electron system.
- Analysis of interatomic distance relaxation.
- Investigation of scale-invariant responses and self-organized criticality.
Main Results:
- Graphene exhibits a scale-invariant response in interatomic distance relaxation upon π-electron system modification.
- Self-organized criticality is identified as a mechanism for delocalized bonding in graphene.
- Graphene belongs to a class of systems where complexity emerges from simple local interactions.
Conclusions:
- The traditional view of delocalization in graphene requires expansion beyond aromatic bonding frameworks.
- Self-organized criticality offers a new perspective on delocalized bonding in graphene.
- Emergent complexity in graphene influences its chemical activity, electron transport, and spin-polarization.
Related Concept Videos
Aromatic Hydrocarbon Cations: Structural Overview
Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
Removing one hydrogen from the intervening CH2 group with both...
Removing one hydrogen from the intervening CH2 group with both...
Aromatic Hydrocarbon Anions: Structural Overview
Neutral hydrocarbons like cyclopentadiene with an odd number of carbon atoms and one intervening CH2 group in the ring are not aromatic. Cyclopentadiene with 4 π electrons does not satisfy the 4n + 2 π electron rule. Additionally, the intervening CH2 group is sp3 hybridized and lacks a vacant p orbital, thereby interrupting the overlap of p orbitals in a continuous manner and preventing the delocalization of π electrons throughout the ring.
Due to the absence of continuous overlap of p...
Due to the absence of continuous overlap of p...
π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds
In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as annulenes. In...
Frost Circles for Different Conjugated Systems
The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
Criteria for Aromaticity and the Hückel 4n + 2 Rule
Like benzene, cyclobutadiene and cyclooctatetraene are cyclic compounds with alternate single and double bonds. However, their chemical behavior differs from benzene, as they are unstable and not aromatic. So, what are the structural characteristics of unsaturated compounds categorized as aromatic?
For the first time, Eric Hückel, a German chemical physicist, derived a set of structural features for a compound to be classified as aromatic. This is now known as Hückel’s rule or the 4n + 2 rule.
For the first time, Eric Hückel, a German chemical physicist, derived a set of structural features for a compound to be classified as aromatic. This is now known as Hückel’s rule or the 4n + 2 rule.
Five-Membered Heterocyclic Aromatic Compounds: Overview
Heterocyclic aromatic compounds are cyclic compounds that are aromatic and have one or more heteroatoms—atoms other than carbon, in the ring. Depending upon the number of atoms present in the ring, they can be either five or six-membered. Examples of five-membered heterocyclic aromatic compounds include pyrrole, furan, thiophene, and imidazole. Pyrrole consists of one nitrogen atom having one lone pair of electrons. Furan and thiophene have one oxygen and one sulfur heteroatom, respectively.

