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Related Concept Videos

Aromatic Hydrocarbon Cations: Structural Overview01:18

Aromatic Hydrocarbon Cations: Structural Overview

4.3K
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...
4.3K
Aromatic Hydrocarbon Anions: Structural Overview01:18

Aromatic Hydrocarbon Anions: Structural Overview

4.3K
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...
4.3K
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

13.6K
According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
13.6K
VSEPR Theory and the Basic Shapes02:52

VSEPR Theory and the Basic Shapes

87.3K
Overview of VSEPR Theory
87.3K
Conformations of Cycloalkanes02:29

Conformations of Cycloalkanes

16.5K
Adolf von Baeyer attempted to explain the instabilities of small and large cycloalkane rings using the concept of angle strain — the strain caused by the deviation of bond angles from the ideal 109.5° tetrahedral value for sp3  hybridized carbons. However, while cyclopropane and cyclobutane are strained, as expected from their highly compressed bond angles, cyclopentane is more strained than predicted, and cyclohexane is virtually strain-free. Hence, Baeyer’s theory that...
16.5K
π Molecular Orbitals of 1,3-Butadiene01:24

π Molecular Orbitals of 1,3-Butadiene

12.6K
Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...
12.6K

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Related Experiment Video

Updated: Mar 24, 2026

Accessing Valuable Ligand Supports for Transition Metals: A Modified, Intermediate Scale Preparation of 1,2,3,4,5-Pentamethylcyclopentadiene
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Accessing Valuable Ligand Supports for Transition Metals: A Modified, Intermediate Scale Preparation of 1,2,3,4,5-Pentamethylcyclopentadiene

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Tight-binding approach to penta-graphene.

T Stauber1, J I Beltrán1,2,3, J Schliemann4

  • 1Instituto de Ciencia de Materiales de Madrid, CSIC, 28049 Madrid, Spain.

Scientific Reports
|March 5, 2016
PubMed
Summary
This summary is machine-generated.

We developed an effective tight-binding model for penta-graphene, providing an analytical solution. This model accurately predicts optical absorption properties, showing large isotropic absorption from 7.5% to 24% at the Γ-point.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Penta-graphene is a novel 2D carbon allotrope with unique electronic properties.
  • Understanding its electronic band structure and optical properties is crucial for potential applications.

Purpose of the Study:

  • To introduce an effective tight-binding model for penta-graphene.
  • To provide an analytical solution for its electronic structure.
  • To investigate its optical absorption characteristics.

Main Methods:

  • Developed an effective tight-binding model focusing on π-orbitals of sp(2)-hybridized carbon atoms.
  • Incorporated energy-dependent hopping elements, Hubbard onsite interaction, and assisted hopping terms.
  • Derived analytical approximations for eigenfunctions and calculated optical absorption.

Main Results:

  • The model successfully reproduces the two highest valence bands of penta-graphene.
  • Inclusion of additional terms allowed good approximation of the two lowest conduction bands.
  • Calculated large isotropic optical absorption ranging from 7.5% to 24% for transitions at the Γ-point.

Conclusions:

  • The proposed tight-binding model offers an effective and analytical approach to study penta-graphene's electronic and optical properties.
  • Penta-graphene exhibits significant isotropic optical absorption, suggesting potential in optoelectronic devices.