Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

VSEPR Theory and the Basic Shapes02:52

VSEPR Theory and the Basic Shapes

62.0K
Overview of VSEPR Theory
62.0K
Exceptions to the Octet Rule02:55

Exceptions to the Octet Rule

31.3K
Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:
31.3K
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

51.6K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
51.6K
VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

40.1K
Effect of Lone Pairs of Electrons on Molecule Geometry
40.1K
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

21.6K
Molecular Orbital Energy Diagrams
21.6K
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

11.4K
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).
11.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Size-dependent superhalogenicity and ring currents of tantalum doped platinum clusters TaPt <sub><i>n</i>-1</sub> <sup>-/0</sup> (<i>n</i> = 2-21).

RSC advances·2026
Same author

NaMgX<sub>3</sub> (X = Cl, Br) for solid electrolyte interphases: atomistic insights into defects, surfaces and doping strategies.

Physical chemistry chemical physics : PCCP·2026
Same author

From Aromatic to Antiaromatic: Charge-Induced Electronic Transformation and Unexpected Stability of B<sub>24</sub>Ni<sub>3</sub><sup></sup>.

The journal of physical chemistry. A·2026
Same author

Isovalent effects on the structural and electronic features of scandium-doped aluminum clusters Sc <sub><i>m</i></sub> Al <sub><i>n</i>-<i>m</i></sub> <sup>+/0/-</sup> with <i>m</i> = 1-2, <i>n</i> = 3-15.

RSC advances·2026
Same author

Composite A<sub>2</sub>M<sub>6</sub>O<sub>13</sub> anodes (A = Li, Na; M = Ti, Zr) for Li-Na dual cation batteries: a theoretical investigation.

RSC advances·2026
Same author

Benchmarking the Ligand-HER2 Interactions Using Machine Learning and Molecular Dynamics Simulations.

ACS omega·2026

Related Experiment Video

Updated: Apr 26, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

7.1K

Quantum rules for planar boron nanoclusters.

Athanasios G Arvanitidis1, Truong Ba Tai, Minh Tho Nguyen

  • 1Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium. athanasios.arvanitidis@chem.kuleuven.be arnout.ceulemans@chem.kuleuven.be.

Physical Chemistry Chemical Physics : PCCP
|July 26, 2014
PubMed
Summary
This summary is machine-generated.

Free particle models reveal quantum bonding rules for planar boron clusters. These rules distinguish between precise in-plane bonding and delocalized out-of-plane bonding, confirmed by DFT calculations.

More Related Videos

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

9.4K
Optimized Fabrication Procedure for High-Quality Graphene-based Moir&#233; Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.8K

Related Experiment Videos

Last Updated: Apr 26, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

7.1K
Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

9.4K
Optimized Fabrication Procedure for High-Quality Graphene-based Moir&#233; Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.8K

Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Planar boron clusters exhibit unique electronic properties.
  • Understanding their bonding is crucial for predicting stability and reactivity.

Purpose of the Study:

  • To derive quantum rules for planar boron clusters using free particle models.
  • To compare these rules with Density Functional Theory (DFT) calculations.
  • To elucidate the nature of in-plane and out-of-plane bonding.

Main Methods:

  • Application of free particle models for quantum rule derivation.
  • Comparison with electronic structure calculations using the DFT method.
  • Analysis of bonding characteristics for clusters with 7-20 boron atoms.

Main Results:

  • Separate quantum rules were established for in-plane and out-of-plane bonding.
  • In-plane bonding shows precise boundary localization and internal 3-center-2-electron (3c-2e) triangular networks.
  • Out-of-plane bonding is highly delocalized, dependent on cluster size and shape.

Conclusions:

  • Free particle models provide a viable method for obtaining quantum bonding rules in boron clusters.
  • The derived rules offer insights into the distinct bonding mechanisms governing planar boron nanostructures.
  • The findings contribute to a deeper understanding of boron cluster chemistry and potential applications.