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

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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...
VSEPR Theory and the Basic Shapes02:52

VSEPR Theory and the Basic Shapes

Overview of VSEPR Theory
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons on Molecule Geometry

You might also read

Related Articles

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

Sort by
Same author

Sustainable nutrition and the case of vegetable oils to match present and future dietary needs.

Frontiers in public health·2023
Same author

A Need for a Paradigm Shift in Healthy Nutrition Research.

Frontiers in nutrition·2022
Same author

Here, the huge rainbow within the COVID-19 storm.

EClinicalMedicine·2020
Same author

Couplings and recouplings of four angular momenta: Alternative 9j symbols and spin addition diagrams.

Journal of molecular modeling·2017
Same author

Topology driven modeling: the IS metaphor.

Natural computing·2015
Same author

Possible effects of pramipexole on neck muscles in a patient with Parkinson's disease.

Oxford medical case reports·2015
Same journal

Porphyrin Aggregation Revisited: From the Four-Orbital Gouterman Model to an Eight-Orbital Framework in Porphin H-Dimers.

The journal of physical chemistry. A·2026
Same journal

Unraveling the Electronic Origin of Selectivity in Ambimodal Transition States with Valence Bond Theory.

The journal of physical chemistry. A·2026
Same journal

Mechanism and Kinetics of the Initial Oxidative Ring-Opening of Corannulene Radicals under Combustion Conditions.

The journal of physical chemistry. A·2026
Same journal

High-Resolution Absorption Spectroscopy of ND<sub>3</sub> between 59,000 and 93,000 cm<sup>-1</sup>.

The journal of physical chemistry. A·2026
Same journal

Twisted-Driven Photoionization of Aligned Chiral Molecules: Signatures of Circular and Helical Dichroism.

The journal of physical chemistry. A·2026
Same journal

Modeling the Clustering of Fumaric/Maleic Acid with Water and Na<sup>+</sup>, Cl<sup>-</sup> Ions.

The journal of physical chemistry. A·2026
See all related articles

Related Experiment Video

Updated: Jun 18, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

Quantum tetrahedra.

Mauro Carfora1, Annalisa Marzuoli, Mario Rasetti

  • 1Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia and INFN, Sezione di Pavia, via A. Bassi 6, 27100 Pavia, Italy. mauro.carfora@pv.infn.it

The Journal of Physical Chemistry. A
|November 11, 2009
PubMed
Summary
This summary is machine-generated.

The Wigner 6j symbol unifies quantum geometry, topological quantum field theory, statistical models, and quantum computing. It merges its roles as a quantum tetrahedron and computational gate in a novel SU(2)-state sum framework.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy
10:28

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy

Published on: May 27, 2018

Related Experiment Videos

Last Updated: Jun 18, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy
10:28

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy

Published on: May 27, 2018

Area of Science:

  • Theoretical Physics
  • Quantum Information Science
  • Mathematical Physics

Background:

  • The Wigner 6j symbol is a fundamental concept in quantum mechanics, particularly in the theory of angular momentum.
  • Its applications span diverse areas including quantum geometry, topological quantum field theory, and statistical lattice models.
  • A dual nature of the 6j symbol has been observed in quantum field theory and quantum computing, appearing as a quantum tetrahedron and a computational gate.

Purpose of the Study:

  • To explore the unifying role of the Wigner 6j symbol across various scientific disciplines.
  • To demonstrate how the seemingly distinct interpretations of the 6j symbol can be integrated.
  • To present a unified framework that bridges quantum computation and state sum models.

Main Methods:

  • Detailed discussion of the Wigner 6j symbol's properties and applications.
  • Analysis of its manifestation as a quantum tetrahedron in geometric contexts.
  • Investigation of its function as a computational gate in quantum information processing.
  • Development of a unified quantum-computational SU(2)-state sum framework.

Main Results:

  • Established the Wigner 6j symbol as a foundational element connecting disparate scientific fields.
  • Demonstrated the convergence of its geometric (quantum tetrahedron) and computational (gate) roles.
  • Successfully merged these dual aspects within a cohesive SU(2)-state sum model.

Conclusions:

  • The Wigner 6j symbol provides a powerful unifying principle in theoretical and computational physics.
  • A novel quantum-computational SU(2)-state sum framework effectively integrates the symbol's diverse properties.
  • This unified approach offers new perspectives for research in quantum geometry, field theory, and computing.