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

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

2.0K
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
2.0K
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.9K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
2.9K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.6K
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
1.6K
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

2.2K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
2.2K
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

14.8K
The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
14.8K
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

49.4K
Overview of Molecular Orbital Theory
49.4K

You might also read

Related Articles

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

Sort by
Same author

Differences in the Impact of Obesity and Bariatric Surgery on Patients Hospitalized for Atrial Flutter and Atrial Fibrillation: A Nationwide Analysis, 2016-2020.

Cureus·2024
Same author

7-Chloro-11a-phenyl-2,3,5,10,11,11a-hexa-hydro-1H-pyrrolo[2,1-c][1,4]benzodiazepine-5,11-dione.

Acta crystallographica. Section E, Structure reports online·2011
Same author

Tensor product approximation with optimal rank in quantum chemistry.

The Journal of chemical physics·2007
Same author

1,2,5-Substituted derivatives of 2-phenylpyrrolidine.

Acta crystallographica. Section C, Crystal structure communications·2004

Related Experiment Video

Updated: Apr 9, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.8K

Singular analysis and coupled cluster theory.

Heinz-Jürgen Flad1, Gohar Harutyunyan2, Bert-Wolfgang Schulze3

  • 1Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, D-85747 Garching, Germany. flad@ma.tum.de.

Physical Chemistry Chemical Physics : PCCP
|June 23, 2015
PubMed
Summary

This study introduces singular analysis and a novel method to approximate Hamiltonians in electronic structure simulations. The research provides an explicit formula for the Green operator, improving accuracy in quantum chemistry calculations.

More Related Videos

Synthesis and Characterization of Supramolecular Colloids
09:26

Synthesis and Characterization of Supramolecular Colloids

Published on: April 22, 2016

10.6K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.1K

Related Experiment Videos

Last Updated: Apr 9, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.8K
Synthesis and Characterization of Supramolecular Colloids
09:26

Synthesis and Characterization of Supramolecular Colloids

Published on: April 22, 2016

10.6K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.1K

Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Mathematical Physics

Background:

  • Accurate derivation of molecular and solid properties requires understanding many-particle Coulomb systems near particle coalescence.
  • Singular analysis offers a framework for studying wavefunction behavior near these singularities.

Purpose of the Study:

  • Introduce the mathematical framework of singular analysis.
  • Present a novel asymptotic parametrix construction for Hamiltonians in many-particle Coulomb systems.
  • Derive an explicit asymptotic formula for the Green operator.

Main Methods:

  • Employ singular analysis to study asymptotic behavior.
  • Construct an approximate inverse (parametrix) for Hamiltonian operators.
  • Analyze the Green operator encoding essential asymptotic information.

Main Results:

  • Developed a novel asymptotic parametrix construction for many-particle Coulomb systems.
  • Derived an explicit asymptotic formula for the Green operator.
  • Demonstrated feasibility through applications to quantum chemistry models, focusing on ladder diagrams.

Conclusions:

  • The developed approach provides an explicit asymptotic formula for the Green operator.
  • The method enhances accuracy in first principles electronic structure simulations.
  • Potential implications for adaptive wavelet approximations in quantum chemistry are discussed.