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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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

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

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...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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...

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Updated: Jul 1, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Connection between GW and Extended Coupled Cluster.

Johannes Tölle1,2, Marios-Petros Kitsaras3, Andreas Irmler4

  • 1Department of Chemistry, University of Hamburg, Hamburg 22761, Germany.

Journal of Chemical Theory and Computation
|June 29, 2026
PubMed
Summary
This summary is machine-generated.

Coupled-cluster (CC) theory and Green's function methods are unified by the extended CC (ECC) ansatz. This framework connects electronic correlation theories, enabling systematic improvements for Green's function approaches.

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Analysis of Complex Molecules and Their Reactions on Surfaces by Means of Cluster-Induced Desorption/Ionization Mass Spectrometry

Published on: March 1, 2020

Area of Science:

  • Quantum chemistry
  • Theoretical physics
  • Computational chemistry

Background:

  • Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) are distinct frameworks for electronic correlation.
  • CC methods use exponential wave function parametrizations for size extensivity.
  • Green's function methods like GW approximation describe excitations via diagrammatic resummations.

Purpose of the Study:

  • Establish a formal correspondence between CC and Green's function theories.
  • Introduce the extended CC (ECC) ansatz as a unified framework.
  • Explore novel avenues for incorporating vertex corrections within CC.

Main Methods:

  • Formal analysis establishing the equivalence between GW approximation and equation-of-motion (EOM) treatment of direct-ring CC doubles (drCCD).
  • Development and application of the extended CC (ECC) ansatz.
  • Investigation of Green's function properties within the ECC framework.

Main Results:

  • Demonstrated formal equivalence between the GW approximation and EOM-drCCD.
  • The ECC ansatz provides a unified framework connecting CC and MBPT.
  • ECC facilitates the incorporation of vertex corrections into CC theory.

Conclusions:

  • The ECC ansatz bridges CC and Green's function methods.
  • This unified framework offers systematic improvability for Green's function approaches.
  • ECC preserves a sum-over-state representation of the self-energy.