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Related Concept Videos

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: 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,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
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...
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Updated: Jun 21, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential

Dipayan Datta1, Debashis Mukherjee

  • 1Department of Physical Chemistry, Indian Association for the Cultivation of Science, Calcutta 700 032, India.

The Journal of Chemical Physics
|August 7, 2009
PubMed
Summary

We developed a new spin-free multireference coupled cluster (CC) method for open-shell systems. This approach accurately calculates state energies for radicals and molecular ions, showing high efficacy compared to other methods and experiments.

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

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Last Updated: Jun 21, 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

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

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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

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of electronic structure for open-shell systems is crucial in chemistry.
  • Existing methods often struggle with the complexity of open-shell electronic configurations.

Purpose of the Study:

  • To present a novel spin-free, state-universal, multireference coupled cluster (CC) formalism.
  • To enable computation of state energies for simple open-shell systems like doublets and biradicals.

Main Methods:

  • Development of a spin-free compact multireference CC formalism.
  • Definition of cluster operators (T(mu), S(e)(mu), S(re)(mu)) based on spin-free unitary generators.
  • Introduction of a new wave operator ansatz with automorphic factors to avoid redundant excitations.

Main Results:

  • The formalism provides a comprehensive account of spin-free cluster operators.
  • The derived CC equations feature direct and normalization terms.
  • Applications to doublet radicals, cations, and ionization energies yielded highly encouraging results.

Conclusions:

  • The developed spin-free multireference CC method is effective for open-shell systems.
  • Results align well with other CC theories, full CI benchmarks, and experimental data.
  • This formalism offers a powerful tool for studying open-shell molecular systems.