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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...
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...
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.
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

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 first.
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

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Related Experiment Video

Updated: Jul 3, 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

Single-reference coupled-cluster theory based on the multi-purpose cluster operator.

Karol Kowalski1,2, Nicholas P Bauman1

  • 1Pacific Northwest National Laboratory, Physical Sciences Division, Richland, Washington 99354, USA.

The Journal of Chemical Physics
|July 2, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new theoretical framework for coupled-cluster (CC) theory, enabling the simultaneous description of multiple electronic states. This advanced method enhances quantum simulations for ground and excited states.

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Last Updated: Jul 3, 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

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

Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • Single-reference coupled-cluster (SR-CC) theory conventionally describes one electronic state.
  • Limitations exist in SR-CC for describing multiple states or states with different symmetries.

Purpose of the Study:

  • To develop a generalized theoretical framework for SR-CC.
  • To extend SR-CC capabilities beyond single-state description.
  • To enable concurrent representation of multiple electronic states.

Main Methods:

  • Developed a generalized SR-CC cluster operator construction.
  • Introduced new SR-CC downfolding formalisms.
  • Established three formal theorems for the extended framework.
  • Proposed a Hermitian variant based on unitary CC representation.

Main Results:

  • The framework allows different cluster operator components to encode states of varying symmetry.
  • The developed formalisms concurrently represent multiple non-orthogonal correlated states.
  • Standard CC downfolding is shown to be a special case of the new framework.
  • A Hermitian variant enables realistic simulations with reduced quantum resources.

Conclusions:

  • The generalized SR-CC framework significantly expands the applicability of CC theory.
  • The new methods facilitate more accurate and efficient quantum simulations of complex electronic systems.
  • This work paves the way for advanced computational studies of ground and excited states.