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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
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.
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...
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...
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...

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Related Experiment Video

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

Explicitly correlated combined coupled-cluster and perturbation methods.

Toru Shiozaki1, Edward F Valeev, So Hirata

  • 1Quantum Theory Project and the Center for Macromolecular Science and Engineering, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA.

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

Coupled-cluster methods incorporating interelectronic distances (R12) accelerate convergence of correlation energies. These R12-based techniques rapidly approach complete basis set limits for molecular properties.

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Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

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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

Published on: January 9, 2014

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Coupled-cluster methods like CCSD and CCSDT are essential for accurate electronic structure calculations.
  • Basis set convergence is a significant challenge in achieving high accuracy in correlated electronic structure calculations.
  • Explicitly correlated methods (R12/F12) incorporate interelectronic distances to accelerate convergence.

Purpose of the Study:

  • To extend coupled-cluster methods (CCSD, CCSDT) with perturbation corrections to include R12 functions.
  • To accelerate the basis-set convergence of correlation energies in quantum chemical calculations.
  • To investigate the performance of these new R12-based methods for molecular properties.

Main Methods:

  • Development and application of R12/F12 schemes within CCSD and CCSDT frameworks.
  • Inclusion of perturbation corrections for triples and quadruples (e.g., CCSD(2)(T)-R12, CCSDT(2)(Q)-R12).
  • Application to dissociation of HF and double dissociation of H2O to test basis-set convergence.

Main Results:

  • R12-based methods demonstrate dramatically accelerated basis-set convergence of correlation energies.
  • Molecular properties converge rapidly to complete basis set limits with respect to excitation rank and perturbation order.
  • While R12 does not improve convergence for triples/quadruples, their errors become comparable to singles and doubles contributions.

Conclusions:

  • R12-based coupled-cluster methods offer a significant pathway to achieve high accuracy with smaller basis sets.
  • These methods provide reliable predictions of molecular properties, rapidly approaching the exact limit.
  • The R12 scheme effectively mitigates basis-set truncation errors in correlated calculations.