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Related Concept Videos

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.
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Distance Corrections01:15

Distance Corrections

To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
Hybridization of Atomic Orbitals I03:24

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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...
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
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Related Experiment Video

Updated: Jun 25, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Long-range-corrected hybrids including random phase approximation correlation.

Benjamin G Janesko1, Thomas M Henderson, Gustavo E Scuseria

  • 1Department of Chemistry, Rice University, Houston, Texas 77005, USA.

The Journal of Chemical Physics
|March 5, 2009
PubMed
Summary

We developed a new method to incorporate long-range random phase approximation (RPA) correlations into density functional theory. This approach accurately models van der Waals interactions and yields good thermochemical results.

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Last Updated: Jun 25, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • A link between random phase approximation (RPA) and coupled cluster theory was recently established.
  • Density functional theory (DFT) is a widely used method in computational chemistry.
  • Accurate modeling of long-range correlation and van der Waals interactions remains a challenge for DFT.

Purpose of the Study:

  • To propose and test a straightforward scheme for integrating long-range RPA correlation into DFT.
  • To improve the accuracy of DFT for systems dominated by van der Waals forces.
  • To provide a computationally feasible method for obtaining reliable thermochemical data.

Main Methods:

  • Building upon the established connection between RPA and coupled cluster theory.
  • Developing a practical method to introduce RPA correlation effects into DFT calculations.
  • Testing the proposed scheme against established theoretical benchmarks.

Main Results:

  • The proposed method successfully incorporates long-range RPA correlation into DFT.
  • The scheme yields accurate thermochemical results for various chemical systems.
  • Van der Waals interactions are modeled with high accuracy using this approach.

Conclusions:

  • The new DFT scheme effectively captures long-range correlation effects.
  • This method offers a significant improvement for modeling van der Waals interactions within DFT.
  • The approach provides a reliable and accurate tool for computational chemistry research.