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Related Concept Videos

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...
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.
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.
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
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...

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Updated: May 29, 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

Long-range-corrected hybrids using a range-separated Perdew-Burke-Ernzerhof functional and random phase approximation

Robert M Irelan1, Thomas M Henderson, Gustavo E Scuseria

  • 1Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA.

The Journal of Chemical Physics
|September 15, 2011
PubMed
Summary

This study enhances computational chemistry methods by replacing local density approximation with generalized gradient approximation functionals. This improves thermodynamic predictions while maintaining accuracy for van der Waals interactions.

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Last Updated: May 29, 2026

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Existing methods combine short-range density functional approximation (DFA) with long-range random phase approximation (RPA) or second-order screened exchange.
  • These methods have shown excellent performance for van der Waals interactions.

Purpose of the Study:

  • To improve the accuracy of thermodynamic property predictions in quantum chemistry calculations.
  • To develop enhanced hybrid methods for electronic structure calculations.

Main Methods:

  • Replacing the short-range local density approximation (LDA) functional with a range-separated generalized gradient approximation (GGA) functional.
  • Combining the modified short-range GGA with long-range RPA or second-order screened exchange.

Main Results:

  • The new GGA-based methods show marked improvement in thermodynamic tests compared to LDA-based methods.
  • The enhanced methods retain the excellent performance for van der Waals interactions.

Conclusions:

  • The developed range-separated GGA methods offer a significant advancement over previous LDA-based approaches.
  • These improved methods provide more accurate predictions for chemical systems, particularly regarding thermodynamics.