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Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
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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...
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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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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...
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.

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Updated: Jun 21, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Long-range-corrected hybrid density functionals including random phase approximation correlation: application to

Benjamin G Janesko1, Thomas M Henderson, Gustavo E Scuseria

  • 1Department of Chemistry, Rice University, Houston, Texas 77005, USA. bjanesko@rice.edu

The Journal of Chemical Physics
|July 24, 2009
PubMed
Summary

A new computational method combining short-range density functional approximation with long-range random phase approximation (RPA) accurately predicts noncovalent interactions. This approach offers a computationally tractable model for complex biological systems.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate prediction of noncovalent interactions is crucial in chemistry and biology.
  • Existing methods may lack accuracy or computational efficiency for complex systems.

Purpose of the Study:

  • To evaluate a hybrid computational method for predicting noncovalent interaction energies.
  • To assess the accuracy and efficiency of the method for various types of molecular complexes.

Main Methods:

  • A combination of short-range density functional approximation and long-range random phase approximation (RPA) was employed.
  • Calculations were performed on diverse sets of noncovalent complexes, including hydrogen-bonded and van der Waals interactions.

Main Results:

  • The hybrid method demonstrated highly accurate interaction energy predictions.
  • Statistical errors were found to be comparable to coupled-cluster methods (CCSD(T)) using moderate basis sets.
  • The approach proved effective for hydrogen-bonded, dipole-dipole, charge transfer, and weakly bound complexes.

Conclusions:

  • The developed computational approach shows significant promise for modeling noncovalent interactions.
  • It offers a computationally tractable solution for studying these interactions in biological systems.