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MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

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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...
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Molecular Orbital Theory II03:51

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Valence Bond Theory02:45

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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...
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Molecular Orbital Theory I02:35

Molecular Orbital Theory I

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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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Related Experiment Video

Updated: Sep 21, 2025

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding
06:44

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding

Published on: March 24, 2018

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Orbital contraction and covalent bonding.

George B Bacskay1

  • 1School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia.

The Journal of Chemical Physics
|June 1, 2022
PubMed
Summary

Orbital contraction, a key aspect of covalent bonding, is quantified using a novel modified atomic orbital (MAO) method. This approach reveals increased kinetic energy within fragments upon bond formation, indicating orbital contraction and deformation in various molecules.

Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Chemical Bonding Theory

Background:

  • Orbital contraction is a fundamental concept in covalent bonding theory, as established by Ruedenberg.
  • Quantifying orbital contraction in molecules beyond simple systems like H2+ and H2 presents computational challenges.
  • Existing methods struggle to precisely measure the effects of bonding on atomic orbitals.

Purpose of the Study:

  • To develop a straightforward method for quantifying orbital contraction in chemical bonds.
  • To apply the modified atomic orbital (MAO) method for calculating kinetic energy changes associated with bonding.
  • To investigate orbital contraction effects across a diverse range of diatomic, polyatomic, and ionic molecules.

Main Methods:

  • Utilized the modified atomic orbital (MAO) method, an atom-centered minimal basis derived from density operators.

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Last Updated: Sep 21, 2025

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  • Re-expanded wave functions using MAOs to enable computation of kinetic energy for free and bonded fragments.
  • Calculated intra- and interfragment kinetic energy changes to quantify orbital contraction and deformation.

    • Main Results:

    • Demonstrated that covalent bond formation consistently leads to an increase in intra-fragment kinetic energy.
    • Observed this kinetic energy increase across numerous diatomic molecules (e.g., H2, N2, O2, Cl2) and polyatomics (e.g., ethane, methanol).
    • Confirmed orbital contraction and/or deformation as a universal consequence of covalent bond formation, also observed in ionic molecules like NaCl.

    Conclusions:

    • The MAO method provides a robust and simple approach to quantifying orbital contraction.
    • Increased intra-fragment kinetic energy is a reliable indicator of orbital contraction and deformation during chemical bonding.
    • This study offers a new computational tool for understanding the fundamental nature of chemical bonds.