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Related Concept Videos

Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory
Atomic Orbitals02:44

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
Valence Bond Theory and Hybridized Orbitals02:38

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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...
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...
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MO Theory and Covalent Bonding02:40

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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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Related Experiment Video

Updated: Jun 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Extremely localized nonorthogonal orbitals by the pairing theorem.

T Zoboki1, I Mayer

  • 1Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University, Budapest P.O. Box 32, H-1518 Budapest, Hungary.

Journal of Computational Chemistry
|October 14, 2010
PubMed
Summary

A new method calculates localized molecular orbitals using Löwdin pairing. This helps assess bonding models and approximate electron correlation in quantum chemistry.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Accurate molecular orbital calculations are crucial for understanding chemical bonding.
  • Existing methods may struggle to provide strictly localized orbitals for detailed analysis.
  • Approximating electron correlation effects locally remains a challenge in computational chemistry.

Purpose of the Study:

  • To develop a method for calculating nonorthogonal and strictly localized molecular orbitals.
  • To assess the adequacy of molecular bonding models against accurate wave functions.
  • To facilitate local approximations of electron correlation.

Main Methods:

  • Utilizing the principles of the Löwdin pairing theorem.
  • Developing a computational approach to derive localized molecular orbitals.
  • Comparing localized orbitals with Linear Combination of Atomic Orbitals - Molecular Orbital (LCAO-MO) wave functions from Hartree-Fock or DFT.

Main Results:

  • Successfully calculated extremely localized, nonorthogonal molecular orbitals.
  • Demonstrated the method's suitability for evaluating bonding model adequacy.
  • Established a foundation for local electron correlation approximations.

Conclusions:

  • The developed method provides a powerful tool for analyzing molecular electronic structure.
  • It enables a rigorous assessment of simplified bonding concepts.
  • The approach is promising for advancing computational efficiency in electron correlation studies.