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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.
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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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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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In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
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Published on: September 2, 2016

"In Situ" Orbital Correlations.

Xuhui Lin1, Huaiyu Zhang2, Changwei Wang3

  • 1Hunan Key Laboratory of Super Microstructure and Ultrafast Process, School of Physics, Central South University, Changsha, Hunan 410083, China.

Accounts of Chemical Research
|June 12, 2026
PubMed
Summary
This summary is machine-generated.

Introducing "in situ" orbital correlation, this study reveals how physical interactions, not just chemical ones, shift molecular orbital energies. This novel approach enhances understanding of chemical reactions and bonding by considering environmental effects on orbital levels.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Chemical Bonding Theory

Background:

  • Traditional orbital correlation diagrams use isolated reactant orbital energies, failing to account for physical interactions.
  • Orbital energy levels are significantly affected by external fields and neighboring molecules, leading to reshuffling.
  • Existing models struggle to explain reactions where frontier molecular orbitals (MOs) alone are insufficient.

Purpose of the Study:

  • To introduce and demonstrate the application of a novel concept: "in situ" orbital correlation.
  • To account for physical effects (electrostatic, Pauli repulsion, van der Waals) on orbital energies during chemical interactions.
  • To provide a more accurate method for understanding chemical reactions, electron transfer, and molecular bonding.

Main Methods:

  • Utilized the block-localized wave function (BLW) method, a variant of ab initio valence bond (VB) theory.
  • BLW self-consistently derives orbital energies in the presence of other species or external fields.
  • Applied "in situ" orbital correlation to analyze CO activation by diboryne, NCCL- anions, and Al-Mg bonding.

Main Results:

  • Demonstrated HOMO-LUMO swaps in B2(NHCR)2 upon CO approach due to Pauli repulsion, enabling orbital compatibility.
  • Revealed orbital swaps in NCC- fragments upon ligand approach, confirming C(0) theory for NCCL- anions.
  • Showed the Al-Mg bond is ionic, not dative covalent, by observing significant HOMO energy decrease and band gap extension upon Mg compound approach.

Conclusions:

  • "In situ" orbital correlation accurately models orbital energy shifts caused by physical interactions.
  • This method provides deeper insights into reaction mechanisms, electron transfer pathways, and bonding nature.
  • The concept fundamentally enriches the understanding of chemical phenomena beyond traditional frontier molecular orbital theory.