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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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Continuous Localized Orbital Corrections to Density Functional Theory: B3LYP-CLOC.

Michelle Lynn Hall1, Jing Zhang, Arteum D Bochevarov

  • 1Department of Chemistry, Columbia University, 3000 Broadway, New York, NY, 10027.

Journal of Chemical Theory and Computation
|February 3, 2011
PubMed
Summary

This study introduces continuous localized orbital corrections (CLOCs) to improve Density Functional Theory (DFT) reaction coordinate accuracy. The new DFT-CLOC method offers highly accurate reaction pathways with minimal computational cost.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Localized Orbital Correction (LOC) methodology enhances thermochemical property accuracy at Density Functional Theory (DFT) stationary points.
  • Extending corrections from stationary points to the entire reaction coordinate (RC) is crucial for accurate chemical process modeling.

Purpose of the Study:

  • To develop and validate continuous localized orbital corrections (CLOCs) for DFT reaction coordinates.
  • To assess the accuracy and computational efficiency of the new DFT-CLOC method across diverse reaction types.

Main Methods:

  • Development of the continuous localized orbital corrections (CLOCs) methodology.
  • Application of DFT-CLOC to various post-Hartree-Fock (post-HF) reaction coordinate profiles.
  • Testing robustness across sigmatropic shifts, Diels-Alder reactions, electrocyclizations, and radical reactions.

Main Results:

  • The DFT-CLOC method significantly improves the accuracy of reaction coordinates compared to uncorrected DFT.
  • The computational cost of DFT-CLOC is only marginally higher than standard DFT calculations.
  • The method demonstrates robustness across a wide range of chemical reaction types.

Conclusions:

  • Continuous localized orbital corrections (CLOCs) provide a computationally efficient and accurate approach for modeling entire reaction coordinates.
  • DFT-CLOC offers a significant advancement for theoretical studies of chemical reactions.