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Radicals, the highly reactive species, gain stability by undergoing three different reactions. The first reaction involves a radical-radical coupling, in which a radical combines with another radical, forming a spin‐paired molecule. The second reaction is between a radical and a spin‐paired molecule, generating a new radical and a new spin‐paired molecule. The third reaction is radical decomposition in a unimolecular reaction, forming a new radical and a spin‐paired...
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The presence of electron-donating, electron-withdrawing, or conjugating groups adjacent to a radical center, imparts electronic stabilization to the radicals. Examples of such electronically-stabilized radicals are triphenylmethyl, tetramethylpiperidine‐N‐oxide, and 2,2‐diphenyl‐1‐picrylhydrazyl. These radicals are remarkably stable and are known as persistent radicals. Some of the persistent radicals can even be isolated and purified.
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Chemical reactivity from linear response eigenfunctions and eigenvalues.

Rémi Grincourt1, Guillaume Hoffmann1, Frédéric Guégan2

  • 1Université Claude Bernard Lyon 1, UMR 5280 CNRS, 5 rue de la Doua, 69100 VIlleurbanne, France.

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|October 3, 2025
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Summary
This summary is machine-generated.

Atom-condensed electron density deformation modes reveal molecular reactivity patterns. These modes, derived from diagonalizing the linear response function matrix, help identify preferred electron flow directions in molecules.

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Area of Science:

  • Quantum chemistry
  • Computational chemistry

Background:

  • The linear response function matrix is crucial for understanding molecular electronic properties.
  • Diagonalization of this matrix yields eigenvectors that form a complete basis set.

Purpose of the Study:

  • To introduce and define atom-condensed Electron Density Deformation Modes.
  • To explore the utility of these modes in identifying molecular reactive regions and electron flow patterns.

Main Methods:

  • Diagonalization of the atom-condensed linear response function matrix.
  • Projection of density deformations onto the obtained eigenvectors.
  • Derivation of relationships between electron density polarization energy and hardness variation.

Main Results:

  • Eigenvectors are interpreted as Electron Density Deformation Modes.
  • These modes describe electron density deformation in response to perturbations.
  • A connection between polarization energy and hardness variation is established.

Conclusions:

  • Electron Density Deformation Modes offer insights into molecular reactivity.
  • These modes can predict preferred electron flow, aiding in the identification of reactive sites.
  • The framework is applicable to practical studies of organic reactions.