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Related Concept Videos

Radical Formation: Addition00:47

Radical Formation: Addition

Radicals can be formed by adding a radical to a spin-paired molecule. This is typically observed with unsaturated species, where the addition of a radical across the π bond leads to the production of a new radical by dissolving the π bond. For example, the addition of a Br radical to an alkene yields a carbon-centered radical.
Similar to charge conservation in chemical reactions, spin conservation is implicit for radical reactions. Accordingly, the product formed must possess an unpaired...
Radical Formation: Overview01:03

Radical Formation: Overview

A bond can be broken either by heterolytic bond cleavage to form ions or homolytic bond cleavage to yield radicals. A fishhook arrow is used to represent the motion of a single electron in homolytic bond cleavage. There are two main sources from which radicals can be formed:
Radicals from spin-paired molecules:
Radicals can be obtained from spin-paired molecules either by homolysis or electron transfer. While two radicals are formed in the former, an electron is added in the latter, also known...
Radical Reactivity: Overview01:11

Radical Reactivity: Overview

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 molecule. These three...
Radicals: Electronic Structure and Geometry01:07

Radicals: Electronic Structure and Geometry

This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Valence Bond Theory02:45

Valence Bond Theory

Overview of Valence Bond Theory

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Related Experiment Video

Updated: May 18, 2026

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization
08:22

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization

Published on: August 6, 2018

Variational fractional-spin density-functional theory for diradicals.

Degao Peng1, Xiangqian Hu, Deepa Devarajan

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.

The Journal of Chemical Physics
|September 25, 2012
PubMed
Summary

A new variational method improves calculations of singlet-triplet energy gaps in diradicals by optimizing orbital occupancies. This approach refines density-functional theory (DFT) for challenging molecular systems.

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Isolating Free Carbenes, their Mixed Dimers and Organic Radicals
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Isolating Free Carbenes, their Mixed Dimers and Organic Radicals

Published on: April 19, 2019

Related Experiment Videos

Last Updated: May 18, 2026

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization
08:22

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization

Published on: August 6, 2018

Isolating Free Carbenes, their Mixed Dimers and Organic Radicals
10:44

Isolating Free Carbenes, their Mixed Dimers and Organic Radicals

Published on: April 19, 2019

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate computation of singlet-triplet energy gaps in diradicals is a significant challenge within density-functional theory (DFT).
  • Existing methods like fractional-spin DFT (FS-DFT) rely on assumptions of equal spin-orbital occupancies for frontier orbitals.
  • Static correlation errors in standard DFT approximations can lead to overestimations of energy gaps.

Purpose of the Study:

  • To introduce and validate a variational extension of FS-DFT (VFS-DFT) for improved diradical energy gap calculations.
  • To investigate the impact of frontier orbital symmetry on optimal occupation numbers.
  • To assess the performance of VFS-DFT and FS-DFT in capturing different electronic states and their accuracy for various diradical systems.

Main Methods:

  • Developed a variational approach (VFS-DFT) that optimizes frontier-orbital occupation numbers for singlet diradicals.
  • The optimization is based on a full configuration-interaction picture, moving beyond the fixed 0.5 occupancy assumption of FS-DFT.
  • Applied VFS-DFT and FS-DFT to analyze diradicals such as O(2), CH(2), and cyclobutadiene.

Main Results:

  • VFS-DFT reduces to FS-DFT for diradicals like O(2) where frontier orbitals belong to the same irreducible representation, yielding optimal 0.5 occupancies.
  • For diradicals with frontier orbitals in different irreducible representations, VFS-DFT finds optimal occupancies varying between 0 and 1.
  • VFS-DFT and FS-DFT calculations overestimate singlet-triplet energy gaps for disjoint diradicals (e.g., cyclobutadiene) due to static correlation errors.

Conclusions:

  • The VFS-DFT method offers a more flexible and accurate approach to calculating singlet-triplet energy gaps for diradicals with varied frontier orbital symmetries.
  • The study highlights the importance of considering orbital symmetry and optimizing occupancies for accurate electronic structure predictions.
  • Both VFS-DFT and FS-DFT still face challenges with static correlation, impacting accuracy for certain diradical types.