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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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The cationic polymerization mechanism consists of three steps: initiation, propagation, and termination. In the initiation step of the polymerization process, the π bond of a monomer gets protonated by the Lewis acid catalyst, which is formed from boron trifluoride and water. The protonation of the π bond generates a carbocation stabilized by the electron‐donating group. In the propagation step, the π bond of the second monomer acts as a nucleophile and attacks the...
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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.
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Stability of Conjugated Dienes01:28

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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
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Updated: Dec 19, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Charge self-localization in π-conjugated polymers by long range corrected hybrid functionals.

Nan Shao1, Qin Wu

  • 1Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA. qinwu@bnl.gov.

Physical Chemistry Chemical Physics : PCCP
|March 4, 2014
PubMed
Summary

Long-range corrected hybrid functionals accurately describe charge self-localization in conjugated polymers. A range parameter of 0.2 bohr(-1) or larger is optimal for accurate calculations, minimizing spin contamination.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Polymer Physics

Background:

  • Accurate description of charge self-localization is crucial for conjugated polymers.
  • Conventional hybrid functionals often exhibit significant spin contamination.
  • Understanding charge localization impacts polymer electronic properties.

Purpose of the Study:

  • To systematically investigate hybrid functionals for charge self-localization in conjugated polymers.
  • To compare long-range corrected (LRC) hybrids with global hybrids.
  • To determine the optimal range parameter for accurate charge localization calculations.

Main Methods:

  • Systematic investigation of hybrid functional capabilities.
  • Comparison of LRC hybrids against conventional global hybrids.
  • Analysis of charge localization dependence on the range parameter.
  • Introduction of a new charge localization length measure.

Main Results:

  • LRC hybrids show significantly less spin contamination than global hybrids.
  • A range parameter of approximately 0.2 bohr(-1) or larger is required for self-localized charges.
  • Charge localization length and related properties (reorganization energy, excitation energy) were analyzed.
  • Convergence of properties with polymer length and range parameter was studied.

Conclusions:

  • LRC hybrid functionals are advantageous for describing charge self-localization in conjugated polymers.
  • A range parameter of 0.2 bohr(-1) is suggested for exploratory studies due to reduced spin contamination.
  • The findings aid in accurate computational modeling of polymer electronic behavior.