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Related Concept Videos

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
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Related Experiment Video

Updated: Jun 8, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Many-electron self-interaction and spin polarization errors in local hybrid density functionals.

Robin Haunschild1, Thomas M Henderson, Carlos A Jiménez-Hoyos

  • 1Department of Chemistry, Rice University, Houston, Texas 77005, USA. H@unschild.de

The Journal of Chemical Physics
|October 15, 2010
PubMed
Summary
This summary is machine-generated.

Local hybrid density functionals were evaluated for systems with noninteger charge and spin. Long-range correction is crucial for cations, while the PSTS functional shows promise for spin polarization errors.

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Last Updated: Jun 8, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Density functional theory (DFT) is essential for materials science.
  • Common DFT failures arise from noninteger electron occupation.
  • Local hybrid functionals have not been extensively studied for these systems.

Purpose of the Study:

  • To investigate the performance of local hybrid density functionals for systems with noninteger charge and spin.
  • To assess many-electron self-interaction error and spin polarization error.
  • To evaluate range-separated variants of local hybrids.

Main Methods:

  • Analysis of recently proposed local hybrid functionals.
  • Testing against systems with noninteger charge (self-interaction error).
  • Testing against systems with noninteger spin state (spin polarization error).

Main Results:

  • Long-range correction effectively mitigates self-interaction error in cations.
  • Full-range local hybrids are adequate for anions, avoiding overcorrection.
  • The PSTS functional demonstrates superior performance in reducing spin polarization errors compared to other local hybrids.

Conclusions:

  • Local hybrid functionals show promise for describing systems with noninteger electron occupation.
  • Careful functional design, including range separation, is key to addressing specific errors.
  • The PSTS functional offers a robust approach for spin-polarized calculations.