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Related Concept Videos

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,...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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 π orbitals.
Coupled Reactions01:17

Coupled Reactions

Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions. 
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions. Cells...

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Related Experiment Video

Updated: Jun 16, 2026

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

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

Published on: May 27, 2020

Estimation of the coupling matrix elements for one-electron transfer systems.

R E Olson, F T Smith, E Bauer

    Applied Optics
    |January 30, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A new semiempirical method estimates coupling matrix elements for Landau-Zener calculations. This approach simplifies predicting electron transfer in charge transfer and ion-ion recombination processes.

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

    • Physical Chemistry
    • Atomic and Molecular Physics
    • Computational Chemistry

    Background:

    • Landau-Zener calculations are crucial for modeling one-electron transfer processes.
    • Accurate estimation of coupling matrix elements (H(12)) is essential for these calculations.
    • Existing methods may require complex inputs or extensive computational resources.

    Purpose of the Study:

    • To develop a simplified, semiempirical method for estimating coupling matrix elements H(12).
    • To provide a computationally efficient approach for Landau-Zener calculations in one-electron transfer problems.
    • To correlate calculated or measured values for improved accuracy.

    Main Methods:

    • A semiempirical method was developed based on a correlation of ninety-nine calculated or measured values.
    • The method estimates coupling matrix elements H(12).
    • It requires only the crossing distance R(x) and basic atomic properties (ionization potentials, electron affinities, energy levels).

    Main Results:

    • A reliable method for estimating H(12) was established.
    • The method is applicable to one-electron transfer problems like charge transfer and ion-ion recombination.
    • The accuracy is based on a correlation of ninety-nine data points.

    Conclusions:

    • The proposed semiempirical method offers a practical approach for estimating H(12) in Landau-Zener calculations.
    • It simplifies the prediction of electron transfer dynamics.
    • Further discussion covers potential applications and inherent limitations of the method.