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Related Concept Videos

π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

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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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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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Spin–Spin Coupling: One-Bond Coupling01:17

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1.2K
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,...
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Spin–Spin Coupling Constant: Overview01:08

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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...
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.3K
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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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A coupled cluster framework for electrons and phonons.

Alec F White1, Yang Gao2, Austin J Minnich2

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

The Journal of Chemical Physics
|December 15, 2020
PubMed
Summary
This summary is machine-generated.

We developed a new coupled cluster theory to model electron-phonon interactions in materials. This approach accurately describes electronic and vibrational properties, advancing computational materials science.

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Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • Electron-phonon interactions are crucial for understanding material properties.
  • Accurate theoretical methods are needed to model these coupled systems.

Purpose of the Study:

  • To develop and apply a coupled cluster framework for electron-phonon systems.
  • To benchmark coupled cluster approximations for accuracy.
  • To implement ab initio calculations for solids.

Main Methods:

  • Equation-of-motion coupled cluster theory.
  • Hubbard-Holstein model for benchmarking.
  • Implementation using crystalline Gaussian type orbitals in PySCF.

Main Results:

  • The coupled cluster framework accurately describes neutral and charged excitations.
  • Coupled cluster approximations perform well for weak to moderate electron-phonon coupling.
  • Preliminary results for finite-size models of diamond with linear coupling are presented.

Conclusions:

  • The developed coupled cluster theory is a powerful tool for studying electron-phonon interactions.
  • The method shows promise for ab initio calculations on solids.
  • Implementation within PySCF facilitates further research.