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¹H NMR: Long-Range Coupling

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.

MO Theory and Covalent Bonding

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

VSEPR Theory and the Effect of Lone Pairs

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Effect of Lone Pairs of Electrons on Molecule Geometry

Spin–Spin Coupling: One-Bond Coupling

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: Two-Bond Coupling (Geminal Coupling)

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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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Related Experiment Video

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Structure and Coordination Determination of Peptide-metal Complexes Using 1D and 2D 1H NMR

Structure and Coordination Determination of Peptide-metal Complexes Using 1D and 2D ¹H NMR

Published on: December 16, 2013

Strong correlations via constrained-pairing mean-field theory.

Takashi Tsuchimochi¹, Gustavo E Scuseria

¹Department of Chemistry, Rice University, Houston, Texas 77005, USA.

The Journal of Chemical Physics

|October 2, 2009

Summary

We developed a new method, constrained-pairing mean-field theory (CPMFT), to accurately model strong electron correlations in materials. This approach captures electron fluctuations and pairings, proving effective for complex systems.

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Area of Science:

Quantum chemistry
Computational condensed matter physics
Strongly correlated electron systems

Background:

Accurately describing strong electron correlations is a major challenge in quantum chemistry and condensed matter physics.
Existing methods often struggle with systems exhibiting significant electron number fluctuations and pairing phenomena.
Developing robust theoretical frameworks is crucial for understanding and predicting material properties.

Purpose of the Study:

To introduce a novel mean-field theory for accurately describing strong electron correlations.
To develop a method that specifically addresses electron number fluctuations and pairings within an active space.
To provide a computationally tractable approach for systems with strong correlation effects.

Main Methods:

Developed constrained-pairing mean-field theory (CPMFT) based on electron number fluctuations and pairings.
Preserved spin and spatial symmetries while allowing for average electron number conservation.
Utilized optimized natural orbitals and occupations obtained from mean-field Hamiltonian diagonalization.
Formulated a two-particle density matrix ansatz exclusively for strong correlations.

Main Results:

CPMFT accurately describes strong electron correlations by incorporating electron number fluctuations and pairings.
The method preserves essential spin and spatial symmetries.
Demonstrated the accuracy of CPMFT through applications to the metal-insulator transition in hydrogen clusters.
Validated CPMFT on molecular dissociation curves, showing its broad applicability.

Conclusions:

CPMFT offers a powerful and accurate approach for studying strongly correlated electron systems.
The method provides a reliable tool for investigating phenomena like metal-insulator transitions and molecular behavior.
CPMFT advances the capability of theoretical chemistry and physics in handling complex electronic structures.