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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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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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: 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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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...
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Valence Bond Theory02:42

Valence Bond Theory

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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...
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sp3d and sp3d 2 Hybridization
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Generalized Spin in the Variance-Based Wave Function Optimization Method within the Doubly Occupied Configuration

Diego R Alcoba1,2, Luis Lain3, Alicia Torre3

  • 1Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

The Journal of Physical Chemistry. A
|August 14, 2024
PubMed
Summary
This summary is machine-generated.

We introduce a generalized spin method for electronic structure calculations, optimizing wave functions and energies for all states. This approach analyzes spin symmetry breakdown in hydrogenic clusters, offering insights into quantum mechanical behaviors.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Electronic Structure Theory

Background:

  • Configuration interaction (CI) methods are fundamental in quantum chemistry for solving the Schrödinger equation.
  • Accurate treatment of electron spin is crucial for understanding molecular properties and spectra.
  • Existing methods may struggle with describing both ground and excited states uniformly, especially concerning spin symmetry.

Purpose of the Study:

  • To implement a generalized spin formulation of the doubly occupied configuration interaction (DECI) methodology.
  • To develop a unified variational treatment for calculating energies of both ground and excited states.
  • To analyze the impact of spin symmetry (Ŝ² and Ŝz) breakdown on energy spectra and spin-related quantities.

Main Methods:

  • Utilized the energy variance of the N-electron Hamiltonian for optimization.
  • Employed a unified variational treatment based on energy variance for wave function optimization and energy calculation.
  • Investigated restricted, unrestricted, and generalized spin methods on model hydrogenic clusters.

Main Results:

  • Successfully optimized N-electron wave functions and calculated their energies using the generalized spin formulation.
  • The energy variance approach enabled a unified description of the entire energy spectra for ground and excited states.
  • Analysis revealed the effects of Ŝ² and Ŝz symmetry breakdown on spectral properties in model systems.

Conclusions:

  • The generalized spin formulation provides a robust framework for electronic structure calculations.
  • The unified variational treatment offers a consistent way to access and describe energy spectra.
  • The study highlights the importance of considering spin symmetry in accurate quantum mechanical simulations.