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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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...
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...
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...
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.
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...

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Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
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A tri-atomic Renner-Teller system entangled with Jahn-Teller conical intersections.

A Csehi1, A Bende, G J Halász

  • 1Department of Information Technology, University of Debrecen, H-4010 Debrecen, P.O. Box 12, Hungary.

The Journal of Chemical Physics
|January 17, 2013
PubMed
Summary
This summary is machine-generated.

This study explores the entanglement of Renner-Teller (RT) and Jahn-Teller (JT) effects in molecular systems. A new Renner-Jahn coupling parameter, η, was discovered, revealing a unique RT/JT effect with its own Hilbert space.

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Published on: February 15, 2016

Area of Science:

  • Theoretical Chemistry
  • Quantum Chemistry
  • Molecular Physics

Background:

  • The Renner-Teller (RT) effect describes the interaction between electronic states and nuclear motion in linear molecules.
  • The Jahn-Teller (JT) effect involves the distortion of non-linear molecules to remove electronic degeneracy.
  • Previous studies examined RT seams along collinear axes, but this work investigates intersecting planar contours.

Purpose of the Study:

  • To investigate the entanglement of Renner-Teller (RT) systems with Jahn-Teller (JT) conical intersections.
  • To develop a new method for calculating adiabatic-to-diabatic angles for intersecting planar contours.
  • To identify and characterize novel coupling terms and parameters arising from RT-JT entanglement.

Main Methods:

  • Analysis of RT systems with planar contours intersecting the collinear axis.
  • Development of a novel approach to compute adiabatic-to-diabatic (mixing) angles.
  • Derivation of non-adiabatic coupling terms (NACTs) expressed via Dirac-δ functions.

Main Results:

  • A unique type of RT-NACTs was formulated using Dirac-δ functions.
  • A novel molecular parameter, the Renner-Jahn coupling parameter (η = 22/π), was discovered, quantifying RT-JT coupling.
  • The entanglement of RT and JT effects leads to a distinct RT/JT effect with a unique Hilbert space.

Conclusions:

  • The entanglement between RT and JT effects creates a new phenomenon, the RT/JT effect.
  • The Renner-Jahn coupling parameter (η) is a universal constant, independent of specific molecular systems.
  • The states involved in the RT/JT effect reside in a Hilbert space distinct from those of the individual RT or JT effects.