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Related Concept Videos

¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.7K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.7K
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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

2.3K
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...
2.3K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.4K
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...
1.4K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.4K
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...
1.4K
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.5K
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...
2.5K
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

2.6K
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
2.6K

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Related Experiment Videos

Quantum interference in multi-branched molecules: The exact transfer matrix solutions.

Yu Jiang1

  • 1Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A. P. 55-534, 09340 México D.F., Mexico.

The Journal of Chemical Physics
|December 10, 2017
PubMed
Summary

We developed a new method to study quantum interference in molecules. This approach simplifies complex molecular systems into single units, enabling the analysis of various resonant transport behaviors.

Related Experiment Videos

Area of Science:

  • Quantum physics
  • Molecular electronics
  • Condensed matter theory

Background:

  • Quantum interference is crucial for electron transport in molecular systems.
  • Complex molecular structures pose challenges for theoretical analysis.
  • Understanding resonant transport phenomena is key to designing molecular electronic devices.

Purpose of the Study:

  • To develop a general formalism for studying quantum interference in single-molecule electronic systems.
  • To simplify the analysis of electron transport through complex molecular structures.
  • To investigate resonant transport behaviors and parity-time (PT)-symmetric transitions in molecular systems.

Main Methods:

  • Transfer matrix formalism
  • Schrödinger equation with Bethe ansatz
  • Kirchhoff's rule for quantum wires

Main Results:

  • A general closed-form expression for transmission and reflection amplitudes of two-port quantum networks.
  • Reduction of complex molecular transport to a single two-port scattering unit.
  • Calculation of transmission coefficients exhibiting Breit-Wigner, Fano, and Mach-Zehnder resonances.
  • Analysis of spectral singularities and PT-symmetric transitions in serially and parallelly coupled systems.

Conclusions:

  • The developed formalism effectively simplifies the study of quantum transport in complex molecules.
  • The method allows for the prediction and analysis of diverse resonant transport phenomena.
  • Coupled PT-symmetric systems can exhibit spectral singularities and phase transitions dependent on coupling configurations.