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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...

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...

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

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.
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Thermal Electrocyclic Reactions: Stereochemistry

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The stereochemistry of electrocyclic reactions is strongly influenced by the orbital symmetry of the polyene HOMO. Under thermal conditions, the reaction proceeds via the ground-state HOMO.
Selection Rules: Thermal Activation
Conjugated systems containing an even number of π-electron pairs undergo a conrotatory ring closure. For example, thermal electrocyclization of (2E,4E)-2,4-hexadiene, a conjugated diene containing two π-electron pairs, gives trans-3,4-dimethylcyclobutene.

Structure of Benzene: Molecular Orbital Model

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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).

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In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as...

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Updated: May 16, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Optimal entanglement distribution within a multi-ring topology.

B C Ciobanu¹, T A Calafeteanu¹, A B Popa¹

¹Computer Science and Engineering Department, National University of Science and Technology POLITEHNICA Bucharest, Bucharest, 60042, Romania.

Scientific Reports

|May 12, 2025

Summary

This summary is machine-generated.

This study optimizes entanglement distribution in multi-ring quantum networks for the Quantum Internet. Algorithms were developed to efficiently manage network resources and minimize request fulfillment time, enhancing network performance.

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Area of Science:

Quantum communication networks
Network topology optimization
Quantum information science

Background:

Entanglement distribution is key for the Quantum Internet.
Multi-ring topologies offer scalability but increase routing complexity.
Efficient entanglement distribution is crucial for network performance.

Purpose of the Study:

To solve the problem of optimal entanglement distribution in multi-ring quantum network topologies.
To analyze two distinct multi-ring network configurations: single-layer routing and multi-layer routing.
To develop algorithms for optimizing time and resources for entanglement resupply requests.

Main Methods:

Analysis of two multi-ring network configurations (single-layer vs. multi-layer routing).
Development of algorithms to determine optimal time and resource allocation for entanglement distribution.
Computer simulations to evaluate the performance of proposed algorithms.

Main Results:

Multi-layer routing offers minimal time-saving benefits for serving requests compared to single-layer routing.
Multi-layer routing may reduce the number of resources required for non-blocking entanglement distribution.
Algorithms provide optimal solutions for time and resource allocation in multi-ring networks.

Conclusions:

The complexity of multi-layer routing in quantum networks provides limited advantages in request serving time.
Resource efficiency can be improved in multi-ring quantum networks by allowing layer switching.
The proposed algorithms offer effective solutions for optimizing entanglement distribution in complex network topologies.