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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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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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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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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

985
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,...
985
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

1.1K
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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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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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...
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Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

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In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
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Related Experiment Video

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Integrator for general spin-s Gross-Pitaevskii systems.

Mudit Jain1, Mustafa A Amin1, Han Pu1

  • 1Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.

Physical Review. E
|December 20, 2023
PubMed
Summary

A new algorithm, i-SPin 2, evolves complex spin systems described by Gross-Pitaevskii equations. It handles diverse interactions and potentials, applicable to Bose-Einstein condensates and dark matter.

Area of Science:

  • Quantum physics
  • Computational physics

Background:

  • Spinor fields in quantum systems are described by Gross-Pitaevskii or nonlinear Schrödinger equations.
  • Simulating these systems requires robust numerical methods to handle complex interactions.

Purpose of the Study:

  • To introduce i-SPin 2, a novel algorithm for evolving general spin-s Gross-Pitaevskii and nonlinear Schrödinger systems.
  • To incorporate a wide range of nonrelativistic interactions, including spin-dependent and spin-orbit couplings.
  • To enable simulations with spatially varying vector potentials affecting spin density.

Main Methods:

  • Development of the i-SPin 2 algorithm, a second-order accurate symplectic method.
  • Inclusion of nonrelativistic interactions up to quartic order (short and long range).

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  • Accommodation of explicit spin-orbit couplings and spatially varying potentials.

    • Main Results:

    • Demonstration of the algorithm's capability to simulate diverse spin systems.
    • Presentation of results for spin-1 Bose-Einstein condensates with varying magnetic fields and spin-orbit coupling.
    • Simulation of spin-1 soliton collisions in dark matter scenarios.

    Conclusions:

    • The i-SPin 2 algorithm provides a versatile tool for simulating complex spinor quantum systems.
    • The method is applicable to both laboratory experiments (e.g., BECs) and astrophysical phenomena (e.g., dark matter).
    • The algorithm is extensible to higher-order accurate methods for advanced simulations.