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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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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Dissolution Dynamic Nuclear Polarization Instrumentation for Real-time Enzymatic Reaction Rate Measurements by NMR
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Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics.

Mikhail Veshtort1, Robert G Griffin

  • 1Department of Chemistry and Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

The Journal of Chemical Physics
|October 14, 2011
PubMed
Summary
This summary is machine-generated.

A new relaxation theory accurately describes proton-driven spin diffusion (PDSD) in rotating solids, enabling precise distance constraints in biomolecules. This theory, validated by simulations and experiments, clarifies spin dynamics and improves internuclear distance measurements.

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Area of Science:

  • Solid-state Nuclear Magnetic Resonance (NMR) spectroscopy
  • Biomolecular structure determination
  • Theoretical physical chemistry

Background:

  • Proton-driven spin diffusion (PDSD) experiments in rotating solids are valuable for distance constraints in large biomolecules.
  • The quantitative relationship between molecular structure and observed spin diffusion is unclear due to a lack of accurate theoretical descriptions.
  • Existing theories struggle to account for complex spin dynamics, including phenomena like rotational resonance (R(2)).

Purpose of the Study:

  • To develop a detailed relaxation theory for PDSD in rotating solids, providing an accurate description of spin dynamics.
  • To extend the theory to the non-Markovian regime, incorporating phenomena such as rotational resonance (R(2)).
  • To validate the theoretical predictions through direct numerical simulations and experimental data.

Main Methods:

  • Development of a non-Markovian kinetic equation for spin dynamics, utilizing a memory function approach based on correlation functions.
  • Derivation of accurate expressions for correlation functions and spin diffusion constants.
  • Numerical simulations of PDSD dynamics using the reversible Liouville-von Neumann equation on small spin systems (e.g., 12 spins).

Main Results:

  • The developed theory accurately describes both conventional and radio-frequency-assisted PDSD experiments, including non-Markovian effects.
  • Numerical simulations confirm an exponential decay of difference magnetization and provide accurate spin diffusion constants, matching theoretical predictions.
  • The theory and simulations show excellent agreement with experimental 2D rotary resonance recoupling proton-driven spin diffusion (R(3)-PDSD) results, enabling accurate internuclear distance measurements up to 4.9 Å.

Conclusions:

  • The new relaxation theory provides a robust and accurate framework for understanding PDSD in rotating solids.
  • This methodology allows for highly accurate internuclear distance extraction from PDSD experiments, overcoming previous limitations.
  • The theory offers a parameter-free alternative to conventional treatments of R(2) relaxation, addressing significant model errors.