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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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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.
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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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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...
2.1K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.6K
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...
1.6K
Valence Bond Theory02:42

Valence Bond Theory

11.5K
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
11.5K
Effects of Temperature on Free Energy02:11

Effects of Temperature on Free Energy

28.7K
The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
28.7K
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

1.3K
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.
1.3K

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Updated: Mar 8, 2026

Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes
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Spin Saturation Transfer Difference NMR SSTD NMR: A New Tool to Obtain Kinetic Parameters of Chemical Exchange Processes

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Ensemble-free configurational temperature for spin systems.

G Palma1, G Gutiérrez2, S Davis3

  • 1Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile.

Physical Review. E
|January 14, 2017
PubMed
Summary
This summary is machine-generated.

A new dynamical temperature estimator was developed for statistical mechanics. This robust estimator accurately measures thermalization and validates simulation algorithms, proving independent of the ensemble used.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Estimating dynamical temperature in arbitrary ensembles is crucial for understanding thermalization processes.
  • Existing methods may lack robustness or direct measures of thermalization and statistical errors.

Purpose of the Study:

  • To derive and validate a novel microscopic estimator for dynamical temperature.
  • To demonstrate the estimator's independence from the chosen statistical ensemble.
  • To assess its utility in testing the ergodicity of numerical simulation algorithms.

Main Methods:

  • Derivation of the estimator within the conjugate variables theorem framework.
  • Numerical simulation of the two-dimensional XY model in the canonical ensemble.
  • Application of a generalized Wolff's unicluster algorithm for critical systems.

Main Results:

  • The derived estimator's average directly yields the inverse temperature.
  • The estimator is proven to be independent of the statistical ensemble.
  • Numerical results confirm the analytical expression's robustness for critical systems.
  • The estimator provides direct measures of thermalization and absolute errors.

Conclusions:

  • The developed microscopic estimator offers a direct, absolute, and stringent test for the ergodicity of simulation algorithms.
  • This estimator enhances the reliability and interpretability of numerical simulations in statistical physics.
  • It provides valuable insights into the thermalization process and associated statistical fluctuations.