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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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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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Free Energy Changes for Nonstandard States03:25

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
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Spin–Spin Coupling: One-Bond Coupling01:17

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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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Atomic Nuclei: Nuclear Spin State Overview01:03

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

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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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Accurate state energetics in spin-crossover systems using pure density functional theory.

Silvia Gómez-Coca1, Eliseo Ruiz1

  • 1Departament de Química Inorgànica i Orgànica and Institut de Recerca de Química Teòrica i Computacional, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain. silvia.gomez.coca@ub.edu.

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A new meta-generalized gradient approximation (meta-GGA) functional accurately calculates spin-state energy differences in transition metal systems. This advance offers a computationally efficient alternative to existing methods for spin-crossover materials.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Accurately calculating the energy difference between spin states in transition metal systems is a significant challenge for electronic structure methods.
  • Spin-crossover systems exhibit small energy differences between high- and low-spin states, often leading to inaccuracies with standard computational approaches.
  • Existing methods like post-Hartree-Fock and density functional theory (DFT) struggle with the precision required for these systems.

Purpose of the Study:

  • To evaluate the accuracy of a novel family of training meta-generalized gradient approximation (meta-GGA) functionals for spin-crossover systems.
  • To identify a functional that can reliably predict spin-state energy differences without the high computational cost of exact exchange terms.

Main Methods:

  • A test set of twenty systems exhibiting spin transitions was employed.
  • The performance of a new meta-GGA functional was assessed against established methods.
  • Comparison was made with the TPSSh hybrid meta-GGA and the r2SCAN meta-GGA functionals.

Main Results:

  • One of the new meta-GGA functionals achieved accuracy comparable to or exceeding the TPSSh hybrid functional for spin energetics.
  • This novel functional outperformed the r2SCAN meta-GGA functional, previously the best alternative to TPSSh.
  • Crucially, the new functional provides these accurate results without incorporating the computationally expensive exact exchange term.

Conclusions:

  • The developed meta-GGA functional offers a highly accurate and computationally efficient solution for calculating spin energetics in transition metal compounds.
  • This breakthrough enables the study of spin-crossover phenomena in larger systems and periodic structures, where exact exchange is often prohibitive.
  • The new functional represents a significant advancement in electronic structure calculations for spin-related properties.