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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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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.
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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.
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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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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:
 
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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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Benchmarking Periodic Density Functional Theory Calculations for Spin-State Energies in Spin-Crossover Systems.

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Calculating spin energetics in materials is challenging. This study proposes an efficient density functional theory method using periodic boundary conditions for accurate spin-crossover energy differences in extended systems.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Solid-state physics

Background:

  • Spin energetics pose significant challenges for electronic structure calculations.
  • Accurately computing small energy differences between spin states in spin-crossover (SCO) compounds is difficult.
  • Most studies focus on single molecules, not the solid-phase SCO properties relevant to experiments.

Purpose of the Study:

  • To develop and validate an efficient computational method for calculating spin-crossover energy differences in extended systems.
  • To assess the performance of various density functional theory (DFT) functionals for SCO energetics in periodic systems.
  • To identify a computationally feasible approach for studying SCO phenomena in solid materials.

Main Methods:

  • Utilized periodic boundary conditions within density functional theory (DFT).
  • Employed geometry optimization with the PBE functional and many-body dispersion (MB) correction.
  • Calculated high- and low-spin energy differences using meta-GGA functionals (r2SCAN, KTBM24) and hybrid functionals (TPSSh).

Main Results:

  • A semiquantitative description of energy differences was achieved for 20 extended systems.
  • The combination of PBE+MB for geometry and KTBM24 for energy (KTBM24//PBE+MB) showed excellent performance.
  • Hybrid functionals like TPSSh provided good results but were computationally expensive due to exact exchange calculations.

Conclusions:

  • The nonhybrid KTBM24//PBE+MB approach offers a computationally advantageous method for studying spin-crossover energetics in periodic systems.
  • This method provides a viable alternative to more computationally demanding hybrid functionals.
  • The findings facilitate accurate theoretical investigations of SCO materials in the solid phase.