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Related Concept Videos

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

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

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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 involved orbitals. The...
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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.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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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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Valence Bond Theory02:42

Valence Bond Theory

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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...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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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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Fast, accurate enthalpy differences in spin crossover crystals from DFT+U.

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Calculating spin crossover material properties is challenging. The DFT+U method accurately predicts enthalpy differences, offering a cost-effective alternative to hybrid functionals for studying these materials.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Solid-State Physics

Background:

  • Spin crossover (SCO) materials are bi-stable systems with potential applications in molecular electronics and sensors.
  • Accurate calculation of the enthalpy difference (ΔH) between high spin (HS) and low spin (LS) states is crucial for predicting SCO behavior.
  • Many conventional density functional theory (DFT) methods struggle to accurately predict the sign and magnitude of ΔH.

Purpose of the Study:

  • To evaluate the performance of DFT+U methods in calculating ΔH for SCO materials.
  • To compare the accuracy of DFT+U with established hybrid functionals like TPSSh.
  • To identify a computationally efficient and accurate method for studying SCO phenomena in crystalline materials.

Main Methods:

  • Benchmarking DFT functionals using a dataset of Fe(II) and Fe(III) SCO materials with experimentally measured ΔH values.
  • Investigating the Liechtenstein and Dudarev formulations of DFT+U.
  • Assessing the mean absolute error (MAE) of predicted ΔH values against experimental data.

Main Results:

  • The hybrid functional TPSSh achieved a MAE of 11 kJ mol⁻¹.
  • Both Liechtenstein and Dudarev DFT+U methods showed improved accuracy over TPSSh.
  • The Dudarev DFT+U method, with Ueff = 1.6 eV, yielded a MAE of 8 kJ mol⁻¹.
  • Excluding a single outlier material, DFT+U achieved chemical accuracy.

Conclusions:

  • DFT+U methods, particularly the Dudarev formulation, offer a promising and accurate approach for calculating ΔH in SCO crystals.
  • DFT+U provides accuracy comparable to meta-hybrid functionals but at a significantly lower computational cost.
  • This makes DFT+U an attractive choice for large-scale studies of spin crossover phenomena in solid-state materials.