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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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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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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.7K
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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¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
7.9K
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

2.1K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
2.1K
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

31.5K
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Range-Separation Parameter in Tuned Exchange-Correlation Functionals: Successive Ionizations and the Fukui Function.

Jonathan D Gledhill1, Frank De Proft2, David J Tozer1

  • 1Department of Chemistry, Durham University , South Road, Durham DH1 3LE, United Kingdom.

Journal of Chemical Theory and Computation
|September 14, 2016
PubMed
Summary
This summary is machine-generated.

The range-separation parameter in exchange-correlation functionals shows system dependence. Tuning this parameter for energy conditions also applies to density conditions, crucial for developing accurate quantum chemistry functionals.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Range-separated exchange-correlation functionals are key in quantum chemistry.
  • The range-separation parameter's system dependence poses challenges for functional development.
  • Koopmans' theorem and conceptual density functional theory (DFT) provide frameworks for understanding electronic structure.

Purpose of the Study:

  • To investigate the system dependence of the range-separation parameter in exchange-correlation functionals.
  • To determine if a parameter optimized for the Koopmans energy condition is suitable for the analogous density condition.
  • To assess the performance of functionals in describing electronic structure properties.

Main Methods:

  • Analyzing the energy versus electron number curve for successively ionized systems.
  • Comparing two formulations of the Fukui function in conceptual DFT.
  • Testing the applicability of an energy-tuned range-separation parameter for density conditions.

Main Results:

  • The range-separation parameter exhibits significant system dependence, leading to non-linear energy-electron number curves.
  • Fukui function formulations show similar trends and low sensitivity to the parameter.
  • Optimal agreement between Fukui function formulations is achieved using the energy-tuned parameter.

Conclusions:

  • The system dependence of the range-separation parameter presents a challenge for developing robust functionals.
  • The range-separation parameter tuned to the Koopmans energy condition is applicable to the analogous density condition.
  • This finding supports the development of more accurate and reliable quantum chemical methods.