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The Pauli Exclusion Principle03:06

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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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...
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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.
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π Electron Effects on Chemical Shift: Overview01:27

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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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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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Related Experiment Video

Updated: Feb 19, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Exact exchange-correlation potentials of singlet two-electron systems.

Ilya G Ryabinkin1, Egor Ospadov2, Viktor N Staroverov2

  • 1Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.

The Journal of Chemical Physics
|November 4, 2017
PubMed
Summary

We present a new analytic method to calculate the exchange-correlation potential for two-electron systems. This approach offers accurate results without the issues found in the Kohn-Sham inversion technique.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Electronic Structure Theory

Background:

  • The exchange-correlation potential (vXC(r)) is crucial for accurate electronic structure calculations.
  • Existing methods like Kohn-Sham inversion can yield unphysical potentials, especially in finite basis sets.
  • Accurate vXC(r) is essential for understanding chemical bonding and material properties.

Purpose of the Study:

  • To develop a non-iterative, analytic method for constructing the exchange-correlation potential (vXC(r)) for singlet ground-state two-electron systems.
  • To provide a computationally efficient and physically meaningful alternative to the Kohn-Sham inversion technique.
  • To demonstrate the method's effectiveness using various two-electron systems and common computational chemistry approaches.

Main Methods:

  • A novel analytic formula for vXC(r) derived from the electronic wave function.
  • Application of the formula to wave functions obtained from common ab initio methods and Gaussian basis sets.
  • Comparison with the Kohn-Sham inversion technique, highlighting differences in potential behavior.

Main Results:

  • The proposed method successfully constructs accurate exchange-correlation potentials for two-electron systems.
  • Unlike Kohn-Sham inversion, this method avoids unphysical oscillations and divergences in the potential when using finite basis sets.
  • Accurate vXC(r) was computed for the helium isoelectronic series, H2, and H3+.

Conclusions:

  • The non-iterative analytic method provides a robust and accurate way to determine the exchange-correlation potential for two-electron systems.
  • This approach overcomes limitations of the Kohn-Sham inversion, particularly concerning basis set effects.
  • The method offers a valuable tool for electronic structure calculations in quantum chemistry and condensed matter physics.