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Related Concept Videos

¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

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The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
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¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.3K
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...
1.3K
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

1.2K
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...
1.2K
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

1.7K
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...
1.7K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.0K
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...
1.0K
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

5.0K
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...
5.0K

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Multi-reference coupled cluster theory using the normal ordered exponential ansatz.

Alexander D Gunasekera1, Nicholas Lee1, David P Tew1

  • 1Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, UK. alexander.gunasekera@chem.ox.ac.uk.

Faraday Discussions
|October 1, 2024
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Summary
This summary is machine-generated.

This study explores spin-adapted coupled-cluster theory for open-shell systems. The research reformulates equations for better accuracy and size-consistency in electronic structure calculations.

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Area of Science:

  • Quantum chemistry
  • Electronic structure theory

Background:

  • Spin-adapted coupled-cluster (CC) theory is crucial for accurately describing open-shell molecular systems.
  • Developing efficient and accurate methods for general open-shell configurations remains a challenge in computational chemistry.

Purpose of the Study:

  • To investigate Lindgren's normal-ordered exponential ansatz for correlating specific spin states.
  • To reformulate the unlinked working equations for improved computational efficiency and accuracy.
  • To analyze the performance of the method for simple molecular systems.

Main Methods:

  • Utilizing automatic equation generation software to implement spin-free excitation operators.
  • Applying intermediate normalization and ensuring size-extensivity in the theoretical framework.
  • Performing calculations with single and double excitations for selected molecular examples.

Main Results:

  • A reformulated, size-extensive version of Lindgren's ansatz was developed.
  • The method's accuracy and size-consistency were evaluated for small molecules.
  • The approach demonstrated potential for accurate electronic structure calculations of open-shell systems.

Conclusions:

  • The reformulated Lindgren's ansatz offers a promising approach for spin-adapted coupled-cluster calculations.
  • The method shows good accuracy and size-consistency for the tested systems.
  • Further development could extend its applicability to more complex open-shell electronic structures.