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Related Concept Videos

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

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

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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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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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

¹H NMR Signal Multiplicity: Splitting Patterns

5.2K
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...
5.2K
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

200
Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
200
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
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.4K
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Selected Nonorthogonal Configuration Interaction with Compressed Single and Double Excitations.

Chong Sun1, Fei Gao2, Gustavo E Scuseria1,2

  • 1Department of Chemistry, Rice University, Houston, Texas 77005-1892, United States.

Journal of Chemical Theory and Computation
|April 19, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new method, selected nonorthogonal configuration interaction with single and double excitations (SNOCISD), to accurately capture dynamic correlations in electronic structure theory. SNOCISD enhances accuracy by compressing excitations, improving calculations for molecular dissociation and condensed matter models.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Electronic structure theory

Background:

  • Accurate treatment of dynamic and static electron correlations is crucial in electronic structure theory.
  • Nonorthogonal configuration interaction (NOCI) effectively handles static correlation but requires dynamic correlation for quantitative accuracy.

Purpose of the Study:

  • To develop a computational framework that incorporates dynamic correlation into NOCI calculations.
  • To improve the accuracy of electronic structure calculations by combining static and dynamic correlation treatments.

Main Methods:

  • A novel framework for compressing orthogonal single and double excitations into a reduced-dimension NOCI (NOCISD).
  • Iterative compression applied to each Slater determinant within a reference NOCI.
  • Refinement of the compressed NOCISD using metric and energy tests, termed selected NOCI with single and double excitations (SNOCISD).

Main Results:

  • The SNOCISD method successfully recovers missing dynamic correlations from the reference NOCI.
  • Validation demonstrated the effectiveness of SNOCISD in accurately describing the dissociation of the nitrogen molecule.
  • The method proved effective for the hole-doped two-dimensional Hubbard model across various interaction strengths.

Conclusions:

  • SNOCISD provides a computationally feasible approach to include dynamic correlation in NOCI.
  • This method offers a significant advancement for achieving quantitative accuracy in electronic structure calculations.
  • The validated applications highlight the broad applicability of SNOCISD in chemistry and condensed matter physics.