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Related Concept Videos

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...
989
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

922
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
922
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

862
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
862
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

939
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...
939
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

1.0K
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...
1.0K
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.2K
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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Analytic Gradient for Spin-Flip TDDFT Using Noncollinear Functionals in the Multicollinear Approach.

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This study introduces a stable method for calculating spin-flip time-dependent density functional theory (TDDFT) gradients using noncollinear functionals. This advance enables accurate geometry optimizations and calculations for excited states, improving computational chemistry methods.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Spin-flip time-dependent density functional theory (SF-TDDFT) is crucial for systems with multiconfigurational character.
  • Current collinear functional implementations face limitations.
  • Noncollinear functionals offer improved symmetry and degeneracy preservation but pose numerical challenges.

Purpose of the Study:

  • To develop and validate analytic gradients for noncollinear spin-flip TDDFT.
  • To address the challenge of calculating third-order derivatives of noncollinear functionals.
  • To enable accurate geometry optimizations and excited-state property calculations.

Main Methods:

  • Application of the multicollinear approach to SF-TDDFT analytic gradients.
  • Calculation of third-order derivatives for generalized gradient approximation (GGA) and meta-GGA functionals.
  • Validation through benchmark tests comparing analytic and numerical gradients.

Main Results:

  • Successful implementation of numerically stable analytic gradients for noncollinear SF-TDDFT.
  • Validation against numerical gradients and spin-conserving states.
  • Demonstration of applications in geometry optimization and excited-state energy calculations.

Conclusions:

  • The multicollinear approach provides stable analytic gradients for noncollinear SF-TDDFT.
  • This method facilitates accurate calculations of excited states and molecular properties.
  • The developed gradients serve as a foundation for further advancements in TDDFT and molecular dynamics.