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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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Valence Bond Theory02:42

Valence Bond Theory

9.2K
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
9.2K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.0K
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...
1.0K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.1K
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
1.1K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.1K
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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Spin-adapted spin-flip-down time-dependent density functional theory.

Chima S Chibueze1, Lucas Visscher1

  • 1Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands.

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|September 4, 2025
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Summary
This summary is machine-generated.

This study introduces novel spin-adapted spin-flip-down time-dependent density functional theory (SFD-TD-DFT) methods to accurately calculate low-lying electronic excitations in high-spin molecular systems. The new restricted open-shell Kohn-Sham (ROKS) methods offer improved accuracy for spin-flip transitions.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Theoretical Spectroscopy

Background:

  • Systems with orbital degeneracy at the Fermi level often exhibit high-spin ground states.
  • Low-lying electronic excitations with lower total spin can be accessed via spin-flip-down transitions.
  • Accurate calculation of these spin-flip excitations is crucial for understanding molecular properties.

Purpose of the Study:

  • To develop and present three spin-adapted spin-flip-down time-dependent density functional theory (SFD-TD-DFT) approaches.
  • To calculate excitation energies for electronic transitions from high-spin ground states.
  • To investigate the role of spin-adaptation and kernel description in these calculations.

Main Methods:

  • Development of three SFD-TD-DFT methods based on restricted open-shell Kohn-Sham (ROKS) formulation within the Tamm-Dancoff approximation (TDA).
  • Utilized different two-electron coupling elements in the kernels of the working equations.
  • Introduced fully spin-adapted ROKS-SFD-TDA methods derived from configuration interaction with single excitations (SF-CIS) and equation-of-motion ansatz (SF-TDA).

Main Results:

  • A noncollinear kernel description is essential for accurate calculation of spin-flip excitations.
  • Fully spin-adapted methods (SF-CIS and SF-TDA) can lead to artificial double counting of correlation effects.
  • The quasi-spin-adapted SF-TDA (Q-SF-TDA) method demonstrates stability, efficiency, and performance comparable to spin-unrestricted SFD-TD-DFT.

Conclusions:

  • The developed ROKS-SFD-TDA methods provide accurate excitation energies for spin-flip transitions in high-spin systems.
  • The Q-SF-TDA method offers a robust and efficient approach for studying these electronic excitations.
  • These advancements contribute to a better theoretical understanding of electronic structure and spectroscopy in degenerate systems.