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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Atomic Nuclei: Nuclear Spin State Overview01:03

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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...
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Free Energy Changes for Nonstandard States03:25

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
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Luminescence, the emission of light by a substance that has absorbed energy, is a process that involves the interaction of molecules with light. The energy-level diagram, or Jablonski diagram, is a graphical representation of these interactions, illustrating the various states and transitions a molecule can undergo. In a typical Jablonski diagram, the lowest horizontal line represents the ground-state energy of the molecule, which is usually a singlet state. This state represents the energies...
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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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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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Related Experiment Video

Updated: Aug 4, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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State-Specific Configuration Interaction for Excited States.

Fábris Kossoski1, Pierre-François Loos1

  • 1Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062 Toulouse, France.

Journal of Chemical Theory and Computation
|April 6, 2023
PubMed
Summary
This summary is machine-generated.

We present state-specific configuration interaction (ΔCI), a novel computational method for excited-state calculations. This systematically improvable approach offers high accuracy, outperforming standard methods for various chemical species.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate excited-state calculations are crucial for understanding photochemistry and spectroscopy.
  • Existing methods often struggle with multireference character inherent in excited states.

Purpose of the Study:

  • Introduce and benchmark a systematically improvable computational method for excited-state calculations.
  • Evaluate the accuracy and applicability of the state-specific configuration interaction (ΔCI) approach.

Main Methods:

  • Developed the state-specific configuration interaction (ΔCI) method, a variant of multireference configuration interaction.
  • Employed state-specific orbitals and determinants for each targeted electronic state.
  • Utilized ΔCISD, ΔCISD+EN2, and ΔCISD+Q models to account for electron excitations and corrections.

Main Results:

  • ΔCI demonstrated significantly higher accuracy compared to standard ground-state-based configuration interaction.
  • ΔCISD models showed performance comparable to Equation-of-Motion Coupled Cluster methods (EOM-CC2 and EOM-CCSD).
  • ΔCISD+Q provided superior accuracy over EOM-CC2 and EOM-CCSD for larger molecular systems.

Conclusions:

  • The ΔCI route is a promising alternative for challenging multireference excited-state problems.
  • It accurately calculates singly and doubly excited states for various species.
  • Current limitations restrict its reliability to relatively low-lying excited states.