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Related Concept Videos

¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

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

¹H NMR: Interpreting Distorted and Overlapping Signals

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

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

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 others.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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. This...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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 in...
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

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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Related Experiment Video

Updated: Jun 25, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Double excitations in finite systems.

P Romaniello1, D Sangalli, J A Berger

  • 1Laboratoire des Solides Irradies UMR 7642, CNRS-CEA/DSM, Ecole Polytechnique, F-91128 Palaiseau, France. pina.romaniello@polytechnique.edu

The Journal of Chemical Physics
|February 5, 2009
PubMed
Summary
This summary is machine-generated.

We introduce a frequency-dependent kernel for time-dependent density-functional theory (TDDFT) to accurately describe double-excitation states in molecules. This approach overcomes limitations of static kernels, improving excited-state calculations.

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Last Updated: Jun 25, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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Published on: May 27, 2020

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Time-dependent density-functional theory (TDDFT) is a standard method for calculating electronic properties.
  • Standard TDDFT approximations struggle to describe excited states with double- and higher-excitation character, especially in open-shell systems.
  • Existing methods often yield excitation energies with only single-excitation character.

Purpose of the Study:

  • To develop a novel frequency-dependent exchange-correlation (xc) kernel for TDDFT.
  • To enable the accurate description of double-excitation states within TDDFT for finite systems.
  • To improve the calculation of excited-state properties, particularly for challenging molecular systems.

Main Methods:

  • Development of a frequency-dependent xc kernel derived from the Bethe-Salpeter equation.
  • Inclusion of a dynamically screened Coulomb interaction W(omega).
  • Application to a two-electron model system to validate the approach.

Main Results:

  • The proposed frequency-dependent xc kernel successfully reproduces double excitations in TDDFT calculations.
  • This method overcomes the limitations of static approximations, which fail to capture double-excitation character.
  • The frequency dependence of the screened Coulomb interaction is crucial for describing these states.

Conclusions:

  • The novel frequency-dependent xc kernel offers a significant advancement for TDDFT.
  • This approach enhances the capability of TDDFT to model complex excited states.
  • Accurate calculation of double excitations is now feasible for finite systems using this method.