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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.0K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

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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...
303
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...
1.1K
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

11.7K
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:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
11.7K
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.6K
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...
1.6K
Atomic Spectroscopy: Absorption, Emission, and Fluorescence01:23

Atomic Spectroscopy: Absorption, Emission, and Fluorescence

1.3K
Atomic spectroscopy is a vital tool in elemental analysis, both qualitatively and quantitatively. It can be broadly divided into optical spectroscopy, mass spectroscopy, and X-ray spectroscopy methods. The optical spectroscopic methods are atomic absorption spectroscopy (AAS), atomic emission spectroscopy (AES), and atomic fluorescence spectroscopy (AFS). The first step in all three methods is atomization, where the solid, liquid, or solution-phase samples are converted into gas-phase atoms and...
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Updated: Sep 16, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excited-state methods based on state-averaged long-range CASSCF short-range DFT.

Benjamin Helmich-Paris1, Erik Rosendahl Kjellgren2, Hans Jørgen Aa Jensen2

  • 1Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany. helmichparis@kofo.mpg.de.

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|July 10, 2025
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Summary
This summary is machine-generated.

Two new methods, SA-CAS-srDFT and CI-srDFT, calculate excited states using density functional theory. CI-srDFT shows improved accuracy for organic molecules, offering a more reliable approach for electronic excitation energy calculations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of excited states is crucial for understanding molecular properties and reactions.
  • Existing methods like CASSCF-DFT have limitations in accuracy and applicability, especially for complex systems.

Purpose of the Study:

  • To develop and evaluate novel state-averaging (SA)-based methodologies for calculating excited states.
  • To compare the performance of these new methods against existing approaches for various molecular systems.

Main Methods:

  • Proposed two distinct state-averaging (SA)-based methodologies: SA-CAS-srDFT and CI-srDFT.
  • Utilized a long-range complete active space self-consistent field (CASSCF) short-range density functional theory (DFT) approach (CAS-srDFT).
  • Employed total one-body and on-top pair density (OTPD) for final energy evaluation and benchmarked against multiconfiguration pair-density functional theory (MC-PDFT).

Main Results:

  • CI-srDFT provides physically correct potential curves for ethylene, unlike SA-CAS-srDFT.
  • CI-srDFT exhibits reduced dependence of excitation energies on the number of states averaged.
  • CI-srDFT achieved a mean absolute error of 0.17 eV for singlet excitation energies of organic chromophores using the sr-ctPBE functional.
  • The developed methods showed impressive accuracy for organic molecules but were not transferable to transition-metal complexes.

Conclusions:

  • CI-srDFT is a more accurate and reliable method for calculating excited states of organic molecules compared to SA-CAS-srDFT.
  • Current CASSCF-DFT and MC-PDFT methods do not consistently improve upon CASSCF excitation energies, particularly for transition-metal complexes.