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π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...
Chemical Shift: Internal References and Solvent Effects01:17

Chemical Shift: Internal References and Solvent Effects

In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
The internal reference compound generally used in NMR spectroscopy is tetramethylsilane (TMS). TMS is preferred because it is chemically inert, soluble in NMR solvents, and easily removable. Also, the highly shielded methyl protons in TMS yield an intense...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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 π orbitals.
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...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
Inductive Effects on Chemical Shift: Overview01:27

Inductive Effects on Chemical Shift: Overview

The protons in unsubstituted alkanes are strongly shielded with chemical shifts below 1.8 ppm. Methine, methylene, and methyl protons appear at approximately 1.7, 1.2 and 0.7 ppm, while the proton signal from methane appears at 0.23 ppm. An electronegative substituent, such as chlorine, withdraws the electron density from the protons, increasing their chemical shift. Progressive substitution of the hydrogens in methane by chlorine shifts the proton signals increasingly downfield, to 3.05 ppm in...

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Updated: Jun 1, 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

Multi-reference state-universal coupled-cluster approaches to electronically excited states.

Xiangzhu Li1, Josef Paldus

  • 1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

The Journal of Chemical Physics
|June 14, 2011
PubMed
Summary

The general model space, state-universal coupled-cluster (GMS-SU-CC) method accurately describes molecular excited states. This approach, including GMS-SU-CCSD(T), shows promise for complex electronic structure calculations.

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Related Experiment Videos

Last Updated: Jun 1, 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

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization
08:22

Measurement of Ultrafast Vibrational Coherences in Polyatomic Radical Cations with Strong-Field Adiabatic Ionization

Published on: August 6, 2018

Area of Science:

  • Quantum Chemistry
  • Computational Spectroscopy
  • Electronic Structure Theory

Background:

  • Accurate description of low-lying excited states is crucial for understanding molecular properties and reactivity.
  • Multi-reference coupled-cluster (MR CC) methods are powerful tools for electronic structure calculations, especially for systems with static and dynamic correlation.

Purpose of the Study:

  • To evaluate the performance of general model space, state-universal coupled-cluster (GMS-SU-CC) methods, including GMS-SU-CCSD and its triple-corrected variant GMS-SU-CCSD(T).
  • To assess the ability of these methods to simultaneously describe multiple electronic states of the same symmetry.
  • To investigate the impact of C-conditions, model space selection, and perturbative triples on the accuracy of excited state calculations.

Main Methods:

  • Application of GMS-SU-CCSD and GMS-SU-CCSD(T) methods to calculate vertical excitation energies.
  • Consideration of C-conditions for incomplete general model spaces.
  • Perturbative inclusion of secondary triple excitations.
  • Comparison with equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), density functional theory (DFT), and experimental data.

Main Results:

  • GMS-type SU-CC approaches demonstrate significant utility in describing low-lying excited states for various molecules, including diatomic (BN) and larger systems (formaldehyde, trans-butadiene, formamide, benzene).
  • The methods effectively handle simultaneous description of multiple states within the same symmetry.
  • The study highlights potential ambiguities arising from large basis sets and the importance of appropriate model space construction.

Conclusions:

  • GMS-type MR-CC methods, particularly GMS-SU-CCSD(T), offer a robust and accurate framework for calculating vertical excitation energies.
  • These approaches provide a valuable alternative to EOM-CCSD for challenging electronic structure problems involving excited states.
  • The findings underscore the potential of GMS-type SU-CC methods for advancing computational spectroscopy and understanding molecular excited states.