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Related Concept Videos

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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...
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...
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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Analytic gradients for the state-specific multireference coupled cluster singles and doubles model.

Eric Prochnow1, Francesco A Evangelista, Henry F Schaefer

  • 1Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany. eric.prochnow@uni-mainz.de

The Journal of Chemical Physics
|August 21, 2009
PubMed
Summary

This study presents analytic energy gradients for state-specific multireference coupled cluster theory, enabling efficient large-scale quantum chemistry calculations. The developed method accurately determines molecular geometries for complex systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Multireference coupled cluster (MRCC) methods are crucial for describing systems with strong electron correlation.
  • State-specific MRCC (SS-MRCC) methods offer a more accurate treatment of excited states and bond-breaking processes.
  • Analytic energy gradients are essential for geometry optimization and reaction pathway exploration in computational chemistry.

Purpose of the Study:

  • To develop and implement analytic energy gradients for the state-specific multireference coupled cluster (SS-MRCC) method.
  • To provide a computationally efficient and scalable approach for calculating energy gradients in complex quantum chemical systems.
  • To validate the implemented method by applying it to determine the equilibrium geometries of pyridyne isomers.

Main Methods:

  • Derivation of energy gradient expressions using a Lagrangian formalism.
  • Implementation of SS-MRCC energy gradients within the singles and doubles approximation, restricted to two determinants.
  • Decomposition of MRCC gradient expressions into single-reference and coupling terms for efficient computation.
  • Utilizing density-matrix notation for seamless integration into quantum chemistry software.

Main Results:

  • A computationally efficient implementation of SS-MRCC analytic energy gradients with O(dN^6) scaling was achieved.
  • The method was successfully applied to compute equilibrium geometries of 2,6-pyridyne isomers and the pyridynium cation.
  • The results obtained were comparable to those from single-reference coupled cluster calculations, demonstrating the method's viability.

Conclusions:

  • The developed analytic energy gradients for SS-MRCC theory are suitable for large-scale computational chemistry applications.
  • This work provides a robust tool for accurate geometry optimizations in systems requiring multireference electronic structure treatments.
  • The findings pave the way for future advancements in multireference coupled cluster theory and its applications in chemistry.