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Related Concept Videos

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.
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...

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Parallel computation of coupled-cluster hyperpolarizabilities.

Jeff R Hammond1, Karol Kowalski

  • 1Department of Chemistry, The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA. jhammond@uchicago.edu

The Journal of Chemical Physics
|May 27, 2009
PubMed
Summary
This summary is machine-generated.

Accurate calculation of molecular static hyperpolarizabilities is crucial for nonlinear optical studies. Coupled-cluster response theory and density functional theory methods were compared, identifying optimal computational approaches for various molecules.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Molecular modeling

Background:

  • Static hyperpolarizabilities are key molecular properties for nonlinear optical (NLO) applications.
  • Accurate theoretical prediction of these properties is essential for designing novel NLO materials.
  • Evaluating the performance of different computational methods is vital for reliable NLO studies.

Purpose of the Study:

  • To assess the accuracy of coupled-cluster response theory and four density functional theory (DFT) methods for calculating static hyperpolarizabilities.
  • To determine appropriate computational methods and basis sets for NLO studies across diverse molecular types.
  • To establish a framework for estimating quantum chemical approximation errors in QM/MM calculations.

Main Methods:

  • Coupled-cluster response theory (CCRT) calculations with large basis sets.
  • Comparison with four common density functional theory (DFT) methods.
  • High-performance computing for large-scale electronic structure calculations.

Main Results:

  • CCRT results served as a benchmark for evaluating DFT method performance.
  • Specific DFT methods and basis sets were identified as suitable for different molecular systems.
  • The study demonstrated the feasibility of large-scale electronic structure calculations on modern supercomputers.

Conclusions:

  • The findings guide the selection of accurate and efficient computational strategies for NLO property prediction.
  • This work provides insights into error estimation for advanced computational chemistry applications.
  • Modern computational resources enable complex quantum chemical calculations for materials science research.