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Related Concept Videos

Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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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.
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Spin–Spin Coupling Constant: Overview

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Evaluation of the spin-orbit interaction within the graphically contracted function method.

Scott R Brozell1, Ron Shepard

  • 1Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.

The Journal of Physical Chemistry. A
|September 10, 2009
PubMed
Summary
This summary is machine-generated.

The study introduces two new methods, SO-GCF and SO-SCGCF, for calculating spin-orbit interactions in quantum chemistry. These methods efficiently construct Hamiltonian matrices, enabling calculations for much larger systems than previously possible.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • The accurate computation of spin-orbit (SO) interactions is crucial for understanding molecular properties.
  • Traditional methods for including SO effects in electronic structure calculations are computationally expensive and limited in scale.
  • The graphically contracted function (GCF) method offers a more efficient approach to constructing wave functions.

Purpose of the Study:

  • To extend the graphically contracted function (GCF) method to incorporate an effective one-electron spin-orbit (SO) operator.
  • To develop and implement two novel algorithms, SO-GCF and SO-SCGCF, for efficient Hamiltonian matrix construction including SO effects.
  • To enable the study of larger and more complex molecular systems with spin-orbit coupling.

Main Methods:

  • Implementation of an effective one-electron spin-orbit operator within the GCF framework.
  • Development of two algorithms: SO-GCF, expanding the wave function in GCFs, and SO-SCGCF, using spin-contracted functions.
  • Utilizing a multiheaded Shavitt graph approach for efficient computation of Hamiltonian matrix elements.

Main Results:

  • The SO-GCF and SO-SCGCF methods allow for Hamiltonian matrix construction scaling as O(N(alpha)(2)omegan(4)).
  • These methods enable calculations for systems with up to N=n=128, corresponding to underlying expansions of over 10^75 configuration state functions (CSFs).
  • The SO-SCGCF method shows slightly faster Hamiltonian matrix construction than SO-GCF for single states, while SO-GCF may be better for multiple states.

Conclusions:

  • The extended GCF methods provide a significant advancement in computational efficiency for treating spin-orbit interactions.
  • These new approaches overcome the limitations of traditional configuration interaction methods for large-scale SO-CI calculations.
  • The developed algorithms offer flexibility for studying single or multiple electronic states with spin-orbit coupling.