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π Electron Effects on Chemical Shift: Overview01:27

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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...
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Related Experiment Video

Updated: May 30, 2026

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

Multi-scale extensions to quantum cluster methods for strongly correlated electron systems.

C Slezak1, M Jarrell, Th Maier

  • 1Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 12, 2011
PubMed
Summary

A new multi-scale approach accurately models strongly correlated electron systems by combining different methods for various length scales. This method shows excellent agreement with quantum Monte Carlo calculations for the Hubbard model.

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Last Updated: May 30, 2026

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory

Background:

  • Strongly correlated electron systems present significant computational challenges.
  • Existing methods struggle to capture correlations across all relevant length scales.

Purpose of the Study:

  • Introduce a numerically implementable multi-scale many-body approach for strongly correlated electron systems.
  • Develop a method that approximates correlations based on their strength at different length scales.

Main Methods:

  • Extend quantum cluster methods to incorporate multi-scale correlation approximations.
  • Treat short length scales explicitly, long scales with dynamical mean-field theory, and intermediate scales diagrammatically.
  • Apply the method to the one-dimensional Hubbard model.

Main Results:

  • The developed multi-scale self-energy demonstrates strong quantitative agreement with quantum Monte Carlo results.
  • Achieved accurate results comparable to more computationally intensive methods.

Conclusions:

  • The multi-scale approach offers an efficient and accurate way to study strongly correlated electron systems.
  • This method provides a viable alternative for complex quantum many-body problems.