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Related Experiment Video

Updated: Jun 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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An algebraic proof of generalized Wick theorem.

Liguo Kong1, Marcel Nooijen, Debashis Mukherjee

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

The Journal of Chemical Physics
|June 25, 2010
PubMed
Summary

This study defines multireference normal order theory and provides algebraic proof for its contraction rules. The generalized theory allows for fewer restrictions, enabling extensions like quasi-normal-order theory.

Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The multireference normal order theory, established by Kutzelnigg and Mukherjee, provides a framework for handling complex electronic structures.
  • Existing theories often rely on specific mathematical properties, such as cumulants, which can limit their applicability.

Purpose of the Study:

  • To explicitly define the multireference normal order theory and provide an algebraic proof for its contraction rules.
  • To relax the restrictions of the original theory, allowing for broader applications.
  • To develop an extended quasi-normal-order theory based on one-particle contractions.

Main Methods:

  • An algebraic proof is presented for the contraction rules governing the product of two normal ordered operators.
  • The proof demonstrates that contractions do not need to be cumulants.

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  • The theory is extended by allowing contractions to be defined up to a certain level.

    • Main Results:

    • A generalized set of contraction rules for multireference normal order theory is established.
    • The proof confirms the validity of these rules even when contractions are not cumulants or are only partially defined.
    • A novel quasi-normal-order theory is developed, incorporating one-body contractions derived from the one-particle reduced density matrix.

    Conclusions:

    • The generalized multireference normal order theory offers a more flexible and less restrictive approach to theoretical chemistry calculations.
    • The developed quasi-normal-order theory provides a simplified yet powerful tool for specific quantum chemical problems.
    • These advancements contribute to more accurate and efficient methods for studying electronic structures in complex systems.