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Combinatorial invariants and covariants as tools for conical intersections.

Itai Ryb1, Roi Baer

  • 1Department of Physical Chemistry and the Lise Meitner Minerva-Center for Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

The Journal of Chemical Physics
|November 20, 2004
PubMed
Summary

Researchers developed new computational tools to analyze conical intersections in molecules. These methods efficiently locate these intersections without complex calculations, simplifying molecular electronic structure analysis.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Molecular Physics

Background:

  • Conical intersections are critical in molecular dynamics and photochemistry.
  • Analyzing these intersections is computationally challenging.
  • Existing methods often rely on complex calculations like nonadiabatic couplings.

Purpose of the Study:

  • Introduce novel computational tools for analyzing conical intersections.
  • Develop an efficient and robust method for locating conical intersections.
  • Provide a gauge-covariant method for adiabatic-diabatic transformations.

Main Methods:

  • Introduced the combinatorial invariant and covariant for analyzing adiabatic electronic states.
  • Developed a method based on the combinatorial invariant to locate conical intersections.

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  • Generalized concepts to higher dimensions for gauge-covariant transformations.

    • Main Results:

    • The combinatorial invariant relates to the Berry phase, indicating the number of conical intersections.
    • A computationally simple and efficient method for locating conical intersections was developed.
    • A gauge-covariant adiabatic-diabatic transformation matrix can be constructed without nonadiabatic couplings.

    Conclusions:

    • The combinatorial invariant and covariant offer practical and robust tools for molecular electronic structure analysis.
    • The developed methods are computationally efficient and readily implementable in standard quantum chemistry codes.
    • These techniques simplify the study of conical intersections and related phenomena.