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Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic.

Jean Christophe Tremblay1, Tucker Carrington

  • 1Département de chimie, Université de Montréal, succursale Centre-ville, Québec, Canada.

The Journal of Chemical Physics
|July 23, 2005
PubMed
Summary
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This study presents a novel non-Hermitian-Lanczos method for calculating resonance energies and widths. This approach efficiently computes eigenvalues using a real matrix, avoiding complex calculations and providing accurate results for molecular systems like HCO.

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Calculating resonance energies and widths is crucial for understanding unstable quantum systems.
  • Existing methods often involve computationally expensive complex matrix operations or parameter searches.
  • Complex Absorbing Potentials (CAPs) are effective but require careful implementation.

Purpose of the Study:

  • To introduce a new, efficient method for computing resonance energies and widths.
  • To avoid complex matrix-vector products in resonance calculations.
  • To achieve accurate resonance properties without extensive parameter tuning.

Main Methods:

  • A non-Hermitian-Lanczos approach is employed to compute eigenvalues of H+W.
  • The method leverages the connection between a CAP-modified Hamiltonian and a real, nonsymmetric matrix U.

Related Experiment Videos

  • A coupled-two-term Lanczos procedure is utilized.

    • Main Results:

    • Accurate resonance energies and widths were obtained for the HCO molecule.
    • The method avoids solving eigenvalue problems for multiple CAP strengths.
    • Computational efficiency is improved by eliminating complex matrix-vector products.

    Conclusions:

    • The non-Hermitian-Lanczos method offers an efficient and accurate alternative for resonance calculations.
    • This approach simplifies the determination of resonance properties.
    • The method shows promise for applications in various quantum mechanical systems.