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Arnaud Leclerc1, Georges Jolicard2

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Summary
This summary is machine-generated.

We introduce a novel wave operator method for calculating eigenvalues and eigenvectors of large parameter-dependent matrices. This adaptive approach efficiently handles complex systems, including non-Hermitian Hamiltonians, offering competitive convergence and constant memory cost.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Calculating eigenvalues and eigenvectors of large parameter-dependent matrices is computationally intensive.
  • Existing methods may struggle with non-Hermitian Hamiltonians or require significant memory.
  • Adaptive techniques are needed to improve efficiency and accuracy.

Purpose of the Study:

  • To develop a new wave operator method for parameter-dependent matrices.
  • To incorporate adaptive active subspaces and projectors for improved efficiency.
  • To handle both Hermitian and non-Hermitian Hamiltonians.

Main Methods:

  • A wave operator method utilizing an adaptive active subspace.
  • Adaptive projectors that dynamically adjust to changing parameters.
  • An iterative algorithm compared against standard wave operator and block-Davidson methods.

Main Results:

  • The proposed method demonstrates competitive performance, converging in a few dozen iterations.
  • Constant memory cost is maintained throughout the calculations.
  • Successful application to a 4D-coupled oscillator model and molecular photodissociation of H2+.

Conclusions:

  • The adaptive wave operator method provides an efficient and accurate approach for large parameter-dependent matrices.
  • The technique is versatile, applicable to both Hermitian and non-Hermitian systems.
  • It offers a promising alternative for complex quantum mechanical calculations, particularly in molecular physics.