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Related Experiment Videos

Select-divide-and-conquer method for large-scale configuration interaction.

Carlos F Bunge1, Ramon Carbó-Dorca

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, México 01000, México. bunge@fisica.unam.mx

The Journal of Chemical Physics
|July 26, 2006
PubMed
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A novel select-divide-and-conquer method approximates configuration interaction (CI) for large N-electron systems. This approach efficiently manages computational resources, achieving high accuracy in electronic structure calculations.

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Physics

Background:

  • Configuration Interaction (CI) methods are crucial for accurate electronic structure calculations.
  • Approximating the full CI space is necessary due to its exponential scaling with system size.
  • Existing methods face challenges in handling large, complex molecular systems.

Purpose of the Study:

  • To present a novel select-divide-and-conquer variational method for approximating CI.
  • To develop a computationally efficient approach for large N-electron systems.
  • To achieve high accuracy in determining energy eigenvalues for complex quantum systems.

Main Methods:

  • A divide-and-conquer strategy is employed to split the N-electron space into manageable subspaces.

Related Experiment Videos

  • Threshold-based selection (tao) is used to partition configurations based on their attributes.
  • Davidson's eigensolver is iteratively applied to progressively larger subspaces.
  • Subspace dimensions are managed to fit within Random Access Memory (RAM) constraints.

    • Main Results:

    • The method achieves high accuracy, with energy eigenvalues consistently above exact eigenvalues.
    • One microhartree accuracy was demonstrated for a problem with 24x10^6 dimensions and 1.2x10^12 non-zero matrix elements.
    • Hamiltonian matrix-element evaluation becomes the rate-determining step in highly accurate calculations.

    Conclusions:

    • The select-divide-and-conquer variational method offers an efficient and accurate way to approximate CI.
    • This approach effectively manages computational complexity for large quantum systems.
    • The method provides a viable pathway for high-accuracy electronic structure calculations in computational chemistry.