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Related Experiment Videos

Atomic-batched tensor decomposed two-electron repulsion integrals.

Gunnar Schmitz1, Niels Kristian Madsen1, Ove Christiansen1

  • 1Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark.

The Journal of Chemical Physics
|April 10, 2017
PubMed
Summary

A new integral format combines Resolution-of-the-Identity (RI) approximation with tensor decomposition for electron repulsion integrals. This method shows good accuracy and scalability for quantum chemistry calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of electron repulsion integrals is crucial for quantum chemistry.
  • Existing methods face challenges with computational scaling and storage requirements.
  • Tensor decomposition techniques offer potential for more efficient integral calculations.

Purpose of the Study:

  • To introduce a novel integral format for 4-index electron repulsion integrals.
  • To combine Resolution-of-the-Identity (RI) approximation with tensor decomposition and atomic batching.
  • To assess the efficiency, storage, and accuracy of the new format.

Main Methods:

  • Decomposition of 3-index RI integral tensors into atom-pair defined sub-tensors.
  • Accelerated decomposition to canonical product (CP) format using singular value decomposition and Tucker decomposition.

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  • Reassembly into full decomposed tensor (RC approach) or maintaining atomic batched format (ABC approach).
  • Comparison of RC and ABC approaches at the MP2 level for efficiency and storage.

    • Main Results:

    • The new integral format integrates RI approximation with tensor decomposition and atomic batching.
    • Both RC and ABC approaches demonstrate good accuracy.
    • The method is not limited to small systems, indicating scalability.
    • Efficiency and storage requirements were compared for RC and ABC at the MP2 level.

    Conclusions:

    • The presented integral format offers a promising approach for calculating electron repulsion integrals.
    • The combination of RI, tensor decomposition, and atomic batching leads to accurate and scalable methods.
    • This work paves the way for more efficient quantum chemistry calculations, including MP2 and coupled cluster methods.