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This study introduces tensor decomposition in the canonical polyadic (CP) format for Coupled Cluster (CC) theory, specifically for the Coupled Cluster Doubles method. This approach aims to reduce computational complexity in electronic structure calculations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Electronic Structure Theory

Background:

  • Previous work established tensor decomposition in the canonical polyadic (CP) format for electronic structure methods, focusing on two-electron integrals and Møller-Plesset perturbation theory (MP2).
  • Coupled Cluster (CC) theory is a powerful but computationally expensive method for accurate electronic structure calculations.

Purpose of the Study:

  • To extend the application of tensor decomposition in the CP format to Coupled Cluster (CC) theory.
  • To present a pilot implementation of CP tensor decomposition for the Coupled Cluster Doubles (CCD) method.
  • To investigate the iterative solution of CC amplitude equations using CP tensor representations.

Main Methods:

  • Utilized tensor decomposition in the canonical polyadic (CP) format for Coupled Cluster (CC) theory.
  • Developed and implemented a pilot version for the Coupled Cluster Doubles (CCD) method.
  • Employed an iterative approach for solving CC amplitude equations with CP tensors and a specialized tensor contraction scheme for efficient rank reduction.

Main Results:

  • Demonstrated the feasibility of using CP tensor format for Coupled Cluster (CC) theory, specifically for the Coupled Cluster Doubles (CCD) method.
  • Presented a tensor contraction scheme that minimizes computational effort during iterative rank reductions.
  • Discussed algorithmic complexity reduction, convergence behavior, truncation errors, and threshold selection for achieving chemical accuracy.

Conclusions:

  • The canonical polyadic (CP) tensor format shows promise for reducing the computational cost of Coupled Cluster (CC) methods.
  • The pilot implementation for Coupled Cluster Doubles (CCD) provides a foundation for further development and application of this technique.
  • Further research is warranted to fully explore the potential of CP tensor decomposition in advancing electronic structure calculations.