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Joonho Lee1,2, Lin Lin3,4, Martin Head-Gordon1,2

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|December 4, 2019
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We developed a new, improvable tensor hypercontraction (THC) factorization using interpolative separable density fitting (ISDF) for accurate quantum chemistry calculations. This method offers a tunable balance between computational cost and accuracy for various electronic structure methods.

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Area of Science:

  • Computational Quantum Chemistry
  • Electronic Structure Theory
  • Method Development

Background:

  • Accurate electronic structure calculations are crucial for understanding molecular properties.
  • Tensor hypercontraction (THC) methods offer a path to reduce computational scaling.
  • Existing THC methods require careful parameterization for accuracy and efficiency.

Purpose of the Study:

  • To present a systematically improvable tensor hypercontraction (THC) factorization.
  • To introduce interpolative separable density fitting (ISDF) as a key component of the THC factorization.
  • To develop and evaluate THC algorithms combined with the resolution-of-the-identity (RI) technique for electronic structure calculations.

Main Methods:

  • Developed a novel THC factorization based on interpolative separable density fitting (ISDF).
  • Integrated ISDF with Becke's atom-centered quadrature grid and the resolution-of-the-identity (RI) technique.
  • Applied the developed THC-RI algorithms to cubic-scaling exact exchange (Hartree-Fock, range-separated hybrids) and quartic-scaling Møller-Plesset perturbation theory (MP2, MP3).

Main Results:

  • Demonstrated that a single ISDF parameter (c_ISDF) controls the accuracy-cost trade-off.
  • Showcased the convergence of THC-RI algorithms to numerically exact RI results across standard Dunning basis sets.
  • Validated the utility of THC-RI for larger systems, including water clusters and C20, for exact exchange and MP2 calculations.

Conclusions:

  • The developed THC-RI factorization provides a systematically improvable and tunable approach for quantum chemistry.
  • Recommendations for optimal c_ISDF parameters are provided for different basis sets and electronic structure methods.
  • Future work should focus on stable THC factorization for wave function amplitudes and virtual orbital spaces in large basis sets.