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Stochastic resolution of identity second-order Matsubara Green's function theory.

Tyler Y Takeshita1, Wenjie Dou2, Daniel G A Smith3

  • 1Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, USA.

The Journal of Chemical Physics
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We developed a new computational method, stochastic resolution of identity Green's function (sRI-GF2), to efficiently study electron correlations in large systems. This approach significantly reduces computational cost, making complex quantum chemistry calculations more accessible.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Second-order Green's function theory (GF2) is crucial for describing electron correlations.
  • Traditional GF2 methods face high computational costs, limiting their application to small systems.
  • Stochastic methods offer a path to reduce computational complexity in quantum chemistry.

Purpose of the Study:

  • To develop a computationally efficient stochastic method for second-order Green's function theory.
  • To reduce the computational scaling of GF2 calculations from O(N^5) to O(N^3).
  • To enable the study of weak correlations in large molecular systems.

Main Methods:

  • Developed a stochastic resolution of the identity (sRI) representation for GF2.
  • Decoupled the second-order Born self-energy using stochastic Coulomb integral resolution.
  • Reduced computational cost via matrix products and contractions.

Main Results:

  • The stochastic resolution of identity Green's function (sRI-GF2) method achieves O(N^3) computational scaling.
  • sRI-GF2 accurately reproduces deterministic GF2 results for small systems.
  • The method demonstrates computational speedup over deterministic GF2 for systems with over 80 atomic orbitals.

Conclusions:

  • sRI-GF2 is a practical and computationally efficient approach for studying weak electron correlations.
  • The method is suitable for large systems with thousands of electrons.
  • This work extends previous stochastic methods and offers an alternative to existing GF2 formulations.