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Stochastic Self-Consistent Second-Order Green's Function Method for Correlation Energies of Large Electronic Systems.

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A new stochastic Green's function approach (sGF2) significantly reduces computational costs for quantum chemistry calculations. This method achieves cubic scaling, making large system size calculations feasible and accurate with minimal error.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • The second-order Matsubara Green's function method (GF2) is a powerful quantum chemistry technique.
  • GF2's computational cost scales steeply with system size, limiting its application.

Purpose of the Study:

  • To develop a more computationally efficient version of the GF2 method.
  • To enable accurate calculations for larger quantum systems.

Main Methods:

  • Developed a stochastic approach to GF2 (sGF2).
  • Reduced the self-energy estimation step's scaling from fifth power to quadratic.
  • Achieved overall cubic scaling for the sGF2 method.

Main Results:

  • The sGF2 method demonstrates numerical stability, efficiency, and accuracy.
  • Stochastic errors are minimal (≤0.1% of correlation energy for large systems).
  • A byproduct is a fast stochastic MP2 (sMP2) method with linear scaling.

Conclusions:

  • sGF2 significantly enhances the feasibility of large-scale quantum chemistry calculations.
  • The method is general and applicable to various systems at different temperatures.
  • sGF2 offers a robust and accurate alternative for electronic structure studies.