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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
|August 3, 2019
Summary
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.
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.
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