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# Stochastic resolution of identity second-order Matsubara Green’s function theory

## Abstract

We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N ^{5}) to O(N ^{3}) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10 ^{3} electrons and more.

- Authors:

- Mercedes-Benz Research and Development North America, Sunnyvale, CA (United States); Univ. of California, Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States)
- Molecular Sciences Software Inst., Blacksburg, VA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Hebrew Univ. of Jerusalem (Israel)
- Univ. of California, Los Angeles, CA (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ., Ramat Aviv (Israel)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

- OSTI Identifier:
- 1577602

- Alternate Identifier(s):
- OSTI ID: 1568913

- Grant/Contract Number:
- AC02-05CH11231; DEAC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 151; Journal Issue: 4; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Stochastic resolution of identity second-order Matsubara Green’s function theory. United States: N. p., 2019.
Web. doi:10.1063/1.5108840.
```

```
Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, & Rabani, Eran. Stochastic resolution of identity second-order Matsubara Green’s function theory. United States. doi:10.1063/1.5108840.
```

```
Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Tue .
"Stochastic resolution of identity second-order Matsubara Green’s function theory". United States. doi:10.1063/1.5108840.
```

```
@article{osti_1577602,
```

title = {Stochastic resolution of identity second-order Matsubara Green’s function theory},

author = {Takeshita, Tyler Y. and Dou, Wenjie and Smith, Daniel G. A. and de Jong, Wibe A. and Baer, Roi and Neuhauser, Daniel and Rabani, Eran},

abstractNote = {We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.},

doi = {10.1063/1.5108840},

journal = {Journal of Chemical Physics},

number = 4,

volume = 151,

place = {United States},

year = {2019},

month = {7}

}

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