# Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory

## Abstract

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Møller–Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(N _{AO3}) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(N _{e} ^{2.4}) for total energies and O(N _{e} ^{3.1}) for forces (N _{e} being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.

- Authors:

- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. of California, Los Angeles, CA (United States)
- Hebrew Univ. of Jerusalem (Israel). Fritz Harber Center for Molecular Dynamics
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ. (Israel), The Sacler Center for Computational Molecular Science

- 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)

- OSTI Identifier:
- 1543624

- Grant/Contract Number:
- [AC02-05CH11231]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Theory and Computation

- Additional Journal Information:
- [ Journal Volume: 13; Journal Issue: 10]; Journal ID: ISSN 1549-9618

- Publisher:
- American Chemical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Physics

### Citation Formats

```
Takeshita, Tyler Y., de Jong, Wibe A., Neuhauser, Daniel, Baer, Roi, and Rabani, Eran. Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory. United States: N. p., 2017.
Web. doi:10.1021/acs.jctc.7b00343.
```

```
Takeshita, Tyler Y., de Jong, Wibe A., Neuhauser, Daniel, Baer, Roi, & Rabani, Eran. Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory. United States. doi:10.1021/acs.jctc.7b00343.
```

```
Takeshita, Tyler Y., de Jong, Wibe A., Neuhauser, Daniel, Baer, Roi, and Rabani, Eran. Fri .
"Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory". United States. doi:10.1021/acs.jctc.7b00343. https://www.osti.gov/servlets/purl/1543624.
```

```
@article{osti_1543624,
```

title = {Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory},

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

abstractNote = {A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Møller–Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(NAO3) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(Ne2.4) for total energies and O(Ne3.1) for forces (Ne being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.},

doi = {10.1021/acs.jctc.7b00343},

journal = {Journal of Chemical Theory and Computation},

number = [10],

volume = [13],

place = {United States},

year = {2017},

month = {9}

}

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