### Abstract

A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H_{2}O, CH_{4}, and C_{6}H_{6} within a few mE_{h} after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.

Original language | English (US) |
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Article number | 4862255 |

Journal | Journal of Chemical Physics |

Volume | 140 |

Issue number | 3 |

DOIs | |

State | Published - Feb 10 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*140*(3), [4862255]. https://doi.org/10.1063/1.4862255