### Abstract

Elongation Hartree-Fock (ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However, it is a simpler method to form the Fock matrix directly from localized molecular orbitals, which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step, almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality, molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.

Original language | Chinese |
---|---|

Pages (from-to) | 91-102 |

Number of pages | 12 |

Journal | Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni*,

*58*(1), 91-102. https://doi.org/10.13471/j.cnki.acta.snus.2019.01.011

**趋于线性标度的增长法:基于局域定域分子轨道的双电子积分.** / Price, David R.; Peng, Liang; Li, Shaopeng; Gu, Fenglong; Aoki, Yuriko.

Research output: Contribution to journal › Article

*Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni*, vol. 58, no. 1, pp. 91-102. https://doi.org/10.13471/j.cnki.acta.snus.2019.01.011

}

TY - JOUR

T1 - 趋于线性标度的增长法:基于局域定域分子轨道的双电子积分

AU - Price, David R.

AU - Peng, Liang

AU - Li, Shaopeng

AU - Gu, Fenglong

AU - Aoki, Yuriko

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Elongation Hartree-Fock (ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However, it is a simpler method to form the Fock matrix directly from localized molecular orbitals, which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step, almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality, molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.

AB - Elongation Hartree-Fock (ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However, it is a simpler method to form the Fock matrix directly from localized molecular orbitals, which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step, almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality, molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.

UR - http://www.scopus.com/inward/record.url?scp=85066807909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066807909&partnerID=8YFLogxK

U2 - 10.13471/j.cnki.acta.snus.2019.01.011

DO - 10.13471/j.cnki.acta.snus.2019.01.011

M3 - 記事

VL - 58

SP - 91

EP - 102

JO - Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni

JF - Zhongshan Daxue Xuebao/Acta Scientiarum Natralium Universitatis Sunyatseni

SN - 0529-6579

IS - 1

ER -