### Abstract

Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the coupled perturbed Hartree–Fock (CPHF) formalism, a key step in the analytical computation of energy first derivatives for configuration interaction (CI) wavefunctions, and energy second derivatives for Hartree–Fock (HF) wavefunctions. One possible computational strategy is to construct Fock‐like matrices for each nuclear coordinate in which the one‐ and two‐electron integrals of the usual Fock matrix are replaced by the integral first derivatives. “Skeleton” matrices are constructed from the unique blocks of electron‐repulsion integral derivatives. The correct matrices are generated by applying a symmetrization operator. The analysis is valid for many wavefunctions, including closed‐ or open‐shell spin‐restricted and spin‐unrestricted HF wavefunctions. To illustrate the method, we compare the computer time required for setting up the coupled perturbed HF equations for eclipsed ethane using D_{3} _{h} symmetry point group and various subgroups of D_{3} _{h}. Computational times are roughly inversely proportional to the order of the point group.

Original language | English |
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Pages (from-to) | 234-240 |

Number of pages | 7 |

Journal | Journal of Computational Chemistry |

Volume | 4 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Chemistry(all)
- Computational Mathematics

### Cite this

*Journal of Computational Chemistry*,

*4*(2), 234-240. https://doi.org/10.1002/jcc.540040214

**Molecular symmetry. IV. The coupled perturbed Hartree–Fock method.** / Takada, Toshikazu; Dupuis, Michel; King, Harry F.

Research output: Contribution to journal › Article

*Journal of Computational Chemistry*, vol. 4, no. 2, pp. 234-240. https://doi.org/10.1002/jcc.540040214

}

TY - JOUR

T1 - Molecular symmetry. IV. The coupled perturbed Hartree–Fock method

AU - Takada, Toshikazu

AU - Dupuis, Michel

AU - King, Harry F.

PY - 1983

Y1 - 1983

N2 - Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the coupled perturbed Hartree–Fock (CPHF) formalism, a key step in the analytical computation of energy first derivatives for configuration interaction (CI) wavefunctions, and energy second derivatives for Hartree–Fock (HF) wavefunctions. One possible computational strategy is to construct Fock‐like matrices for each nuclear coordinate in which the one‐ and two‐electron integrals of the usual Fock matrix are replaced by the integral first derivatives. “Skeleton” matrices are constructed from the unique blocks of electron‐repulsion integral derivatives. The correct matrices are generated by applying a symmetrization operator. The analysis is valid for many wavefunctions, including closed‐ or open‐shell spin‐restricted and spin‐unrestricted HF wavefunctions. To illustrate the method, we compare the computer time required for setting up the coupled perturbed HF equations for eclipsed ethane using D3 h symmetry point group and various subgroups of D3 h. Computational times are roughly inversely proportional to the order of the point group.

AB - Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the coupled perturbed Hartree–Fock (CPHF) formalism, a key step in the analytical computation of energy first derivatives for configuration interaction (CI) wavefunctions, and energy second derivatives for Hartree–Fock (HF) wavefunctions. One possible computational strategy is to construct Fock‐like matrices for each nuclear coordinate in which the one‐ and two‐electron integrals of the usual Fock matrix are replaced by the integral first derivatives. “Skeleton” matrices are constructed from the unique blocks of electron‐repulsion integral derivatives. The correct matrices are generated by applying a symmetrization operator. The analysis is valid for many wavefunctions, including closed‐ or open‐shell spin‐restricted and spin‐unrestricted HF wavefunctions. To illustrate the method, we compare the computer time required for setting up the coupled perturbed HF equations for eclipsed ethane using D3 h symmetry point group and various subgroups of D3 h. Computational times are roughly inversely proportional to the order of the point group.

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U2 - 10.1002/jcc.540040214

DO - 10.1002/jcc.540040214

M3 - Article

VL - 4

SP - 234

EP - 240

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 2

ER -