### Abstract

Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the analytic computation of the energy Hessian matrix. A "skeleton" Hessian matrix is calculated from the unique blocks of electron repulsion integrals. The true Hessian matrix is generated by projecting the symmetric component out of the skeleton Hessian. The analysis is valid for many wave functions, including closed- or open-shell restricted and unrestricted Hartree-Fock wave functions, multiconfiguration Hartree-Fock wave functions, and configuration interaction wave functions. We also extend the use of translational invariance previously used for energy gradient calculations. To illustrate the method, we compare the computer time required for the two-electron contribution to the Hessian matrix of eclipsed ethane, using Pople's 6-31G** basis set and D_{3h} symmetry and various subgroups D_{3h}. Computational times are roughly inversely proportional to the order of the point group.

Original language | English |
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Pages (from-to) | 332-336 |

Number of pages | 5 |

Journal | Journal of Chemical Physics |

Volume | 75 |

Issue number | 1 |

Publication status | Published - 1981 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*75*(1), 332-336.

**Molecular symmetry. III. Second derivatives of electronic energy with respect to nuclear coordinates.** / Takada, Toshikazu; Dupuis, Michel; King, Harry F.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 75, no. 1, pp. 332-336.

}

TY - JOUR

T1 - Molecular symmetry. III. Second derivatives of electronic energy with respect to nuclear coordinates

AU - Takada, Toshikazu

AU - Dupuis, Michel

AU - King, Harry F.

PY - 1981

Y1 - 1981

N2 - Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the analytic computation of the energy Hessian matrix. A "skeleton" Hessian matrix is calculated from the unique blocks of electron repulsion integrals. The true Hessian matrix is generated by projecting the symmetric component out of the skeleton Hessian. The analysis is valid for many wave functions, including closed- or open-shell restricted and unrestricted Hartree-Fock wave functions, multiconfiguration Hartree-Fock wave functions, and configuration interaction wave functions. We also extend the use of translational invariance previously used for energy gradient calculations. To illustrate the method, we compare the computer time required for the two-electron contribution to the Hessian matrix of eclipsed ethane, using Pople's 6-31G** basis set and D3h symmetry and various subgroups D3h. 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 analytic computation of the energy Hessian matrix. A "skeleton" Hessian matrix is calculated from the unique blocks of electron repulsion integrals. The true Hessian matrix is generated by projecting the symmetric component out of the skeleton Hessian. The analysis is valid for many wave functions, including closed- or open-shell restricted and unrestricted Hartree-Fock wave functions, multiconfiguration Hartree-Fock wave functions, and configuration interaction wave functions. We also extend the use of translational invariance previously used for energy gradient calculations. To illustrate the method, we compare the computer time required for the two-electron contribution to the Hessian matrix of eclipsed ethane, using Pople's 6-31G** basis set and D3h symmetry and various subgroups D3h. Computational times are roughly inversely proportional to the order of the point group.

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M3 - Article

VL - 75

SP - 332

EP - 336

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

ER -