### Abstract

For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two‐electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre–Elder procedure. We compare SCF calculations on the phosphorus molecule using T_{d} symmetry with those using various subgroups of T_{d}. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry‐related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.

Original language | English |
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Pages (from-to) | 613-625 |

Number of pages | 13 |

Journal | International Journal of Quantum Chemistry |

Volume | 11 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1977 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*,

*11*(4), 613-625. https://doi.org/10.1002/qua.560110408

**Molecular symmetry and closed‐shell SCF calculations. I.** / Dupuis, Michel; King, Harry F.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 11, no. 4, pp. 613-625. https://doi.org/10.1002/qua.560110408

}

TY - JOUR

T1 - Molecular symmetry and closed‐shell SCF calculations. I

AU - Dupuis, Michel

AU - King, Harry F.

PY - 1977

Y1 - 1977

N2 - For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two‐electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre–Elder procedure. We compare SCF calculations on the phosphorus molecule using Td symmetry with those using various subgroups of Td. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry‐related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.

AB - For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two‐electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre–Elder procedure. We compare SCF calculations on the phosphorus molecule using Td symmetry with those using various subgroups of Td. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry‐related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.

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U2 - 10.1002/qua.560110408

DO - 10.1002/qua.560110408

M3 - Article

VL - 11

SP - 613

EP - 625

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 4

ER -