### Abstract

The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton-Raphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy-free internal coordinates. This procedure, already used for the geometry optimization of porphine, C_{20}N_{4}H _{14}, is illustrated here at the ab initio self-consistent-field level for the four-membered ring azetidine, for bicyclo[2.2.2]octane, and for the four-ring system C_{16}O_{2}H_{22}, the skeleton of taxol.

Original language | English |
---|---|

Pages (from-to) | 2856-2860 |

Number of pages | 5 |

Journal | The Journal of Chemical Physics |

Volume | 96 |

Issue number | 4 |

Publication status | Published - 1992 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*96*(4), 2856-2860.

**Geometry optimization in redundant internal coordinates.** / Pulay, P.; Fogarasi, G.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 96, no. 4, pp. 2856-2860.

}

TY - JOUR

T1 - Geometry optimization in redundant internal coordinates

AU - Pulay, P.

AU - Fogarasi, G.

PY - 1992

Y1 - 1992

N2 - The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton-Raphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy-free internal coordinates. This procedure, already used for the geometry optimization of porphine, C20N4H 14, is illustrated here at the ab initio self-consistent-field level for the four-membered ring azetidine, for bicyclo[2.2.2]octane, and for the four-ring system C16O2H22, the skeleton of taxol.

AB - The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton-Raphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy-free internal coordinates. This procedure, already used for the geometry optimization of porphine, C20N4H 14, is illustrated here at the ab initio self-consistent-field level for the four-membered ring azetidine, for bicyclo[2.2.2]octane, and for the four-ring system C16O2H22, the skeleton of taxol.

UR - http://www.scopus.com/inward/record.url?scp=36449004262&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36449004262&partnerID=8YFLogxK

M3 - Article

VL - 96

SP - 2856

EP - 2860

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -