### Abstract

A nondiagrammatic formulation of the analytical first derivative of the coupled‐cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree‐Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(^{1}) = X for first‐order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non‐perturbation‐dependent set of equations can be solved instead. This and the first‐order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

Original language | English (US) |
---|---|

Pages (from-to) | 245-254 |

Number of pages | 10 |

Journal | International Journal of Quantum Chemistry |

Volume | 26 |

Issue number | 18 S |

DOIs | |

State | Published - 1984 |

Externally published | Yes |

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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*,

*26*(18 S), 245-254. https://doi.org/10.1002/qua.560260825

**Analytical gradients for the coupled‐cluster method.** / Adamowicz, Ludwik; Laidig, W. D.; Bartlett, R. J.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 26, no. 18 S, pp. 245-254. https://doi.org/10.1002/qua.560260825

}

TY - JOUR

T1 - Analytical gradients for the coupled‐cluster method

AU - Adamowicz, Ludwik

AU - Laidig, W. D.

AU - Bartlett, R. J.

PY - 1984

Y1 - 1984

N2 - A nondiagrammatic formulation of the analytical first derivative of the coupled‐cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree‐Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first‐order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non‐perturbation‐dependent set of equations can be solved instead. This and the first‐order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

AB - A nondiagrammatic formulation of the analytical first derivative of the coupled‐cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree‐Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first‐order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non‐perturbation‐dependent set of equations can be solved instead. This and the first‐order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

UR - http://www.scopus.com/inward/record.url?scp=84987058293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987058293&partnerID=8YFLogxK

U2 - 10.1002/qua.560260825

DO - 10.1002/qua.560260825

M3 - Article

AN - SCOPUS:84987058293

VL - 26

SP - 245

EP - 254

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 18 S

ER -