### Abstract

An analytical method was elaborated to compute the second derivative of the Hartree-Fock energy with respect to the unit cell length (Ỹ) in stereoregular polymers. The evaluation of Ỹ was performed in a single-shot calculation once the optimal geometry is known. The formulas necessary to calculate cell and mixed Hessians of individual one- and two-electron integrals were implemented efficiently. A seven-step CPHF procedure was used to obtain the derivatives of the density matrix in a fashion consistent with the SCF procedure. Using an adapted long-range effects scheme and efficient quadrature methods for transforming k-space density matrix and its derivatives into their real-space counterparts, an accuracy of 10^{-9} a.u. was obtained on the final Hessian elements.

Original language | English |
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Pages (from-to) | 373-388 |

Number of pages | 16 |

Journal | The journal of chemical physics |

Volume | 118 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2003 |

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### Cite this

*The journal of chemical physics*,

*118*(1), 373-388. https://doi.org/10.1063/1.1523909

}

*The journal of chemical physics*, vol. 118, no. 1, pp. 373-388. https://doi.org/10.1063/1.1523909

**Analytic ab initio determination of the elastic modulus in stereoregular polymers : Analytical integral derivatives, long-range effects, implementation, and examples.** / Jacquemin, Denis; André, Jean-Marie; Champagne, Benoît.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analytic ab initio determination of the elastic modulus in stereoregular polymers

T2 - Analytical integral derivatives, long-range effects, implementation, and examples

AU - Jacquemin, Denis

AU - André, Jean-Marie

AU - Champagne, Benoît

PY - 2003/1/1

Y1 - 2003/1/1

N2 - An analytical method was elaborated to compute the second derivative of the Hartree-Fock energy with respect to the unit cell length (Ỹ) in stereoregular polymers. The evaluation of Ỹ was performed in a single-shot calculation once the optimal geometry is known. The formulas necessary to calculate cell and mixed Hessians of individual one- and two-electron integrals were implemented efficiently. A seven-step CPHF procedure was used to obtain the derivatives of the density matrix in a fashion consistent with the SCF procedure. Using an adapted long-range effects scheme and efficient quadrature methods for transforming k-space density matrix and its derivatives into their real-space counterparts, an accuracy of 10-9 a.u. was obtained on the final Hessian elements.

AB - An analytical method was elaborated to compute the second derivative of the Hartree-Fock energy with respect to the unit cell length (Ỹ) in stereoregular polymers. The evaluation of Ỹ was performed in a single-shot calculation once the optimal geometry is known. The formulas necessary to calculate cell and mixed Hessians of individual one- and two-electron integrals were implemented efficiently. A seven-step CPHF procedure was used to obtain the derivatives of the density matrix in a fashion consistent with the SCF procedure. Using an adapted long-range effects scheme and efficient quadrature methods for transforming k-space density matrix and its derivatives into their real-space counterparts, an accuracy of 10-9 a.u. was obtained on the final Hessian elements.

UR - http://www.scopus.com/inward/record.url?scp=0037255208&partnerID=8YFLogxK

U2 - 10.1063/1.1523909

DO - 10.1063/1.1523909

M3 - Article

VL - 118

SP - 373

EP - 388

JO - The journal of chemical physics

JF - The journal of chemical physics

SN - 0021-9606

IS - 1

ER -