Analytic ab initio determination of the elastic modulus in stereoregular polymers: Analytical integral derivatives, long-range effects, implementation, and examples

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Résumé

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.

langue originaleAnglais
Pages (de - à)373-388
Nombre de pages16
journalThe journal of chemical physics
Volume118
Numéro de publication1
Les DOIs
étatPublié - 1 janv. 2003

Empreinte digitale

modulus of elasticity
Polymers
Elastic moduli
Derivatives
space density
polymers
cells
quadratures
shot
self consistent fields
electrons
Electrons
evaluation
geometry
Geometry
energy

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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.",
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