Molecular symmetry. III. Second derivatives of electronic energy with respect to nuclear coordinates

Toshikazu Takada, Michel Dupuis, Harry F. King

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the analytic computation of the energy Hessian matrix. A "skeleton" Hessian matrix is calculated from the unique blocks of electron repulsion integrals. The true Hessian matrix is generated by projecting the symmetric component out of the skeleton Hessian. The analysis is valid for many wave functions, including closed- or open-shell restricted and unrestricted Hartree-Fock wave functions, multiconfiguration Hartree-Fock wave functions, and configuration interaction wave functions. We also extend the use of translational invariance previously used for energy gradient calculations. To illustrate the method, we compare the computer time required for the two-electron contribution to the Hessian matrix of eclipsed ethane, using Pople's 6-31G** basis set and D3h symmetry and various subgroups D3h. Computational times are roughly inversely proportional to the order of the point group.

Original languageEnglish
Pages (from-to)332-336
Number of pages5
JournalJournal of Chemical Physics
Volume75
Issue number1
Publication statusPublished - 1981

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Hessian matrices
Wave functions
wave functions
Derivatives
symmetry
musculoskeletal system
electronics
Point groups
Ethane
energy
Electrons
subgroups
Invariance
ethane
configuration interaction
invariance
electrons
gradients

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Molecular symmetry. III. Second derivatives of electronic energy with respect to nuclear coordinates. / Takada, Toshikazu; Dupuis, Michel; King, Harry F.

In: Journal of Chemical Physics, Vol. 75, No. 1, 1981, p. 332-336.

Research output: Contribution to journalArticle

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