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

Toshikazu Takada, Michel Dupuis, Harry F. King

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


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
JournalThe Journal of Chemical Physics
Issue number1
Publication statusPublished - 1981

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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