Numerical solution of the Sinanoǧlu equation using a multicentre radial-angular grid

So Hirata, Toru Shiozaki, Cole M. Johnson, James D. Talman

Research output: Contribution to journalArticlepeer-review


The pair functions that minimise the correlation energy of second-order many-body perturbation (MP2) theory (the Hylleraas functional) are obtained as solutions to the corresponding Sinanoǧlu equation by expanding them on a six-dimensional, multicentre, radial-angular grid of two electrons. Cusps in the pair functions at the nuclei are described numerically accurately by the multicentre grid. A cusp in each singlet pair function at the coalescence of the two electrons is taken into account analytically by a correlation factor. With a grid of approximately 10,000 points per atom, the MP2 correlation energies for atoms and polyatomic molecules are obtained usually within 0.1 mEh of the complete-basis-set results. The correlation factor, auxiliary basis functions, and a judicious choice of integration algorithms are all necessary to stabilise the grid-based MP2 and underlying Hartree–Fock (HF) calculations. The auxiliary basis set, in particular, largely restores the hermiticity and diagonal dominance of the Fock matrix as well as furnishes virtual orbitals used in a resolution-of-the-identity approximation to lower the dimension of some integrals. The results of the grid-based HF and MP2 calculations without a correlation factor are found to suffer from large, nonsystematic errors frequently.

Original languageEnglish (US)
Pages (from-to)510-525
Number of pages16
JournalMolecular Physics
Issue number5
StatePublished - Mar 4 2017


  • Many-body perturbation theory
  • correlation hole
  • density functional theory
  • explicit correlation
  • quadrature grid

ASJC Scopus subject areas

  • Biophysics
  • Molecular Biology
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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