Application of diophantine integration to hartree–fock and configuration interaction calculations

D. E. Ellis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

167 Scopus citations


The methods of open and closed Diophantine integration have been applied to obtain matrix elements relevant to unrestricted Hartree‐Fock (uhf) and configuration interaction (ci) calculations for atoms and molecules. In the present formulation matrix elements of the effective Hamiltonian are evaluated directly without the intermediate step of generating molecular integrals. The method appears to be superior to conventional techniques for large polyatomic systems; it can handle arbitrary analytic or numerical basis sets, and is easily adapted to include operators such as the spin–orbit interaction in the Hamiltonian. Preliminary results for both uhf and ci methods are quite encouraging, showing that reasonably accurate energies and wave functions can be obtained with moderate computational effort. Results of calculations on the Sc2F and MnF6 complexes, as well as several small atoms and molecules, are briefly discussed. Importance sampling and the use of distribution functions is shown to accelerate convergence of the integrals.

Original languageEnglish (US)
Pages (from-to)35-42
Number of pages8
JournalInternational Journal of Quantum Chemistry
Issue number2 S
StatePublished - Jan 1 1968

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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