Is the divide-and-conquer Hartree-Fock method valid for calculations of delocalized systems?

Tomoko Akama, Atsuhiko Fujii, Masato Kobayashi, Hiromi Nakai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


Recently, we applied Yang's divide-and-conquer (DC) method to the Hartree-Fock (HF) and hybrid density functional theories and assessed its reliability in calculations of bond-alternating polyene chains. In this paper, we investigate the cut-off behaviour of the HF exchange interaction in the DC-HF method by comparing the results of bond-alternating polyene chains with those of more delocalized uniform polyene chains. The cut-off error of the uniform chain is much larger than that of the bond-alternating chain because of the delocalized electronic structure of the uniform polyene chain. We also estimate the exponential decay coefficient of the cut-off error in the DC scheme and compare it with that of the real-space one-particle density matrix, which can be represented by the band gap in the insulator limit. It can be concluded that the cut-off derived from the DC-HF method can be reduced to an arbitrary magnitude of error by adopting an appropriate buffer radius corresponding to the band gap.

Original languageEnglish
Pages (from-to)2799-2804
Number of pages6
JournalMolecular Physics
Issue number19-22
Publication statusPublished - 2007 Oct 21


  • Delocalized system
  • Divide-and-conqure method
  • Hartree-Fock exchange
  • Linear-scaling method

ASJC Scopus subject areas

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


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