Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation

Hai Anh Le*, Toru Shiozaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We present an efficient algorithm for computing the exact exchange contributions in the Hartree-Fock and hybrid density functional theory models on the basis of the fast multipole method (FMM). Our algorithm is based on the observation that FMM with hierarchical boxes can be efficiently used in the exchange matrix construction, when at least one of the indices of the exchange matrix is constrained to be an occupied orbital. Timing benchmarks are presented for alkane chains (C400H802 and C150H302), a graphene sheet (C150H30), a water cluster [(H2O)100], and a protein Crambin (C202H317O64N55S6). The computational cost of the far-field exchange evaluation for Crambin is roughly 3% that of a self-consistent field iteration when the multipoles up to rank 2 are used.

Original languageEnglish (US)
Pages (from-to)1228-1234
Number of pages7
JournalJournal of Chemical Theory and Computation
Issue number3
StatePublished - Mar 13 2018

ASJC Scopus subject areas

  • Computer Science Applications
  • Physical and Theoretical Chemistry


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