Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations

Toru Shiozaki, Muneaki Kamiya, So Hirata*, Edward F. Valeev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


The explicitly correlated coupled-cluster singles and doubles (CCSD-R12) and related methods-its linearized approximation CCSD(R12) and explicitly correlated second-order Møller-Plesset perturbation method-have been implemented into efficient computer codes that take into account point-group symmetry. The implementation has been largely automated by the computerized symbolic algebra SMITH that can handle complex index permutation symmetry of intermediate tensors that occur in the explicitly correlated methods. Unlike prior implementations that invoke the standard approximation or the generalized or extended Brillouin condition, our CCSD-R12 implementation is based on the nontruncated formalisms [T. Shiozaki, Phys. Chem. Chem. Phys. 10, 3358 (2008)] in which every diagrammatic term that arises from the modified Ansatz 2 is evaluated either analytically or by the resolution-of-the-identity insertion with the complementary auxiliary basis set. The CCSD-R12 correlation energies presented here for selected systems using the Slater-type correlation function can, therefore, serve as benchmarks for rigorous assessment of other approximate CC-R12 methods. Two recently introduced methods, CCSD(R12) and CCSD (2) R12 -, are shown to be remarkably accurate approximations to CCSD-R12.

Original languageEnglish (US)
Article number071101
JournalJournal of Chemical Physics
Issue number7
StatePublished - 2008

ASJC Scopus subject areas

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


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