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

J. Chem. Phys. 129, 071101 (2008); doi:10.1063/1.2967181

Published 21 August 2008

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Toru Shiozaki,1,2 Muneaki Kamiya,1 So Hirata,1 and Edward F. Valeev3
1Quantum Theory Project and The Center for Macromolecular Science and Engineering, Department of Chemistry and Department of Physics, University of Florida, Gainesville, Florida 32611-8435, USA
2Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
3Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061-0002, USA

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 et al., 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)<sub>[overline R12]</sub>, are shown to be remarkably accurate approximations to CCSD-R12. ©2008 American Institute of Physics
History: Received 8 July 2008; accepted 14 July 2008; published 21 August 2008; corrected 25 August 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/071101/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.bw
    Coupled-cluster theory
  • 31.15.xp
    Perturbation theory in atomic and molecular physics
  • YEAR: 2008

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ISSN:
0021-9606 (print)   1089-7690 (online)
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