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Higher-order explicitly correlated coupled-cluster methods

J. Chem. Phys. 130, 054101 (2009); doi:10.1063/1.3068302

Published 2 February 2009

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Toru Shiozaki,1,2 Muneaki Kamiya,1 So Hirata,1 and Edward F. Valeev3
1Department of Chemistry and Department of Physics, Quantum Theory Project and The Center for Macromolecular Science and Engineering, 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
Efficient computer codes for the explicitly correlated coupled-cluster (CC-R12 or F12) methods with up to triple (CCSDT-R12) and quadruple excitations (CCSDTQ-R12), which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra SMITH. Together with the explicitly correlated coupled-cluster singles and doubles (CCSD-R12) method reported earlier [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], they form a hierarchy of systematic approximations (CCSD-R12<CCSDT-R12<CCSDTQ-R12) that converge very rapidly toward the exact solutions of the polyatomic Schrödinger equations with respect to both the highest excitation rank and basis-set size. Using the Slater-type function exp(−gammar12) as a correlation function, a CC-R12 method can provide the aug-cc-pV5Z-quality results of the conventional CC method of the same excitation rank using only the aug-cc-pVTZ basis set. Combining these CC-R12 methods with the grid-based, numerical Hartree–Fock equation solver [T. Shiozaki and S. Hirata, Phys. Rev. A 76, 040503(R) (2007)], the solutions (eigenvalues) of the Schrödinger equations of neon, boron hydride, hydrogen fluoride, and water at their equilibrium geometries have been obtained as −128.9377±0.0004, −25.2892±0.0002, −100.459±0.001, and −76.437±0.003  Eh, respectively, without resorting to complete-basis-set extrapolations. These absolute total energies or the corresponding correlation energies agree within the quoted uncertainty with the accurate, nonrelativistic, Born–Oppenheimer values derived experimentally and/or computationally. ©2009 American Institute of Physics
History: Received 17 November 2008; accepted 17 December 2008; published 2 February 2009
Permalink: http://link.aip.org/link/?JCPSA6/130/054101/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.bw
    Coupled-cluster theory
  • 33.15.Bh
    General molecular conformation and symmetry; stereochemistry
  • 31.15.xr
    Self-consistent-field methods in atomic and molecular physics
  • YEAR: 2009

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