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Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states

J. Chem. Phys. 126, 244106 (2007); doi:10.1063/1.2741262

Published 26 June 2007

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Toru Shiozaki
Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan

Kimihiko Hirao
Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan and CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan

So Hirata
Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435
Second- and third-order perturbation corrections to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) incorporating excited configurations in the space of triples [EOM-CCSD(2)T and (3)T] or in the space of triples and quadruples [EOM-CCSD(2)TQ] have been implemented. Their ground-state counterparts—third-order corrections to coupled-cluster singles and doubles (CCSD) in the space of triples [CCSD(3)T] or in the space of triples and quadruples [CCSD(3)TQ]—have also been implemented and assessed. It has been shown that a straightforward application of the Rayleigh-Schrödinger perturbation theory leads to perturbation corrections to total energies of excited states that lack the correct size dependence. Approximations have been introduced to the perturbation corrections to arrive at EOM-CCSD(2)T, (3)T, and (2)TQ that provide size-intensive excitation energies at a noniterative O(n7), O(n8), and O(n9) cost (n is the number of orbitals) and CCSD(3)T and (3)TQ size-extensive total energies at a noniterative O(n8) and O(n10) cost. All the implementations are parallel executable, applicable to open and closed shells, and take into account spin and real Abelian point-group symmetries. For excited states, they form a systematically more accurate series, CCSD<CCSD(2)T<CCSD(2)TQ<CCSD(3)T<CCSDT, with the second- and third-order corrections capturing typically ~80% and 100% of such effects, when those effects are large (>1  eV) and the ground-state wave function has single-determinant character. In other cases, however, the corrections tend to overestimate the triples and quadruples effects, the origin of which is discussed. For ground states, the third-order corrections lead to a rather small improvement over the highly effective second-order corrections [CCSD(2)T and (2)TQ], which is a manifestation of the staircase convergence of perturbation series. ©2007 American Institute of Physics
History: Received 22 February 2007; accepted 24 April 2007; published 26 June 2007
Permalink: http://link.aip.org/link/?JCPSA6/126/244106/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.Dv
    Coupled cluster theory (atoms and molecules)
  • 31.25.Jf
    Electron-correlation calculations for atoms and ions: excited states
  • YEAR: 2007

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