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Cumulant decomposition of reduced density matrices, multireference normal ordering, and Wicks theorem: A spin-free approach

J. Chem. Phys. 131, 174109 (2009); doi:10.1063/1.3256237

Published 4 November 2009

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K. R. Shamasundar
Institut für Theoretische Chemie, Pfaffenwaldring 55, 70569 Stuttgart, Germany
We propose a spin-free approach to the cumulant decomposition of reduced density matrices of singlet and spin-rotation or SU(2) invariant ensemble of nonsinglet states as in [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999); 116, 4787 (2002)]. We provide a simple recursive procedure to obtain expressions which relate different spin components of spin-orbital reduced density matrices and cumulants of such states to the spin-free counterparts. These results are used to set up a spin-summation procedure to arrive at a definition of spin-free cumulants of any order. Alternatively, an analytic formula for the spin-free form resulting from a spin summation involving product of two spin-orbital cumulants is derived and its utility in spin-free cumulant decomposition of reduced density matrices is demonstrated. This leads to suitable definitions of spin-free analog of multireference normal ordering and the associated Wicks theorem. The results of this formulation are expected to be useful in investigations of spin-free multireference internally contracted coupled-cluster methods where cumulant approximations to the active reduced density matrices are employed. ©2009 American Institute of Physics
History: Received 4 May 2009; accepted 8 October 2009; published 4 November 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/174109/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.E-
    Density-functional theory (atoms and molecules)
  • 31.15.bw
    Coupled-cluster theory
  • YEAR: 2009

PUBLICATION DATA

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