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A natural orbital functional based on an explicit approach of the two-electron cumulant

Authors

  • M. Piris

    Corresponding author
    1. Faculty of Chemistry, Donostia International Physics Center (DIPC), University of the Basque Country UPV/EHU, P.K. 1072, 20080 Donostia, Spain and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Euskadi, Spain
    • Faculty of Chemistry, Donostia International Physics Center (DIPC), University of the Basque Country UPV/EHU, P.K. 1072, 20080 Donostia, Spain and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Euskadi, Spain
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Abstract

The cumulant expansion gives rise to an useful decomposition of the two-matrix in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one-matrices. The cumulant can be approximated in terms of two matrices, Δ and Π, which are explicit functions of the occupation numbers of the natural orbitals. It produces a natural orbital functional (NOF) that reduces to the exact expression for the total energy in two-electron systems. The N-representability positivity necessary conditions of the two-matrix impose several bounds on the matrices Δ and Π. Appropriate forms of these matrices lead to different implementations of the NOF known in the literature as PNOFi (i = 1–5). The basic features of these functionals are reviewed here. The strengths and weaknesses of the different PNOFs are assessed. © 2012 Wiley Periodicals, Inc.

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