Variational energy functionals of the Green function and of the density tested on molecules

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Nils Erik Dahlen and Robert van Leeuwen
Theoretical Chemistry, Materials Science Centre, Rijksuniversiteit Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Ulf von Barth
Department of Physics, Lund University, Sölvegatan 14 A, SE-22362 Lund, Sweden

Received 7 March 2005; published 31 January 2006

Wehave calculated total energies of atoms and diatomic molecules fromthe Luttinger-Ward functional, using self-energy approximations to second order aswell as the GW approximation. In order to assess thevariational quality of this functional, we have also solved theDyson equation self-consistently. The Luttinger-Ward functional is compared to thevariational functional due to Klein, and we demonstrate that thevariational property of the latter functional is inferior to thatof the Luttinger-Ward functional. We also show how to obtainvariational density functionals from the functionals of the Green function.These orbital functional schemes are important for systems where density-functionaltheory using local functionals of the density necessarily fails. Wederive an optimized effective potential (OEP) scheme that is basedon the Luttinger-Ward functional and, unlike the conventional OEP schemes,produces energies in good agreement with the values obtained fromthe self-consistent Green function. Our calculations show that, when appliedto molecules, the Luttinger-Ward functional is more sensitive to thequality of the input Green function than when applied toatoms, but the energies are remarkably close to the self-consistentvalues when the Hartree-Fock Green function is used as input.This Luttinger-Ward functional is therefore a simple and efficient methodfor studying the merits of various self-energy approximations while avoidingthe computationally demanding task of solving the Dyson equation self-consistently.

URL:	http://link.aps.org/doi/10.1103/PhysRevA.73.012511
DOI:	10.1103/PhysRevA.73.012511
PACS:	31.10.+z; 31.15.Ew; 31.15.Lc 31.10.+z Theory of electronic structure, electronic transitions, and chemical binding in atoms and molecules 31.15.Ew Density-functional theory (atoms and molecules) 31.15.Lc Quasiparticle methods (atoms and molecules) YEAR: 2006
KEYWORDS:	variational techniques, total energy, density functional theory, SCF calculations, HF calculations, molecular electronic states, Green's function methods

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