Generalized density-functional theory: Conquering the N -representability problem with exact functionals for the electron pair density and the second-order reduced density matrix |
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Authors: | Paul W Ayers and Mel Levy |
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Institution: | (1) Department of Chemistry, McMaster University, L8S 4M1 Hamilton, Ontario, Canada;(2) Department of Physics, North Carolina A&T University, 27411 Greensboro, NC, USA;(3) Department of Chemistry, Tulane University, 70118 New Orleans, LA, USA |
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Abstract: | Using the constrained search and Legendre-transform formalisms, one can derive “generalized” density-functional theories,
in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both
approaches, theN-representability problem is solved by the functional, and the variational principle is with respect to all pair densities
(density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower
bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests
that it is easier to approximate functionals than it is to approximate the set ofN-representable densities sheds some light on the significance of this work. |
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Keywords: | Density-functional theory N-representability problem electron pair density |
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