Phys. Rev. A 63, 022506 (2001) [8 pages]Differentiation of density functionals that conserves the normalization of the densityReceived 28 October 1999; revised 25 July 2000; published 9 January 2001 The formula for differentiation of functional A[ρ] with respect to ρ(r) while keeping the normalization ∫ρ(r)dr of ρ(r) fixed is derived, and basic properties arising from it are concerned. The results are then generalized for time-dependent theories. One of the essential consequences of normalization conservation for functional differentiation, namely, that it ruins the symmetry in r of multiple derivatives, is shown to give the resolution of the causality paradox of response functions in time-dependent density-functional theory. The formula for the differentiation of functionals A[ρ] that conserves the shape of ρ(r) is also presented. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.63.022506
DOI:
10.1103/PhysRevA.63.022506
PACS:
31.15.Ew, 02.30.Sa, 02.30.Xx
See AlsoErratum: Tamás Gál, Erratum: Differentiation of density functionals that conserves the normalization of the density [Phys. Rev. A 63, 022506 (2001)], Phys. Rev. A 63, 049903 (2001). Erratum: Tamás Gál, Erratum: Differentiation of density functionals that conserves the normalization of the density [Phys. Rev. A 63, 022506 (2001)], Phys. Rev. A 74, 029901 (2006). |
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