Differentiation of density functionals that conserves the normalization of the density
Abstract
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 timedependent 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 timedependent densityfunctional theory. The formula for the differentiation of functionals A[ρ] that conserves the shape of ρ(r) is also presented.
 Publication:

Physical Review A
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevA.63.022506
 Bibcode:
 2001PhRvA..63b2506G
 Keywords:

 31.15.Ew;
 02.30.Sa;
 02.30.Xx;
 Densityfunctional theory;
 Functional analysis;
 Calculus of variations