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It contains the coupling-constant-averaged pair correlation function, which is a functional of the electron density rho(r) and paramagnetic current density j(p)(r). On the basis of this expression, the local density approximation and its modifications for E-xc[rho,j(p)] are proposed within the CDFT. In addition, we present sum rules and bounds on E-xc[rho,j(p)] by considering the behaviors of the basic variables and E-xc[rho,j(p)] under the various types of the nonuniform coordinate scaling of electrons. 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