A rigorous approach of density functional theory DFT for open-shell Ž . multifermionic systems is devised, using a local-scaling transformation LST scheme Ž .
N involving a single scalar function f r . Within the orbit induced by a model wave Ž . function MWF ⌿, the total energy of space or spin degenerate or nondegenerate states Ž . is expressed as an exact functional of the single-particle density r . In the first step, it is Ž . shown how the reduced density functions and matrices RD Fs and Ms of any order Ž . Ž . s s 1, . . . , N y 1 of an open or closed N-fermion system can be expressed as Ž functionals of the one-fermion charge density. The spatial components which depend on . the spin configuration of the fermions of the RD Fs and Ms of orders 1 and 2, and the resulting charge and spin distribution and correlation densities, are functionals of the one-fermion charge density. We form the manifolds of the charge and spin distribution and correlation energy functionals, from which the theory can be extended to degenerate states of a spinless Hamiltonian. For multielectronic systems, the spin densities and spin᎐pair correlations as well as the spin᎐orbit and spin᎐spin interactions are determined Ž . by the function r . In the second step, it is shown how the expectation values of s-particle operators, in particular those of spin-including mono-and biparticle operators,