SPIN-DENSITY FUNCTIONAL THEORY .7. EULER- LAGRANGE EQUATION FOR RHO(R)

In two previous papers we expressed the total energy of the spin multi plicities of a multifermionic system within an orbit induced by a loca l-scale transformation with scalar function f (r), as an exact functio nal of the components of the single-particle density p (r). In this pa per we provide an integro-differential equation implicit in p (r) and show how to solve it interatively using f (r). We also show how to der ive a similar equation explicit in f (r) after expressing the total en ergy as a functional of f.