SPIN-DENSITY FUNCTIONAL THEORY - VIII - E ULER-LAGRANGE EQUATION FOR F(R)

In the previous paper we expressed the Euler-Lagrange variational equa tion for the non-relativistic energy of spin multiplicities of a multi fermionic system, implicit in the charge distribution rho(r), and show ed how to solve it iteratively -- and derive optimal values of observa bles, including the spin distribution sigma(r) -- through using the sc alar function f( r) of the local-scaling transformation of the orbit. In the present paper we derive a similar equation, more explicit but a lso more complex, for the total energy expressed as a functional of f( r), and compare the problems raised by the different approaches.