Density- and spin-density-functional theories through spin-free wave functions

It is proven that entirely spin-free wave functions can be utilized in the basic definitions of the universal functionals in density-functional theory and spin-density-functional theory. Then, for the purpose of approximating these functionals, it is shown that the knowledge of certain properties of the functionals, such as those involving the coordinate scaling of just one of the spin densities, is made feasible precisely because the wave functions in the functional definitions are free of explicit spins. Among the examples, a conjectured spin-density scaling relation for the correlation energy is studied.