DENSITY-FUNCTIONAL THEORY FOR OPEN-SHELL SYSTEMS USING A LOCAL-SCALING TRANSFORMATION SCHEME .2. EULER-LAGRANGE EQUATION FOR F(R) VERSUS THAT FOR RHO(R)

Following the previous article (Part I), we express the total nonrelat ivistic energy for spin manifolds of open-shell multielectronic system s, within an orbit theta(N) induced by a model wave function (MWF) <(P si)under bar> using a single local-scaling transformation (LST) as an exact functional of the single-particle density rho(r) or, alternative ly, of the LST scalar function f(r). We derive the corresponding Euler -Lagrange variational equations: one implicit in rho(r), which can be solved iteratively through steps involving f(r), and one explicit in f (r), derived from the total energy as a functional of f(r). Both equat ions fulfill the space and spin symmetries characterizing the system. The problems arising from the specificities of these two highly nonlin ear integrodifferential equations are discussed. The optimal charge de nsity rho(r) derived from these equations is N- and upsilon-representa ble and determines the optimal spin density sigma(r) as well. Accurate optimal values of all observables can be derived from this scheme usi ng standard procedures. (C) 1997 John Wiley & Sons, Inc.