DENSITY-FUNCTIONAL THEORY FOR OPEN-SHELL SYSTEMS USING A LOCAL-SCALING TRANSFORMATION SCHEME .1. SINGLE-DENSITY ENERGY FUNCTIONAL

A rigorous approach of density functional theory (DFT) for open-shell multifermionic systems is devised, using a local-scaling transformatio n (LST) scheme involving a single scalar function f(r). Within the orb it theta(N) induced by a model wave function (MWF) <(Psi)under bar>, t he total energy of space or spin degenerate or nondegenerate states is expressed as an exact functional of the single-particle density rho(r ). In the first step, it is shown how the reduced density functions an d matrices (RD Fs and Ms) of any order (s = 1, ..., N - 1) of an (open or closed) N-fermion system can be expressed as functionals of the on e-fermion charge density. The spatial components (which depend on the spin configuration of the fermions) of the RD Fs and Ms of orders 1 an d 2, and the resulting charge and spin distribution and correlation de nsities, are functionals of the one-fermion charge density. We form th e manifolds of the charge and spin distribution and correlation energy functionals, from which the theory can be extended to degenerate stat es of a spinless Hamiltonian. For multielectronic systems, the spin de nsities and spin-pair correlations as well as the spin-orbit and spin- spin interactions are determined by the function rho(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, are functionals of the monoparticle density rho(r). We give general e xpressions for the expectation values of spin-free, spin-field, spin-o rbit and spin-spin interaction operators in degenerate states. We show how to express the energy functional of the spin manifolds of a syste m described by a Schrodinger Hamiltonian. The use of an LST, which pre serves spin symmetry, to build this functional must fulfill certain co nditions in order to maintain the space symmetry of the system. We inv estigate the dependence of the Weizsaecker and extended Thomas-Fermi k inetic energy terms and of the Coulomb attraction, repulsion, and exch ange potential energy terms on the choice of the MWF, i.e., on the ind uced orbit and on the spin configuration of the system. (C) 1997 John Wiley & Sons, Inc.