Density functional theory for open-shell systems using a local-scaling transformation scheme. I. Single-density energy functional

Abstract

A rigorous approach of density functional theory (DFT) for open-shell multifermionic systems is devised, using a local-scaling transformation (LST) scheme involving a single scalar function f(r). Within the orbit θN induced by a model wave function (MWF) _Ψ, the total energy of space or spin degenerate or nondegenerate states is expressed as an exact functional of the single-particle density ρ(r). In the first step, it is shown how the reduced density functions and 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 one-fermion charge density. The spatial components (which depend on the spin configuration of the fermions) of the RD Fs and Ms of orders 1 and 2, and the resulting charge and spin distribution and correlation densities, are functionals of the one-fermion charge density. We form the manifolds of the charge and spin distribution and correlation energy functionals, from which the theory can be extended to degenerate states of a spinless Hamiltonian. For multielectronic systems, the spin densities and spin–pair correlations as well as the spin–orbit and spin–spin interactions are determined by the function ρ(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 ρ(r). We give general expressions for the expectation values of spin-free, spin–field, spin–orbit and spin–spin interaction operators in degenerate states. We show how to express the energy functional of the spin manifolds of a system described by a Schrödinger Hamiltonian. The use of an LST, which preserves spin symmetry, to build this functional must fulfill certain conditions in order to maintain the space symmetry of the system. We investigate the dependence of the Weizsaecker and extended Thomas–Fermi kinetic energy terms and of the Coulomb attraction, repulsion, and exchange potential energy terms on the choice of the MWF, i.e., on the induced orbit and on the spin configuration of the system. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 241–256, 1997