RIGOROUS FORMULATION OF A KOHN AND SHAM THEORY FOR STATES WITH SPECIAL SYMMETRIES

By defining functionals over all states in the Hilbert space, we deriv e the Kohn and Sham (KS) equations for the ground state. Density funct ionals are defined as an intermediate step and they are restricted to single state representable densities. We do not make any use of the on e-to-one correspondence between density and ground state. The resultin g noninteracting state is not necessarily a single Slater determinant. Some necessary theorems for developing a KS theory for the lowest ene rgy states transforming :according to the irreducible representation ( Irrep) of a symmetry group of a Hamiltonian are presented. We show tha t the part of the lowest energy density having the same symmetry as th e external potential determines uniquely the lowest energy state of an Irrep of the symmetry group. (C) 1998 John Wiley & Sons, Inc. Int J Q uant Chem 69: 461-467, 1998.