Fukutome Symmetry Classification of the Kohn]Sham Auxiliary One-Matrix and Its Associated State or Ensemble

Ž . ABSTRACT: The Kohn]Sham KS procedure for variational minimization of the Hohenberg]Kohn density functional utilizes a one-particle reduced density matrix of assumed diagonal form, hence depends implicitly on a set of auxiliary states. Originally, the auxiliary state was assumed to be a single determinant with doubly occupied spin orbitals, i.e., of the same form as in ‘‘restricted’’ Hartree]Fock theory. The pragmatic and formal extension of the KS procedure to noninteger occupation numbers requires extension to more general forms of the auxiliary state or even its replacement by an auxiliary ensemble. Though attention has been given to the symmetry properties of the KS one-matrix, its spin and time-reversal symmetries have not been classified along the lines of Fukutome’s treatment of the generalized Hartree]Fock problem. Here we show Ž . that, in the context of constrained search density functional theory DFT , Fukutome’s analysis goes through essentially unaltered. We then consider the broken symmetry consequences for the case that the KS one-matrix is restricted to a single-determinantal KS auxiliary state. Q 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 451]460, 1998