— —   Fukutome Symmetry Classification of the Kohn  Sham Auxiliary One-Matrix and Its Associated State or Ensemble B. WEINER, 1 S. B. TRICKEY 2 1 Department of Physics, Pennsylvania State University, Dubois, Pennsylvania 15801 2 Quantum Theory Project, Department of Physics, University of Florida, Gainesville, Florida 32611 Received 3 June 1997; revised 7 October 1997; accepted 21 November 1997 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.  1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 451460, 1998 Key words: broken symmetry; general spin orbitals; symmetry dilemma; spin symmetry; symmetry in density functional theory Background reatments of the various symmetry properties T Ž . of fermion density functional theory DFT seem to be relatively infrequent, though several subtle aspects of the theory are involved. The Correspondence to: S. B. Trickey. Contract grant sponsor: U.S. Army Research Office. Contract grant number: DAA HO4-95-1-0326. Ž . original DFT papers are Hohenberg and Kohn HK  Ž .  1 and Kohn and Sham KS 2 ; for general refer-   ences see also Refs. 3  14 . Omitting the substantial but not directly rele- vant literature on the multiplet problem, early consideration of symmetry issues in DFT includes the observation that the X  approximation for the Ž . exchange correlation XC potential does not have the spin symmetry of the full, nonrelativistic   Hamiltonian 15, 16 . In both calculational and formal pursuits of this problem, Dunlap studied ( ) International Journal of Quantum Chemistry, Vol. 69, 451 460 1998  1998 John Wiley & Sons, Inc. CCC 0020-7608 / 98 / 040451-10