  Brueckner orbitals, and the density of the Brueckner reference-state, are
shown to satify the same cusp condition -- involving the nuclear charges -- as
natural- and Hartree--Fock-orbitals. Using the cusp condition, the density of a
determinantal state can be used to determine the external potential, if the
determinantal state is from either Hartee--Fock or Brueckner-orbital theory, as
well as, determinant states obtained by many other formalisms that are defined
by a one-body operator, if a portion of the one-body operator -- the portion
not associated with the kinetic energy or external potential -- generates a
well behaved function when acting on an occupied orbital. Using this
relationship involving a determinant and its external potential, a variation of
Reference--State One--Particle Density--Matrix Theory (physics/0308056) is
formulated, where the trial wavefunctions are universal, in the Kohn-Sham
sense, since they do not depend on the external potential. The resulting
correlation-energy functionals, are also, universal, except for a relatively
small term involving the portion of the expectation value of the external
potential with the trial wavefunctions that appears beyond the first order. The
same approximate energy functionals that were shown to be valid for the
previous v-dependent, Reference--State One--Particle Density--Matrix Theory
(physics/0308084), are shown to be valid for the current approach, except that
the use of the LYP and Colle--Salvetti functional appear more natural within
the current approach, since these functionals are universal ones. And since the
BLYP and B3LYP functionals contain the LYP functional, these approaches are
also better suited with the current approach.
