  Uniqueness of effective interaction defined in an extension of the Kohn-Sham
theory is proved, if the model with a non-degenerate ground state exists and to
reproduce a correlation function as well as the single-particle density of an
electron system. The two-body interaction term is regarded as a Hubbard-type
short range interaction term. The interaction strength is a functional of an
element of a two-body reduced density matrix of the electron system. The
uniqueness theorem gives a basic principle for effective description of
electron systems.
