  A self-consistent calculation scheme for correlated electron systems is
created based on the density-functional theory (DFT). Our scheme is a
multi-reference DFT (MR-DFT) calculation in which the electron charge density
is reproduced by an auxiliary interacting Fermion system. A short-range
Hubbard-type interaction is introduced by a rigorous manner with a residual
term for the exchange-correlation energy. The Hubbard term is determined
uniquely by referencing the density fluctuation at a selected localized
orbital. This strategy to obtain an extension of the Kohn-Sham scheme provides
a self-consistent electronic structure calculation for the materials design.
Introducing an approximation for the residual exchange-correlation energy
functional, we have the LDA+U energy functional. Practical self-consistent
calculations are exemplified by simulations of Hydrogen systems, i.e. a
molecule and a periodic one-dimensional array, which is a proof of existence of
the interaction strength U as a continuous function of the local fluctuation
and structural parameters of the system.
