  We propose a method that incorporates explicit derivative discontinuity of
the total energy with respect to the number of electrons and treats both
delocalization and static correlation effects in density functional
calculations. Our approach is motivated by the exact behavior of the ground
state total energy of electrons and involves minimization of the
exchange-correlation energy with respect to the Fock space density matrix. The
resulting density matrix minimization (DMM) model is simple to implement and
can be solved uniquely and efficiently. In a case study of KCuF$_3$, a
prototypical Mott-insulator with strong correlation, LDA+DMM correctly
reproduced the Mott-Hubbard gap, magnetic ordering and Jahn-Teller distortion.
