This expression satisfies Koopmans' theorem for the closed-shell case ( D pp = 0 or 2). However, this identity does not hold for active MOs. In an extreme case, D tt = 1, the Fock matrix element can be written as an average of IP and EA, but this characteristic of the Fock matrix leads to overestimation of the perturbation energy for open-shell states. To satisfy the Koopmans' theorem-like identity, Ghigo et al. introduced a shift. When an electron is excited into a partially occupied orbital, we want the Fock matrix element to be the negative of EA: