  We show that a naive treatment of open-shell systems in hybrid density
functional calculations ignoring the spin dependence causes significant errors
due to a kind of self interaction that is not emerged in spin-dependent
calculations. As numerical examples, we compare the results of the LDA, GGA,
and PBE0 calculations on the ionization potential and electron affinity of
C$_{60}$ molecule and the GGA and HSE calculations on the singly charged
monovacancy in crystalline Si.
