  We provide a new derivation of a formula for the Fukui function of
density-functional chemical reactivity theory which incorporates the
discontinuities in the Kohn-Sham reference system. Orbital relaxations are
described in terms of the exchange-correlation (XC) kernel, i.e., the
derivative of the XC potential with respect to the density and it is shown that
in order to correctly measure the reactivity toward a nucleophilic reagent a
discontinuity of the XC kernel has to be taken into account. The importance of
this finding is illustrated in model molecular systems.
