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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694103]
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