The Fukui Function concept of the theory of chemical reactivity is identified as the negative asymptotic exchange-correlation hole, when one electrons wanders far away from the rest of the molecule. The appropriate two-electron measures of the electron density responses for an electrophilic, nucleophilic, and radical attacks are proposed, and the exact correspondence with, the electron density of the Frontier Orbitals is established for the hypothetical Kohn-Sham system. (c) 2005 Elsevier B.V. All rights reserved.