In a recent paper [J. Chem. Phys. 105, 6171 (1996)], nonlinear chemical responses of a system to a simultaneous change of its external potential and of its number of electrons have been formulated in terms of the ground-state electronic density for a given model of the Hohenberg-Kohn functional, In the present work, an exact one-electron formulation of all the chemical responses is derived in terms of the Kohn-Sham orbitals of the unperturbed system, The present formulation encompasses the band-structure formulation of the linear Fukui function derived recently [M.H. Cohen. M.V. Ganduglia-Pirovano, and J. Kudrnovsky, J. Chem. Phys. 101, 8988 (1993)] and providers an exact orbital expression of the linear hardness. The latter is compared to the hardness matrix used in the construction of ab initio pseudo-potentials [M. Teter, Phys. Rev, B 48, 5031 (1993)]. In addition, the relation between the covalent radius of atoms and the linear and nonlinear hardnesses is discussed.