Kohn-Sham orbital formulation of the chemical electronic responses, including the hardness

In a recent paper J. Chem. Phys. 105, 6471 (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. Kudrnovský, J. Chem. Phys. 101, 8988 (1994) and provides 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.