Chemical hardnesses of atoms and molecules from frontier orbitals

It is demonstrated that the chemical hardness of molecules is exactly the screened interaction energy of the electrons in the frontier (HOMO, LUMO) orbitals, whereas the derivative of the Kohn-Sham potential relative to the electron number is a screened local hardness measuring the local reactivity of molecules and solids. It is also shown that the hardness of two interacting molecules involves the screened interaction between their respective HOMO and LUMO orbitals. The formula are applied to the Thomas-Fermi model.