CHEMICAL-POTENTIAL, HARDNESS, HARDNESS AND SOFTNESS KERNEL AND LOCAL HARDNESS IN THE ISOMORPHIC ENSEMBLE OF DENSITY-FUNCTIONAL THEORY

New relations among reactivity descriptors are provided within the rec ently introduced modified isomorphic ensemble of density functional th eory. In addition, expressions for the softness and hardness kernel ar e derived in the canonical, grand canonical, isomorphic and grand isom orphic ensemble. There results a new definition for the local hardness , eta(r)=[partial derivative u(r)/partial derivative N](sigma) = eta(s igma)-g(r), where g(r) = [partial derivative v(r)/partial derivative N ](sigma) and sigma = rho/N is the shape factor. This identifies the lo cal hardness as a function measuring the response of the system's exte rnal potential to a perturbation in electron number at a constant shap e factor. Furthermore, it is shown that one cannot represent both loca l softness and local hardness unambiguously with one representation. ( C) 1997 American Institute of Physics.