Application of the regional density functional theory: The chemical potential inequality in the HeH+ system

The chemical potential inequality and the principle of maximum hardness alo ng the reaction coordinate in the ion-atom reaction system He + H+ --> HeH are discussed in term of the regional density functional theory. The regio nal properties such as the regional transfer potentials tau(P, Q), the regi onal excitation potentials epsilon(P, Q), and the regional hardnesses theta (P,) (Q) are calculated along the reaction coordinate using regional Hellma nn-Feynman forces, and we prove numerically that the regional chemical pote ntials, mu(P) and mu(Q), are not necessarily equal to each other nor to the chemical potential mu of the whole system by means of the difference rule, tau(P) - tau(Q) = mu(P) - mu(Q), where P denotes an electron-acceptor regi on and Q denotes an electron-donor region. The electronic state is in the g round state along the reaction path and attains the maximum hardness at the nuclear equilibrium point where the reaction stops. The regional chemical potentials come close but are not equalized even at the nuclear equilibrium point. (C) 1999 John Wiley & Sons, Inc.