Relations among several nuclear and electronic density functional reactivity indexes

An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the ‘‘Quantum Chemical le Chatelier Principle.’’ Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given. © 2003 American Institute of Physics. @DOI: 10.1063/1.1615763#