The nuclear Fukui function and Berlin’s binding function in density functional theory

The recently introduced nuclear Fukui function φα is formally identified as a reactivity index of the density functional theory (according to the postulated criterion of |dμ|) and is shown to constitute the conformational contribution to a change in the molecular electronic chemical potential μ, through the relation dμ|N=∫ f(r)dν(r)dr=−∑αφαdRga, with φα=(∂Fα/∂N)ν=−(δμ/δRα)N, where N is the number of electrons, f(r) the electronic Fukui function, ν(r) the external potential at point r, Rα the space coordinate of nucleus α, and Fα the force on nucleus α. Scaling of the nuclear coordinates with a factor λ, as a particular conformational change, links the nuclear Fukui function with Berlin’s binding function B(r) for polyatomic molecules, dμλ|N=dλ∫ f(r)B(r)dr=−∑αφα. This relation is instructing for interpretative purposes: changes in electron density are weighted by the binding function, which, according to Berlin’s theorem, separates the system in binding and antibinding regions.