Electronic and nuclear chemical reactivity

Abstract

The local softness and the Fukui function emerge from density functional theory as measures of local electronic reactivity. We obtain here an exact linear integral relation between the Fukui functions of insulators or molecules and the probability density of the frontier orbitals of Kohn–Sham theory. The same linear map holds between the local softness and the local Kohn–Sham density of states at the Fermi level for metals. The kernel in those relations is the inverse of the transpose of the potential response function (PRF) of Kohn–Sham theory. The PRF has the form of the static Hartree dielectric function with an exchange and correlation interaction added to the bare Coulomb interaction. The exact static dielectric function also has the Hartree form, but with a renormalized polarization propagator. The map is norm preserving for systems with energy gaps such as insulators and molecules and norm reducing or screening for systems with a finite density of states above the ground state such as normal metals and Anderson insulators. Nuclear reactivities are defined in analogy with the more familiar electronic reactivities and are more directly relevant to reaction pathways. The former are linearly related to the frontier orbital densities or the local density of states through a kernel which is just the electron–nuclear Coulomb force screened by the PRF. This shows explicitly how the frontier orbital density or the local density of states drives the nuclear reactivity. The limitations of such definitions of chemical reactivity are discussed and directions for improvement indicated.