Fukui Functions from the Relaxed Kohn−Sham Orbitals

Abstract

The global Fukui function of a molecular system, f(r) = (∂ρ(r)/∂N)v, where ρ is the ground-state density of a system containing N electrons moving in the external potential v(r), is calculated within a single Kohn−Sham calculation. It is determined by adding to the rigid (frontier orbital) term, relevant for the electron removal (dN < 0) or addition (dN > 0), the density relaxation contribution determined from the N-differentiated Kohn−Sham equations. The only approximation introduced is a neglect of the exchange−correlation terms in the N-derivative of the effective one-body potential. The corresponding equations resulting from the basis set expansion of orbitals are derived, and illustrative results for CO, HCN, H2CO are reported. The predicted Fukui functions for pyrrole, furane, and tiophene are used to diagnose reactivity toward an electrophilic attack. The contour maps of f(r) and the resulting condensed Fukui function indices are compared with the corresponding |ΔN| = 1 and the “exact” |ΔN| → 0 finite difference predictions.