Fukui Functions from the Relaxed Kohn−Sham Orbitals

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 (d N < 0) or addition (d N > 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, H 2 CO 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 |Δ N | = 1 and the “exact” |Δ N | → 0 finite difference predictions.