Variation of Local Reactivity during Molecular Vibrations, Internal Rotations, and Chemical Reactions

Conceptual density functional theory (DFT) [1-7] has been quite successful in explaining chemical bonding and reactivity through various global and local reactivity descriptors as described in the previous chapters. The Fukui function (FF) [4,5] is an important local reactivity descriptor that is used to describe the relative reactivity of the atomic sites in a molecule. The FF [4,5] is defined as

f (~r ) ¼ [dm=dv(~r )]N ¼ @r(~r )=@N½ v(~r ) (23:1)

where r(~r ) is the density of an N-electron system and the chemical potential and external potential are denoted m and v(~r ), respectively. As proposed by Yang and Mortier [6], the condensed FFs, { f ak }, may be expressed using a finite difference method, giving:

fþk ¼ qk(N þ 1) qk(N) for nucleophilic attack (23:2a) fk ¼ qk(N) qk(N 1) for electrophilic attack (23:2b)

f ok ¼ qk(N þ 1) qk(N 1)½ =2 for radical attack (23:2c)

where qk is the electronic population of atom k. The electronic populations of the Nþ 1-electron and N 1-electron species are computed at the optimized geometry of the N-electron molecule, so that the condensed FF measures the change in atomic population at fixed molecular geometry.