QUANTUM COMPUTATIONAL STUDIES ON PORPHYCENE - Theoretical and Computational Research in the 21st Century - page 166

Governing nucleophilic attack, f + ( r ) ≈ ρ (LUMO) ( r ) (22)

Governing neutral attack f 0 ( r ) ≈ ½[ ρ (HOMO) ( r ) + ρ (LUMO) ( r )] (23)

The Fukui function has been used in several works as a natural de-
scriptor of site selectivity. Within the Li and Evans reactivity and selectiv-
ity rules [29], “ for soft-soft interactions, the preferred reactive site in a
molecule should have the highest value of the Fukui function, whereas the
hard-hard interactions are supposed to be described through the mini-
mum value of this local index” often the reactivity in molecules with only
one reactive site can be correctly characterized.
However, for polyfunctional systems where more than one site can be
attacked, the Fukui function seems to fail, predicting the selectivity of
hard-hard interactions as hard-hard interactions are charge controlled and
soft-soft interactions are frontier controlled, the Fukui function is not ex-
pected to describe well the hard-hard interactions. Using the properties of
Fukui function, more powerful descriptor of chemical reactivity and site
selectivity have been proposed by Chattaraj et al. [30].

9.2.2 LOCAL HARDNESS AND LOCAL SOFTNESS

In addition to the knowledge of global softness ( S ), different local soft-
nesses were used to describe the reactivity of atoms in molecule. The local
softness is generally defined [28] as

S k α = Sf k α (24)

where α = +, − and 0 represent the local softness quantities which describe
the nucleophilic, electrophilic, and radical attacks, respectively.

S + = Sf + for nucleophilic attack (25)

S - = Sf - for electrophilic attack (26)

S 0 = Sf 0 for radical attack (27)

where S is the total softness of the molecule.
The purpose of mathematical defi nitions of a local softness is to pro-
vide a quantitative representation of qualitative concepts.