THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 38

LUMO. The normalized electron densities of these frontier orbitals are
called the frontier function or the Fukui function, f ( r ).
The Fukui function, f ( r ) describes the sensitivity of chemical potential
to local change in external potential and is considered as the measure of
reactivity at a local point( r ) and defi ned by Parr and Yang [60] as follows:

f ( r )= (δρ( r )/δN) v(r) (51)

In order to point out the preferred direction of attack of a reagent (R)
approaches to S, Parr and Yang [60] assumed that “the preferred direction
is the one for which the initial │dμ│for the species S is a maximum.”
They considered three cases:
For governing nucleophilic attack, the positive Fukui function was
given by the following equation:

f + ( r ) = (δρ( r )/δN) + v(r) when μ S > μ R (52)

the negative Fukui function for governing electrophilic attack was given
as

f - ( r ) = (δρ( r )/δN) - v(r) when μ R > μ S (53)

and the neutral Fukui function for governing the radical attack was given
by the following equation:

f 0 ( r ) = (δρ( r )/δN) 0 v(r) when μ S ≈ μ R (54)

where μ S and μ R are the chemical potentials of R and S , respectively.
A “frozen core” approximation now gives dρ = dρ valence , and the above
equations can be approximated to

f + (r) = ρ HOMO for donor molecule (55)

f - ( r ) = ρ LUMO for acceptor molecule

(56)

f 0 (r) = ½(ρ HOMO + ρ LUMO ) for both donor and acceptor molecule (57)
f 0 (r) is for the case where there is electron transfer in both direction as
found in (σ + π) bonding. The magnitude of the Fukui functions at the