Semi-empirical AM-1 Studies on Porphyrin - Modern Trends in Chemistry and Chemical Engineering - page 127

The electrophilicity index, ω is a descriptor of reactivity that allows a quantitative
classifi cation of the global electrophilic nature of a molecule within a relative scale.
Parr and Yang [27] suggested that electronegativity squared divided by hardness mea-
sures the electrophilic power of a ligand its prosperity to “soak up” electrons.
Thus,
ω = μ 2 /2η (11)
It is further anticipated that electrophilicity index should be related to electron
affi nity, because both electrophilicity index and electron affi nity measures capacity
of an agent to accept electrons. Electron affi nity refl ect capability of an agent to ac-
cept only one electron from the environment, whereas electrophilicity index measures
the energy lowering of a ligand due to maximal electron fl ow between the donor and
acceptor. The electron fl ows may be either less or more than one. Thus the electro-
philicity index provides the direct relationship between the rates of reaction and the
electrophilic power of the inhibitors [28].

THE LOCAL REACTIVITY PARAMETERS
The Fukui functions play a prominent role in the field known as conceptual Density
Functional Theory (DFT) [29]. Yang and Parr [30] based on the original ideas of Fu-
kui, Yonezawa, and Shingu [31], introduced Fukui function which reflect the response
of a molecular system towards a change in the number of electrons (N) of the molecu-
lar system under consideration. The Fukui functions are a measure of local reactivity
and defined as:

f (r) = (∂ρ (r)/∂N) v . (12)

where ρ(r) is the electron density.
It is transparent from the above equation that the Fukui functions measured the
response of the electron density at every point r, in front of a change in the number of
electrons, N under the constant external potential, v. The sites with the largest value for
the Fukui functions are those with the largest response, and as such the most reactive
sites within a molecule. In chemistry, often chemical reactivity and molecular proper-
ties in general are preferably interpreted in terms of the atoms composing molecular
structure. It is then logical to introduce the so called atom condensed Fukui functions.
This means that some way of calculating the change in the total atomic electron den-
sity of an atom “a” with respect to N is needed. Since the nuclear change of an atom
is a constant, one of the easiest ways is to use the concept of atomic charges, which
introduces the following expression for atom condensed Fukui function:
f α = - (∂q a /∂N)v (13)
Yang and Mortier [32] were the fi rst to use such atom condensed Fukui functions,
and used Mulliken charges to obtain values for the above defi ned atom condensed
Fukui functions.
Now, let us discuss the operational defi nitions of Fukui functions and local soft-
nesses.
In Frontier Orbital theory, the two orbitals, the HOMO, and the LUMO, are the
most important in correlating the molecular reactivity and suggesting orientation of a