The Time Evolution of the Electronegativity - Modern Trends in Chemistry and Chemical Engineering - page 27

χ(r) = δEv(ρ)/δρ(r) (1)
Parr et al. [12] noted that the energy is minimized only if the electronegativity is
equalized, because if there are two place in the molecule with different electronegativ-
ity, then transferring a small amount of electron density q, from the atom having lower
electronegativity to the atom with greater electronegativity will lower the energy. Parr
and Bartolotti [13] gave a proof of the electronegativity equalization principle from
a sound density functional theoretical [14, 15] background. The term “chemical po-
tential” as it occurs in thermodynamics [16] has long been accepted as a perspicuous
description of the escaping tendency of a component from a phase. Parr et al. [12]
identifi ed electronegativity as the negative of the chemical potential of the system.
They also pointed out that both parameters can be adopted at the molecular level be-
cause they have the very same properties in the charge equalization procedure. Parr et
al. [12] correlated charge transfer, the electronegativity difference, and the energetic
effect of the charge transfer with the geometric mean principle of electronegativity
equalization [11].
Let us consider the formation of a molecule AB, in its ground state, from the con-
stituent ground state gaseous atoms A and B have the chemical potentials μ AB , μ 0 A ,
and μ 0 B , the electron densities ρ AB , ρ 0 A , and ρ 0 B , the numbers of electrons N, N 0 A , and
N 0 B , and the nuclear potentials υ AB , υ 0 A , and υ 0 B respectively. Of course, the chemical
potentials, υ AB of the product molecule is υ AB = υ 0 A + υ 0 B , and the number of electrons
N = N 0 A + N 0 B .
The number of electrons which fl ow from B to A during the formation of AB mol-
ecule is given [13] as:

ΔN = (½ γ)ln (μ 0 B /μ 0 A ) (2)

The γ is not always constant rather it changes in a fairly narrow range of 2.15 ±
0.59 [13].
The energy difference ΔE, is correlated with the standard chemical potential dif-
ference of the atoms A and B (μ 0 A - μ 0 B ) and the number of electron transferred ΔN as
follows:

ΔE = (μ 0 A - μ 0 B ) ΔN (3)

Ray, Samuels, and Parr [17] fi rst derived the necessary algorithms for the equal-
ized molecular electronegativity and other descriptors such as bond distance, force
constants, and so forth using the Simple Bond Charge (SBC) model [18-21). For a
diatomic molecule AB with the equilibrium bond length R AB, if we consider Z A and Z B
as the charge on atom A and B in the diatomic molecule AA having the bond length 2r A
and the charge on B in BB having the bond length 2r B respectively and δ is the amount
of charge transferred during the process of the molecule formation, then (Z A + δ) and
(Z B - δ) will be the charges on nuclei A and B in the molecule AB.
Pasternak [21] defi ned the electronegativity of a bonded atom A in a molecule as:

χ A = C(Z A /r A ) (4)