Time Evolution of the Electronegativity - Modern Trends in Chemistry and Chemical Engineering - page 5

Now, Mulliken's assumption was that the difference between A + B - and A - B + can
be neglected as they are not truly ionic. So the involved energies, ∆ E (A + B - ) , ∆ E (A - B + )
can be equalized.

∆ E (X + Y - ) = ∆ E (X - Y + ) (10)

that is, IP X - EA Y = IP Y - EA X (11)

or, IP X + EA X = IP Y + EA Y (12)

The equation (12) reveals that the sum of ionization energy and electron affi nity of
each separate atom becomes equal when they are combined to form the complex, XY.
Hund [56] stated that the quantities average of IP and EA , that is, ( IP + EA )/2, is an
approximate criterion for their equal participation in a chemical bond.
Using this idea, Mulliken [55] took an arithmetic mean of the fi rst ionization en-
ergy and electron affi nity as a qualitative defi nition of electronegativity for any species
X (atom, molecule, or radical in its state of interaction):

χ X ≈ ( IP X + EA X )/2 (13)

It is more usual to use a linear transformation to transform these absolute values
into values which resemble the more familiar Pauling values. Plotting the (I + A) with
Pauling electronegativity values, the electronegativity scale was designed as

χ = a ( IP + EA ) + b (14)

where a and b are the constants.
Putting “ IP ” and “ EA ” in electron volt and using the method of least square fi tting,
the “a” and “b” values are computed as a = 0.187 and b = 0.17.
Coulson [57] opined that Mulliken's measure of electronegativity is better and
more precise than Pauling's electronegativity data.
Mulliken's Electronegativity Scale is absolute and more fundamental because it
only depends on the fundamental energy value of the isolated atom. Also, it is more
precise because it bears the modern density functional defi nition of electronegativity
[58, 59].

χ DFT = -(∂E/∂N) v (15)

From the energy versus number of electron curve (E vs. N curve), it is transparent
that the change in energy, ΔE, is associated with two electrons changes. If we consider
S as a neutral species having energy E N , and having a total number of N electrons, then
the corresponding cation and anion, S + and S - have the energy E N-1 and E N+1 and the
number of electrons N-1 and N+1 respectively.
Putz [48] showed that the density function electronegativity (χ DFT ) approximates
the former Mulliken electronegativity formula (χ M ).

χ DFT = -(∂E/∂N) v = -(E N+1 - E N-1 )/2 = ( IP + EA )/2 = χ M (16)