THE TIME EVOLUTION OF THE HARD AND SOFT ACIDS AND BASES THEORY - Theoretical and Computational Research in the 21st Century - page 30

This expresses the hardness (η) of the corresponding system [46]

η = ½(∂ 2 E /∂ N 2 ) v = ( I − A )/2 (29)

It is important to mention here that Huheey [49] identified the parameter
' b ' as inverse charge capacitance. The capacitance ( C ) of a spherical con-
denser is equal to 4πε 0 . Komorowski [50] proposed hardness as inverse of
capacitance, that is,

η = 1/C = (4πε 0 ) −1 (30)

Pearson [51] proceeded further to evaluate I and A in terms of orbital en-
ergies of the highest-occupied molecular orbital, HOMO and the lowest
unoccupied molecular orbital, LUMO by connecting it with Hartree-Fock
SCF theory and invoking Koopmans' theorem,

η = (-ε HOMO + ε LUMO )/2 (31)

and

χ = -(ε HOMO + ε LUMO )/2 (32)

It is transparent from Figure (1.4) that a soft molecule has a small
HOMO-LUMO energy gap and a hard molecule has a large HOMO-
LUMO energy gap.
The soft acids and bases have the properties that guarantee that the
HOMO is relatively high in energy while the LUMO is relatively low in
energy. Hard acids and bases have the opposite characteristics.
On the basis of the quantum theory of polarizability, Pearson [9(c)]
pointed out that, in the presence of an 'electric fi eld, exited states of a sys-
tem are mixed with the ground state in such a way as to lower the energy.
The smaller the excitation energy, the greater the effect. Thus, a small
energy gap, (I-A) means high polarizability and soft acids and bases will
be easily polarized.