Handbook of Solvents - George Wypych - ChemTech - Ventech!

10.2 Effect of polymer/solvent acid-base interactions 575
The principle states that hard acid prefers to interact with a hard base, and vice versa, a
soft acid with a soft base. A hard-hard interaction is fast because of large Coulombic attraction,
a soft-soft interaction is fast because of large orbital overlap between HOMO and
LUMO. However the problem is, what is the physical meaning of hardness?
10.2.1.2.3 Density functional theory
Parr and al. 12 gave in 1988 a theoretical support to the absolute hardness. In the density functional
theory two basic parameters were introduced. Any chemical system can be characterized
by its chemical potential, µ, and its absolute hardness, η. The chemical potential
measures the escaping tendency of an electronic cloud, while absolute hardness determines
the resistance of the species to lose electrons. The exact definitions of these quantities are:
∂
∂
μ = η
∂
∂
⎛ ⎞
⎜ ⎟ =
⎝ ⎠
⎛ 2
E
1 E ⎞
and ⎜
⎟
2
N
2
⎟
⎝ N ⎠
ν ν
[10.2.3]
where :
µ chemical potential
η absolute hardness
E electronic energy
N number of electrons
ν potential due to the nuclei plus any external potential.
However, according to frontier orbital method, 13 the relationship between η and the
HOMO and LUMO energies is reduced to:
1
η≈− −
2
( E E )
HOMO LUMO [10.2.4]
where :
η absolute hardness
EHOMO energy level of the HOMO orbital
ELUMO energy level of the LUMO orbital.
Of course the absolute softness is the reciprocal of the absolute hardness. The apparent
success of the density-functional theory is to provide two parameters from which we can
calculate the number of electrons transferred, resulting mainly from the charge transfer between
two molecules, i.e., from electrons flow until chemical potential reaches an equilibrium.
As a first approximation, the number of electron transferred is given 14 by:
N Trans
μ −μ
=
2
B A
( η −η
)
A B
[10.2.5]
where:
Ntrans number of electrons transferred
µ A chemical potential of the acid
µ B chemical potential of the base
ηA absolute hardness of the acid
ηB absolute hardness of the base.
This number varies from 0 to 1 and it is in most cases a fractional number. As an
example 15 for the interaction between Cl2 and substituted aromatic compounds, Ntrans varies