Chemistry Reference
In-Depth Information
The local hardness η(r) and local softness s(r) are defined as
η=
δµ
δρ
(r)
and
(3.58)
(r)
v(r)
δρ
δµ
s(r)
=
.
(3.59)
(r)
v(r)
The local hardness and local softness are interconnected through this inverse
relationship:
∫
η
(r)s(r)dr1
=
.
(3.60)
The most commonly cited scale producing the most successful correlations (i.e.,
highest correlation coefficients, r) is the one computed by Pearson and Mawby
(Pearson and Mawby 1967). This scale involves the so-called softness parameter
(σ
P
) defined for a metal ion in terms of the coordinate bond energies of its metal
fluoride, CBE(F), and metal iodide, CBE(I).
CBEF CBEI
CBEF
()
−
()
σ=
(3.61)
()
The softness parameter (σ
P
) is a measure of the ability of a metal ion to give up its
valence electrons (Jones and Vaughn 1978; Williams and Turner 1981). A hard metal
ion retains its valence electrons very strongly and is not readily polarized, whereas
a soft metal ion is relatively large, does not retain its valence electrons firmly, and
is easily polarized (Vouk 1979). For ions of a given charge, softness increases as
σ
P
decreases. The σ
P
is probably the most widely used parameter in studies of
metal ion toxicities (Williams et al. 1982; Turner et al. 1983; Tan et al. 1984; Babich
et al. 1986; Khangarot and Ray 1989; Segner et al. 1994; Magwood and George 1996;
McCloskey et al. 1996; Enache et al. 1999; Ownby and Newman 2003). These and
additional studies are discussed in Chapter 5.
Other softness parameters used by various studies are the following:
• Ahrland softness parameter (σ
A
)
(Ahrland 1968) is correlated with total ion-
ization potential for the formation of M
n+
(g) and the dehydration energy −Δ
H
o
.
The larger the difference between the total ionization potential for the forma-
tion of M
n+
(g) and the dehydration energy −Δ
H
o
are, the softer the ion is.
• The softness parameter of Misono and Saito (Y') (Misono and Saito 1970)
is based on the use of a regression model where the log of stability con-
stants of halogeno-complexes of metal ions (Log k) is a function of two
parameters. One parameter corresponds to hardness (X) and the other to
softness (Y),
log K = α'X + β'Y' + γ'
(3.62)
