Chemistry Reference
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t HE c ovalEnt i ndEx (
)
2
m
3.4.3
Xr
2
m ( X m is electronegativity and r is ionic radius) reflects the degree of covalent
interactions in the metal-ligand complex relative to ionic interactions (Nieboer and
Richardson 1980). In QSAR studies, the covalent index is commonly used in com-
bination with ionic index Z 2 / r or with the constant for the first hydrolysis |log KOH|
(see Section 3.5). The subscript “m” refers to the most common (Mulliken) measure
of electronegativity. Sometimes other measures are used in the literature and some-
times the “m” is omitted, e.g., the covalence index in Chapter 8 does not include the
“m” subscript because the Pauling, Mulliken or Allred-Rochow scales for electro-
negativity might be pertinent.
The Xr
m and i ionic, i ndEx Z 2 / r
The combined use of the covalent and ionic indices was proposed by Nieboer
and Richardson (1980) to correlate with metal bioactivity. Based on the ionic
indices and covalent indices, Nieboer and Richardson (1980) classified metals
and metalloids into three classes: A, B, and borderline (see Table  3.1 ) . This clas-
sification is related to atomic properties and the solution chemistry of metal ions,
and demonstrates the potential for grouping metal ions according to their binding
preferences.
The hard acceptors, or class A group ions (oxygen-seeking), are expected to inter-
act with oxygen-containing ligands. The soft acceptors, or class B group ions (nitro-
gen/sulfur-seeking), form stable bonds with S- and N-containing ligands. The metals
from class B (e.g., Ag + , Tl + , Hg 2+ , Cd 2+ ) are often very toxic. Between the two major
classes are the borderline elements represented primarily by metal ions from the first
series of transition metals.
The combined use of the two indices has been applied in QSAR studies to predict
the relative toxicity of metal ions (McCloskey et al. 1996) or to predict biosorption
capacity (Can and Jianlong 2007).
3.4.4
c ombination of c ovalEnt i ndEx Xr
3.4.5 p olariZability and c HEmical s oftnEss p aramEtEr
A widely applied concept in the evaluation of metal ion interaction is that of hardness
and softness. In general terms, hard and soft suggest the resistance to deformation in
response to electric forces. Thus, hard ions have greater resistance to deformation of
the electron cloud and soft ions have lesser resistance to deformation. Quantitative
scales for metal ion hardness or softness were developed in the 1960s, starting with
the HSAB theory developed by Pearson (see Section 3.3.1).
HSAB theory is rather qualitative and summarizes the general affinity of a Lewis
acid (the metal ion) for a Lewis base (the ligand) in a manner independent of the
acidity or basicity of the species. The general trend is that hard metal ions bind pref-
erentially to hard ligands, whereas the soft metal ions bind to soft ligands. This prin-
ciple reflects the degree of covalency in the metal-ligand bond. The combinations
between strong species are predominantly ionic, while the combinations between
soft species are predominantly covalent.
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