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3.2 Thermodynamic Considerations in Self-Assembly
Spontaneous reactions tend to minimize the free energy D
G
of a chemical system at given
experimental conditions. In mononuclear coordination compounds, the formation of
favourable interactions between metal ions and ligands overcomes the energy-consuming
desolvation processes of reagents. The structure of the resulting complexes depends on
the concentration and inherent properties of the metal ions and ligands involved. When
describing the self-assembly of supramolecular architectures including helicates, the
same thermodynamic principles are taking place. Let us consider in detail the physico-
chemical description of simple mononuclear complexes that are well experienced in coor-
dination chemistry and that are often used as building blocks in supramolecular chemistry.
These basic concepts will then be extended to the appropriate thermodynamic description
of polynuclear compounds and illustrated with examples of helicates.
3.2.1 Mononuclear Coordination Complexes
Basic physico-chemical principles can be briefly summarized in the following three point-
s that are closely interconnected [2,8]. To maximize the energetic gain associated with the
complexation of one metal ion (i.e., a receptor), the number of its interactions with
x
-dentate ligands must be also maximal. An optimal arrangement of coordinating ligands
around metal ions with respect to their intrinsic properties is known in coordination chem-
istry as
stereochemical matching
[1]. Ideally, a metal ion with the coordination number
CN
may accommodate
CN
/
x
ligands. The coordinating atoms must be spatially disposed
in such a way as to respect the coordination geometry of the metal ion. At this point,
molecular recognition takes place and selects only complementary polydentate ligands.
As an example, let us take a copper cation, which is commonly employed for the assem-
bly of double-stranded helicates. The satisfaction of its tetrahedral coordination prefer-
ences requires the coordination of two bipyridine-based chelating ligands (Figure 3.1).
The mononuclear copper complex forms the maximum of possible coordination bonds
provided by the bidentate ligand and reaches its maximum occupancy state with a maxi-
mal energetic gain. The copper coordination sphere is saturated with the bidentate ligand
Y
Y
[Cu(CH
3
CN)
4
]
+
+
2
+
4 CH
3
CN
N
N
X
X
Point group
T
d
12
3
4
1
C
2v
2
1
1
D
2v
4
C
∝
h
1
3
1
ext
σ
int
σ
1
1
mix
σ
(12·3
4
·1) (2·1·1)
2
(4·1·1)(1·3·1)
4
Cu,L
=
= 12
ω
1,2
Figure 3.1 Reaction scheme for the formation of a simple copper(I) complex. The statistical
factors v
M;L
m
are assessed with the symmetry number method [10].
;
n
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