Chemistry Reference
In-Depth Information
The basic principles of this approach were formulated in 2005 [15a,b] as an extension of
the site-binding model. The main difference compared with the site-binding model is the
explicit considerations of inter- and intramolecular reactions and homocomponent inter-
actions. Although the complexity of modelling with the thermodynamic additive free
energy model (TAFEM) increases, this thermodynamic description is applicable to the
stability constant of any species formed by self-assembly.
The total free energy related to the formation of a supramolecular assembly (Equa-
tion 3.1) is obtained as the sum of the elementary energetic contributions intervening in
the process, which can be expressed with the general Equation 3.12.
n
RT
X
RT
X
X
inter
intra
ln
k
i
þ
D
G
M;L
m
M;L
m
ln
k
i
j
D
E
M;M
¼
RT
ln
v
:
EM
j
;
n
;
ij
i
¼
1
j
¼
1
i
<
X
l
D
E
L;L
þ
ð
3
:
12
Þ
kl
k
<
The related global stability constant is then obtained as the product of all microscopic
parameters using straightforward transformations (Equation 3.13).
ij
Y
tot
intra
Y
Y
Y
k
i
EM
j
kl
ð
u
M;M
u
L;L
Ln;L
M;L
m
;
n
b
m
;
n
¼ v
3
:
13
Þ
i
¼1
j
¼1
i
<
j
k
<
l
M;L
m
n
(Equation 3.2), micro-
scopic binding affinities for inter- (
k
i
) and intramolecular reactions (
k
i
Note that all these energetic parameters [statistical factors
v
;
EM
), homocom-
ponent interactions D
E
M;M
and D
E
L;L
] were discussed in Section 3.1 in terms of basic
principles applicable to complexation processes.
The application of this innovative approach can be illustrated for the assembly of dinu-
clear triple-stranded helicates (i.e., with lanthanides [15c]), which represent the most fre-
quently occurring type of helicates. Figure 3.16 schematically shows the structures of all
possible microspecies in the system, their point groups (necessary for calculating symme-
try numbers) and the thermodynamic model of their microscopic constants. In the present
case, the expression for microconstants is identical to the macroscopic stability constants.
However, in more complex systems, the expression for the macroconstant is obtained as
the sum of microconstants [15].
The number of stability constants available for modelling is often limited: (i) due to the
lack of reliable experimental data for existing complexes or (ii) because of the thermo-
dynamic instability of elusive complexes. Therefore, the analysis of real systems and
obtaining physically meaningful parameters often requires making reasonable simplifica-
tions and reducing the number of thermodynamic parameters by: (i) empirical estima-
tions, (ii) theoretical predictions or (iii) by an independent evaluation of reference
processes. For instance, the combination of thermodynamic data collected for the series
of different but structurally related di-, tri- and tetranuclear europium helicates allowed
the establishment of a reasonably simplified set of thermodynamic descriptors. The
applied hypotheses are the following: (i) binding affinities and interligand and inter-
metallic interactions are identical in all microspecies, taking into account the same inter-
metallic distances, (ii) long-range intermetallic distances are modelled with Coulomb's
:
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