C. R. Rice, T. Riis-Johannessen et al.
À
Á
DECuCu ¼ RT ln uCuCu ¼ þ21:6kJmolꢀ1
ð16Þ
same time; at least one of them is constrained so that its hy-
drogen is directed towards the metal, hindering any poten-
The term uCuCu, from which the intermetallic interaction
value of DECuCu ¼ þ21:6kJmolꢀ1 is derived, equates to Erco-
laniꢄs allosteric cooperativity index a.[12] This parameter is
typically expressed as the ratio of the (statistically correct-
ed) experimental formation constant of a given multi-com-
ponent assembly to its equivalent hypothetical (non-cooper-
ative) one. The value of a will be greater than 1 in the case
of positive cooperativity and less than 1 in the case of nega-
tive cooperativity.[12] In the present case the value of a is
given by Equation (17):
ꢀ
tial Cu N interaction.
We have applied the extended site-binding model[10] to es-
timate the degree to which the binding of a first CuII ion by
L affects its affinity for a second CuII ion. This approach
allows the cumulative formation constants for equilibria
(1)–(4) to be modelled by one or more microscopic interac-
tion parameters and a statistical factor (w). The latter (w)
can be computed using a well-established procedure[11]
based on the symmetries of the participating species (see
Cu
aza
Cu
bipy
the Supporting Information). Defining 1) f and f as the
microscopic affinities of CuII for the aza-crown and bipy
ꢀ
ꢁ
À
Á
LL/RT
sites, respectively, and 2) a Boltzmann factor uLL =eꢀDE
a ¼ bC2;u1;L=wCu;L = fCu ꢂ fCu ¼ 10ꢀ3:7 ðꢃ 1Þ
ð17Þ
2;1
bipy
aza
as the inter-ligand interaction between the two coordinating
bipy units (in, for example, [Cu(L)2]2+ and [Cu3(L)2]6+), we
can express the cumulative formation constants of
[Cu(L)2]2+ and [Cu(L)]2+ as the following:
which indicates that severe negative cooperativity accompa-
nies the successive binding of two CuII ions to the ditopic re-
ceptor L. Although electrostatic repulsion between the en-
tering cations cannot be ruled out as a possible source of
this energy cost, such effects are known to be largely com-
pensated for by favourable solvation changes associated
with the increase in total charge when polymetallic recep-
tors undergo a sequential increase in nuclearity.[13] It is more
probable, therefore, that the repulsive interaction has a
structural basis: as seen in the solid state, when the bipy
unit acts as a bidentate chelate the resulting planarity forces
the two “inner” nitrogen atoms at the 3,3’-positions to ap-
proach one another, causing one to be an axially elongated
donor and outright preventing the other from coordinating
CuII at all. The corresponding energy cost of
DECuCu ¼ þ21:6kJmolꢀ1 thus reflects the entropic and en-
thalpic losses associated with the aza-crown being able to
coordinate through only three of its nitrogen atoms when
the bipy site is bound to a CuII ion. This applies irrespective
of the order in which the two sites are occupied: The struc-
tural rearrangements caused by secondary binding of CuII to
ꢀ
À
ꢁ
Cu;L
1;2
Cu;L
1;2
Cu
bipy
ð5Þ
ð6Þ
b
b
¼ w
¼ w
ꢂ
f
2ꢂuLL
Á
Cu;L
1;1
Cu;L
1;1
Cu
aza
ꢂ f
CuCu
Introduction of a second Boltzmann factor, uCuCu =eꢀDE
/
RT, accounting for the energy cost incurred by simultaneous
binding of both the bipy and aza-crown sites, likewise allows
us to write the following Equations (7) and (8):
ꢀ
ꢀ
ꢁ
ꢁ
2 À
Á À Á À
Á
2
2
Cu;L
3;2
Cu;L
3;2
Cu
bipy
Cu
aza
b
b
¼ w
¼ w
ꢂ
ꢂ
f
f
ꢂ uLL ꢂ f
ꢂ uCuCu
ð7Þ
ð8Þ
À
Á À
Á
Cu;L
2;1
Cu;L
2;1
Cu
bipy
Cu
aza
ꢂ f
ꢂ uCuCu
for [Cu3(L)2]6+ and [Cu2(L)]4+, respectively. Converting
Equations (5), (6), (7) and (8) into their logarithmic forms
then gives four simultaneous equations from which we cal-
culate the following values (see the Supporting Information
for full details):
ꢀ
the bipy site will require one of the Cu Naza bonds to break.
Alternatively, if the bipy unit is considered as the primary
binding site, the aza-crown is already locked in a conforma-
tion that prevents it from binding a second CuII ion through
all four N-donors.
Cu
bipy
log ðf Þ ¼ 7:8
ð9Þ
ð10Þ
ð11Þ
ð12Þ
Cu
In conclusion, we have presented structural and thermo-
dynamic evidence to show how the binding mode and affini-
ty of a ditopic aza-crown/bipy ligand can be influenced by
allosteric interactions. The results provide an interesting in-
sight into the mechanism of site interaction in artificial allo-
steric systems: the two sites are mechanically coupled
through conformational restraints. Possible applications for
regulating the catalytic activity in for example, dioxygen ac-
tivation and phosphodiester cleavage reactions are currently
being explored.
log ðf Þ ¼ 10:3
aza
log ðuLLÞ ¼ 0:02
log ðuCuCuÞ ¼ ꢀ3:7
Subsequent conversion into absolute energies gives the fol-
lowing final values:
ꢀ
ꢁ
Cu
bipy
DgCu;bipy ¼ RT ln f
¼ ꢀ44:9kJmolꢀ1
ð13Þ
À
Á
Cu
aza
DgCu;bipy ¼ RT ln f
¼ ꢀ59:3kJmolꢀ1
ð14Þ
ð15Þ
Acknowledgements
À
Á
DEL;L ¼ RT ln uLL ¼ ꢀ0:1kJmolꢀ1
We thank the University of Huddersfield for funding (CES).
3466
ꢂ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2012, 18, 3464 – 3467