The Delicate Balance of Preorganisation and Adaptability in Multiply Bonded Host–Guest Complexes

Article abstract of DOI:10.1002/chem.201605092

Rigidity and preorganisation are believed to be required for high affinity in multiply bonded supramolecular complexes as they help reduce the entropic penalty of the binding event. This comes at the price that such rigid complexes are sensitive to small geometric mismatches. In marked contrast, nature uses more flexible building blocks. Thus, one might consider putting the rigidity/high-affinity notion to the test. Multivalent crown/ammonium complexes are ideal for this purpose as the monovalent interaction is well understood. A series of divalent complexes with different spacer lengths and rigidities has thus been analysed to correlate chelate cooperativities and spacer properties. Too long spacers reduce chelate cooperativity compared to exactly matching ones. However, in contrast to expectation, flexible guests bind with chelate cooperativities clearly exceeding those of rigid structures. Flexible spacers adapt to small geometric host–guest mismatches. Spacer–spacer interactions help overcome the entropic penalty of conformational fixation during binding and a delicate balance of preorganisation and adaptability is at play in multivalent complexes.

Full text of DOI:10.1002/chem.201605092

A Journal of
Accepted Article
Title: The delicate balance of preorganisation and adaptability in
multiply bonded host-guest complexes
Authors: Larissa K. S. von Krbek, Andreas J. Achazi, Stefan Schoder,
Marius Gaedke, Tobias Biberger, Beate Paulus, and
Christoph A Schalley
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The delicate balance of preorganisation and adaptability in
multiply bonded host–guest complexes
Larissa K. S. von Krbek,[a] Andreas J. Achazi,[b] Stefan Schoder,[a] Marius Gaedke,[a] Tobias Biberger,[a]
Beate Paulus,*[b] and Christoph A. Schalley*[a]
Abstract: Rigidity and preorganisation are believed to be required
for high affinity in multiply bonded supramolecular complexes as
they help reducing the entropic penalty of the binding event. This
comes at the price that such rigid complexes are sensitive to small
geometric mismatches. In marked contrast, nature uses more
flexible building blocks. Thus, one might consider putting the rigidity-
high affinity notion to the test. Multivalent crown/ammonium
complexes are ideal for this purpose as the monovalent interaction is
well understood. A series of divalent complexes with different spacer
lengths and rigidities has thus been analysed to correlate chelate
cooperativities and spacer properties. Too long spacers reduce
chelate cooperativity compared to exactly matching ones. However,
in contrast to expectation, flexible guests bind with chelate
cooperativities clearly exceeding those of rigid structures. Flexible
spacers adapt to small geometric host/guest mismatches. Spacer-
spacer interactions help overcoming the entropic penalty of
conformational fixation during binding and a delicate balance of
preorganisation and adaptability is at play in multivalent complexes.
reason, why many natural multivalent complexes do not exhibit
such a high degree of preorganisation, but exhibit at least some
flexibility allowing for adaptability. DNA for example has a highly
flexible backbone, yet it is very stable when doubly stranded
(due to multivalent binding enhancement). This concept is also
used in foldamers[16-19] and Hunter and co-workers[20-21] recently
reported a synthetic DNA analogue binding with high chelate
cooperativities despite of its flexible backbone. Sufficient
adaptability to small geometric mismatches between the multiply
bonded interaction partners may thus be advantageous for
strong multiple host–guest interactions.
Here, we address this question systematically by
investigating several series of divalent crown ether/ammonium
complexes and quantify the effects of spacer length and spacer
flexibility on the chelate cooperativity of the complex. Chelate
cooperativity[7-8, 22-24] is a term that accounts for the likeliness of a
multiply bonded, i.e. multivalent, structure to form a fully bonded
1:1 complex instead of oligomers. Fundamental studies of this
type will provide quantitative design rules to guide the
construction of supramolecular assemblies and receptors.
Recently, we demonstrated[25-26] the well-studied crown
ether/ammonium binding motif[10-11, 27-30] to be especially suitable
for our purpose as the monovalent interaction is a reliable, well
understood binding motif.[31-33] Furthermore, these systems
exhibit a limited molecular size suitable for computational
analysis by density functional theory.[25-26, 31, 34] In our previous
studies, we investigated[25-26] the cooperativities in two virtually
identical divalent complexes with flexible linkers that exhibited
significantly different, but very high chelate cooperativities. The
present study aims at a more general view on multivalent
interactions in such host-guest complexes. We expected to find
the highest cooperativities for rigid linkers. However, the
opposite was the case. Maximum chelate cooperativity was
observed for the flexible structures. This indicates that there is a
delicate balance between preorganisation and adaptability of a
system.
Introduction
Preorganisation and complementarity are paradigmatic concepts
in supramolecular chemistry, which are believed to be the key to
exceptionally strong multiply bonded[1-9] structures. Cram[10-11]
introduced the concept of preorganisation to supramolecular
12]
chemistry and Whitesides and co-workers[2,
extended this
principle to multivalent biological systems. Preorganised, rigid
systems supposedly suffer from a lower entropic penalty upon
binding compared to more flexible, less preorganised
systems.[13-14] Indeed, there are intriguing examples of highly
cooperative multivalent binding in rigid supramolecular
systems;[1-8] for example Anderson’s[8] huge zinc porphyrin
wheels that are synthesised around multivalent templates. The
preorganisation and linker rigidity in these systems leads to a
four orders of magnitude increase of binding affinity compared to
noncyclic porphyrin oligomers. However, such rigid structures
are very sensitive towards geometric mismatches between the
binding partners. Even a slight structural discrepancy can lead to
a drastic drop in binding affinity.[12, 15] This is likely an important
Results and Discussion
Conceptual approach
Before discussing the results obtained, we briefly describe the
general conceptual approach that was taken in this work. This
approach has been described previously[26] and details can be
found in the SI. Briefly, to quantify the multivalent binding
enhancement compared to the corresponding monovalent
counterparts, two different chelate cooperativity factors β and β'
were defined by Hunter and Anderson[22] as well as Ercolani and
Schiaffino,[23] respectively (eqs. 1 and 2, respectively, for a
[a]
L. K. S. von Krbek, M. Sc.; A. J. Achazi, M. Sc., S. Schoder, M. Sc.;
M. Gaedke, M. Sc.; T. Biberger, Prof. Dr. B. Paulus, Prof. Dr. C. A.
Schalley
Institut für Chemie und Biochemie, Freie Universität Berlin
Takustraße 3, 14195 Berlin, Germany
E-mail: c.schalley@fu-berlin.de
Supporting information for this article is given via a link at the end of
the document.
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divalent complex a, Figure 1, middle). The cooperativity factor β
quantifies the likeliness of an open singly bound divalent
complex to close to the doubly bound form. Factor β' describes
how prone the open complex is to oligomerisation, if an
additional host is offered. This is why the cooperativity factor β'
is normalised by the host concentration.
Both cooperativity factors indicate positive chelate
cooperativity, i.e. predominant formation of closed complex,
if β > 1 and β' > 1 (ln β > 0 and ln β' > 0, respectively). In
case of factors smaller than 1, the divalent complex
predominantly exists in its open form which is prone to
cooperativity remains. This DMC can also be described as the b
+ c  a + 2 d equilibrium (Figure 1, bottom). As all components
appear on both sides of the equilibrium, the equilibrium constant
K is only affected by chelate cooperativity. EM can be calculated
from the set of all four binding constants Ka – Kd (eq. 3). These
binding constants can be expressed as products of the intrinsic
monovalent binding constant Kmono and the statistical factors,[38-
40]
derived by the direct count method[38-39] or—with the same
40]
result—Benson’s symmetry number method.[38,
If these
products are inserted into the definition of K (eq. 3), it becomes
clear that K is only dependent on EM in these cases.
oligomerisation,
cooperativity. The absence of chelate cooperativity is
thus
exhibiting
negative
chelate
)
(
(
)
(
)
(3)
(
)
(
)
indicated by β = 1 and β'= 1.
(4)
(5)
(
)
or
(1)
(2)
(
)
(
)
or (
)
[
]
[
]
The four individual binding constants Ka
–
Kd are
The effective molarity EM is the key variable in both
cooperativity factors. In the two-step association process of a
experimentally accessible in four separate isothermal titration
calorimetry (ITC) experiments. The advantage of ITC is that it
measures the association constant K, the association enthalpy
ΔH and the association entropy ΔS in the same experiment.
Hence, the DMC can also be applied to ΔH and ΔS (eqs. 4, 5).
This provides detailed insight into residual enthalpies ΔΔH and
entropies Δ(T ΔS) of divalent complexes. These values exhibit
larger errors due to error propagation and their discussion later
on will focus on trends rather than precise values.
divalent complex
a
(Figure 1), EM accounts for the
intramolecular ring closure in the second binding step. EM
cannot be measured directly, but can be quantified by double
mutant cycle analyses (DMC; Figure 1, top).[5, 26, 31-33, 35-37] The
DMC connects
a divalent complex a to two monovalent
complexes d via two pathways of two consecutive mutations. By
comparison of the four complexes a – d derived from the
mutations, all secondary allosteric effects cancel and the chelate
Figure 1. Top: Double mutant cycle for the thermodynamic analysis of chelate cooperativity of a divalent complex. Bottom: Evaluation of the effective molarity EM.
The individual binding constants for each of the four complexes, Ka – Kd can be independently measured in four titration experiments. Each of them can be
expressed in a term using the monovalent binding constant Kmono. As the crown ether can be approached by the ammonium ion from both sides, Kmono is the
intrinsic monovalent binding constant after correction of the apparent one by a statistical factor of 2 to be consistent with the statistical factors of the other
complexes. From the four binding constants, the equilibrium constant K for the b + c → a + 2d equilibrium can be calculated and is equivalent to EM in the cases
under study here as all statistical factors cancel. Adapted with permission from Ref. [26] (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim).
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Chart 1. Divalent guests GX, divalent host H and their complexes GX@H as well as monovalent reference compounds mG1, mG2, mH and their complexes
mG1@mH and mG2@mH. Divalent guests GX exhibit spacers of different lengths and degrees of flexibility between their ammonium binding sites. The different
degrees of flexibility are colour coded: flexible = blue, “semi-rigid” = violet, rigid = red. Three more flexible guests bearing ether chains instead of alkyl were
investigated as well. Results of those are reported in the SI. Note that there is only one monovalent reference system for G6–G11.
For a correlation of linker length and flexibility with chelate
cooperativity, DFT-optimised structures were used. DFT
structure optimisation is done here with a dispersion corrected
matches the green line, which indicates the N–N distance in the
+
(NH4 )2@H 2:1 complex. Consequently, the selection of
guests should be appropriate to get a more general view on
the role of spacer length (and flexibility) on cooperativity.
The guests under investigation can be divided into four
groups: (i) Too short guest G1 which most likely cannot
meta-GGA functional and
a triple-zeta basis set (TPSS-
D3(BJ)/def2-TZVP).[41-50] This method provided good geometric
structures in previous studies[25-26, 43] (for a detailed description of
the computational methods see SI).
bridge the distance between the two crown ethers in
therefore, is mostly singly bound. (ii) Short guests G2
H
,
and,
G6
This approach was established in earlier studies.[26] In this
work, we took a known divalent [18]crown-6 host with a rigid
linker scaffold (H) and investigated its association to different
divalent primary ammonium ions (Chart 1). We systematically
altered the linker length and flexibility in the ammonium guests
to quantify the effect of both on the chelate cooperativity of the
complex. Three different groups of guest spacer flexibilities were
taken into account: flexible alkyl spacers (blue), less flexible,
“semi-rigid” aryl ether spacers (violet) and rigid aryl/alkynyl
spacers (red). We did not alter the host structure to have a
reliable benchmark in all systems.
,
To test, whether the guest spacer lengths selected for this
study cover the whole range from too short to longer-than-
necessary spacers, the calculated N–N distances of the
host-guest complexes GX
@H−2OTs were compared to
those of the unbound, relaxed guests GX−2OTs (Figure 2).
+
The (NH4 )2@H 2:1 complex provides the N
unstrained host-guest structure. The orange line in Figure 2
indicates the trend of relaxed N N distances in the free divalent
guests. As long as the guests are too short, the N N distances
–N distance for an
Figure 2. Comparison of N–N distances in unbound guests GX−2OTs (one
representative structure in top right corner) and in complexes GX@H−2OTs.
The orange line corresponds to N–N(unbound guest) = N–N(complex). The
green line corresponds to the N–N distance in (NH4+)2@H (structure in bottom
right corner). Guest with N–N distances shorter than that of the host
benchmark (14.0 Å) show linear behaviour along the orange trendline, while
longer guests show asymptotic behaviour towards the green line. According to
this correlation, G7 and G11 are expected to exhibit the highest chelate
cooperativities.
–
–
for the host-guest complexes follow this line until a good length
fit is achieved.
For guests that have too long spacers, the N
–N distances in
the divalent complexes is more or less constant and nicely
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G9 and G10 to which
conformations to accommodate shorter guests. (iii) Guests
G7 and G11 with (almost) optimal N distances. (iv) Guests
G3 G4 G5 and G8 with too long spacers which have to
contract to bind to . Hence, complexes G7 and
G11 with optimal spacer lengths are expected to exhibit
the highest chelate cooperativities. They furthermore exhibit
more rigid spacer scaffolds that are expected to be
preferable for high-affinity divalent binding and high chelate
cooperativity. Shorter guests spacers (ii) should exhibit
reduced chelate cooperativities as the complexes can be
expected to be strained with unfavourable enthalpic effects.
Longer spacers (iv) are expected to be entropically
unfavourable due to a higher degree of conformational
fixation in the complex. Also, there might be enthalpic
penalties from unfavourable gauche conformations along
the alkyl chain.
H
can adapt by changing the crown
Analysis of chelate cooperativities
The thermodynamic binding data of the complexes GX@H were
determined by isothermal titration calorimetry (ITC) in 1:1 (v/v)
mixtures of chloroform and methanol.
N–
[51]
,
,
The data were fitted to
H
@H
a 1:1 binding isotherm. The resulting association constants are
summarised in Table 1. Double mutant cycle analyses of the
divalent complexes provide their effective molarities EM and
their chelate cooperativity factors β and β' (Table 1). Figure 3a
depicts the cooperativities plotted in logarithmic form (ln β and ln
β') against the deviations of the N–N distances of the complexes
against the corresponding relaxed distances. To facilitate the
analysis, we roughly distinguish two cases (i) If the guest is
more flexible than the host (G1–G8), one expects mainly the
guest to adapt to the host. The host adapts to the guest as well,
but with less pronounced geometrical changes. Energetically,
the deformation of the host contributes however more to the
@
H
strain (examples in Figure 3b). For these guests, the N–N
distances of the relaxed complex ((NH4 )2@
+
H
) are compared to
Synthesis and complex characterisation
the N–N distances of the complexes GX@H−2OTs. (ii) If the
host structure is more flexible than the guest structure (G9–G11),
it is more reasonable to compare the N–N distances of the
complexes GX@H−2OTs with the N–N distances of the
unbound guests GX−2OTs.
Several observations are made from the plots in Figure 3a.
First of all, both cooperativity factors result in similar trends and
we can conclude that it does not make a significant difference
for the interpretation of chelate cooperatives in the present
study, which of the two definitions of chelate cooperativity is
used.
The synthesis of monovalent guests mG1 and mG2,[25] divalent
host H[26] as well as divalent guest G3[26] and their complexes
was reported before. The other 10 divalent guests were obtained
as described in the SI. Complex formation was achieved by
mixing the two binding partners in a 1:1 molar ratio in 1:1
(v/v) mixtures of chloroform and methanol. Exclusive
formation of doubly bound 1:1 complexes was
1
demonstrated by H NMR (see SI). As expected, the only
exception is G1
@H, which is at least partially open. ESI
mass spectrometric experiments substantiate the 1:1
stoichiometry and exclude the formation of 2:2 complexes
or larger oligomers (see SI).
Table 1. Association constants of divalent complexes Ka and the corresponding normalised monovalent reference constants obtained from ITC titrations
(CHCl3/MeOH 1:1 (v/v), 298 K (for complete data sets including 1:2 and 2:1 complexes of two monovalent and one divalent component, see SI, Tables S2-S15).
Effective molarities EM, chelate cooperativity factors β[22] and β'[23], as well as residual enthalpies ΔΔH and entropies Δ(T ΔS) were obtained by complete DMC
analysis (eqs. 1 - 5)
[25]
Kmono
Ka
EM
[mM]
ΔΔH
Δ(T ΔS)
complex
β
β' [a]
[103 M−1
]
[103 M−1
]
[kJ mol−1
]
[kJ mol−1
]
G1
G2
@
@
H
H
2.0 ± 0.2
2.0 ± 0.2
2.0 ± 0.2
2.0 ± 0.2
2.0 ± 0.2
4.3 ± 0.4
4.3 ± 0.4
4.3 ± 0.4
4.3 ± 0.4
4.3 ± 0.4
4.3 ± 0.4
14 ± 1.4
700 ± 70
1.3 ± 0.3
430 ± 100
880 ± 200
200 ± 40
96 ± 22
20 ± 4
2.5 ± 0.6
860 ± 210
1,800 ± 430
400 ± 100
190 ± 50
85 ± 21
0.16 ± 0.04
54 ± 12
110 ± 30
25 ± 6
3.0 ± 4.0
−(4.1 ± 3.6)
−(11.1 ± 4.0)
−(2.3 ± 3.6)
−(3.7 ± 3.5)
5.3 ± 4.3
7.9 ± 3.9
−(6.4 ± 3.6)
−(11.5 ± 4.1)
−(6.4 ± 3.7)
−(9.6 ± 3.5)
−(4.4 ± 4.4)
−(3.6 ± 4.5)
−(2.5 ± 3.8)
−(0.2 ± 3.9)
−(10.5 ± 3.8)
−(5.8 ± 3.8)
G3
@
H23
2,700 ± 270
620 ± 62
G4
G5
G6
G7
G8
G9
@
H
H
H
H
H
H
@
@
@
@
@
300 ± 30
12 ± 3
300 ± 30
2.5 ± 0.6
13 ± 3
1,400 ± 140
1,100 ± 110
220 ± 22
110 ± 20
51 ± 11
11 ± 5
460 ± 110
220 ± 50
45 ± 21
1.8 ± 4.5
6.4 ± 1.5
2.6 ± 1.2
15 ± 3
5.0 ± 3.7
11.0 ± 3.7
−(5.7 ± 3.7)
3.1 ± 3.8
G10
G11
@
H
H
1,500 ± 150
380 ± 38
120 ± 30
28 ± 8
500 ± 120
120 ± 36
@
1.94 ± 0.25
[a] The concentration in the ITC vessel, by which the cooperativity factor β' is normalised, was 2 mM in all cases, except G9 and G11, where it was 1 mM, because
of solubility problems.
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Figure 3. (a) Correlations of chelate cooperativity factors ln β (left) and ln β' (right) to (i) the differences in N–N distances of complex GX@H−2OTs and relaxed
complex (NH4+)2@H (N–N(complex) − N–N(2 NH4+)) for guests G1–G8 (blue & purple lines) or to (ii) the differences in N–N distances of unbound guests
GX−2OTs and complex GX@H−2OTs (N–N(unbound guest) − N–N(complex)) for guests G9–G11 (red lines). Shorter guest spacers correspond to lower values
on the x axis. Values below x = 0 correspond to a contracted conformation of host or rigid guest compared to their relaxed structures. Values of x > 0 correspond
to a stretched conformation of host or rigid guest compared to their relaxed structures. For x =1, the more rigid component of the complex is in a relaxed structure,
resulting in the highest chelate cooperativities. (b) Representative DFT calculated structures of relaxed host (NH4+)2@
well as their complexes with H for an assessment of the impact of guest spacer length and flexibility on the chelate cooperativity of the whole complex.
H, unbound guests G3, G5, G6 and G11 as
The second finding is that a separate consideration of the
series of flexible, semi-rigid and rigid guests is required to obtain
a clearer picture: In each of the three series the highest chelate
cooperativity is found for the guest with the best size match (G3
among the flexible guests, G7 in the semi-rigid and G10 in the
rigid series). Consequently, flexibility and spacer length are two
factors that are intimately interdependent and can, thus, not be
considered separately. To compare lengths is only reasonable
for guests of similar rigidity.
A third observation is that there appears to be no significant
difference in the chelate cooperativity between the “semi-rigid”
and the rigid guests as expressed in the almost identical chelate
cooperativity factors of G7 and G10. Clearly, however, a small
deviation from the optimal length causes a sharper drop in
chelate cooperativity for the rigid than the semi-rigid guests.
High rigidity thus comes at the price of a higher sensitivity of the
binding interactions to small geometric mismatches between
host and guest. Slightly stretching or compressing the guests
scaffold even by only 0.5 Å results in a decrease of the
cooperativity factors by one order of magnitude.
Most strikingly and in marked contrast to the expectation
discussed above, semi-rigid G7 and rigid G11 do not exhibit the
highest chelate cooperativities, even though they are close to
perfect in spacer length and require less conformational fixation
upon divalent binding than the flexible guests. Instead, two
flexible guests G2 (slightly too short) and G3 (slightly too long)
exhibit the highest chelate cooperativities. Even flexible guest
G4, with a spacer significantly longer than required to bridge
between binding sites exhibits chelate cooperativities β similar to
and β' higher than G7 and G10. Although the semi-rigid guest
G8 fits better to the host in length, it can still not compete with
G4 neither in β nor in β'. Similarly, the chelate cooperativity
drops somewhat below that of G4 for the longest flexible guest
G5, but is still in the same order of magnitude as compared to
G8 and G11. Unexpectedly, flexible guests thus clearly exceed
the more rigid ones in chelate cooperativity over a broader
length range, even when the latter ones are expected to fit better
to the host geometrically. Generally, the complexes with flexible
guests are less affected by variations of the spacer length than
the complexes with more rigid guests (G6–G11, purple/red lines).
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Analysis of residual enthalpies and entropies
and entropy factors that contribute to chelate cooperativity.
Density functional theory aided the analysis of the
thermochemical data by providing the structural parameters
required.
These results contradict the widely accepted notion that flexible
scaffolds are unfavorable for multivalent binding as they suffer
from a higher entropic penalty upon ring closure than more rigid
structures. To address this point, we investigated residual
enthalpies ΔΔH and entropies −Δ(TΔS) of the divalent
complexes under study with respect to spacer lengths and
flexibilities. A correlation of residual enthalpies and entropies to
the structural parameters used in Figure 3a elucidates the
impact of both parameters on the chelate cooperativities of
the complexes (Figure 4). In contrast to expectation, the
impact of the residual enthalpy ΔΔH on the chelate
cooperativity is generally larger than the impact of the residual
entropy −Δ(TΔS). Within the series of “semi-rigid” guest
scaffolds (G6–G8, purple lines), residual enthalpies and
entropies do not change significantly. Within the other two series,
the highest entropic penalties −Δ(T ΔS) are surprisingly paid by
the complexes exhibiting the highest chelate cooperativities, i.e.
G3@H and G10@H. These unfavourable entropies are
compensated by even more negative residual enthalpies ΔΔH,
which stabilise the complex. They are likely caused by
secondary interactions between guest and host spacers, such
as C–H···π and π···π interactions, and a low amount of strain in
the matching doubly bound host-guest complex. This provides
clear evidence, that the common notion that the entropic penalty
of the ring closure step is the main drawback in multivalent
binding needs to be regarded more carefully.
In complexes combining a host with a rigid scaffold with
guests of different spacer lengths and flexibilities, the flexible
guests are favoured over the more rigid ones, almost
irrespective of their spacer length as long as the spacers are
long enough to permit divalent binding. Our results therefore
clearly underline the importance of a certain flexibility and
adaptability for achieving strong divalent binding and high
chelate cooperativities. The underlying reason is the much more
pronounced effect that slight structural mismatches have on
complexes of rigid host and guest components. They exhibit
high chelate cooperativities only, when the geometries of host
and guest exactly match each other.
Furthermore, the cyclisation into the divalent complexes
under study is mainly driven by enthalpy, in particular favourable
secondary spacer–spacer interactions between host and guest
play a role. The entropic penalty for too long, but flexible spacers
resulting from their conformational fixation in the doubly bound
state is in contrast only a minor effect.
In contrast to supramolecular paradigms such as the principle of
preorganisation, a delicate balance between preorganisation
and adaptability is at play, when multiply bonded structures are
concerned. As it appears, flexible systems have been
underestimated so far with respect to their ability to achieve high
multivalent binding strengths and favourable chelate
cooperativity. When developing multivalent complexes, these
results encourage the supramolecular chemist to include less
rigid spacers in the design of the building blocks. This is of
interest also because solubility problems connected to the often
well-packing and easily precipitating rigid molecules can more
easily be circumvented and because the synthesis of more
flexible chains is often easier to accomplish.
Conclusions
Three series of divalent crown ether/ammonium complexes have
been investigated by isothermal titration calorimetry with respect
to their chelate cooperativities including an analysis of enthalpy
Figure 4. Correlations of residual enthalpies ΔΔH (left) and residual entropies −Δ(TΔS) (right) to (i) the differences in N–N distances of complex
+
GX
@
H
−2OTs and relaxed host (NH4+)2@H (N–N(complex) − N–N(2 NH4
)
) for guests G1
–
G8 (blue & purple lines) or to (ii) the differences in N–N
G11 (red lines).
distances of unbound guests GX−2OTs and complex GX
@
H
−2OTs (N–N(unbound guest) − N–N(complex)) for guests G9–
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Acknowledgements
The authors thank the Deutsche Forschungsgemeinschaft for
generous financial support (SFB 765). Support by the High-
Performance Computing facilities of the Freie Universität Berlin
(ZEDAT) is acknowledged. Furthermore, the authors thank
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Keywords: multivalency • chelate cooperativity •
preorganisation-adaptability dichotomy • isothermal titration
calorimetry • density functional theory
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10.1002/chem.201605092
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Entry for the Table of Contents
Layout 1:
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Adaptability beats rigidity:
Larissa K. S. von Krbek, Andreas J.
Thermochemical (ITC) and
Achazi, Stefan Schoder, Marius Gaedke,
Tobias Biberger, Beate Paulus,* and
Christoph A. Schalley*
computational (DFT) analyses on
various crown/ammonium complexes
with different guest-spacer lengths
and flexibilities revealed a delicate
interplay of preorganisation and
adaptability. Flexible and rigid spacers
equally suffer entropic penalty upon
binding, but flexible spacers are able
to compensate for mismatches
between host and guest. Furthermore,
spacer-spacer interactions render
flexible spacers favourable.
Page No. – Page No.
The delicate balance of
preorganisation and adaptability in
multiply bonded host–guest
complexes
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