Steric desolation enhances the effective molarities of intramolecular H-bonding interactions

Article abstract of DOI:10.1039/c2ob25372k

Free energy contributions due to intramolecular phosphonate diester-phenol H-bonds have been measured for 20 different supramolecular architectures in cyclohexanone solution. High throughput UV/Vis titrations were used in combination with chemical double mutant cycles to dissect out the contributions of different functional group interactions to the stabilities of over 100 different zinc porphyrin-pyridine ligand complexes. These complexes have previously been characterised in toluene and in 1,1,2,2-tetrachloroethane (TCE) solution. Intramolecular ester-phenol H-bonds that were measured in these less polar solvents are too weak to be detected in cyclohexanone, which is a more competitive solvent. The stability of the intermolecular phosphonate diester-phenol H-bond in cyclohexanone is an order of magnitude lower than in TCE and two orders of magnitude lower than in toluene. As a consequence, only seven of the twenty intramolecular phosphonate diester-phenol interactions that were previously measured in toluene and TCE could be detected in cyclohexanone. The effective molarities (EM) for these intramolecular interactions are different in all three solvents. Determination of the EM accounts for solvent effects on the strengths of the individual H-bonding interactions and the zinc porphyrin-pyridine coordination bond, so the variation in EM with solvent implies that differences in the solvation shells make significant contributions to the overall stabilities of the complexes. The results suggest that steric effects lead to desolvation of bulky polar ligands. This increases the EM values measured in TCE, because ligands that fail to replace the strong interactions made with this solvent are unusually weakly bound compared with ligands that make intramolecular H-bonds.

Full text of DOI:10.1039/c2ob25372k

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PAPER
Steric desolvation enhances the effective molarities of intramolecular
H-bonding interactions†‡
Elena Chekmeneva, Christopher A. Hunter,* Maria Cristina Misuraca and Simon M. Turega
Received 21st February 2012, Accepted 27th March 2012
DOI: 10.1039/c2ob25372k
Free energy contributions due to intramolecular phosphonate diester–phenol H-bonds have been
measured for 20 different supramolecular architectures in cyclohexanone solution. High throughput UV/
Vis titrations were used in combination with chemical double mutant cycles to dissect out the
contributions of different functional group interactions to the stabilities of over 100 different zinc
porphyrin–pyridine ligand complexes. These complexes have previously been characterised in toluene
and in 1,1,2,2-tetrachloroethane (TCE) solution. Intramolecular ester–phenol H-bonds that were measured
in these less polar solvents are too weak to be detected in cyclohexanone, which is a more competitive
solvent. The stability of the intermolecular phosphonate diester–phenol H-bond in cyclohexanone is an
order of magnitude lower than in TCE and two orders of magnitude lower than in toluene. As a
consequence, only seven of the twenty intramolecular phosphonate diester–phenol interactions that were
previously measured in toluene and TCE could be detected in cyclohexanone. The effective molarities
(EM) for these intramolecular interactions are different in all three solvents. Determination of the EM
accounts for solvent effects on the strengths of the individual H-bonding interactions and the zinc
porphyrin–pyridine coordination bond, so the variation in EM with solvent implies that differences in the
solvation shells make significant contributions to the overall stabilities of the complexes. The results
suggest that steric effects lead to desolvation of bulky polar ligands. This increases the EM values
measured in TCE, because ligands that fail to replace the strong interactions made with this solvent are
unusually weakly bound compared with ligands that make intramolecular H-bonds.
We have been developing methods for quantifying functional
group interactions in cooperative recognition interfaces that inter-
act via multiple contacts.7 Although it is possible to make
reasonably accurate predictions of the stabilities of simple com-
plexes that are held together by single point interactions like H-
bonds,8 systems that make multiple non-covalent contacts are
less well-understood. In addition, the effect of solvent on such
processes is an area that is largely unexplored, and development
of reliable models for understanding solvation in complex
systems represents a major challenge for supramolecular chem-
istry.9 This paper describes a quantitative investigation of solvent
effects on chelate cooperativity.
Introduction
Synthetic supramolecular complexes provide the ideal platform
for exploring the fundamentals of non-covalent chemistry in
relatively simple well-defined systems. Synthetic constructs have
been used to measure functional group interactions,1 long range
secondary interactions,2 the role of desolvation,3 and cooperative
effects in multivalent systems.4 The results have a direct bearing
on processes that range from the structures of biomacromolecules
to the properties of molecular materials and the development of
new catalysts.5 Supramolecular complexes also provide well-
characterised tractable systems for benchmarking molecular
simulation methods for making predictions of the structures and
thermodynamic properties of non-covalent systems.6
Approach
Metalloporphyrin–ligand complexes of the type shown in Fig. 1
provide an ideal platform for systematic studies of chelate co-
operativity in a relatively complicated but tractable molecular
recognition interface.7 Chemical double mutant cycles (DMC)
can be used to dissect out the free energy contributions due to
individual H-bonding interactions in these systems.10 The
approach is illustrated in Fig. 2. By comparing the properties of
Department of Chemistry, University of Sheffield, S3 7HF, UK. E-mail:
C.Hunter@shef.ac.uk; Fax: +44 114 2229346; Tel: +44 114 2229476
†Electronic supplementary information (ESI) available: Details of the
partially bound states analysis, statistical factors σ, values of K EM,
H-bond occupancy. See DOI: 10.1039/c2ob25372k
‡This article is part of the Organic & Biomolecular Chemistry 10th
Anniversary issue.
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single mutants (complexes B and C) with the double mutant
(complex D), it is possible to measure all secondary interactions
between the H-bonding groups and the core zinc porphyrin–pyri-
dine units. Thus eqn (1) gives the free energy contribution (ΔΔG
°) due to the phosphonate diester–phenol H-bond in complex A
in Fig. 2 without any contribution from these secondary inter-
actions. Experimental measurement of the free energies of intra-
molecular H-bonding interactions as a function of porphyrin and
ligand geometry provides insight into the relationship between
supramolecular architecture and the magnitude of chelate co-
operativity in these systems.
Fig. 1 Structure of a complex formed between a zinc porphyrin
(black) and a pyridine ligand (grey), which forms four intramolecular
H-bonds (blue).
ΔΔG° ¼ ΔGA° ꢀ ΔGB° ꢀ ΔGC° þ ΔGD°
ð1Þ
We have previously reported experiments on a family of
closely-related complexes where this analysis was applied to 48
different recognition interfaces involving zinc porphyrin–pyri-
dine coordination, phosphonate diester–phenol H-bonds, ester–
phenol H-bonds and ether–phenol H-bonds.7 These measure-
ments of chelate cooperativity were carried out in toluene and in
TCE solutions. Although the difference in polarity is rather
subtle, changing the solvent from toluene to TCE had a surpris-
ingly large effect on the effective molarities for the intramolecu-
lar interactions in these systems.7b In an attempt to understand
the origin of this solvent effect on chelate cooperativity, we have
investigated the same systems in a significantly more polar
solvent, cyclohexanone. This paper reports experiments in this
solvent and compares the results with the data obtained in
toluene and TCE.
Results and discussion
Fig. 2 Chemical double mutant cycle (DMC) for measurement of the
free energy contribution of the phosphonate diester–phenol H-bond to
the stability of complex A.
Figs. 3 and 4 show the porphyrins and ligands used to investi-
gate solvent effects on chelate cooperativity. The synthesis of
Fig. 3 Zinc porphyrin receptors P1a–P4a (R = OH) and P1b–P4b (R = OMe).
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Table 1 H-bond parameters and association constants (M−1) for the
1
formation of intermolecular complexes measured by H NMR titrations
in d10-cyclohexanone, d2-TCE and in d8-toluene at 298 K (Kref) and
a
calculated using eqn (2) (Kcalc
Solvent
Cyclohexanone 7·8
)
Complex αD βA αS
βS
Kref
Kcalc
b
3.8 5.4 1.5 5.8
3.8 5.4 2.0 1.3
3.8 5.4 1.0 2.2
3.8 8.9 1.5 5.8
0.06
2
3
TCE
Toluene
7·8
7·8
2
3
3
1
1
1
Cyclohexanone 7·9
2
TCE
Toluene
7·9
7·9
3.8 8.9 2.0 1.3 13
3.8 8.9 1.0 2.2 140 10 180
1
23
a H-bond parameters from ref. 8. b This complex is not sufficiently stable
to determine the association constant in cyclohexanone.
Fig. 5 Compounds used to measure Kref, the association constant for
the formation of intermolecular H-bonds.
ꢀRT ln Kcalc ¼ ꢀðαD ꢀ αSÞðβA ꢀ βSÞ þ 6 kJ molꢀ1
ð2Þ
Fig. 4 Phosphonate diester ligands, L1a–L6a, ester ligands, L1b–
L6b, and control ligands with no H-bonding groups, L4c–L6c.
where Kcalc is the intermolecular association constant at T =
298 K, αD and βA are the H-bond parameters of the H-bond
donor (D) and H-bond acceptor (A), αS and βS are the H-bond
donor and acceptor parameters of the solvent, and the constant
of 6 kJ mol−1 was experimentally determined in carbon tetra-
chloride solution.8
these compounds was described previously.7 Four of the zinc
porphyrin receptors are equipped with four phenol H-bond
donor sites located at different positions around the periphery of
the metal binding site, P1a–P4a (Fig. 3). The corresponding
methoxy porphyrins, P1b–P4b, serve as control compounds that
can not make H-bonds. The ligands are all based on pyridine
carboxylic acids that allow attachment of up to four H-bonding
groups at various positions on the ligand. Ligands L1a–L6a are
equipped with phosphonate diester groups, and the correspond-
ing ethyl ester ligands, L1b–L6b, serve as controls for the con-
struction of DMCs for the measurement of phosphonate diester–
phenol H-bonds. Ligands L4c, L5c and L6c are used as non H-
bonding mutants for construction of DMCs for the measurement
of ester–phenol H-bonds. Previous work showed that intramole-
cular H-bonding interactions are at the limit of detection for
ligand L1a in TCE.7b As we will see, the H-bonding interactions
are much weaker in cyclohexanone, so L1a and L1b are
excluded from this study.
H-bonding interactions between 7 and 8 could not be detected
in cyclohexanone solution, and this is consistent with the very
low association constant predicted by eqn (2). Although some of
the association constants in Table 1 are too low to be measured
with a high degree of accuracy, the values of Kcalc are all in good
agreement with the experimental values of Kref, which provides
confidence in the reliability of the values of the intermolecular
association constants in Table 1. The phosphonate diester–
phenol H-bond in cyclohexanone is an order of magnitude less
stable than in TCE and two orders of magnitude less stable than
in toluene. The phosphonate diester is such a strong H-bond
acceptor that it can compete effectively with a polar solvent like
cyclohexanone for interactions with H-bond donors, whereas the
carboxylic acid ester is a much weaker H-bond acceptor and can
not.
Solvent effects on intermolecular H-bonding
Cyclohexanone is a significantly more polar solvent than toluene
and TCE (Table 1). In particular, the H-bond acceptor parameter
β of cyclohexanone is much higher which means that the phenol
H-bond donor groups will be more strongly solvated in cyclo-
hexanone. The effect on the stability of intermolecular phospho-
nate diester–phenol H-bonds was measured experimentally using
High throughput titration analysis of binding
The association constants for all porphyrin–ligand combinations
were measured using a UV/Vis plate-reader that allows routine
determination of large numbers of association constants. The
zinc porphyrins have an intense UV/Vis absorption band at
420 nm, which shifts by around 10 nm when a pyridine ligand
binds to the zinc, and this provides a convenient spectroscopic
probe of binding. The titration data fit well to a 1 : 1 binding iso-
therm in all cases, and the results are collected in Table 2. The
stability of the complexes in cyclohexanone is low. This leads to
1
the compounds shown in Fig. 5 and H NMR titrations in d2-
TCE, d8-toluene and d10-cyclohexanone (Kref in Table 1). It is
also possible to estimate the values of intermolecular association
constants for the formation of complexes involving a single H-
bond using eqn (2) (Kcalc in Table 1).8a
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Table 2 Association constants (K/M−1) for the formation of 1 : 1 complexes measured using UV/Vis titrations in cyclohexanone at 298 K (with
percentage errors at the 95% confidence limit based on multiple repeats of the measurement)
Porphyrin
Ligand P1a
P2a
P3a
P4a
P1b
P2b
P3b
P4b
L2a
L3a
L4a
L5a
L6a
L2b
L3b
L4b
L5b
L6b
L4c
L5c
L6c
1.5 × 102 (45%) 6.7 × 101 (40%) 2.3 × 102 (16%) 5.8 × 101(17%) 5.8 × 101 (58%) 3.6 × 101 (35%) 5.1 × 101 (25%) 6.3 × 101 (36%)
a
a
a
a
5.4 × 101 (52%) 2.3 × 101 (32%) 4.9 × 101 (30%) 3.4 × 101 (34%)
7.7 × 102 (14%) 7.3 × 102 (16%) 6.7 × 102 (6%) 5.9 × 102 (4%) 3.9 × 102 (28%) 3.5 × 102 (12%) 3.7 × 102 (4%) 3.6 × 102 (14%)
7.7 × 102 (4%) 9.3 × 102 (14%) 5.0 × 102 (8%) 5.9 × 102 (8%) 1.3 × 102 (41%) 2.1 × 102 (7%) 1.9 × 102 (9%) 2.4 × 102 (34%)
2.9 × 102 (14%) 4.7 × 102 (14%) 2.4 × 102 (4%) 1.9 × 102 (6%) 1.1 × 102 (14%) 9.7 × 101 (8%) 9.7 × 101 (2%) 1.1 × 102 (2%)
6.3 × 101 (38%) 9.7 × 101 (26%) 8.2 × 101 (30%) 1.2 × 102 (20%) 6.9 × 101 (35%) 6.2 × 101 (14%) 9.4 × 101 (15%) 7.6 × 101 (2%)
2.9 × 101 (38%) 2.9 × 101 (36%) 4.6 × 101 (33%) 3.3 × 101 (35%) 2.6 × 101 (55%) 2.6 × 101 (59%) 2.8 × 101 (66%) 3.2 × 101 (34%)
5.8 × 102 (20%) 5.8 × 102 (4%) 5.3 × 102 (21%) 5.0 × 102 (28%) 4.6 × 102 (24%) 4.8 × 102 (6%) 5.2 × 102 (12%) 5.0 × 102 (12%)
2.0 × 102 (48%) 4.5 × 102 (10%) 4.2 × 102 (14%) 3.6 × 102 (16%) 1.8 × 102 (10%) 2.5 × 102 (39%) 2.8 × 102 (20%) 2.5 × 102 (14%)
1.1 × 102 (14%) 3.0 × 102 (38%) 2.8 × 102 (24%) 2.9 × 102 (16%) 1.2 × 102 (20%) 1.8 × 102 (14%) 1.8 × 102 (10%) 1.9 × 102 (10%)
6.3 × 102 (6%) 6.4 × 102 (8%) 5.7 × 102 (10%) 5.0 × 102 (4%) 5.8 × 102 (23%) 4.2 × 102 (11%) 4.9 × 102 (10%) 4.7 × 102 (12%)
1.9 × 102 (8%) 2.2 × 102 (8%) 1.9 × 102 (10%) 1.8 × 102 (2%) 1.3 × 102 (26%) 1.5 × 102 (40%) 1.4 × 102 (12%) 1.5 × 102 (2%)
2.2 × 102 (4%) 2.7 × 102 (22%) 1.9 × 102 (18%) 1.9 × 102 (12%) 1.6 × 102 (10%) 1.7 × 102 (6%) 1.6 × 102 (14%) 1.6 × 102 (18%)
a These complexes are not sufficiently stable for accurate measurement of the association constant.
Fig. 6 compares the association constants measured in cyclo-
hexanone with those reported previously in toluene (Fig. 6a) and
in TCE (Fig. 6b).7 The association constants in cyclohexanone
are three to four orders of magnitude lower than in toluene and
one to two orders of magnitude lower than in TCE. In toluene
and TCE, the values of log K span a wide range due variation in
the contributions from intramolecular H-bonding interactions.
The range of values in cyclohexanone is significantly narrower,
because cyclohexanone competes with both the zinc–pyridine
and the H-bond interactions. The most stable complexes in
toluene and TCE have larger contributions due to intramolecular
H-bonds, and so they are more strongly affected by changing the
solvent to cyclohexanone.
In general, there is a reasonable correlation between the
association constants measured in the three solvents, but there
are some outliers. The outliers highlighted in Fig. 6a are the
complexes of L3a with P1a–P4a (yellow) and L6a with P1a–
P4a (red). These complexes are also highlighted in Fig. 6b,
where there are fewer discrepancies. We have previously noted
that the properties of the L3a and L6a complexes are different in
toluene and TCE. The complexes of these ligands with P1b–
P4b, which can not make intramolecular H-bonds, also gave
anomalously low association constants in TCE, and this suggests
that steric effects may be significant for these ligands. Data for
the complexes formed between L3a and P1b–P4b are missing
from Fig. 6, because these complexes were not sufficiently stable
to allow determination of association constants, which suggests
that the behaviour in cyclohexanone is similar to TCE.
Fig. 6 Comparison of the 1 : 1 association constants (log K/M−1) for
porphyrin–ligand complexes in cyclohexanone with the corresponding
values measured in (a) toluene and in (b) TCE. Data for the complexes
of L3a with P1a–P4a (yellow) and complexes of L6a with P1a–P4a
(red) are highlighted. The lines correspond to log K (toluene) = log K
(cyclohexanone) and log K (TCE) = log K (cyclohexanone).
DMC analysis of intramolecular H-bonding
Fig. 7 shows the data in Table 2 with the complexes organised
according to their role in the DMC used to measure intramolecu-
lar phosphonate diester–phenol H-bonds. In general, the com-
plexes that can make phosphonate diester–phenol H-bonds
(complex A, blue data in Fig. 7) are more stable than the other
complexes.
relatively large errors, and the complexes of L3a with P1b–P4b
were not sufficiently stable to determine association constants.
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Fig. 7 Association constants (K/M−1) for formation of 1 : 1 complexes
(phosphonate ligand–hydroxyporphyrin complexes in blue, phosphonate
ligand–methoxyporphyrin complexes in green, control ligand–hydroxy-
porphyrin complexes in yellow, control ligand–methoxyporphyrin com-
plexes in red).
Fig. 9 DMC for evaluating the thermodynamic contribution of phos-
phonate diester–phenol H-bonds to the stability of a porphyrin–ligand
complex.
Table 3 Total free energy contributions due to phosphonate diester–
phenol H-bonding interactions (ΔΔG°/kJ mol−1) determined using the
chemical double mutant cycle in Fig. 9 and data obtained at 298 K in
cyclohexanone. Complexes that do not make detectable H-bonds are
shadeda
a Average error over the data set
1 kJ mol−1 b These values were
.
estimated using ΔGA° − ΔGB° rather than the full DMC.
Fig. 8 DMC for evaluating the thermodynamic contribution of ester–
phenol H-bonds to the stability of a porphyrin–ligand complex.
values for these interactions by using the top arm of the DMC,
i.e. ΔGA° − ΔGB°, and these values are quoted in Table 3.
Only seven of the twenty different supramolecular architec-
tures studied show detectable H-bonding interactions (Table 3).
This result is very different from the results in toluene and TCE,
where H-bonding could be measured in all twenty complexes.
Solvent competition clearly has a dramatic effect on intramolecu-
lar H-bonding in these systems. Comparison of the results for
ligands that have two symmetrical side arms (L3a and L6a) with
the corresponding one-armed ligands (L2a and L5a) reveals
some interesting features in the data in the Table 4. In toluene,
the free energy contributions due to H-bonding for the two-
armed ligands are double those for the one-armed ligands. This
implies that the two-armed ligands make two identical H-bonds.
In cyclohexanone, this is clearly not the case. With the exception
of the L6a·P2a complex, the free energy contributions due to H-
bonding are actually lower for the two-armed ligands compared
with the one-armed ligands. In other words, addition of the
second side arm destabilises the complexes in cyclohexanone.
Similar effects were observed in TCE,7b and as explained above,
it is possible that the discrepancies may be due to adverse steric
interactions in the complexes involving the bulkiest ligands, L3a
and L6a.
Ester–phenol H-bonds. Fig. 8 shows the DMC used to
measure the free energy contributions due to intramolecular
ester–phenol H-bonds. In toluene and TCE, H-bonding to the
ester groups contributes up to 6 kJ mol−1 to the overall stability
of a complex, but in cyclohexanone, the values of ΔΔG° from
the DMC analysis were all 0 1 kJ mol−1. This is consistent
with the data for intermolecular ester–phenol H-bonds in
Table 1, which suggests that the ester is not sufficiently polar to
compete with cyclohexanone for H-bonding interactions.
Phosphonate diester–phenol H-bonds. Fig. 9 shows the DMC
used to measure the free energy contributions due to phospho-
nate diester–phenol H-bonds. Although we were not able to
reliably quantify ester–phenol H-bonding interactions using the
DMC in Fig. 8, the DMC in Fig. 9 factors out any small contri-
butions due to interactions with the ester groups, and this allows
measurement of the phosphonate diester–phenol interactions in
the presence of ester–phenol interactions. The results are sum-
marised in Table 3. Accurate values for ligand L3a are not avail-
able, because the association constants for the interaction of L3a
with P1b–P4b, complex C in the DMC, were too low to be
measured reliably. However, it is possible to obtain approximate
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Table 4 Values of ΔGC° − ΔGD° for the DMC in Fig. 9 (kJ mol−1).
Complexes where there is no detectable difference in free energy are
shadeda
.
a Average error over the data set 1 kJ mol−1 b Association constants for
complex were too low to be measured reliably for L3a in
C
cyclohexanone.
It is possible to obtain an estimate of the magnitude of poten-
tial steric interactions, by comparing complexes C and D in the
DMC in Fig. 9. These complexes can not make intramolecular
H-bonds, so the difference ΔGC° − ΔGD° is dominated by sec-
ondary effects, like changes in solvation and steric interactions.
Table 4 shows the values for the phosphonate diester ligands in
the three different solvents. In most cases, the values are close to
or within the experimental error. However, there are consistent
differences for all of the complexes involving L2a and L3a in
TCE. A positive value of the free energy difference in Table 4
means that addition of the phosphonate diester group destabilises
the complex. L2a and L3a are the ligands that position the phos-
phonate diester groups closest to the central core of the complex,
so they are expected to show the largest steric effects. The
effects do not depend on the structure of the porphyrin but do
depend on the solvent. The values are roughly twice as large for
the two armed ligand, L3a, compared with the one-armed
ligand, L2a, which is consistent with an additive effect associ-
ated with solvation of the phosphonate diester groups in TCE.
Fig. 10 shows a possible explanation. TCE is a better H-bond
donor than the other two solvents (Table 1), and strong solvation
of the phosphonate diester by TCE significantly increases the
effective size of the ligand. Disruption of these solvent inter-
actions may be required for binding to P1b–P4b (complex C in
Fig. 10). When L2a and L3a bind to P1a–P4a, the interactions
with solvent are replaced by H-bonding interactions with the
phenol groups (dark blue sites in complex A in Fig. 10). Com-
parison of complexes A and C in effect measures H-bonding
interactions with a phosphonate diester that is partially desol-
vated. The evaluation of EM below compares the properties of
complexes A, B, C and D in Fig. 10 with the intermolecular H-
bonding interactions given by Kref. Desolvation of the phospho-
nate diester groups in the intermolecular process involves the
same process as in formation of complex A, so these contri-
butions cancel out in the evaluation of EM. However, desolva-
tion of the phosphonate diester groups in complex C does not
Fig. 10 Desolvation of porphyrin–ligand complexes. The complexes
are labelled according to their role in the DMC in Fig. 9. The porphyrin
receptors are grey, the ligands are green and solvent is pale blue. The H-
bonding sites are red on the ligand, dark blue on the porphyrin and the
corresponding non H-bonding mutant sites are shown as green and grey
circles respectively. Binding of L3a to P1b in TCE involves fitting a
sterically demanding ligand into the binding pocket (complex C), and
this leads to partial desolvation of the phosphonate diester groups. In
complex A of the DMC, interactions of the phosphonate diester groups
with TCE in the free state are replaced by H-bonds with the phenol
groups. Complexes B and D involve the smaller control ligand, L3b, so
changes in the solvation shell are less dramatic. The top box shows that
the intermolecular binding interaction used to measure Kref involves the
same desolvation process as formation of complex A, which cancels out
in the calculation of EM. However, desolvation of the phosphonate
diester groups on formation of complex C does not cancel out in this
analysis and leads to an anomalously high value of EM in TCE.
cancel out and makes an additional contribution to the value of
EM. The result is that the values of EM measured for L2a and
L3a in TCE are unusually high, because they contain a contri-
bution from ligand desolvation in complex C. A TCE–phospho-
nate diester CH·O H-bond is worth 18 kJ mol−1 according to the
H-bond parameters in Table 1 (αSβD), so the effects of this
phenomenon are potentially large.
Returning to the data in Table 3, there are two interpretations
of the small values of ΔΔG° observed for the two-armed ligands:
either the two-armed ligand makes one H-bond of a similar
strength to the one-armed ligand, or the two-armed ligand makes
two weaker H-bonds. These possibilities can be distinguished
1
using H NMR spectroscopy. The signals due to the porphyrin
pyrrole protons provide a sensitive probe of the number of intra-
molecular H-bonds formed in a complex.7b For ligands that
make only one H-bond, the pyrrole signals of the complex are
singlets, but if more than one H-bond is made, splitting of the
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Fig. 12 Stepwise equilibria in the formation of a porphyrin–pyridine
complex containing an intramolecular phosphonate diester–phenol H-
bond. K0 is the intermolecular association constant for formation of the
zinc–nitrogen interaction. KrefEM is the equilibrium constant for for-
mation of the intramolecular H-bond. Kref is the equilibrium constant for
formation of the corresponding intermolecular H-bond. EM is the effec-
tive molarity for the intramolecular interaction.
Fig. 11 Pyrrole region of 400 MHz 1H NMR spectra of free P1a
(black), 1 : 1 mixtures with the one-armed ligand, L5a (red), and the
two-armed ligand, L6a (blue), recorded at mM concentrations in d2-
TCE (a) and in d10-cyclohexanone (b).
This expression can be generalised to complexes where mul-
tiple intramolecular H-bonds are possible by summing over all
possible bound states (eqn (4) and (5)).
pyrrole signal is observed due to slow exchange between the six
different types of atropisomer that make different interactions
with the ligand. Fig. 11 compares the H NMR spectra of the
P1a·L5a and P1a·L6a complexes recorded in TCE and in cyclo-
hexanone. In TCE, the P1a·L6a complex makes two H-bonds,
and the pyrrole signal accordingly appears as a multiplet. In
cyclohexanone, no splitting is observed, which implies that the
two-armed ligand, L6a, does not make a second H-bond with
P1a.
Kobs ¼ fK0
ð4Þ
1
where
f ¼ 1 þ
X
σiKiEMi
i
ð5Þ
N
N
X
Y
þ
σijKiEMiKjEMj þ ::: þ σij:::N
KiEMi
i;j
i
and K0 is the intermolecular association constant for formation
of the zinc–nitrogen interaction, Ki is the association constant for
formation of the relevant intermolecular H-bond, EMi is the
effective molarity for formation of the intramolecular interaction,
and σ are statistical factors that describe the degeneracies of the
partially and fully bound states.
Differences in the zinc–nitrogen interaction, K0, from one
complex to another, cancel out in the DMC, so the values of
EMi can be related to the experimentally measured value of ΔΔG°
by eqn (6).
Effective molarities
By comparing the intermolecular association constants measured
for the reference compounds in Table 1 with the free energy con-
tributions due to intramolecular H-bonding in the porphyrin–
ligand complexes in Table 3, it is possible to determine the effec-
tive molarities (EM) for the intramolecular processes.11 Fig. 12
illustrates the relevant equilibrium for a complex that makes one
intramolecular H-bond. The bound state is a population weighted
distribution of the fully bound complex, where the zinc–nitrogen
and phosphonate diester–phenol interactions are both made, and
the partially bound state, where only the coordination bond is
made. The other partially bound state, where the coordination
bond is broken and the H-bond is formed, is not populated to
any significant extent in these systems, because the coordination
bond is so much stronger than the H-bond (see Tables 1 and 2).
Thus the observed association constant for the complex in Fig. 1
is given by eqn (3).
fAfD
o
eꢀðΔΔG =RTÞ
¼
ð6Þ
fBfC
The values of Kref in Table 1 were used as Ki in eqn (5), and
the DMC free energy differences in Table 3 were used to solve
eqn (6) for the values of EMi for the intramolecular H-bond
interactions in all of the complexes (Table 5). The ESI† contains
full details of the analysis of the partially bound states and stat-
istical factors, σ, for each DMC. The value of Kref is 3 M−1 for
the phosphonate diester–phenol H-bond, and EM is less than
1 M for all of the complexes, so there are significant populations
of partially bound states in all of these systems.
Kobs ¼ ð1 þ Kref EMÞK0
ð3Þ
where K0 is the intermolecular association constant for por-
phyrin–ligand coordination, Kref is the association constant for
formation of the corresponding intermolecular H-bond, and EM
is the effective molarity for the intramolecular interaction.
The calculation of EM factors out any contributions from
differences in the properties of the individual H-bonding inter-
actions and should simply reflect the ease with which the system
is able to form intramolecular contacts. In other words, the value
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Table 5 Effective molarities (EM/mM) for intramolecular phosphonate
diester–phenol H-bonds measured at 298
in cyclohexanone.a
K
Complexes that do not make detectable H-bonds are shaded
a Average error over the data set 50%. b These complexes do not make
detectable H-bonds. c These complexes do not make any additional H-
bonds compared with the one-armed ligands L2a and L5a.
Fig. 14 Comparison of free energy contributions due to intramolecular
H-bonds (ΔΔG°) measured experimentally in cyclohexanone and pre-
dicted using the values of EM measured in toluene (a) and in TCE (b).
Data for ester–phenol H-bonds in red and phosphonate diester–phenol
H-bonds in blue. Complexes that are outliers in TCE are highlighted in
dark blue on both graphs. The lines correspond to ΔΔG° (experiment) =
ΔΔG° (predicted).
measured in toluene and cyclohexanone (Fig. 13a). Although
there are only five data points, the trends in the values of EM
measured in cyclohexanone are similar to TCE (Fig. 13b). There
is one outlier in Fig. 13b: the P1a·L2a complex has the highest
EM of all of the complexes in TCE, but the value in cyclohexa-
none is significantly lower. The difference may be due to partial
desolvation of L2a in complex C of the DMC in TCE as illus-
trated in Fig. 10.
The small number of complexes that gave measurable intra-
molecular interactions in cyclohexanone raises question marks
over the validity of the comparisons in Fig. 13. However, it is
possible to compare the experiments in different solvents in a
different way. Values of EM were measured in toluene and in
TCE for all twenty complexes studied here. These values can be
used in conjunction with the values of Kref in Table 1 and eqn
(5) and (6) to predict the values of ΔΔG° that would be expected
in cyclohexanone, if the values of EM were identical to those
found in toluene or in TCE. Fig. 14 shows the results. The ester–
phenol interactions (red points) are all predicted to be small in
agreement with the experimental results in cyclohexanone. The
agreement is less good for the phosphonate diester–phenol
Fig. 13 Comparison of effective molarities (EM) for formation of
intramolecular phosphonate diester–phenol H-bonds in cyclohexanone
with the corresponding values measured in toluene (a) and in TCE (b).
The lines correspond to log EM (cyclohexanone) = log EM (toluene)
and log EM (cyclohexanone) = log EM (TCE).
of EM might be expected to be a function of the supramolecular
architecture and independent of the solvent. This is true for the
ester–phenol interactions measured in toluene and TCE,7b which
are practically identical in the two solvents and show little vari-
ation with supramolecular architecture. However, the values of
EM for the phosphonate diester–phenol H-bonds measured in
TCE span nearly two orders of magnitude and are very different
from those measured in toluene. Fig. 13 compares the values of
EM measured in cyclohexanone with the corresponding values
in toluene and TCE. There is no correlation between the values
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interactions (blue points). The toluene EM values predict rela-
tively small values of ΔΔG° in cyclohexanone (Fig. 14a), and
the agreement with the experimental results is reasonable. The
TCE EM values generally overestimate the values of ΔΔG° in
cyclohexanone, and there are some particularly large discrepan-
cies, P1a·L3a, P1a·L2a and P1a·L6a (dark blue points in
Fig. 14b). These complexes have the highest values of EM
measured in TCE but this is clearly not the case in the cyclohex-
anone. The toluene EM values accurately predict the properties
of these outliers (dark blue points in Fig. 14a). This implies that
the values of EM measured in TCE are anomalous due to partial
desolvation of the bulky ligands in complex C of the DMC as
illustrated in Fig. 10.
These results show that there are specific solvation effects that
contribute as much as 8 kJ mol−1 to differences in the stabilities
of these complexes. These solvent effects are not related to the
properties of the primary functional groups involved in ligand
coordination or H-bonding, since these contributions are factored
out in the determination of EM. Rather the variations are related
to differences in the way in which the complexes as a whole are
solvated.
data, but there are significant discrepancies for TCE. Differences
of up to 8 kJ mol−1 are found between the experimental free
energy contribution due to intramolecular H-bonding in cyclo-
hexanone and the value estimated based on the EM measured in
TCE. The EM values measured in TCE appear to be anoma-
lously high, and this is ascribed high to partial desolvation of the
phosphonate diester groups of sterically crowded ligands in
complex C of the DMC.
These experiments indicate that there are substantial solvent
effects on the value of EM. Although some complexes show
similar behaviour in two of the solvents, there is no consistency
across all of the complexes in all three solvents studied. The
determination of EM factors out solvent effects on H-bond
strength and the zinc porphyrin–pyridine interaction, so these
variations must be due to changes in the stability of the solvation
shell as a whole. These results highlight the complexity of sol-
vation phenomena, and the collection of a large body of exper-
imental data on these relatively simple model systems should
prove useful for the development of reliable simulation tech-
niques for tackling more complex molecular recognition pro-
cesses in solution.
Conclusions
Experimental
We have used chemical double mutant cycles to quantify intra-
molecular H-bonding interactions in cyclohexanone. The results
are compared with previous experiments on the same complexes
in toluene and in TCE. The results show that there are significant
solvent effects in these systems. In both toluene and TCE, all
twenty of the porphyrin–ligand complexes studied here make
intramolecular phosphonate diester–phenol H-bonds, and six of
the complexes also make ester–phenol H-bonds. Cyclohexanone
is a much more polar solvent and competes more strongly for
interactions with the phenol H-bond donors on the porphyrin
receptors. As a result, no ester–phenol interactions could be
detected in cyclohexanone, and only seven of the twenty com-
plexes gave phosphonate diester–phenol H-bonds that were
strong enough to measure. Measurements of intermolecular
phosphonate diester–phenol interactions show that this H-bond
is an order of magnitude less stable in cyclohexanone compared
with TCE and two orders of magnitude less stable compared
with toluene, and this accounts qualitatively for the solvent
effects on complex stability.
NMR titrations
NMR titrations were carried out by preparing a 2 ml sample of
host at known concentration (10–13 mM). Then, 0.6 ml of this
solution was removed, and a 1H NMR spectrum was recorded. A
1 ml solution of guest (3500 mM) was prepared using the host
solution, so that the concentration of host remained constant
throughout the titration. Aliquots of guest solution were added
successively to the NMR tube containing the host, and the NMR
spectrum was recorded after each addition. Changes in chemical
shift were analyzed by fitting to a 1 : 1 binding isotherm in
Microsoft Excel. Each titration was repeated at least three times,
and the experimental error is quoted as twice the standard
deviation.
UV/Vis absorption titrations
A more detailed analysis used DMCs to determine the contri-
butions of intramolecular H-bonds to the overall stabilities of the
porphyrin–ligand complexes. The intermolecular association
constants were used to convert these measurements into effective
molarities (EM) for the intramolecular interactions. The values
of EM measured in cyclohexanone show no correlation with the
values measured in toluene but compare well with the values
measured in TCE. There are only five data points in cyclohexa-
none, but the values of EM measured in toluene and TCE can be
used to calculate expected stabilities of the complexes in cyclo-
hexanone, assuming that EM is an intrinsic property of the
complex and can be transferred between solvents. This allows
comparison of all twenty values of ΔΔG° measured in
cyclohexanone with the results from toluene and TCE. There is
reasonable agreement between the toluene and cyclohexanone
UV/Vis titrations were carried out by preparing a 10 ml sample
of porphyrin at known concentration (4–7 μM) in spectroscopic
grade solvent. A 10 ml solution of ligand (20–350 mM) was pre-
pared using spectroscopic grade solvent. The porphyrin solution
(150 μl) was added to a Hellma quartz 96 well plate, and UV/
Vis spectra were recorded using a BMG FLUOstar Omega plate
reader. Aliquots of ligand solution (3, 6 or 10 μl) were added
successively to the wells containing the porphyrin solutions, and
the UV/Vis spectra were recorded after each addition. Changes
in absorbance were fit to a 1 : 1 binding isotherm in Microsoft
Excel to obtain the association constant. Each titration was
repeated at least three times, and the experimental error is quoted
as twice the standard deviation.
We thank the Royal Society for a Newton International
Fellowship (EC).
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