Stepwise effective molarities in porphyrin oligomer complexes: Preorganization results in exceptionally strong chelate cooperativity

Article abstract of DOI:10.1021/ja209254r

Complexes of zinc porphyrin oligomers with multivalent ligands can be denatured by adding a large excess of a monodentate ligand, such as quinuclidine. We have used denaturation titrations to determine the stabilities of the complexes of a cyclic zinc-porphyrin hexamer with multidentate ligands with two to six pyridyl coordination sites. The corresponding complexes of linear porphyrin oligomers were also investigated. The results reveal that the stepwise effective molarities (EMs) for the third through sixth intramolecular coordination events with the cyclic hexamer are extremely high (EM = 10 ²-10³ M), whereas the values for the linear porphyrin oligomers are modest (EM ? 0.05 M). The speciation profiles for the denaturation reactions demonstrate that intermediate species are not significantly populated and that these equilibria are well described by a highly cooperative two-state model.

Full text of DOI:10.1021/ja209254r

ARTICLE
pubs.acs.org/JACS
Stepwise Effective Molarities in Porphyrin Oligomer Complexes:
Preorganization Results in Exceptionally Strong Chelate Cooperativity
Hannah J. Hogben, Johannes K. Sprafke, Markus Hoffmann, Mizosz Pawlicki, and Harry L. Anderson*
Department of Chemistry, University of Oxford, Chemistry Research Laboratory, Mansfield Road, Oxford OX1 3TA, United Kingdom
S Supporting Information
b
ABSTRACT: Complexes of zinc porphyrin oligomers with
multivalent ligands can be denatured by adding a large excess
of a monodentate ligand, such as quinuclidine. We have used
denaturation titrations to determine the stabilities of the com-
plexes of a cyclic zincꢀporphyrin hexamer with multidentate
ligands with two to six pyridyl coordination sites. The corre-
sponding complexes of linear porphyrin oligomers were also
investigated. The results reveal that the stepwise effective
molarities (EMs) for the third through sixth intramolecular
coordination events with the cyclic hexamer are extremely high (EM = 102ꢀ103 M), whereas the values for the linear porphyrin
oligomers are modest (EM ≈ 0.05 M). The speciation profiles for the denaturation reactions demonstrate that intermediate species
are not significantly populated and that these equilibria are well described by a highly cooperative two-state model.
’ INTRODUCTION
When two molecules bind noncovalently through more than
one point of interaction, the overall thermodynamic stability of
the resulting complex can be substantially greater than would
result from a single-point interaction.1ꢀ3 This principle of multi-
valency underlies all biological molecular recognition and supra-
molecular self-assembly. The synergy between interactions
which causes the increased stability of closed multivalent com-
plexes is called “chelate cooperativity”.2,3a It originates from the
chelate effect, and it can be attributed to the fact that inter-
molecular interactions require an extra loss of translational and
rotational entropy when compared with intramolecular interac-
tions. A key parameter for quantifying the chelate cooperativity
between two interactions is the effective molarity, EM, which is
just the equilibrium constant for forming the chelated complex
(Kchel) divided by the product of the two single-site binding
constants (KAKB), as illustrated in Figure 1 and the following
equation:1,2,4
Figure 1. Formation of a chelated complex between two two-site
species illustrates the definition of effective molarity, EM. This analysis
assumes that the binding sites act independently when they bind
monodentate ligands, i.e., that the system does not exhibit allosteric
cooperativity.4
recently, several authors have questioned whether too much
emphasis is placed on the use of rigid preorganized structures for
molecular recognition. It has been suggested that the effort
required to create a rigid receptor is often not sufficiently re-
warded by high binding constants, that values of EM for
supramolecular systems rarely exceed about 1 M, and that these
modest effective molarities can be achieved using flexible hostꢀ
guest systems, which are easier to synthesize.7,10,13 Here we show
that rigid preorganized host and guest structures can achieve EM
values which greatly exceed those encountered in flexible sys-
tems, even when the binding sites are many atoms apart.
K
chel
EM ¼
ð1Þ
KAKB
In practice, the value of EM is difficult to predict or calculate
(except in the case of cyclization of a completely flexible chain,
when EM µ iꢀ3/2, where i is the number of segments in the
chain).5ꢀ10 This problem is a serious obstacle to predicting the
stability of noncovalent complexes.
The principle of preorganization, pioneered by Cram in the
early 1980s,11 states that EM can be maximized by designing
a receptor with a well-defined shape, so that it is locked in
the correct conformation for binding. This concept has had a
huge influence on the design of synthetic receptors;12 however,
The chelate effect was discovered in the context of the
coordination of diamines, such as 1,2-diaminoethane, to metal
cations. Bidentate ligands typically bind metal ions more strongly
Received: October 1, 2011
Published: November 17, 2011
r
2011 American Chemical Society
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Chart 1. Structures of the Complexes Investigated during This Studya
aSee the stability constants in Table 1. Ar is 3,5-di-tert-butylphenyl in c-P6 and 3,5-bis(octyloxy)phenyl in l-P02, l-P03, l-P04, and l-P06. THS is
Si(C6H13)3.
than the corresponding monodentate ligands by a factor of
EM ≈ 50ꢀ100 M.14 The equilibrium for dehydration of succinic
acid to succinic anhydride is more favorable than the corresponding
process for acetic acid by a factor of EM ≈ 105 M,1 and the
formation of cyclic disulfides exhibits chelate effects of up to
EM ≈ 103 M.15 However, these equilibria involve formation of
covalent five- and six-membered rings. Larger ring sizes are
generally associated with much lower effective molarities, and
most supramolecular multivalent systems display thermody-
namic effective molarities in the range of 0.01ꢀ10 M.3c,6ꢀ10,16ꢀ24
Here we analyze a supramolecular system exhibiting effective
molarities of up to about 103 M. Recently, we reported that
the cyclic zinc porphyrin hexamer c-P6 forms an exceptionally
stable 1:1 complex with the hexapyridyl template T6.25,26 Here we
present a detailed analysis of this binding process. By comparing
the stability constants of the 1:1 complexes of ligands featuring
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Scheme 1. Synthesis of Ligands T2ꢀT5
at 298 K) to displace the multidentate ligands (Figure 4). For
example, in the denaturation of c-P6 TN, Kdn is defined by eq 2,
where [Q] is the concentration of quinuclidine. The correspond-
ing binding isotherm is given by eq 3
3
Figure 2. Stepwise equilibria defining the effective molarities EM2ꢀ
EM6 (a) for formation of c-P6 T6 and (b) for formation of l-P06 T6. K1
3
3
is the microscopic binding constant for coordination of a pyridyl group
to one face of a zinc site. For simplicity, isomers of intermediate
complexes are not shown, but their formation is taken into account by
the statistical factors. (See the Supporting Information for calculation of
the statistical factors.)
½c-P6 Q 6ꢁ½TNꢁ
3
K
¼
ð2Þ
dn
N
½c-P6 TNꢁ½Q ꢁ
3
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N
ꢀK ½Q ꢁ
dn
2N
N
2
two to six binding sites, T2, T3, T4, T5, and T6, with both cyclic
hexamer c-P6 and linear oligomers l-P02, l-P03, l-P04, and l-P06
(Chart 1), we have determined the individual stepwise effective
molarities for coordination of the second, third, fourth, fifth, and
sixth site of the template, EM2ꢀEM6 (Figure 2). The c-P6/T6
system is highly preorganized and has excellent geometrical com-
plementarity,26 resulting in very high EM values and an overall 1:1
association constant of 1036 Mꢀ1, which is beyond the range of those
of previously studied supramolecular systems.27 In contrast, the linear
hexamer l-P06 is less well preorganized for binding these ligands, and
its effective molarities, EM2ꢀEM6, are all around 0.05 M.
þ
K
½Q ꢁ þ 4K ½Q ꢁ ½Pꢁ0
dn dn
A ꢀ A0
¼
Af ꢀ A0
2½Pꢁ0
ð3Þ
where A is the absorption at a given point in the titration, A0 is the
initial absorption at [Q] = 0, Af is the asymptotic final absorption
at [Q] = ∞, and [P]0 is the total concentration of 1:1 porphyrin
oligomer template complex at the start of the titration. Binding
isotherms derived from changes in absorption at selected wave-
lengths were analyzed by simulation with eq 3 to give the smooth
curves plotted in Figure 4, with just three free parameters (A0, Af,
and Kdn).
’ RESULTS
The derivation of eq 3 assumes that the concentration of free
quinuclidine [Q] can be approximated to the total concentration
of quinuclidine, which is valid since [Q] . [P]0 throughout the
fitted regions of the denaturation curves. Our analysis also
assumes that the denaturation processes are essentially all-or-
nothing two-state equilibria (i.e., that intermediate partially
denatured species do not build up to high concentrations). This
assumption is supported by the isosbestic nature of the UV/vis
titrations (Figure 4) and by the good fits of this simple model to
the experimental isotherms. The calculated speciation profiles also
confirm that a two-state model is consistent with the results (see the
Discussion). The resulting values of Kdn are listed in Table 1.
Denaturation constants were used to calculate the formation
constants Kf via the thermodynamic cycle shown in Figure 3
using the following equation:
Synthesis. Ligands T2ꢀT5 were synthesized using the mod-
ular approach outlined in Scheme 1. Aldol condensation of a
benzil derivative (blue) with a ketone (black) gave a tetracyclone
that was converted to the corresponding ligand by DielsꢀAlder
cyclization with a tolan derivative (red) (see the Supporting
Information for experimental details).28 Ligand T6, porphyrin
nanoring c-P6, and the linear porphyrin oligomers l-P0N (N = 1,
2, 3, 4, and 6) were synthesized as reported previously.25,26,29
UV/Vis Titrations. The 1:1 complexes shown in Chart 1 were
generated by titrating solutions of the porphyrin oligomers in
chloroform with the ligands TN. These UV/vis titrations gave
sharp end points (see the Supporting Information), but the
complexes are mostly too stable (Kf > 108 Mꢀ1) for their as-
sociation constants to be determined from their formation curves.
Thus, denaturation was used to determine Kf indirectly via the
denaturation constant Kdn. A large excess of quinuclidine was
titrated into solutions of the 1:1 complex (ca. 10ꢀ6 M in CHCl3
N
KQ
Kf ¼
ð4Þ
K
dn
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Table 1. Equilibrium Constants for the Porphyrin Oligomer Complexes Shown in Chart 1a
N
complex
Kdn
log Kf
Kσ
log Kchem,N
log EMN
log EMN
2
3
4
5
6
2
3
4
5
6
l-P02 T2
(4.4 ( 1.3) ꢂ 104 Mꢀ1
(6.3 ( 1.9) ꢂ 107 Mꢀ2
(6.0 ( 1.8) ꢂ 1010 Mꢀ3
(3.1 ( 0.9) ꢂ 1013 Mꢀ4
(2.5 ( 0.8) ꢂ 1016 Mꢀ5
(570 ( 170) Mꢀ1
7.5 ( 0.2
10.4 ( 0.3
13.5 ( 0.4
16.9 ( 0.5
20.1 ( 0.5
8.4 ( 0.2
8
6.6 ( 0.2
9.2 ( 0.3
ꢀ1.3 ( 0.3
ꢀ1.3 ( 0.2
ꢀ1.3 ( 0.2
ꢀ1.3 ( 0.2
ꢀ1.3 ( 0.2
ꢀ0.81 ( 0.3
1.2 ( 0.2
ꢀ1.3 ( 0.3
ꢀ1.4 ( 0.2
ꢀ1.2 ( 0.2
ꢀ1.2 ( 0.2
ꢀ1.6 ( 0.2
ꢀ0.81 ( 0.3
3.1 ( 0.2
3
l-P03 T3
16
32
3
l-P04 T4
12.0 ( 0.4
14.8 ( 0.5
17.2 ( 0.5
6.8 ( 0.2
3
l-P06 T5
128
768
48
3
l-P06 T6
3
c-P6 T2
3
c-P6 T3
(14 ( 4) Mꢀ2
15.6 ( 0.3
22.3 ( 0.4
29.6 ( 0.5
36.1 ( 0.5
96
13.6 ( 0.3
20.0 ( 0.4
27.0 ( 0.5
33.2 ( 0.5
3
c-P6 T4
(1.2 ( 0.4) Mꢀ3
192
384
768
1.6 ( 0.2
2.6 ( 0.2
3
c-P6 T5
(2.3 ( 0.7) ꢂ 10ꢀ2 Mꢀ4
2.0 ( 0.2
3.2 ( 0.2
3
c-P6 T6
(2.7 ( 0.8) ꢂ 10ꢀ3 Mꢀ5
2.1 ( 0.2
2.4 ( 0.2
3
a Errors estimated from at least two replicates. See the Supporting Information for calculation of Kσ. Logarithms are decadic.
Effective Molarities. Consideration of the thermodynamic
cycles in Figure 2 shows that Kchem,N for a system with N inter-
actions is the product of N ꢀ 1 effective molarities, as expressed
by the following equation:35
m¼N
Y
N
K
¼ K1
EMm
ð6Þ
chem, N
m¼2
The stepwise effective molarities for the Nth interaction EMN
can thus be calculated using the following equation:
Figure 3. Thermodynamic cycle relating the formation constant of the
template complex (Kf) to the denaturation constant (Kdn) and binding
constant of each porphyrin unit for quinuclidine (KQ).
K
chem, N
EMN
¼
ð7Þ
K
chem,Nꢀ1K1
The reference constant KQ was approximated to the binding
constant for coordination of quinuclidine to porphyrin monomer
l-P01 (KQ = 1.2 ꢂ 106 Mꢀ1) for the linear oligomer complexes and
coordination of quinuclidine to cyclic hexamer c-P6 (KQ =3.6 ꢂ 105
Mꢀ1) for the cyclic complexes.30 Figure 4 shows that the absorption
spectra of the complexes with multidentate ligands are generally
red-shifted and more structured compared to the quinuclidine-
bound oligomers at the end of the titration due to the more
rigid structures and reduced porphyrinꢀporphyrin dihedral angles
in the template complexes.31,32 The denaturation curves become
increasingly sigmoidal and cooperative as the number of coordina-
tion sites increases for both linear and cyclic complexes. The change
in the shape of the UV/vis spectra during denaturation is most
dramatic with the linear porphyrin oligomers (Figure 4aꢀe) due to
the greater change in conformation compared with that of the
preorganized cyclic hexamer (Figure 4fꢀj).
The geometric average of all the effective molarities contributing
to the stability constant of a complex with N interactions is
defined by eq 8 and calculated by eq 9.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m¼N
Y
N
ꢀ 1
EMN
¼
EMm
ð8Þ
m¼2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K
N
ꢀ 1
chem, N
K1
EMN
¼
ð9Þ
N
The K1 in eqs 6ꢀ9 and Figure 2 is a reference single-site
microscopic binding constant (statistically corrected for binding
to one face of a porphyrin monomer). We estimated K1 using the
binding of 4-phenylpyridine to the porphyrin monomer l-P01
(K1 = 1.0 ꢂ 104 Mꢀ1) for the linear oligomers and to cyclic
hexamer c-P6 (K1 = 6.0 ꢂ 103 Mꢀ1) for the cyclic complexes.
Values of Kf, Kchem, EMN, and EMN are listed in Table 1 as
decadic logarithms. The effective molarities have significant
uncertainties because each value of EM is calculated from four
Statistical Factors. To understand the stability constants of
different complexes, it is useful to factor out statistical contri-
butions.33 Thus, a measured equilibrium constant Keq can be
factorized into its statistical component Kσ and its statistically
corrected value Kchem according to eq 5,34 where for each species
i, Qi is the partition coefficient, Q0i is the statistically corrected
partition coefficient, and σi is the symmetry number. In Table 1, Kf is
the measured formation constant from eq 4, Kσ is the corresponding
statistical factor from eq 5 (see the Supporting Information for
details), and Kchem,N is the statistically corrected value of Kf.
experimentally determined binding constants (Kdn,N, Kdn,Nꢀ1
K1, and KQ).
,
’ DISCUSSION
The stepwise effective molarities EMN for binding the linear
oligomers l-P0N are small and show little variation from EM2 to
EM6 (range 0.03ꢀ0.07 M; Figure 5a, green curve); thus, the
average effective molarities EMN for these linear systems are
essentially independent of N (range 0.04ꢀ0.05 M; Figure 5b).
The first effective molarity for c-P6 is also low (EM2 = 0.15 M),
K
s
eq
wA þ xB
yC þ zD
F
R
s
y
z
x
QC QD
QAwQB
QAwQB Q0C Q0D
y
z
x
K
¼
¼
¼ K K
ð5Þ
eq
σ
chem
w
x
y
z
QC QD Q0A Q0B
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Figure 4. UV/vis denaturation titrations of linear (aꢀe, green) and cyclic (fꢀj, red) complexes (all in CHCl3 at 298 K). The spectra are shown on the
left with the spectra of the complexes in thick black lines and the end spectra (of the quinuclidine-saturated oligomers) in green (linear) and red (cyclic)
lines. On the right are shown the experimental (black circles) and calculated (colored lines) binding isotherms, fitted to eq 3.
but the following effective molarities EM3ꢀEM6 are several
orders of magnitude larger (range 280ꢀ1700 M; Figure 5a, red
curve). The variation in the values of EM3ꢀEM6 is comparable
with the experimental error, while the average effective molarities
EMN increase from EM3 to EM6 due the decreasing contribution
from EM2.
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Figure 6. Gibbs free energies of complex formation of linear (black
circles) and cyclic (black squares) complexes as a function of the number
of interactions N. The error bars are smaller than the data points and
thus are not shown. Linear fits to the data are shown as a green and a red
line for linear and cyclic complexes, respectively.
rotation of the porphyrins about the acetylene links, by prevent-
ing rotation of the bound guest, and by preventing low-frequency
vibrations; changes in solvation may also make an important
contribution.
The statistically corrected Gibbs free energy of complex
formation ΔGf increases linearly with the number of interactions
N for the linear oligomers (Figure 6). For the cyclic hexamer
complexes, ΔGf increases more steeply after a discontinuity at
N = 2. This discontinuity reflects the dramatic increase in EM in
c-P6 when N > 2. These plots of ΔGf against N provide an
alternative approach to estimating the geometrical average
effective molarities by the following equation:
Figure 5. Stepwise (a) and geometric average (b) effective molarities
for formation of linear (black circles, green lines) and cyclic (black
squares, red lines) complexes as a function of N. Red and green lines are
guides to the eye.
ΔGf ¼ ꢀ RT ln K
chem, N
¼ ꢀ RT lnðEMN ꢀ 1K1NÞ
The high effective molarities exhibited by the cyclic hexamer,
compared to the linear oligomers, reflect enthalpic and entropic
preoganization. Butadiyne-linked porphyrin oligomers l-P0N are
shape-persistent rods, and the length of linear hexamer l-P06
(ca. 7 nm) is well below the persistence length (ca. 19 nm),36,37
so there must be a significant enthalpy cost associated with
bending this molecule into a cyclic conformation, whereas the
geometry of c-P6 is almost ideal for binding T6.26 According to
¼ RT ln EM ꢀ N RTðln EM þ ln K1Þ
ð10Þ
The gradient of the line for the linear oligomers gives EM = 0.034 M,
which is in excellent agreement with the average effective
molarity of l-P06 T6 determined using eq 9 (EM6 = 0.032 M).
3
For the cyclic oligomers, the linear region of the plot, for
N = 2ꢀ6, gives EM = 730 M, which is close to the geometric
average of EM3ꢀEM6 (700 M), confirming the high effective
molarities for N = 3ꢀ6.
Ercolani’s terminology, formation of the complexes c-P6 TN, in
3
contrast to formation of the complexes of the linear oligomers,
displays interannular cooperativity.3a
A key assumption underlying the analysis presented here is
that the denaturation titrations (Figure 4) can be analyzed as all-
or-nothing two-state equilibria, so that each denaturation curve can
be fitted by eq 3 using just three free parameters (A0, Af, and Kdn).
It would be impossible to analyze these titrations without making
this assumption because a full set of partially bound species
would lead to too many free variables. This assumption is sup-
ported by the isosbestic nature of the UV/vis titrations (Figure 4)
and by the good fits to the calculated binding curves. Knowledge
of the effective molarities (Table 1) allows us to check whether
this two-state assumption is consistent with the results by
calculating speciation curves for the denaturation reactions
(see the Supporting Information for details). These calculations
confirm that denaturation is essentially a two-state process for
both linear and cyclic oligomer complexes; for example, the
It is surprising that EM2 for c-P6 is only about 3 times larger
than EM2 for l-P02. This probably reflects the significant loss of
entropy on formation of the second bond in the cyclic complex;
while formation of the first bond could occur inside or outside
the nanoring, the second binding event can only occur inside the
cavity. For subsequent coordination events, the ligand is fixed in
place and the advantage of preorganization is maximized.
For the cyclic hexamer c-P6, the ratio EM3/EM2 is 8800. This
corresponds to a huge increase in ligand affinity after the second
zincꢀpyridyl bond has been formed. The intermediate with two
zincꢀpyridyl interactions must be particularly rigid, so that little
entropy is lost on formation of a third zincꢀligand bond, and this
factor of about 104 is too large to arise from restricted rotation
about a single bond.10,38 The formation of two zincꢀnitrogen
interactions probably increases the rigidity of the host by preventing
speciation curves for denaturation of c-P6 T6 are plotted in
3
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Journal of the American Chemical Society
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factor of the cyclization process;3a if we used this definition, our
values of EM would be larger by about a factor of 3.
The highly cooperative nature of the binding of cyclic
porphyrin hexamer c-P6 with hexadentate ligand T6 is evident
from the denaturation of this complex with quinuclidine, both
from the sigmoidal shape of the denaturation curve (Figure 7a)
and from the low concentrations of partially bound intermediate
complexes seen in the speciation profiles (Figure 7b). The strong
chelate cooperativity is caused both by the high effective molarity
and by the high single-site binding constant (K1).2,3a For
c-P6 T6, K1(EM) = 7.8 ꢂ 105, which means that all the intramolec-
3
ular coordination steps in Figure 2a are extremely favorable.
All the effective molarities reported here are thermodynamic
values for equilibrium processes. Ligand T6 is also a very effective
template for directing the synthesis of c-P6, which implies that it
will be interesting to compare stepwise kinetic and thermody-
namic effective molarities in this system.
’ ASSOCIATED CONTENT
S
Supporting Information. Synthesis and characterization
b
of new compounds, UV/vis titrations and binding data for
reference compounds and for the formation of linear oligomer
complexes, derivation of binding equations, error analysis and
calculation of statistical factors, calculation of speciation profiles,
and complete ref 26. This material is available free of charge via
the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
harry.anderson@chem.ox.ac.uk
Figure 7. Speciation profiles for denaturation of c-P6 T6 (2 μM) with
3
quinuclidine: (a) molar fraction of species in the course of the titration
(N is the number of template-bound binding sites of the nanoring) and
measured difference in absorption (791ꢀ850 nm) in the course of the
titration; (b) same speciation profile on a logarithmic scale. The
concentrations of the species with N = 1ꢀ4 are too low to be visible
on the linear scale of plot a.
’ ACKNOWLEDGMENT
We thank the European Commission for support (through
THREADMILL, Grant MRTN-CT-2006-036040, studentship
to J.K.S., and Grant MEIF-CT-2006-041629, fellowship to M.P.)
and the EPSRC Mass Spectrometry Service (Swansea) for the
mass spectra. We are grateful to Melanie C. O’Sullivan for
valuable discussion.
Figure 7. The two most abundant species in the course of the
titration are the fully template-bound nanoring complex (N = 6)
and the quinuclidine-saturated nanoring (N = 0). The only other
species that reaches noticeable concentrations is the five-pyridyl-
bound complex (N = 5; peak mole fraction 0.04). Figure 7b
shows that other partially denatured species with one to four
coordinated pyridines (N = 1ꢀ4) are formed in very low con-
centrations. The presence of two dominant species in this equi-
librium, accounting for 96% of the material, justifies the use of an
all-or-nothing binding model and illustrates the high coopera-
tivity of the binding process.
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Whitesides, G. M. J. Am. Chem. Soc. 2007, 129, 1312–1320.
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’ CONCLUSIONS
This work demonstrates that rigid preorganized shape-
complementary multivalent hostꢀguest systems can exhibit high
effective molarities (up to 103 M) and very high association
constants (up to 1036
M
ꢀ1). An effective molarity of 103 M
matches the upper limit to EM estimated from the entropy of the
zincꢀporphyrin pyridine interaction,3c,17 but systems exhibiting
such high effective molarities have not been previously reported.
The effective molarities reported here are statistically corrected.
Other authors often use the symbol EM to indicate the product
of the microscopic effective molarity multiplied by the statistical
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Journal of the American Chemical Society
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(26) The crystal structure of c-P6 T6 shows that the c-P6 nanoring
3
is too large for a perfect fit to the T6 ligand by a factor of 2.5%. This
crystal structure also shows that the geometry of the Znꢀpyridine
coordination sphere in c-P6 T6 is normal, with no signs of strain-
3
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(27) In a preliminary study25 we determined the stability of the
complex c-P06 T6 with octyloxy side chains and reported Kf = 6.6 ꢂ
3
1038 M, whereas here we report Kf = 1.2 ꢂ 1036 M for c-P6 T6 with tert-
3
butyl side chains. The difference between these values originates largely
from the difference in side chains. The statistically corrected geome-
trically averaged effective molarity determined for c-P06 T6 was log EM6 =
3
2.0, which is similar to the value of log EM6 = 2.1 reported here for
c-P6 T6.
3
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