Physical basis of self-assembly. Part 2. A theoretical and experimental study of the self-assembly of a zinc meso-pyridyl porphyrin

Article abstract of DOI:10.1039/b101033f

A previously reported theoretical treatment for self-assembly macrocyclisations occurring under thermodynamic control has been tested experimentally. The fundamental quantities on which the treatment is based are the effective molarity (EM) of the self-assembling cyclic n-mer and the equilibrium constant for the intermolecular model reaction between monofunctional reactants (K_inter). Provided that estimates of EM and K_inter are available, this treatment can be used to predict not only whether the self-assembly process is more or less favoured, but also the distribution of all the species present in solution. Since K_inter values are approximately known from the literature, we have proposed a method, based on molecular modelling techniques, to estimate the EM. The method has been applied to the self-assembly of Zn(PyP₃P), where PyP₃P is 5-(4-pyridyl)-10,15,20-triphenylporphyrinato dianion. An EM greater than 0.1 mol L^-1 has been estimated for its cyclotetramerisation by PM3 calculations, suggesting that self-assembly should be favoured in solvents like toluene and chloroform. Self-assembly of Zn(PyP₃P) has been studied in these solvents by UV/visible spectroscopy. The data are consistent with the formation of the cyclotetramer, and at variance with the model of linear polymerisation. The experimental values of the EM were little affected by the nature of the solvent (EM values were 20 mol L^-1 in toluene and 15 mol L^-1 in chloroform), indicating that the solvent affects the process of self-assembly mainly through the value of K_inter.

Full text of DOI:10.1039/b101033f

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Physical basis of self-assembly. Part 2.¤ A theoretical and
experimental study of the self-assembly of a zinc meso-pyridyl
porphyrin
Gianfranco Ercolani,* Marcella Ioele and Donato Monti
Dipartimento di Scienze e T ecnologie Chimiche, Universita di Roma T or V ergata, V ia della
Ricerca ScientiÐca, 00133 Roma, Italy. E-mail: ercolani=uniroma2.it; Fax: ]3906 72594328
Received (in London, UK) 29th January 2001, Accepted 29th March 2001
First published as an Advance Article on the web 16th May 2001
A previously reported theoretical treatment for self-assembly macrocyclisations occurring under thermodynamic
control has been tested experimentally. The fundamental quantities on which the treatment is based are the e†ective
molarity (EM) of the self-assembling cyclic n-mer and the equilibrium constant for the intermolecular model
reaction between monofunctional reactants (K ). Provided that estimates of EM and K
treatment can be used to predict not only whether the self-assembly process is more or less favoured, but also the
are available, this
inter
inter
distribution of all the species present in solution. Since K
values are approximately known from the literature,
inter
we have proposed a method, based on molecular modelling techniques, to estimate the EM. The method has been
applied to the self-assembly of Zn(PyP P), where PyP P is 5-(4-pyridyl)-10,15,20-triphenylporphyrinato dianion.
3
3
An EM greater than 0.1 mol L~1 has been estimated for its cyclotetramerisation by PM3 calculations, suggesting
that self-assembly should be favoured in solvents like toluene and chloroform. Self-assembly of Zn(PyP P) has been
3
studied in these solvents by UV/visible spectroscopy. The data are consistent with the formation of the
cyclotetramer, and at variance with the model of linear polymerisation. The experimental values of the EM were
little a†ected by the nature of the solvent (EM values were 20 mol L~1 in toluene and 15 mol L~1 in chloroform),
indicating that the solvent a†ects the process of self-assembly mainly through the value of K
.
inter
Zn(PyP P) [PyP P \ 5-(4-pyridyl)-10,15,20-triphenylporphy-
Introduction
3
3
rinato dianion] as a building block because its structure is
relatively simple and, most stimulating for us, its self-assembly
behaviour has given rise to some controversy which requires
further investigation. In fact, Fleischer and Shachter reported
Self-assembly consists of the spontaneous generation of a well-
deÐned, discrete supramolecular architecture from a given set
of components under thermodynamic equilibration.1 Applica-
tion of this phenomenon to macrocyclisation is attractive,
since cyclisation of a large molecule by the usual synthetic
methods, employing kinetically controlled reactions, is fre-
quently a tedious and low-yield process. Numerous examples
of self-assembling systems can be found in the literature,
however the physicochemical basis of self-assembly has not,
with some exceptions,2h5 received adequate attention.
We have recently reported a theoretical treatment for self-
assembly macrocyclisations occurring under thermodynamic
control.5 The fundamental quantities on which the treatment
is based are the e†ective molarity6h8 (EM) of the self-
assembling cyclic n-mer and the equilibrium constant for the
intermolecular model reaction between monofunctional reac-
a study on the aggregation of Zn(PyP P) both in solution and
3
in the solid state:9 X-ray crystallography of Zn(PyP P)
3
showed that the pyridyl nitrogen is bound to the metal centre
of an adjacent porphyrin to form a linear polymeric aggregate.
Since a spectrophotometric study of Zn(PyP P) in CHCl
3
3
solution showed a good Ðt to a model involving reversible
linear polymerisation, it was concluded that the linear poly-
meric structure is present not only in the solid state, but also
in solution. However, Hunter et al. pointed out that the stabil-
ity constant for the formation of the polymeric assembly in
solution obtained by Fleischer and Shachter is unusually large
for pyridine coordination of a zinc porphyrin and suggested,
by analogy with the behaviour of their macrocyclic porphyrin
tants (K ). Knowledge of these quantities would not only
inter
allow prediction of whether the self-assembly process is more
or less favoured, but also the distribution of all the species
present in solution. It appears, therefore, that it is crucial to
have methods that allow an estimate of both K
inter
can generally be made on the
and EM.
In fact, an estimate of K
inter
basis of literature data, whereas an estimate of the EM is more
difficult. The present paper has the twofold aim of both
proposing a method, based on molecular modelling tech-
niques, to obtain a rough estimate of the EM and testing our
previously reported treatment experimentally. In search of a
suitable system for such an investigation, we were attracted by
¤ For part 1, see: ref. 5.
DOI: 10.1039/b101033f
New J. Chem., 2001, 25, 783È789
783
This journal is ( The Royal Society of Chemistry and the Centre National de la Recherche ScientiÐque 2001

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oligomers, that Zn(PyP P) probably forms a cyclic tetrameric
[C ] \ EMxn
(4)
3
n
structure in solution, c-[Zn(PyP P)] .10 Imamura et al.
3
4
One of the principal results of our treatment is that in order
reported a variable temperature 1H NMR study of Zn(PyP P)
3
in CDCl and found that at [40 ¡C the spectrum is the same
3
for self-assembly to be virtually complete [C (%) [ 99%]
in a certain range of initial monomer concentration the fol-
lowing condition must be veriÐed.
n
max
as that of c-[Ru(PyP P)(CO)] , with sharp pyridyl and b-
3
4
pyrrole signals that broaden at 25 ¡C.11 They concluded that
at low temperature the cyclic tetramer is the major com-
ponent and that a fast exchange, relative to the NMR time
scale, occurs at 25 ¡C between cyclic and linear structures.
However, it is still not clear whether the cyclic tetramer is the
prevalent species at room temperature.
EMK
inter
P 185n
(5)
If, in addition, n O 4, the acyclic fraction is essentially com-
posed of the monomer only; in this case, Scheme 1 reduces to
eqn. (6), and eqn. (1) to eqn. (7)
EMKn
inter
Results and discussion
Theoretical considerations
nM A88B C
(6)
1
n
x
Before illustrating our results, it is useful to brieÑy recall the
principal features of the previously reported theoretical treat-
ment for self-assembly macrocyclisations.5 Consider a bifunc-
[M ] \ nEMxn ]
(7)
1 0
K
inter
would allow a prediction
An estimate of both EM and K
inter
tional monomer AÈB (M ) bearing two di†erent functional
using eqn. (5) of whether the process of self-assembly is more
or less favoured. In fact, K can generally be estimated from
1
groups, each capable of reacting with the other only in a
reversible addition reaction. After equilibration, a system ini-
tially composed of monomer units M contains, in principle,
inter
literature data. For example, the interaction between zinc
tetraphenylporphyrin (ZnTPP) and pyridine has been studied
by various authors in several solvents. A list of the available
association constants is reported in Table 1. These values,
which appear to be signiÐcantly a†ected by the nature of
1
an inÐnite number of cyclic oligomers C as well as an inÐnite
i
number of linear oligomers M , i being the degree of polym-
i
erisation. If the monomer, however, has a rigid structure
predisposed12 in such a way that formation of all the cyclic
oligomers except one (the cyclic n-mer) is prevented by strain,
the equilibration scheme can be simpliÐed as shown in
Scheme 1.
solvent, provide an estimate of the equilibrium constant K
for the process under consideration. An estimate of the EM is
inter
more difficult, depending on the structural features of both M
n
and C . However, as a rule of thumb, a relatively high EM,
n
say [0.1 mol L~1, is a result of the absence of signiÐcant
strain in the cyclic oligomer C (the main factor a†ecting the
n
enthalpic component of the EM) and of a small number of
rotatable bonds in the linear oligomer M (the main factor
n
a†ecting the entropic component of the EM).7 To ascertain
whether signiÐcant strain energy is present in the self-
Scheme 1 Equilibria for the self-assembly of the cyclic oligomer C
assembled cyclic oligomer C , the enthalpy change (* H) for
n
accompanied by linear polymerisation.
n
r
the isodesmic equilibrium23 reported in eqn. (8) has to be
The mass balance equation relative to Scheme
1
is
evaluated. The presence of strain would be signalled by a sig-
expressed by eqn. (1).5
niÐcantly positive * H value.
r
x
EM
[M ] \ nEMxn ]
(1)
is
M ] M A8B C ] 2M
(8)
1 0
K
(1 [ x)2
n
2
n
1
inter
where [M ] is the initial monomer concentration, K
1 0
inter
In the case under consideration, eqn. (8) becomes:
the equilibrium constant for the intermolecular model reac-
tion between the functional groups A and B, assumed to be
identical for all the associations between the linear oligomers,
EM is the equilibrium e†ective molarity (deÐned as
[Zn(PyP P)] ] [Zn(PyP P)] H
3
4
3
2
c-[Zn(PyP P)] ] 2Zn(PyP P) (9)
3
4
3
K
/K
, where K
refers to the equilibrium of cyclisa-
intra inter
intra
tion of the acyclic n-mer M to yield the cyclic n-mer C ) and
n
n
x, conÐned to the range 0 O x \ 1, is the fraction of reacted
end groups in the acyclic part of the polymer. The Ðrst term in
the right-hand side of eqn. (1) is the weighted concentration of
C , whereas the second term is the weighted concentration of
n
the acyclic fraction. Of course, in the absence of cyclic oligo-
mers eqn. (1) reduces to eqn. (2).
x
[M ] \
(2)
1 0
K
(1 [ x)2
inter
Note that since x \ K [M ], eqn. (2) is equivalent to the
inter
1
mass balance equation reported by Fleischer and Shachter
[eqn. (10) of their paper].9,13
Although eqn. (1) cannot be solved analytically, knowing
[M ] , K
and EM, it is possible to obtain a numerical
1 0
inter
solution for x by the NewtonÈRaphson method.14 In turn,
knowledge of x allows the concentrations of all the species
present in solution to be found, since eqn. (3) and eqn. (4)
hold.
xi
A way of estimating the reaction enthalpy is by using
quantum mechanical calculations. To this end, we have
[M ] \
(3)
i
K
inter
784
New J. Chem., 2001, 25, 783È789

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resorted to semi-empirical methods, since the structural com-
plexity of the species involved prohibits the use of accurate ab
initio calculations. The PM3 semi-empirical molecular orbital
method24 has been used to calculate the geometry and heat of
formation of all the species involved in eqn. (9) (see Experi-
mental for details). There is evidence in the literature25 that
both PM3 and AM1 semi-empirical methods predict geo-
metrical parameters for zinc porphyrins which are close to
those observed in X-ray studies, however, since PM3 per-
formed better than AM1 as far as heats of formation are con-
cerned, it was the method of choice. Earlier, Stewart reported
a root mean square error of 7.9 kcal mol~1 for absolute values
of heats of formation obtained by PM3 employing 276 com-
pounds containing H, N, O and C.24 Although there are indi-
cations that in the case of zinc porphyrins the error could be
even larger (ca. 25 kcal mol~1),25 owing to the isodesmic
nature of the equilibrium in eqn. (9), most of systematic errors
should cancel out. The calculated reaction enthalpy turned
out to be * H \ [2.2 kcal mol~1. A negative * H value
containing the twisting bond as in the case of symmetric tops,
but about the axis parallel to the bond and passing through
the centre of mass of the top. A computer program has been
written that calculates I for each rotor from the atomic coor-
r
dinates of the PM3 optimised structure of the linear tetramer.
The following
I
values (in amu AŽ 2) were obtained:
r
1.39 ] 104; 2.39 ] 104; 7.92 ] 103. The geometrical mean of
these values gives an average I value per rotor of 1.38 ] 104
r
amu A
Ž
2. The entropy of an internal rotation depends not only
on the reduced moment of inertia of the rotating groups but
also on the potential energy barrier to rotation (the entropy
decreases on increasing the barrier).29 Taking the dimer
[Zn(PyP P)] as a model compound, we have evaluated the
adiabatic potential energy curve relative to the internal rota-
tion about the N(pyridyl)ÈZn bond by PM3 calculations (see
Experimental for further details). The energy barrier turned
out to be very low (0.59 kcal mol~1), thus the internal rotation
about N(pyridyl)ÈZn can be considered virtually free at room
temperature. According to statistical thermodynamics, the
entropic contribution of a free internal rotation is given by
eqn (11).29
3
2
r
r
should be interpreted as due either to a self-template e†ect
stabilising the cyclic tetramer or to a strain factor present in
the linear tetramer that is released upon ring closure.
A
8p3I kT
B
However, since the * H value is rather small, and since there
r
S \ R 0.5 ln
[ ln p ] 0.5
(11)
r
int
h2
are no evident structural features that suggest either of the
two possible e†ects, we are more inclined to believe that the
where T is the absolute temperature, p is the symmetry
number for internal rotation, and R, k and h are the usual
int
negative * H value is trivially due to the approximate nature
r
of the PM3 method. We assume therefore, as is more likely,
fundamental constants. Considering that for the three rotors
that the reaction in eqn. (9) occurs without any appreciable
real enthalpy change and, therefore, the EM should be domi-
nated by entropy only.
under examination p \ 1, the average entropy per rotor at
int
25 ¡C turns out to be 14 cal mol~1 K~1. If one assumes that
upon ring closure internal rotations are frozen and this
entropy is completely lost,29 the EM will decrease by a factor
exp(S/R), i.e. by a factor of about 103 per rotor. The resulting
EM (B0.1 mol L~1), however, should be considered as a
lower limit because complete, or almost complete, freezing of
torsional motion, although usual in small ring compounds, is
unlikely in a macrocyclic structure such as c-[Zn(PyP P)]
The entropic component of the EM is more difficult to
evaluate. Page and Jencks were the Ðrst to recognise that the
entropic advantage of an intramolecular reaction with respect
to the corresponding intermolecular one is due to the signiÐ-
cant losses of translational plus rotational entropy that occur
in the latter.26 They estimated that such an advantage can be
translated into a maximum EM value of about 108 mol L~1.
The presence of rotatable bonds in the chain undergoing ring
closure involves a decrease in the EM because of restriction of
torsional motion in the cyclic structure. In the case of short
alkane chains, this decrease has been estimated to be about a
factor of 10 per rotor.7,8,26,27 The linear oligomer
[Zn(PyP P)] is characterised by the presence of three rotors,
3
4
because of new low frequency vibrations.29,30 In spite of this
uncertainty, from the estimated values of K and EM, it can
be concluded from eqn. (5) that in a solvent like toluene a
inter
large fraction of Zn(PyP P) should be present in the cyclic
3
tetrameric form. As a result, we initially chose this solvent to
carry out the experimental study of self-assembly. We then
extended the study to chloroform to gain information about
possible solvent e†ects.
3
4
namely the three N(pyridyl)ÈZn bonds, however the decrease
of the EM per rotor is expected to be much greater than a
factor of 10 because of the larger moments of inertia of the
rotating groups with respect to the simple aliphatic chain. To
Self-assembly in toluene
estimate the reduced moment of inertia of each rotor (I ) an
approximate method, recommended for asymmetric top rota-
Binding studies were carried out at 25.0 ¡C using UV/visible
spectroscopy. Our Ðrst goal was the evaluation of the equi-
r
tions, has been used.28 The method is based on eqn. (10)
librium constant K
, and the very intense absorptions of
inter
Zn(PyP P) in the 410È440 nm region (Soret band) were used
3
I I
to this end. We recorded the spectra of Zn(PyP P) at a con-
1 2
I \
(10)
3
r
I ] I
centration of about 2 lM upon addition of increasing
1
2
amounts of pyridine up to [Py] B 10 mM. Analysis of the
absorbance data at j 422 and 430 nm vs. pyridine concentra-
tion led to well-behaved 1 : 1 complexation curves which gave
a binding constant of the expected order of magnitude
where I and I are the moments of inertia of the two rotating
1
2
groups about the axis of internal rotation. The moment of
inertia of each top is computed, however, not about the axis
(K
\ 4.1 ^ 0.2 ] 103 L mol~1).
Table 1 Equilibrium constants for the addition of pyridine to
ZnTPP at 298 K
inter
Dilution studies were carried out in the concentration range
[Zn(PyP P)] B 0.04È7 lM. Plots of the apparent molar
3
Solvent
K/mol L~1
Ref.
absorptivity in the 405È445 nm region, reported in Fig. 1,
show a well-deÐned isosbestic point. There is evidence in the
literature that cyclotetrameric complexes, such as c-[Ru
(PyP P)(CO)] , show broadening of the Soret bands because
of the excitonic interactions between the porphyrin subunits
which are aligned parallel.11 This implies that the molar
absorptivity of a coordinated metalloporphyrin subunit in an
ordered cyclic tetrameric structure is di†erent from that in a
random linear polymer. The isosbestic point in Fig. 1, is there-
fore not compatible with a model involving the simultaneous
benzene
benzene
benzene
benzene
benzene
toluene
chloroform
cyclohexane
methylene chloride
4800
6030
3900
6460
5300
6030
610
15
16
17
18
19
20
18
21
22
3
4
25100
6900
New J. Chem., 2001, 25, 783È789
785

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Fig. 1 Plots of the apparent molar absorptivity (e) of Zn(PyP P) B
3
0.04È7 lM in toluene. The arrows indicate how e changes with
Fig. 2 Plot of the apparent molar absorptivity (e) at j 422 nm as a
increasing Zn(PyP P) concentration.
function of Zn(PyP P) concentration in toluene. The points are
3
3
experimental and the curve is calculated (see text).
presence of signiÐcant amounts of the monomer, the cyclic
tetramer and the linear polymer, whereas it would be compat-
ible either with a model involving an equilibrium between the
monomer and the cyclic tetramer [eqn. (6)] or with a model
involving linear polymerisation without formation of cyclic
species, i.e. the model of Fleischer and Shachter.9
Considering that the Ðrst summation is simply [M ] , and
1 0
substituting eqn. (3) for [M ] into the second summation, eqn.
i
(15) becomes:
(e [ e ) =
0
=
; xi
A \ e [M ] ]
1 0
(16)
=
K
inter i/1
Let us consider how the absorbance depends on the analyti-
Since the summation appearing in the right-hand side of eqn.
(16) is equal to x/(1 [ x), eqn. (16) is transformed into eqn.
(17).
cal concentration of Zn(PyP P) in the two model cases. In the
3
Ðrst case, the absorbance (A) would be given by eqn. (12)
A \ e [M ] ] 4e [C ]
(12)
0
1
=
4
(e [ e )
x
0
=
A \ e [M ] ]
1 0
(17)
where e and e are the molar absorptivities of the free
=
K
(1 [ x)
0
=
inter
monomer M and of a coordinated porphyrin subunit in the
1
To obtain A as a function of [M ] only, one should solve
cyclic tetramer C . Considering the mass balance equation,
[M ] \ [M ] ] 4[C ], and eqn. (3), eqn. (12) is transformed
into eqn. (13).
1 0
4
eqn. (2) for x, and introduce the resulting expression into eqn.
1 0
1
4
(17). Also, in the case of eqn. (2) a simple analytical solution is
not available, and one must resort to the NewtonÈRaphson
method.14 A nonlinear least-squares procedure based on eqn.
(17) and on the NewtonÈRaphson solution of eqn. (2) was
carried out. The input data were the absorbance data at j 422
x
A \ e [M ] ] (e [ e )
(13)
=
1 0
0
=
K
inter
To obtain A as a function of [M ] only, one should solve
nm as a function of [M ] , whereas K
treated as adjustable parameters. The following optimised
, e and e were
1 0
1 0
inter
0
=
eqn. (7) with n \ 4 for x, and introduce the resulting expres-
sion into eqn. (13). Although it is not possible to obtain a
simple analytical solution of eqn. (7), it can be solved numeri-
cally by the NewtonÈRaphson method.14 A nonlinear least-
squares procedure based on eqn. (13) and on the
NewtonÈRaphson solution of eqn. (7) with n \ 4 was carried
out. The input data were the absorbance data at j 422 nm as
parameters were obtained: K
inter
e \ 3.5 ^ 0.1 ] 105 L mol~1 cm~1; e \ [4.0 ^ 2.4 ] 104
\ 8.5 ^ 1.2 ] 104 L mol~1;
0
=
L mol~1 cm~1. It appears not only that the value of K
is
inter
more than one order of magnitude greater than the experi-
mental value, but also that e , being negative, is completely
=
unrealistic. By imposing a more realistic value of e , K
=
inter
a function of [M ] , K
was held Ðxed at 4.1 ] 103 L
increases; for example, by assuming e \ 1 ] 105 L mol~1
1 0
inter
=
mol~1, the EM, e and e were treated as adjustable param-
cm~1,
K
\ 3.4 ^ 0.3 ] 105
L
mol~1. In conclusion,
0
=
inter
eters to improve the Ðt of calculated to experimental absorb-
ance data. Fig. 2 reports the experimental apparent molar
absorptivities (e) and the curve calculated on the basis of eqn.
(7) and (13) with the following optimised parameters:
although the quality of the Ðt is analogous for the two models,
the model of linear polymerisation can be unequivocally ruled
out because the required parameters for the best Ðt are not
realistic. By contrast, the model involving a simple equi-
librium between the monomer and the cyclic tetramer is sup-
ported by realistic values of the molar absorptivities and by
the fact that the EM is greater than our estimated lower limit
of 0.1 mol L~1, as expected. Furthermore, the product EM
EM \ 20 ^ 5 mol L~1; e \ 3.3 ^ 0.1 ] 105 L mol~1 cm~1;
0
e
\ 1.5 ^ 0.1 ] 105 L mol~1 cm~1.
=
In the second case, considering that in each linear i-mer the
zinc of one of the terminal subunit is not coordinated, the
absorbance would be given by eqn. (14)
K
(\8.2 ] 104) largely satisÐes the condition shown in
inter
eqn. (5) with n \ 4, thus justifying the validity of the simpliÐed
model in eqn. (6) instead of the more complex one shown in
Scheme 1. Since the model in eqn. (6) holds, a lower self-
assembly concentration (lsac) of 7.1 ] 10~6 mol L~1 can be
calculated from eqn. (18).5
=
A \ ; (e ] (i [ 1)e ) É [M ]
(14)
0
=
i
i/1
where e and e are the molar absorptivities of an uncoordi-
0
=
nated and a coordinated porphyrin subunit, respectively, in
the linear oligomers. From eqn. (14), eqn. (15) is immediately
obtained.
2
lsac \
(18)
n1@(n~1)EM1@(n~1)Kn@(n~1)
inter
=
=
The lsac has been deÐned as the initial monomer concentra-
A \ e ; i[M ] ] (e [ e ) ; [M ]
(15)
=
i
0
=
i
tion at which the complex is half-assembled, i.e. when the yield
i/1
i/1
786
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Fig. 4 Plots of the apparent molar absorptivity (e) of Zn(PyP P) B
3
Fig. 3 Distribution curves of the monomer M and of the cyclic
7È200 lM in chloroform. The arrows indicate how e changes with
1
tetramer
C
as
a
function of the analytical concentration of
increasing Zn(PyP P) concentration.
4
3
Zn(PyP P). Solid and dashed curves refer to toluene and chloroform
3
solutions, respectively.
show well-deÐned isosbestic points. The considerations made
for the results in toluene also apply here. A nonlinear least-
squares procedure based on eqn. (13) and on the NewtonÈ
is 50%.5,31 More elaborate calculations, involving the solu-
tion of eqn. (1), (3) and (4), allow the evaluation of the dis-
tribution curves of the various species present in solution. The
Raphson solution of eqn. (7) with n \ 4 and K
\ 1.3 ] 103
inter
L mol~1 was carried out. Absorbance data at j 547 and 562
solid curves in Fig.
3 are the distribution curves of
nm were taken into account as a function of [M ] . Fig. 5
1 0
the cyclic tetramer and the monomer in toluene. Since the
weighted fraction of the linear polymer (excluding the
monomer) is negligibly low (always lower than 0.016), the lsac
coincides with the intersection of the two curves. Note that
satisfaction of the condition in eqn. (5) implies that there is a
range of initial monomer concentrations at which the process
of self-assembly is more than 99% complete. This range begins
reports the experimental apparent molar absorptivities (e) and
the curves calculated on the basis of eqn. (7) and (13) with the
following optimised parameters: at j 547 nm, EM \ 11 ^ 1
mol L~1, e \ 1.41 ^ 0.02 ] 104 L mol~1 cm~1, e \ 5.50
0
=
^ 0.02 ] 103 L mol~1 cm~1; at j 562 nm, EM \ 15 ^ 4 mol
L~1, e \ 6.2 ^ 0.3 ] 103 L mol~1 cm~1, e \ 1.37 ^ 0.01
0
=
] 104 L mol~1 cm~1. From these results, an average EM
value of 15 ^ 5 mol L~1 can be obtained. This value can be
considered identical within the experimental errors to that
obtained in toluene, conÐrming, beyond our most optimistic
expectations, the independence of the EM from solvent e†ects.
Best Ðts of the same absorbance data with the model of
linear polymerisation described by eqn. (17) and (2) yielded the
at [M ] \ 2 ] 10~3 mol L~1, as shown in Fig. 3.
1 0
It is worth noting that either formation of a cyclic trimer or
pentamer Ðts the data almost as well as formation of the cyclic
tetramer, thus, one cannot tell on the basis of absorbance data
only which is the cyclic oligomer actually present in solution.
However, in the present case, 1H NMR evidence from
Imamura et al.,11 as well as the computational study reported
here, strongly support the formation of the cyclic tetramer.
following optimised parameters: at j 547 nm, K
\ 2.9
inter
^ 0.6 ] 105 L mol~1, e \ 2.6 ^ 0.2 ] 104 L mol~1 cm~1,
0
e
\ 4.3 ^ 0.1 ] 103 L mol~1 cm~1; at j 562 nm, K
\ 3.8
=
inter
^ 0.8 ] 105 L mol~1, e \ [5 ^ 2 ] 103 L mol~1 cm~1,
Self-assembly in chloroform
0
e
\ 1.47 ^ 0.1 ] 104 L mol~1 cm~1. They also appear
=
Binding studies were carried out at 25.0 ¡C with UV/visible
spectroscopy using the same procedures illustrated for
unrealistic in this case.
The dashed curves in Fig. 3, calculated from eqn. (1), (3) and
(4), are the distribution curves of the cyclic tetramer and the
monomer in chloroform; the weighted fraction of the linear
polymer (excluding the monomer) is also negligibly low
toluene. The equilibrium constant K
(\1.3 ^ 0.2 ] 103 L
inter
mol~1) was obtained by analysing the changes in absorbance
at j 549 and 562 nm (Q bands) of Zn(PyP P) B 20 lM upon
3
addition of increasing amounts of pyridine up to [Py] B 10
mM.
Since the EM represents the intramolecular reactivity
(K ) corrected for the inherent reactivity of end-groups
intra
(K ), its value should be little a†ected by solvent e†ects.
inter
This has been largely veriÐed in practice7 and is the rationale
for our believing that a theoretical gas phase estimate of the
EM is also meaningful for intramolecular processes occurring
in solution. By assuming for CHCl the same EM value
3
obtained in toluene (\20 mol L~1), one can predict, from
eqn. (5), that the process of self-assembly of Zn(PyP P) should
3
be strongly favoured in CHCl as well, and that it should be
3
described by the model in eqn. (6). Accordingly, one can esti-
mate from eqn. (18) the value of the lsac in CHCl that should
3
be B3 ] 10~5 mol L~1, that is, about Ðve times greater than
that in toluene. Dilution studies were therefore carried out in
the concentration range [Zn(PyP P)] B 7È200 lM by follow-
3
ing the absorbances corresponding to the Q bands (at these
concentrations Soret bands display absorbance values which
are too high for our purposes). Plots of the apparent molar
absorptivity in the 500È650 nm region, reported in Fig. 4,
Fig. 5 Plots of the apparent molar absorptivity (e) at j 547 (A) and
562 nm (B) as a function of Zn(PyP P) concentration in chloroform.
3
The points are experimental and the curves are calculated (see text).
New J. Chem., 2001, 25, 783È789
787

View Article Online
(\0.025) in this case. The calculated lsac (\3.6 ] 10~5 mol
L~1) is in excellent agreement with the predicted value. The
range of initial monomer concentrations at which the process
energy surface is rather Ñat and this caused severe difficulties
in localising the global minimum conformation. After some
unsuccessful attempts, we decided to consider the structure
with the three N(pyridyl)ÈZn bonds in the anti conformation
as a plausible representative of the lowest energy conforma-
tion. To constrain the structure in the anti conformation and
to speed up the geometry optimisation we chose, on the basis
of the results obtained with the linear dimer, to impose a
plane of symmetry coplanar with all the pyridyl rings
of self-assembly is more than 99% complete begins in CHCl
3
at [M ] \ 0.12 mol L~1.
1 0
Conclusions
Values of EM can be roughly estimated by molecular model-
ling techniques in the case of rigid subunits undergoing self-
assembly into fairly rigid cyclic oligomeric structures. Such
estimates should be sufficient in most cases to establish the
feasibility of the self-assembly process. Application of the
(D H¡ \ 1272.95 kcal mol~1). An attempt to optimise the
f
geometry of the cyclic tetramer c-[Zn(PyP P)] without sym-
3
4
metry constraints failed at an intermediate stage of the calcu-
lation because of the inability of the program to achieve
self-consistency. However, by imposing C symmetry, which
method to Zn(PyP P) gave indications that self-assembly
4
3
should be a reasonable assumption, the geometry opti-
should occur in solution to yield a cyclic tetramer. This has
misation went on to completion. The optimised structure of
been found to be consistent with an UV/visible study of the
self-assembly process both in toluene and in chloroform. The
experimental values of the EM were, as expected, little a†ected
by the nature of the solvent indicating that the solvent a†ects
the process of self-assembly mainly through the value of
c-[Zn(PyP P)] resulted in C symmetry with the zinc atoms
3
4
4h
forming a square with sides of 9.86 A in length (* H¡ \
f
1263.70 kcal mol~1).
Synthesis of Zn(PyP P)
K
. These results revise the conclusions of other authors9
3
inter
who suggested that Zn(PyP P) yields a linear polymer in solu-
tion.
The porphyrin derivative Zn(PyP P) was synthesised by a
3
3
modiÐcation34 of the earlier published procedure,9 as follows:
to a solution of 26 mL (0.256 mol) of benzaldehyde and 6.0
mL (0.063 mol) of 4-pyridinecarboxaldehyde in 250 mL of
reÑuxing propionic acid, a solution of 17.5 mL (0.252 mol) of
freshly distilled pyrrole in 50 mL of propionic acid was added
dropwise over a period of 30 min. The reaction mixture was
stirred at reÑux temperature for additional 3 h, then cooled to
room temperature and allowed to stand overnight. The crys-
talline residue, separated from the bulk of the reaction mixture
by Ðltration, was thoroughly washed with methanol. 2.5 g
of shiny dark-purple crystals, consisting of a mixture of two
Experimental
Materials and methods
Reagents (Aldrich, Merck or Fluka) were of the highest grade
available and were used without further puriÐcation. Solvents
were dried, distilled and degassed prior to use, using standard
procedures.32 Spectrophotometric grade chloroform (Uvasol,
Merck) was stored over activated molecular sieves, and passed
through an aluminium oxide (activated, basic, Brockmann 1,
Aldrich) column prior to use, in order to remove traces of
acids. Silica gel 60 (70È230 mesh) was used for column chro-
matography. 1H-NMR spectra were recorded with a Bruker
AC 300 P (300 MHz) spectrometer. Routine UV/visible
spectra were measured on a Varian Cary 1E Spectrophotom-
eter, whereas more delicate measurements were performed on
a Perkin Elmer k18 spectrophotometer equipped with a ther-
mostatted cell holder. Mass spectra (FAB) were recorded on a
VG Quattro spectrometer using m-nitrobenzyl alcohol (NBA,
Aldrich) as a matrix in positive ion mode. PM3 calculations
were performed with the GAUSSIAN 98 software package.33
Structure visualisation and manipulation was carried out with
version 4.0 of the molecular modelling package HYPER-
CHEM (Hypercube Inc., Gainesville, FL).
products, was chromatographed on SiO . Elution with
2
chloroform gave a Ðrst moving band consisting of the tetra-
phenylporphyrin, H TPP, by-product. The desired porphyrin
2
was subsequently eluted with a 1% methanolÈchloroform
mixture to give 0.9 g (1.5 mmol, 3% yield) of H PyP P as a
2
3
purple crystalline solid, which was puriÐed by dissolving in
dichloromethane and adding hexane until complete precipi-
tation. The Zn-metallation of the free base was accomplished
according to the literature5 to give, after work-up and
dichloromethaneÈhexane crystallisation (as above), 870 mg
(80% yield) of Zn(PyP P). The identity of the porphyrin pro-
3
ducts was conÐrmed by UV/visible, 1H-NMR and FAB mass
spectroscopies.
Determination of K
inter
The intermolecular equilibrium constants K
via spectrophotometric titration by adding a pyridine solution
were obtained
inter
PM3 calculations
to a solution of Zn(PyP P) in a 1 cm path length quartz
cuvette, using microliter syringes. The porphyrin was present
The PM3 optimised structure of Zn(PyP P) resulted in C
3
3
2v
symmetry with the C axis passing through the zinc and the
2
in the ligand at the same concentration as that in the cuvette,
to avoid dilution e†ects. Titrations were carried out at 25.0 ¡C
up to a pyridine concentration of about 1 ] 10~2 mol L~1.
Titrations in toluene were followed at j 422 and 430 nm
nitrogen of the pyridyl group, the porphyrin ring is planar and
the meso aromatic rings are orthogonal to the porphyrin
plane (* H¡ \ 323.95 kcal mol~1). As to the dimer,
f
[Zn(PyP P)] , since there is the possibility of internal rota-
3
2
([Zn(PyP P)] B 2 ] 10~6 mol L~1). Titrations in chloroform
tion about the N(pyridyl)ÈZn bond, the corresponding adia-
3
were followed at j 549 and 562 nm ([Zn(PyP P)] B 2 ] 10~5
batic potential energy curve was evaluated in the range
3
mol L~1). The association constants K
nonlinear least-squares curve Ðtting of the absorbance data to
were evaluated by
0¡ O h O 180¡. The lowest energy minimum (* H¡ \ 640.83
inter
f
kcal mol~1), corresponds to the conformation in which the
a standard equation for 1 : 1 complexation.35
two pyridyl rings are coplanar (h \ 0, 180¡); this conformation
resulted in C symmetry, with the symmetry plane coplanar
Self-assembly studies
s
with pyridyl rings. Another relative energy minimum 0.02 kcal
mol~1 was found at h \ 90¡. Two maxima of practically the
same relative energy (0.59 kcal mol~1) were found at h \ 45
and 135¡. Since the barrier height is very low, the internal
rotation can be considered virtually free at room temperature.
As to the linear tetramer [Zn(PyP P)] , owing to the almost
UV/visible self-assembly macrocyclisation studies of
Zn(PyP P) were performed at 25.0 ¡C by adding aliquots of a
3
concentrated stock solution of the title porphyrin (2.5 ] 10~4
mol L~1 in toluene; 1.80 ] 10~3 mol L~1 in chloroform) to a
1 cm quartz cell containing 2.5 mL of solvent (toluene or
chloroform). The UV/visible spectra after each addition were
3
4
free rotation about the N(pyridyl)ÈZn bonds, its potential
788
New J. Chem., 2001, 25, 783È789

View Article Online
Rowan, D. G. Hamilton, P. A. Brady and J. K. M. Sanders, J.
Am. Chem. Soc., 1997, 119, 2578.
recorded in digital format. Nonlinear least-squares Ðttings of
the absorbance data to both the models of simple cyclisation
and linear polymerisation were carried out by appositely
written computer programs (see Results and discussion for
further details). The programs, coded in BASIC, are based on
the Gauss method and have been adapted from a published
coding,36 the principal variation being in the routine of func-
tion evaluation that calls for a subroutine performing the
numerical solution of the appropriate algebraic equation by
the NewtonÈRaphson method.
13 Owing to a misprint in eqn. (10) in this paper, however, this
equivalence is not readily recognised (the power 2 was erron-
eously printed inside, instead of outside, the parenthesis).
14 H. Margenau and G. M. Murphy, T he Mathematics of Physics
and Chemistry, 2nd edn., Van Nostrand, Princeton, 1962, p. 492.
15 J. R. Miller and G. D. Dorough, J. Am. Chem. Soc., 1952, 74,
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16 C. H. Kirksey, P. Hambright and C. B. Storm, Inorg. Chem.,
1969, 8, 2141.
17 S. J. Cole, G. C. Curthoys, E. A. Magnusson and J. N. Phillips,
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Moments of inertia
18 G. C. Vogel and L. A. Searby, Inorg. Chem., 1973, 12, 936.
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20 P. Bhyrappa, V. Krishnan and M. Nethaji, J. Chem. Soc., Dalton
T rans., 1993, 1901.
Reduced moments of inertia were evaluated by an approx-
imate literature method28 (see Results and discussion for
further details) implemented into an appositely written
MatLab (The MathWorks, Natick, MA) script. This script
extracts the atomic coordinates, by dynamic data exchange,
from the appropriate structure displayed in the HYPER-
CHEM program, and performs the relevant calculations.
21 G. C. Vogel and J. R. Stahlbush, Inorg. Chem., 1977, 16, 950.
22 M. Nappa and J. S. Valentine, J. Am. Chem. Soc., 1978, 100, 5075.
23 An isodesmic reaction is one with the same number and types of
bonds on both sides. Isodesmic reactions allow extensive cancel-
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semi-empirical methods through parameterisation: W. J. Hehre,
L. Radom, P. v. R. Schleyer and J. A. Pople, Ab Initio Molecular
Orbital T heory, Wiley, New York, 1986.
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New J. Chem., 2001, 25, 783È789
789