Quantitative Evaluation of the Catalytic Activity of Dendrimers with only One Active Center at the Core: Application to the Nitroaldol (Henry) Reaction

Article abstract of DOI:10.1021/ja039888s

One reference tertiary amine and three families of structurally related trialkylamines and dendrimers have been synthesized, characterized, and studied by molecular dynamics simulations. The catalytic activity of these amines in the nitroaldol (Henry) reaction between 2-nitroethanol and benzaldehyde has been measured by FT-IR spectroscopy. It is found that, in this kind of molecule with only one catalytic center at the core, the efficiency of the catalytic process decreases with the size and/or the degree of ramification of the dendrimer. According to these results, there is a linear departure from the behavior predicted by the hard sphere collision theory (HSCT) as the size of the dendrimer increases. Therefore, the behavior of structurally related dendrimers can be quantified in terms of their molecular weight and reagent accessible surfaces.

Full text of DOI:10.1021/ja039888s

Published on Web 04/03/2004
Quantitative Evaluation of the Catalytic Activity of Dendrimers
with Only One Active Center at the Core: Application to the
Nitroaldol (Henry) Reaction
Aizpea Zubia, Fernando P. Coss´ıo,* In˜aki Morao, Marina Rieumont, and
Xabier Lopez*
Contribution from the Kimika Fakultatea, Euskal Herriko Unibertsitatea, P.K. 1072,
20080 San Sebastian-Donostia, Spain
Received December 1, 2003; E-mail: qopcomof@sq.ehu.es (F.P.C.); poplopex@sq.ehu.es (X.L.)
Abstract: One reference tertiary amine and three families of structurally related trialkylamines and
dendrimers have been synthesized, characterized, and studied by molecular dynamics simulations. The
catalytic activity of these amines in the nitroaldol (Henry) reaction between 2-nitroethanol and benzaldehyde
has been measured by FT-IR spectroscopy. It is found that, in this kind of molecule with only one catalytic
center at the core, the efficiency of the catalytic process decreases with the size and/or the degree of
ramification of the dendrimer. According to these results, there is a linear departure from the behavior
predicted by the hard sphere collision theory (HSCT) as the size of the dendrimer increases. Therefore,
the behavior of structurally related dendrimers can be quantified in terms of their molecular weight and
reagent accessible surfaces.
Introduction
and reaction rates in Diels Alder reactions catalyzed by bis-
(oxazoline)copper (II) dendrimers. These authors found that the
The potential of dendritic molecules as catalysts was recog-
nized almost since the beginning of this field of research.1,2 In
principle, one of the advantages of dendrimers in catalysis is
the possibility of recovering the homogeneous catalytic mac-
romolecule by microfiltration or precipitation. The second one
consists of the possibility of developing tailor-made environ-
ments that, if appropriately designed, could produce results not
affordable to low size analogues.
The design of dendritic catalysts offers multiple possibilities
of installing the active centers. If the dendrimer incorporates
only one catalytic point, this site can be at the core of the macro-
molecule3 or it can occupy a focal point in a dendritic sector.
Similarly, multiple catalytic centers can be incorporated inside
the dendritic structures3 or can be encapsulated without any
covalent bond between the active sites and the macromolecule.
Finally, the catalytic points can be installed on the periphery.4
Although the scope of reactions catalyzed by dendrimers is
very large,1-4 attempts to measure quantitatively the catalytic
activity of different generations of dendrimers are very scarce
to date. Thus, Chow et al.5 have reported different selectivities
formation constant of the dienophile-catalyst complex de-
creased gradually from the lower to the higher generations. In
addition, the reaction rate constants remained essentially invari-
able from the zeroth to second generation, whereas it dropped
suddenly for the third generation. This result was rationalized
in qualitative terms by assuming that the size of the dendritic
sectors in the bulkiest catalyst induces a change in the
accessibility of the catalytic site. Similarly, Seebach et al.6 found
a slight decreasing of the catalytic activity of different TADDOL
derivatives with the generation number in the diethyl zinc
addition to benzaldehyde, with an abrupt variation for the
bulkiest dendrimer. In the same vein, Diederich et al.7 measured
quantitatively a decay of the catalytic activity of dendritic
thiazolio-cyclophanes in the course of the oxidation of naftalene-
2-carboxaldehyde. More recently, Astruc et al. have observed
negative dendritic effects in the catalysis of the Sonogashira
reaction between terminal alkynes and vinyl halides8 and in the
ring opening metathesis polymerization of norbornene.9
Quantitative measurement of positive dendritic effects in
catalysis is also scarce. For example, Detty et al. have reported
an increasing activity per peripheric catalytic site in the oxidation
of bromide by hydrogen peroxide.10 In a related approach,
Twyman and Martin11 measured a 25-fold rate enhancement in
the aminolysis of p-nitrophenyl acetates with a PAMAM
(1) (a) Astruc, D.; Chardac, F. Chem. ReV. 2001, 101, 2991. (b) Janssen, H.
M.; Meijer, E. W. Chem. ReV. 1999, 99, 1665. (c) Newkome, G. R.; He,
E.; Moorefield, C. N. Chem. ReV. 1999, 99, 1689. For seminal contributions
in this field, see, inter alia: (d) Knapen, J. W. J.; van der Made, A. W.; de
Wilde, J. C.; van Leeuwen, P. W. N. M.; Wijkens, P.; Grove, D. M.; van
Koten, G. Nature 1994, 372, 659. (e) Brunner, H.; Fu¨rst, S. Tetrahedron
1994, 50, 4303. (f) Brunner, H. J. Organomet. Chem. 1995, 500, 39.
(2) (a) Hecht, S.; Fre´chet, J. M. J. Angew. Chem., Int. Ed. 2001, 40, 74. (b)
Oosterom, G. E.; Reek, J. N. H.; Kamer, P. C. J.; van Leeuwen, P. W. N.
M. Angew. Chem., Int. Ed. 2001, 40, 1828.
(5) (a) Mak, C. C.; Chow, H.-F. Macromolecules 1997, 30, 1228. (b) Chow,
H.-F.; Mak, C. C. J. Org. Chem. 1997, 62, 5116.
(6) Rheiner, P. B.; Seebach, D. Chem.-Eur. J. 1999, 5, 3221.
(7) Habicher, T.; Diederich, F.; Gramlich, V. HelV. Chim. Acta 1999, 82, 1066.
(8) Heuze´, K.; Me´ry, D.; Gauss, D.; Astruc, D. Chem. Commun. 2003, 2274.
(9) Gatard, S.; Nlate, S.; Cloutet, E.; Bravic, G.; Blais, J.-C.; Astruc, D. Angew.
Chem., Int. Ed. 2003, 42, 452.
(3) Twyman, L. J.; King, A. S. H.; Martin, I. K. Chem. Soc. ReV. 2002, 31,
69.
(4) (a) Reek, J. N. H.; de Groot, D.; Oosterom, G. E.; Kamer, P. C. J.; van
Leeuwen, P. W. N. M. ReV. Mol. Biotechnol. 2002, 90, 159. (b) van Koten,
G.; Jastrzebski, J. T. B. H. J. Mol. Catal. A 1999, 146, 317.
(10) Francavilla, C.; Bright, F. V.; Detty, M. R. Org. Lett. 1999, 1, 1043.
9
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J. AM. CHEM. SOC. 2004, 126, 5243-5252
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A R T I C L E S
Zubia et al.
dendrimer with respect to an equivalent amount of N-acetyl
ethylenediamine. Alternatively, Fre´chet et al. proposed a dif-
ferent strategy based upon the installation of a catalytic center
at the core of the dendrimer and on the generation of an inside-
outside polarity gradient. This favors the interaction between
the reactants and the catalytic center and prevents product
inhibition of the active site. This strategy to generate positive
dendritic effects proved to be successful in the conversion of
cyclopentadiene to cis-2-cyclopentene-1,4-diol catalyzed by
dendritic ambiphilic singlet oxygen sensitizers.12 In this case,
the gradient was established between an hydrophobic core and
a polar environment. An inverse design was also successful in
the catalysis of E1-type13 and esterification reactions.14 Finally,
a very recent paper of Liu and Breslow15 reports quantitative
measurements of large rate enhancements in the catalytic
transamination of piruvic and phenylpiruvic acids by PAMAM
dendrimers incorporating one pyridoxamine unit at the core.
Our group16 reported that dendrimers derived from triethy-
lamine catalyze the nitroaldol (Henry) reaction. Similarly, Smith
et al.17 found that dendrimers containing a tertiary amine and
dendritic branches derived from L-lysine catalyze the same
reaction. In both cases, the activity of the catalysts decreased
with the generation number, in agreement with most of the
above-mentioned results.
In all these precedents the description of the features of the
different generations of catalysts was based upon plausible and
qualitative arguments. Within this context, we decided to study
the possibility of correlating the kinetic behavior of one family
of structurally related dendritic catalysts with some of their
structural parameters. This correlation could eventually help in
the design of other catalysts. To facilitate the study, we designed
our dendritic catalysts taking into account the following
requirements: (i) one single and structurally simple catalytic
center at the core, (ii) highly symmetric branches and periphery,
and (iii) different branching indexes and generations without
significant changes in the neighborhood of the catalytic site.
Therefore, the aim of the present work has been to measure
the catalytic activity of structurally related triethanolamine-
derived dendrimers with different generation numbers and
branching indexes, in an attempt to correlate the catalytic activity
with different parameters of the dendritic molecules. As we did
in our previous work,16 the reaction studied is the nitroaldol
(Henry) reaction, which can be catalyzed by amines.18
Figure 1. Basic features of dendrimers designed for the catalysis of the
nitroaldol (Henry) reaction. Lines connecting the branching and terminal
units are alkoxylidene groups.
(Figure 1). In all of these tertiary amines, terminal benzyloxy
groups provided a common hydrophobic periphery.
In all cases, the synthesis of the catalyst was accomplished
by Williamson reaction between triethanolamine 1 and different
benzyl bromides (Schemes 1-3). In the simplest case, the
tribenzyloxyethylamine A0 was obtained in 61% yield after 24
h of reaction at room temperature in the presence of 3 equiv of
benzyl bromide. The synthesis of the linear congener MA1 was
accomplished in 75% yield after 48 h of reaction at room
temperature. Similarly, the second-generation analogue MA2
was obtained in 53% yield under the same reaction conditions.
Bromides 2 and 3 (Scheme 1) were readily prepared using the
hydroxy benzylic alcohol strategy developed by Fre´chet19 (see
Supporting Information).
The synthesis of dendrimers DA1 and DA2 was carried out
in the same way from 1 and bromides19 4 and 5 (Scheme 2).
As in the monosubstituted series, the yield of the second-
generation dendrimer DA2 was lower than that obtained for its
first-generation congener DA1. The reaction times required for
these yields were 72 and 48 h, respectively.
Dendrimers TA1 and TA2 were prepared in the same way
from 1 and bromides 6 and 7, respectively. These halides were
prepared in turn following the methodology developed by
Fre´chet and using the starting materials reported by Percec20
(Scheme 3). To improve the yield of the last Williamson
reaction, we used the bromides instead of the chlorides used
by Percec et al.20 in the synthesis of these 3,4,5-trisubstituted
benzyl halides. The full details of the preparation and charac-
terization of 6 and 7 are reported in the Supporting Information.
The characterization of these triethanolamine-derived den-
drimers showed the different dynamic properties of these
compounds depending on the generation number and/or the
branching index. Thus, the nonaromatic region of their 1H NMR
spectra shows a progressive broadening of the two triplets
corresponding to the ethylene moieties surrounding the catalytic
centers (see Supporting Information). Similarly, the intensities
Results and Discussion
Chemical Synthesis of the Catalysts. All the catalysts
prepared were based on the methodology reported in our
previous work,16 but incorporated different branching units.
Thus, around a single catalytic center at the core (a nitrogen
atom) surrounded by a common triethanol moiety, different
generations of substituted benzyloxy units were incorporated
(11) Twyman, L. J.; Martin, I. K. Tetrahedon Lett. 2001, 42, 1123.
(12) Hecht, S.; Fre´chet, J. M. J. J. Am. Chem. Soc. 2001, 123, 6959.
(13) Piotti, M. E.; Rivera, F.; Bond, R.; Hawker, C. J.; Fre´chet, J. M. J. J. Am.
Chem. Soc. 1999, 121, 9471.
(14) Liang, C. O.; Helms, B.; Hawker, C. J.; Fre´chet, J. M. J. Chem. Commun.
2003, 2524.
(15) Liu, L.; Breslow, R. J. Am. Chem. Soc. 2003, 125, 12110.
(16) Morao, I.; Coss´ıo, F. P. Tetrahedron Lett. 1997, 38, 6461.
(17) Davis, A. V.; Driffield, M.; Smith, D. K. Org. Lett. 2001, 3, 3075.
(18) (a) Luzzio, F. A. Tetrahedron 2001, 57, 915. (b) Rosini, G. In Compre-
hensiVe Organic Synthesis; Trost, B. M., Ed.; Pergamon: New York, 1991;
Vol. 2, pp 321-340.
(19) (a) Hawker, C. J.; Fre´chet, J. M. J. J. Am. Chem. Soc. 1990, 112, 7638. (b)
Hawker, C. J.; Fre´chet, J. M. J. J. Chem. Soc., Chem. Commun. 1990, 1010.
(20) (a) Balagurusamy, V. S. K.; Ungar, G.; Percec, V.; Johansson, G. J. Am.
Chem. Soc. 1997, 119, 1539. (b) Percec, V.; Cho, W. D.; Mosier, P. E.;
Ungar, G.; Yeardley, D. J. P. J. Am. Chem. Soc. 1998, 120, 11061.
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A R T I C L E S
Scheme 1. Synthesis of Amines A0, MA1, and MA2a
a
Reagents and conditions: (i) NaH (3.2 equiv), RBr (3.2 equiv), THF/DMF, room temperature.
and the chemical shifts of the different benzyl methylene groups
permitted in most cases the assignation of the different signals.
Measurement of the Catalytic Activity. The model reaction
to study the catalytic power of our dendrimers was the Henry
reaction between benzaldehyde 8 and nitro ethanol 9 to yield
nitroaldols syn- and anti-10 (Scheme 4). Given that the
mechanism of this reaction consists of multiple steps,18,21 kinetic
treatment by means of an analytic rate equation is very
complicated and difficult to analyze. To overcome this draw-
back, we decided to work under pseudo-first-order conditions,
with a large excess of 9.22 Therefore, we measured the
disappearance of 8 according to eq 1, where kobs is the observed
rate coefficient.
d[8]
dt
-
) kobs[8]
(1)
Experimentally, we monitored the IR signal corresponding to
the carbonyl group of 8 as it is shown in Figure 2A, using the
stretching vibration of the C-N triple bond of benzonitrile as
internal standard (see Supporting Information). Therefore, after
measuring carbonyl absorbances at different times, we used the
following expression to calculate kobs
:
(21) Lecea, B.; Arrieta, A.; Morao, I.; Coss´ıo, F. P. Chem.-Eur. J. 1997, 3, 20.
(22) Steindfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and
Dynamics; Prentice Hall: Upper Saddle River, NJ, 1999; pp 40-41.
ln(At - A∞) ) ln(A0 - A∞) - kobs
t
(2)
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A R T I C L E S
Zubia et al.
Scheme 2. Synthesis of Amines DA1 and DA2a
a
Reagents and conditions: (i) NaH (3.2 equiv), RBr (3.2 equiv), THF/DMF, room temperature.
where A0, At, and A∞ indicate initial absorbance and absorbancies
at times t and ∞, respectively. Given that the direct measurement
of A∞ is difficult and not reliable, we used the Kezdy-
Swinbourne method to estimate it.23,24 According to this method,
absorbancies at times t and t + τ can be written in the forms
expression:
At ) A∞[1 - exp(kobsτ)] + At+τ exp(kobsτ)
(5)
Since the first term on the right of eq 5 is time independent, a
plot of At versus At+τ will be linear, with a slope of exp(kobsτ).
In addition, since at t ) ∞ At ) At+τ, intersection of this line
with the 45° line yields the value of A∞, which can be used to
calculate kobs from eq 2. As an example, in Figure 2B,C we
have included the results of one series of experiments involving
the reaction depicted in Scheme 4 with TA2 as catalyst. As it
At ) (A0 - A∞) exp(- kobst) + A∞
(3)
(4)
A
t+τ ) (A0 - A∞) exp[- kobs(t + τ)] + A∞
Dividing eqs 3 and 4 and solving for At leads to the following
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Dendrimers with Only One Active Center at the Core
A R T I C L E S
Scheme 3. Synthesis of Amines TA1 and TA2a
a
Reagents and conditions: (i) NaH (3.2 equiv), RBr (3.2 equiv), THF/DMF, room temperature.
can be seen, under our experimental conditions, the reaction
follows pseudo-first-order kinetics, with good linear correlations
in both the At vs At+τ and ln(At - A∞) vs t representations. The
same behavior was observed in the seven series of experiments
involving catalysts described in Schemes 1-3. The observed
rate coefficients are displayed in Table 1. In this table we have
also included the stereochemical outcome of these reactions.
According to our results, we have obtained a syn:anti ratio of
ca. 2:1 in all cases, except when TA2 was used as catalyst, in
which the syn:anti ratio was slightly higher (2.6:1). The
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A R T I C L E S
Zubia et al.
a,b
Table 1. Pseudo-First-Order Rate Coefficients (kobs
)
for the
Reaction between Benzaldehyde 8 and Nitroethanol 9 To Yield
Racemic syn- and anti-2-Nitro-1-phenyl-1,3-propanediol 10c
(Scheme 4)
catalyst
k
obs (10-4 s-1
)
syn/anti
A0
12.11 ((0.25)
10.85 ((0.34)
5.53 ((0.31)
8.25 ((0.62)
3.70 ((0.15)
1.89 ((0.43)
1.03 ((0.14)
66:34
69:31
67:33
68:32
66:34
67:33
72:28
MA1
MA2
DA1
DA2
TA1
TA2
a
b
Calculated from FT-IR data by means of eqs 2 and 5. Numbers in
parentheses correspond to standard deviation from the average value. Each
c
series of experiments was carried out in triplicate. Determined by 1H
NMR in the crude reaction mixtures (see refs 16 and 25).
involving only A0, DA1, and DA2 compounds, we conclude
that in our series of benzyloxy-based catalytic dendrimers neither
the generation number nor the branching index has any
significant impact on the stereocontrol of the reaction.
Computation of Structural Parameters of Catalysts. To
gain a better understanding on the behavior of the dendrimers
previously reported, we carried out several calculations of
structurally significant parameters. All these computational
studies were based upon molecular dynamics (MD)26 and used
the MM3 method27 developed by Allinger et al. as implement
in the MacroModel28 package. To account partially for the
solvent effects,29 a dielectric constant of ꢀ ) 4.89 was
introduced, within a Born-generalized model for the electrostatic
contribution to solvation energy and a solvent accessible surface
(SAS)-based computation of the cavitation energy.30 Therefore,
this treatment does not account for specific solvent effects such
as hydrogen bonds. The value of ꢀ was chosen to account for
a low polarity dielectric medium, representative in average of
a mixture formed by the reactants and the hydrophobic branches
of the dendrimer. All MD simulations were performed with
SHAKE31 to constrain the C-H bonds. The temperature was
set up to 298 K. The system was equilibrated for 1 ns with
time steps of 1 fs. This equilibration time is 10 times longer
than the expected value for the relaxation time of dendrimers
of this size.32a The production run was started from this point
and lasted another nanosecond with time steps of 1 fs. In all
cases, we observed that during the production period, the energy
Figure 2. (A) FT-IR spectra of the carbonyl region of benzaldehyde at
different reaction times corresponding to the reaction between benzaldehyde
and nitroethanol catalyzed by dendrimer TA2. The arrow indicates the loss
in absorbance at increasing reaction times. (B) Absorbances at times t and
t + τ (At and At+τ, respectively, with τ ) 120 min) for the same reaction.
Intersection of the line with the 45° line yields the calculated A∞ value
(see text). (C) ln(A-A∞) versus time representation of the values measured
for the same reaction under pseudo-first-order conditions.
Scheme 4. Nitroaldol Reaction between Benzaldehyde and
Nitroethanol Catalyzed by Amines A0, MA1-2, DA1-2, and TA1-2
(23) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms; McGraw-
Hill: New York, 1981; pp 24-30.
(24) (a) Kezdy, F. J.; Kaz, J.; Bruylants, A. Bull. Soc. Chim. Belg. 1958, 67,
687. (b) Swinbourne, E. S. J. Chem. Soc. 1960, 2371.
(25) Eyer, M.; Seebach, D. J. Am. Chem. Soc. 1985, 107, 3601.
(26) (a) Haile, J. Molecular Dynamics Simulations; Wiley: New York, 1992.
(b) Cramer, C. J. Essentials of Computational Chemistry; Wiley: Chich-
ester, U.K., 2002; pp 63-94 and references therein.
(27) (a) Bowen, J. P.; Allinger, N. L. In ReViews in Computational Chemistry;
Lipkowitz, K. B.; Boyd, E. D., Eds.; VCH Publishers: New York, 1991;
Vol. 2, pp 81-97. (b) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem.
Soc. 1989, 111, 8551. (c) Lii, J.-H.; Allinger, N. L. J. Am. Chem. Soc.
1989, 111, 8576.
(28) (a) MacroModel, version 7.0; Schro¨dinger: Portland, OR. (b) Mohamadi,
F.; Richards, N. G. J.; Guida, W. C.; Liskamp, R.; Lipton, M.; Caulfield,
C.; Chang, G.; Hendrickson, T.; Still, W. C. J. Comput. Chem. 1990, 11,
440.
(29) For related studies showing the importance of solvent effects on the
conformation of dendrimers, see for example: (a) Hecht, S.; Vladimirov,
N.; Fre´chet, J. M. J. J. Am. Chem. Soc. 2001, 123, 18. (b) Chai, M.; Niu,
Y.; Youngs, W. J.; Rinaldi, P. L. J. Am. Chem. Soc. 2001, 123, 4670.
(30) Still, W. C.; Tempczyk, A.; Hawley, R. C.; Hendrickson, T. J. Am. Chem.
Soc. 1990, 112, 6127.
structural assignment of compounds 10 was made by comparison
of our 1H NMR data and those reported by Eyer and Seebach25
(Scheme 4). Therefore, as an extension of our preliminary study
(31) Rickaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977,
23, 327.
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Dendrimers with Only One Active Center at the Core
A R T I C L E S
dendrimers A0, MA1-2, DA1-2, and TA1-2 during the produc-
tion time. As can be seen, the fluctuation of Rg obtained for the
MA1-2 dendrimers is considerably larger than that obtained for
the more rigid compound TA2, which has a larger atom density
at the periphery.
The square of the radius of gyration is related to the trace of
the diagonalized tensor of inertia ID of the molecule by means
of the following expression:
2
ML1
0
0
2
2
tr(ID) ) tr 0
ML2
0
) MRg
(8)
(
)
2
0
0
ML3
As a convention, the components Li are taken to satisfy the
following expression:
L21 > L22 > L23
(9)
To correlate the shape of a given dendrimer with these
magnitudes, it is useful to define the asphericity b in the form35
1
2
b ) L21 - (L22 + L23)
(10)
Thus, b is related to the anisotropy of the molecule with
respect to the principal axes. For a perfect sphere, L1 ) L2 )
L3, and therefore b ) 0.
Similarly, acylindricity c can be defined as35
Figure 3. Evolution of the radius of gyration (Rg, in Å) along the production
time of molecular dynamics simulations on catalysts A0, MA1-2, DA1-2,
and TA1-2.
c ) L22 - L23
(11)
Therefore, for a perfect cylinder, L2 ) L3 and c ) 0.
and temperature of the whole system were equilibrated.32 During
the production run, the coordinates were saved each picosecond,
which implies a total of 1000 structures. These structures were
used to calculate the averages of the properties specified below.
To calculate these properties, programs based on the DYNAMO
library33 were written.
To interpret the structural data obtained for dendrimers A0,
MA1-2, DA1-2, and TA1-2, we compared these data with those
computed for three reference molecules (see Table 1 of the
Supporting Information). These molecules are n-pentane, neo-
pentane (2,2-dimethylpropane), and hexaethynyl benzene as
examples of linear chain, spheric globular molecule, and star-
disk structures, respectively. In addition, we also computed the
maximum radius (Rmax) of these molecules, defined as the
maximum distance from the central nitrogen atom to the most
distant atom:
The first property computed from our MD data was the radius
of gyration Rg, whose norm is given by34
N
1/2
m (r - g)(r - g)
∑
i
i
i
i)1
Rg )
(6)
Rmax ) max |rN - ri|
(12)
N
[
]
m
∑
i
where rN and ri are the position vectors of the nitrogen and the
i atom. These data are reported in Table 2.
i)1
According to our results, the radii of gyration grow according
to the generation and/or the branching numbers, whereas the
averaged Rmax values are almost constant for each generation,
irrespective of the degree of branching. To facilitate the
visualization of the shape of dendrimers A0, MA1-2, DA1-2,
and TA1-2, we report in Figure 4 their relative asphericities,
acylindricities, and components of the diagonalized tensor of
inertia together with the values corresponding to the model
molecules mentioned before. Inspection of Figure 4 reveals that,
in both representations, most dendrimers are grouped in couples.
Thus, A0 and MA1 are structurally similar to each other,
where mi is the mass of atom i (i ) 1,2...N), ri is its position
vector, and g is the position vector of the center of masses:
N
m r
∑
i
i
g ) i)1
(7)
N
m
∑
i
i)1
In Figure 3, we report the fluctuation of the Rg values for
(32) For recent studies on MD simulation on dendrimers, see for example: (a)
Naidoo, K. J.; Hughes, S. J.; Moss, J. R. Macromolecules 1999, 32, 331.
(b) Teobaldi, G.; Zerbetto, F. J. Am. Chem. Soc. 2003, 125, 7388. (c)
Karatajos, K.; Adolf, D. B.; Davies, G. R. J. Chem. Phys. 2001, 115, 5310.
(d) Lee, I.; Athey, B. D.; Wetzel, A. W.; Meixner, W.; Baker, J. R., Jr.
Macromolecules 2002, 35, 4510.
(33) Field, M. J. A Practical Introduction to the Simulation of Molecular Systems;
Cambridge University Press: Cambridge, 1999.
(34) Mattice, W. L. In Dendritic Molecules: Concepts, Syntheses, PerspectiVes;
Newkome, G. R.; Moorefield, C. N.; Vo¨gtle, F., Eds.; VCH: Weinheim,
Germany, 1996; pp 1-36.
(35) Theodorov, D. N.; Suter, U. W. Macromolecules 1985, 18, 1206.
9
J. AM. CHEM. SOC. VOL. 126, NO. 16, 2004 5249

A R T I C L E S
Zubia et al.
between structural properties of dendrimers A0, MA1-2, DA1-
2, and TA1-2 and the observed rate coefficients in the catalysis
of the nitroaldol reaction depicted in Scheme 4. With this
purpose, we have adapted the hard-sphere collision theory36 to
the structurally more complex dendrimers.
According to this theory, the kinetic constant kcoll associated
with the collision of two reagents to give a chemical transfor-
mation is given by
8kT 1/2
πµ
kcoll ) σ*
NA exp(- ∆Ea/RT)
(13)
(
)
where σ* is the reactive collision cross section which can be
expressed as
σ* ) Pσ
(14)
with P being the steric factor and σ the spheric collision cross
section.
In eq 13, µ is the reduced mass of the reactants described by
eq 15:
m1m2
µ )
(15)
m1 + m2
and ∆Ea is the activation energy, the remaining symbols of eq
13 having their usual meaning.
The crucial point to evaluate kcoll by means of eq 13 is the
calculation of σ*. One possible estimate is to assume that σ is
linearly related to the average solvent accessible surface SAS
.
As the probe radius we have selected the average Csp3-H
distance of 1.10 Å, since this is the bond to be broken as a
consequence of the effective collision of the nitroalkane and
the catalyst. In Figure 5 we report the evolution of SAS along
the production time for all the catalysts, as well as one
representation of this surface for dendrimer TA2.37 In addition,
for a given family of structurally related catalyst, P can be taken
as inversely proportional to the molecular weight Mw of the
catalyst. Therefore, for the dendrimers described above, the
reactive cross section σ* can be approximated as
SAS
σ* ) Rna
(16)
Mw
Figure 4. A) Representation of averaged asphericities b and acylindricities
2
c relative to the averaged square of the radius of gyration Rg for the
where na stands for the number of active sites, R being a
proportionality constant. In our series of dendrimers, na ) 1
for all catalysts.
different catalysts with respect to model spheric, linear chain, and disk-star
reference molecules. (B) Same representation but considering the relative
averaged Li2 components of the diagonalized tensor of inertia with respect
to the largest one L21 .
If the catalytic centers of the dendrimers (the amino groups)
have similar ability to abstract the proton of the nitroalkane
molecule, the activation energy would be very similar. Under
these conditions, the effective collision will be determined by
the reactive cross section. Therefore, if the zeroth superscript
denotes the parameter of amine A0, the relative kinetic constant
of a given dendrimer with respect to A0 can be approximated
as
occupying a halfway position between the linear chain and the
disk-star structure. Similarly, DA1 and MA2 exhibit similar
shapes, very similar to the disk-star geometry. Finally, the struc-
tural parameters of TA1 and TA2 are between those correspond-
ing to the disk-star geometry and the sphere. Quite surprisingly,
the structure most similar to the spheric shape is DA2, which
must be related to the larger conformational freedom of this
dendrimer. In summary, our results show that the dendrimers
prepared cover a wide range of shapes, including structures
similar to disk-star geometries as well as other dendrimers with
different degrees of asphericity and acylindricity.
SAS M°w µ° 1/2
kcoll
≈
(17)
(
)
k°coll
µ
S°AS Mw
Correlation between Geometric Features and Catalytic
Properties. The next step in our study was to find a correlation
where the Mw and SAS values can be taken from the data
included in Table 2.
9
5250 J. AM. CHEM. SOC. VOL. 126, NO. 16, 2004

Dendrimers with Only One Active Center at the Core
A R T I C L E S
2
Table 2. Molecular Weights (Mw, Da), Averaged Squares of Radius of Gyration ( Rg , Å2), Maximum Radii ( RMax , Å), Normalized
2
2
2
Asphericities ( b / Rg ) and Acylindricities ( c / Rg ), Ratios of Principal Moments of the Gyration Tensor ( Li
/
L21 ), and Solvent Accessible Surfacesa ( SAS , Å2) of Dendrimers A0, MA1-2, DA1-2, and TA1-2b
dendrimer
M
w
R 2
Rmax
b / R 2
c / R 2
L32 / L12
L22 / L12
SAS
g
g
g
A0
419.56
737.93
52.77
119.76
277.45
145.41
250.34
169.06
375.52
8.86
14.68
21.04
14.07
19.25
14.88
21.83
0.22
0.21
0.23
0.23
0.10
0.17
0.17
0.15
0.15
0.05
0.04
0.05
0.06
0.05
0.38
0.41
0.47
0.49
0.69
0.55
0.56
0.69
0.72
0.58
0.58
0.80
0.68
0.67
729.79
1189.88
1684.96
1668.99
3456.70
2017.85
5738.21
MA1
MA2
DA1
DA2
TA1
TA2
1056.30
1056.30
2329.75
1373.62
4239.29
a
b
Computed with a probe radius of 1.1 Å. All magnitudes were computed according to eqs 6-12; see text.
Figure 6. Relative rate coefficients(kobs/k°obs) versus parameters of
amines A0, MA1-2, DA1-2, and TA1-2. Kinetic parameters correspond to
the reaction between benzaldehyde and nitroethanol. The 45° line corre-
sponds to the behavior described by eq 17. SAS , MW, and µ stand for the
averaged solvent accessible surface of the catalysts (with probe radius of
1.1 Å), molecular weight of the catalysts, and the reduced mass of the
catalysts and nitroethanol, respectively. The zero superscript corresponds
to amine A0. Gray and white colors indicate regions occupied by cooperative
and noncooperative dendrimers, respectively (see text).
can write the following expression:
SAS M°w µ° 1/2
kobs
) φ
+ θ
(18)
(
)
k°obs
µ
S°AS Mw
with φ ) 3.8 and θ ) -2.2, the regression factor being r2 )
0.921. It is noteworthy that the catalytic behavior of the smallest
molecule MA1 is described by eq 17, whereas the departure
from this behavior is larger as the generation number and/or
the branching index increases. Therefore, we can describe the
behavior of an ensemble of structurally related catalytic den-
drimers in terms of a sole parameter. Although further studies
should test if the model presented here is general, we can
anticipate that noncooperative catalytic dendrimers will lie in
the region colored in white in Figure 6, whereas cooperative
Figure 5. (A) Solvent accessible surfaces (SAS, in Å2, with a probe radius
of 1.1 Å; see text) of catalysts A0, MA1-2, DA1-2, and TA1-2 along the
production time during the molecular dynamics simulations. (B) One view
of the solvent accessible surface of dendrimer TA2 with a probe radius of
1.1 Å. Regions occupied by nitrogen, oxygen, carbon, and hydrogen atoms
are represented in blue, red, light blue, and white, respectively.
(36) (a) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford,
1998; pp 820-825. (b) Berry, R. S.; Rice, S. A.; Ross, J. Physical
Chemistry; Oxford University Press: New York, 2000; pp 906-910.
(37) The graphic representations of the solvent accessible surfaces were obtained
by means of the Visual Molecular Dynamics program. See: Umpherey,
W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33.
In Figure 6 we have represented the relative parameters
included in eq 17 versus the experimentally observed kinetic
parameters kobs (vide supra). We have found that there is a linear
departure from the behavior described by eq 17. Therefore, we
9
J. AM. CHEM. SOC. VOL. 126, NO. 16, 2004 5251

A R T I C L E S
Zubia et al.
(s, 6H), 3.55 (t, J ) 6.5 Hz, 6H), 2.81 (t, J ) 6.5 Hz, 6H). 13C NMR
(δ, ppm, CDCl3): 159.8, 140.8, 136.7, 128.3, 127.7, 127.3, 106.2, 101.0,
72.7, 69.7, 68.6, 54.5. Anal. Calcd for C69H69NO9: C, 78.44; H, 6.59;
N, 1.33. Found: C, 78.07; H, 6.55; N, 1.34. MS calcd for C69H69NO9:
1055.50; found (MALDI-TOF): m/z 1056.68 [M + H]+.
dendrimers will exhibit a behavior not reducible to eqs 17 or
18 and will lie in the region marked in gray in the figure.
Therefore, the models reported in this article can be used as a
general criterion to measure the relative catalytic power of
different types of dendrimers.
DA2: 50% yield. 1H NMR (δ, ppm, CDCl3): 7.40-7.20 (m, 60H),
6.67 (d, J ) 2.2 Hz, 12H), 6.59 (d, J ) 2.2 Hz, 6H), 6.57 (t, J ) 2.2
Hz, 6H), 6.52 (t, J ) 2.2 Hz, 3H), 5.05 (s, 24H), 4.90 (s, 12H), 4.37
(s, 6H), 3.50 (t, J ) 6.1 Hz, 6H), 2.76 (t, J ) 6.1 Hz, 6H). 13C NMR
(δ, ppm, CDCl3): 160.0, 159.8, 140.9, 139.2, 136.7, 128.4, 127.9, 127.5,
106.2, 101.4, 101.1, 72.9, 69.9, 69.7, 68.7, 54.7. Anal. Calcd for
Conclusions
From the results reported in this article the following
conclusions can be drawn. (i) Dendrimers with one active site
at the core and with shapes varying from linear to spheric can
exhibit catalytic power, which decreases as the generation
number and/or the degree of branching increases, provided that
the dendritic regions do not participate in the chemical
transformation under consideration. (ii) In this kind of nonco-
operative dendrimers and, at least in the case studied, the impact
of the shape of the dendrimer on the stereochemical outcome
is low to negligible. (iii) For the reaction studied in this article,
there is a linear correlation between the rate coefficient and a
combined parameter derived from the solvent accessible surface,
the molecular weight, and the reduced mass. The slope of the
linear regression thus obtained can be used to measure the
effectiveness and the cooperative effects in different types of
structurally related catalytic dendrimers.
C153H141NO21: C, 78.86; H, 6.11; N, 0.60. Found: C, 79.05; H, 6.07;
N, 0.59. MS calcd for C153H141NO21: 2329.75; found (MALDI-TOF):
m/z 2330.89 [M + H]+.
TA1: 79% yield. 1H NMR (δ, ppm, CDCl3): 7.41-7.21 (m, 45H),
6.52 (s, 6H), 5.04 (s, 12H), 4.98 (s, 6H), 4.41 (s, 6H), 3.52 (t, J ) 5.3
Hz, 6H), 2.84 (t, J ) 5.3 Hz, 6H). 13C NMR (δ, ppm, CDCl3): 152.9,
137.9, 137.1, 134.1, 128.5, 128.4, 128.1, 127.8, 127.7, 127.4, 107.1,
75.2, 73.1, 71.1, 68.8, 54.7. Anal. Calcd for C90H87NO12: C, 78.62; H,
6.39; N, 1.02. Found: C, 78.40; H, 6.42; N, 1.00. MS calcd for C90H87-
NO12: 1373.62; found (MALDI-TOF): m/z 1374.33 [M + H]+.
TA2: 27% yield. 1H NMR (δ, ppm, CDCl3): 7.32-7.07 (m, 135H),
6.74 (s, 6H), 6.70 (s, 12H), 6.63 (s, 6H), 4.89 (s, 54H), 4.80 (s, 6H),
4.74 (s, 12H), 4.38 (s, 6H), 3.56 (t, J ) 5.8 Hz, 6H), 2.86 (t, J ) 5.8
Hz, 6H). 13C NMR (δ, ppm, CDCl3): 152.9, 138.0, 137.8, 136.8, 134.4,
133.4, 132.6, 128.3, 128.2, 128.0, 127.7, 127.6, 127.4, 107.5, 106.7,
75.1, 73.0, 71.4, 71.0, 70.8, 69.0, 54.8. Anal. Calcd for C279H249NO39:
C, 79.02; H, 5.93; N, 0.33. Found: C, 78.89; H, 6.01; N, 0.34. MS
calcd for C279H249NO39: 4239.29; found (MALDI-TOF): m/z 4240.77
[M + H]+.
Experimental Section
General Method for the Preparation of Catalytic Amines. A
solution of triethanolamine (0.47 g, 3.15 mmol) in dry THF (10 mL)
under argon atmosphere was cooled with an ice/water bath. NaH (0.40
g, 10.0 mmol) was added, and the suspension was stirred for 10 min.
A solution of the corresponding bromide (10.0 mmol) in dry THF (30
mL) and dry DMF (10 mL) was slowly added, and the mixture was
stirred at room temperature. After completion of the reaction, Et2O (60
mL) was added, and the organic layer was washed with H2O (3 × 25
mL), dried over Na2SO4, and evaporated under reduced pressure. The
crude products were purified by column chromatography with ethyl
acetate as eluent, yielding the amines as syrups that were fully
characterized.
Procedure for the Kinetic Experiments. To a mixture of freshly
purified and distilled benzaldehyde38 (0.051 mL, 0.5 mmol), 2-nitro-
ethanol (0.359 mL, 5.0 mmol), and benzonitrile (0.051 mL, 0.5 mmol),
the corresponding catalyst (7.5 × 10-3 mmol) was added at 25 °C. At
certain times (see the Supporting Information for additional details),
aliquots were withdrawn with a micropipet, placed on a KBr disk, and
immediately analyzed by IR spectroscopy. The decay of the CdO st.
band (1724-1672 cm-1) of the starting aldehyde was monitored with
respect to the internal standard (benzonitrile, CtN st. band, 2266-
2200 cm-1). At the end of each experiment, the diastereomeric ratio of
the products was calculated by 1H NMR spectroscopy on crude reaction
mixtures, according to literature spectroscopic data.25
1
A0: 61% yield. H NMR (δ, ppm, CDCl3): 7.31-7.28 (m, 15H),
4.48 (s, 6H), 3.55 (t, J ) 6.0 Hz, 6H), 2.84 (t, J ) 6.0 Hz, 6H). 13C
NMR (δ, ppm, CDCl3): 138.3, 128.2, 127.5, 127.4, 73.0, 68.7, 54.5.
Anal. Calcd for C27H33NO3: C, 77.28; H, 7.94; N, 3.34. Found: C,
77.26; H, 7.91; N, 3.36. MS calcd for C27H33NO3: 419.25; found
(MALDI-TOF): m/z 420.25 [M + H]+.
Acknowledgment. We thank the Ministerio de Ciencia y
Tecnolog´ıa of Spain (Project BQU2001-0904) and the Gobierno
Vasco-Eusko Jaurlaritza (Grant 9/UPV 00170.215-13548/2001)
for financial support. A.Z. also thanks the Gobierno Vasco-
Eusko Jaurlaritza for a grant.
MA1: 75% yield. 1H NMR (δ, ppm, CDCl3): 7.41-7.28 (m, 15H),
7.21 (d, J ) 2.1 Hz, 6H), 6.90 (d, J ) 2.1 Hz, 6H), 5.05 (s, 6H), 4.45
(s, 6H), 3.55 (t, J ) 5.54 Hz, 6H), 2.85 (t, J ) 5.54 Hz, 6H). 13C NMR
(δ, ppm, CDCl3): 159.6, 137.3, 132.6, 129.2, 128.5, 127.9, 127.4, 115.1,
72.8, 70.0, 69.7, 54.6. Anal. Calcd for C48H51NO6: C, 78.11; H, 6.98;
N, 1.89. Found: C, 77.80; H, 7.02; N, 1.90. MS calcd for C48H51NO6:
737.37; found (MALDI-TOF): m/z 738.32 [M + H]+.
Supporting Information Available: Full experimental details
and characterization of bromides 2, 3, 4, 5, 6, and 7 and their
precursor alcohols and esters, kinetic measurements, ratios of
averaged principal moments of the radius of gyration tensor,
relative asphericities, and acylindricities of reference molecules
hexamethyl benzene, n-pentane, and neopentane (PDF). This
material is available free of charge via the Internet at
http://pubs.acs.org.
MA2: 53% yield. 1H NMR (δ, ppm, CDCl3): 7.42-7.18 (m, 27H),
7.02-6.87 (m, 12H), 5.06 (s, 6H), 4.95 (s, 6H), 4.42 (s, 6H), 3.57 (t,
J ) 5.6 Hz, 6H), 2.84 (t, J ) 5.6 Hz, 6H). 13C NMR (δ, ppm, CDCl3):
159.5, 137.0, 131.1, 129.2, 129.1, 128.5, 127.9, 127.4, 114.9, 114.7,
72.7, 70.0, 69.7, 54.5. Anal. Calcd for C69H69NO9: C, 78.44; H, 6.59;
N, 1.33. Found: C, 79.03; H, 6.55; N, 1.31. MS calcd for C69H69NO9:
1055.50; found (MALDI-TOF): m/z 1056.62 [M + H]+.
JA039888S
DA1: 70% yield. 1H NMR (δ, ppm, CDCl3): 7.41-7.29 (m, 30H),
6.58 (d, J ) 2.2 Hz, 6H), 6.50 (t, J ) 2.2 Hz, 3H), 4.95 (s, 12H), 4.41
(38) Armarego, W. L. F.; Perrin, D. D. Purification of Laboratory Chemicals;
Butterworth-Heinemann: Oxford, 1996; p 99.
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5252 J. AM. CHEM. SOC. VOL. 126, NO. 16, 2004