Cyclopropanation reactions catalysed by dendrimers possessing one metalloporphyrin active site at the core: Linear and sigmoidal kinetic behaviour for different dendrimer generations

Article abstract of DOI:10.1016/j.tet.2016.01.013

Experimental and computational studies on dendrimers possessing a Fe(porphyrin) catalytic core and polyether dendritic arms show that these macromolecules promote efficiently the (2+1) cycloaddition between a model alkene and diazomethane. The reaction is

Full text of DOI:10.1016/j.tet.2016.01.013

Accepted Manuscript
Cyclopropanation reactions catalysed by dendrimers possessing one
metalloporphyrin active site at the core: linear and sigmoidal kinetic behaviour for
different dendrimer generations
Petr Vinš, Abel de Cózar, Iván Rivilla, Kateřina Nováková, Ronen Zangi, Josef
Cvačka, Iosune Arrastia, Ana Arrieta, Pavel Drašar, José I. Miranda, Fernando P.
Cossío
PII:
S0040-4020(16)30013-8
10.1016/j.tet.2016.01.013
TET 27420
DOI:
Reference:
To appear in: Tetrahedron
Received Date: 28 July 2015
Revised Date: 9 December 2015
Accepted Date: 7 January 2016
Please cite this article as: Vinš P, de Cózar A, Rivilla I, Nováková K, Zangi R, Cvačka J, Arrastia I,
Arrieta A, Drašar P, Miranda JI, Cossío FP, Cyclopropanation reactions catalysed by dendrimers
possessing one metalloporphyrin active site at the core: linear and sigmoidal kinetic behaviour for
different dendrimer generations, Tetrahedron (2016), doi: 10.1016/j.tet.2016.01.013.
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ACCEPTED MANUSCRIPT
Cyclopropanation reactions catalysed by dendrimers possessing one
metalloporphyrin active site at the core: linear and sigmoidal kinetic behaviour
for different dendrimer generations
Petr Vinš,a Abel de Cózar,bcd Iván Rivilla,b Kateřina Nováková,e Ronen Zangi,bc Josef
Cvačka,e Iosune Arrastia,bd Ana Arrieta,b Pavel Drašara, José I. Miranda, f and
Fernando P. Cossío*bd
Graphical Abstract:
Abstract: Experimental and computational studies on dendrimers possessing a
Fe(porphyrin) catalytic core and polyether dendritic arms show that these
macromolecules promote efficiently the (2+1) cycloaddition between a model alkene
a University of Chemistry and Technology in Prague, Department of Chemistry of
Natural Compounds, Technická 5, 16628 Prague 6, Czech Republic
b Departamento de Química Orgánica I, and Centro de Innovación en Química
Avanzada (ORFEO-CINQA), Universidad del País Vasco / Euskal Herriko
Unibertsitatea (UPV/EHU), Pº Manuel Lardizabal 3, 20018 San Sebastián /
Donostia, Spain
c Ikerbasque, Basque Foundation for Science, 48013, Bilbao, Spain
d Donostia International Physics Center (DIPC), Pº Manuel Lardizabal, 20018, San
Sebastián / Donostia, Spain
e Institute of Organic Chemistry and Biochemistry AS CR, v.v.i., Flemingovo nám. 2,
16610 Prague 6, Czech Republic
f SGIker, NMR Facility, Universidad del País Vasco / Euskal Herriko Unibertsitatea
(UPV/EHU), Pº Manuel Lardizabal 3, 20018 San Sebastián / Donostia, Spain
* Corresponding author. Tel. +34 943 015442; fax: +34 943 015270; e-mail:
fp.cossio@ehu.es
1

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and diazomethane. The reaction is kinetically efficient and competitive with smaller
catalysts. Lower generations of dendrimers exhibit a normal hyperbolic kinetic
behaviour, whereas third- and fourth-generation dendrimers show a sigmoidal kinetic
profile, compatible with cooperative effects most likely due to aggregation
phenomena. This behaviour resembles that observed for Fe(porphyrin) containing
biomolecules such as cytochromes and haemoglobin.
Introduction
Catalytic dendrimers1 constitute an active research field, which has been intensively
studied in the past two decades. These efforts have resulted in the development of
novel catalysts possessing one metallic centre2 and well-defined macromolecular
organocatalysts.3 These macromolecular entities possess several interesting properties
in homogeneous catalysis such as easier catalyst recovery by precipitation4 or nano-
and ultrafiltration.5 Despite the fact that the separation of catalysts immobilized on
solid supports will remain easier, there are other advantages of the dendritic approach.
For example, higher overall activities of the homogenous systems, uniformity of
catalyst structure and also the possibility of higher catalyst loading in the case of
dendrimers with catalytic sites on the peripheries or branching points.
Installing a catalytic site onto a dendritic moiety either at the core or at the
periphery can result in distinct catalytic properties with respect to polymeric or small
molecule analogues. This variation has been termed as a “dendrimer effect”.6 In the
case of core-functionalized dendrimers, the growth of the structure can enhance the
catalytic performance by creation of tailored microenvironment in its centre. But also
it can reduce the efficiency of the catalyst by rendering the central function hardly
accessible for the substrate. Such activity decrease can be either successive,7 or also
abrupt, showing very similar behaviour for lower generations and swift downturn
after a trespass of certain molecule size limit 8 . Quantitative measurements of
dendrimer catalyst activity in dependence on the generation number are not very
frequent; however, there are several examples of such studies,9,10 showing different
effects coming from dendron size to catalytic performance.
In previous work, we studied dendrimers with one active site10, 11 or one
fluorophore12 at the core. We observed negative, i.e., non-cooperative dendrimer
effects with increasingly high generation numbers. Moreover, Morandi and Carreira13
have recently published a very interesting study on the cyclopropanation of alkenes.
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14
We thought that this formal (2+1) cycloaddition
involving very reactive
intermediates and relatively small substrates could be an interesting system to observe
dendrimer effects in which the steric hindrance of the dendritic catalysts could be less
relevant than in previously studied reactions.
According to the Morandi-Carreira approach, the cyclopropanation of various
styrene derivatives is performed in 6 M KOH in an open vial, with continuous
addition of a water soluble diazomethane precursor, which provides this reactive
intermediate under basic conditions, and under catalysis by Fe(III)
tetraphenylporphyrin chloride (Fe(TPP)Cl) complex. 15 The approach successfully
avoided hazardous isolation and handling of diazomethane.16
Within the context established by the precedents discussed above, in this paper
we present our results on the dendrocatalytic version of the Morandi-Carreira
reaction. In particular, we will focus our research on the catalytic behaviour of
different generations of dendritic porphyrin-based17 catalysts in order to assess the
possibility of finding emergent properties for higher generations of these
macromolecules.
Results and discussion
Synthesis of catalytic dendrimers. The general procedure followed for the synthesis
of the catalysts is shown in Scheme 1 and was based on convergent strategy18 for the
synthesis of dendrimers. Thus, Fréchet-type disubstituted benzyloxy dendrons were
prepared first up to the fourth generation. These dendritic wedges were obtained in
the form of bromides (Br-Dn, n=1-4, see Scheme 1) following the original
procedure.19
Subsequent conjugation of bromides Br-Dn with 5,10,15,20-tetrakis(4-hy-
droxyphenyl)porphyrin (TPP-(OH)4, 1) was carried out under conventional
Williamson etherification conditions using K2CO3 as base and DMF as solvent, to
yield dendrimeric porphyrins 2c-f (generations G1-G4, see Scheme 1). Lower-weight
analogous porphyrins tetrakis(4-methoxyphenyl)porphyrin 2a and tetrakis(4-
benzyloxyphenyl)porphyrin 2b (0th generation dendrimer G0) were prepared for the
shake of completeness and continuity using methyl iodide and benzyl bromide as
Williamson electrophiles, respectively. Metallated porphyrins 3a-f including
dendrimer generations G’0-G’4 were obtained by addition of ferrous chloride to
porphyrins 2a-f in refluxing solution of THF. Under these reaction conditions, Fe(II)
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intermediates were exposed to air and therefore the corresponding Fe(III)Cl-porphyrin
derivatives20 were obtained as stable compounds. Metallated porphyrins 3a-f were
characterized by HRMS (compounds 3a-c) or by MALDI-TOF-MS (dendrimers 3d-f)
as well as by UV-Visible spectroscopy. Non-metallated precursors 2a-f were analysed
1
by H-NMR and 13C-NMR spectroscopy (see the Experimental Section and the
Supplementary data for further details).
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HO
OH
RO
OR
RO
OR
N
H
N
Fe
N
N
H
Cl
a
b
N
N
N
N
N
N
H
N
H
N
OH
OR
HO
OR
RO
RO
3a: R=Me
3b: R=Bn (G'0)
1
2a: R=Me
2b: R=Bn (G0)
c
O
RO
OR
RO
OR
1
D1
O
N
N
H
Cl
b
N
N
N
Fe
N
N
H
N
O
O
2
O
O
OR
OR
RO
RO
2c: R=D1 (G1)
2d: R=D2 (G2)
2e: R=D3 (G3)
2f: R=D4 (G4)
3c: R=D1 (G'1)
3d: R=D2 (G'2)
3e: R=D3 (G'3)
3f: R=D4 (G'4)
1
D2
O
O
O
O
4
O
O
O
O
3
3
O
O
O
O
O
O
O
2
O
O
2
O
O
O
O
O
O
O
O
1
1
D3
D4
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
Scheme 1. Synthesis of dendrimeric catalysts 3a-f. Reagents and conditions: a)
K2CO3, DMF, MeI (for 2a) or BnBr (for 2b); b) FeCl2, THF, O2 (air); c) K2CO3,
DMF, Br-Dn (n=1-4).
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Catalytic properties. Once we had prepared compounds 3a-f, we studied their
behaviour as catalysts in the cyclopropanation of substituted styrene 4 (1-chloro-4-
(prop-1-en-2-yl)benzene) with diazomethane in deuterated chloroform. Following the
Morandi-Carreira procedure,13 diazomethane was generated in situ from 3-(N-methyl-
N-nitrososulfamoyl)benzoate 6 (Scheme 2). The reaction mixtures were analysed by
1H-NMR using 1,2,3-trimethoxybenzene (TMB) as internal standard for the
integration of the appropriate diagnostic signals corresponding to the internal
standard, the reactant 4 and the (2+1) cycloadduct 1-(4-chlorophenyl)-1-
methylcyclopropane 5 (Figure 1).
Scheme 2. Cyclopropanation of styrene 4 (1-chloro-4-(prop-1-en-2-yl)benzene) with
sodium 3-(N-methyl-N-nitrososulfamoyl)benzoate 6 catalysed by metalloporphyrins
3a-f. TMB: 1,2,3-trimethoxybenzene.
Figure 1. Example of 1H-NMR spectrum recorded for the reaction between styrene 4
and in situ generated diazomethane to yield cyclopropane derivative 5 in the presence
of catalyst 3b (G’0, 2 mol %) at room temperature and after a reaction time of 40 min.
TMB: 1,2,3-trimethoxybenzene.
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According to the mechanism accepted for this kind of reactions, precursor 6
generates one equivalent of diazomethane in a solution of KOH in water (Scheme 3)
with the concomitant formation of highly polar salt 7, which remains in the aqueous
phase. In situ formed diazomethane passes to the organic phase and reacts with the
catalytic metalloporphyrin 3’ to yield the corresponding carbene-Fe complex. It has
been proposed that reactive and unstable Fe(II) species are the actual active catalysts.
21
Indeed, it has been suggested21a,c that the diazomethane reactant can reduce the
Fe(III)Cl complex 3 to the corresponding Fe(II) derivative 3’. In addition, the Fe-
carbene intermediate can exist in at least two different spin states as a bridged
complex.22 denoted as A in Scheme 3, which is in equilibrium with the corresponding
axial isomer B. This latter intermediate interacts with the alkene to yield the (2+1)
cycloadduct 5, with the concomitant release of porphyrin 3’, thus completing the
catalytic cycle.
Scheme 3. Catalytic cycle for the cyclopropanation of alkene 4 to yield cyclopropane
5 in the presence of diazomethane precursor 6 and metalloporphyrins 3.
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The reaction was performed in a biphasic system (water/CDCl3).13 Using this
approach, hydrophobic catalyst and substrate were dissolved in a small quantity of
chloroform, which was vigorously stirred together with an aqueous solution of KOH.
The reaction vessel was a flask that permitted a flow-off of excessive gas phase
during the addition process through injected needle. Compound 6 was slowly added
into the reaction system by means of an automatic syringe, providing diazomethane
under basic conditions. In situ generated diazomethane participated in the
cyclopropanation reaction after its phase transfer into the droplets of chloroform. In
the organic phase it was consumed by the metalloporphyrin catalyst 3 to form the
corresponding metal-carbene intermediate, which reacted with the styrene substrate 4.
Due to the slow addition of 6, diazomethane was present in the reaction system in
substoichiometric quantity. On the contrary, the substrate in the organic phase was in
local excess.
Since Morandi and Carreira13 used a 2 mol % of Fe(TTP)Cl catalyst in the
original work, we started our study on dendrimeric analogues by testing the 4
®5
reaction with loadings of 1-10 mol % of Fe(TPP)Cl at an addition rate of 1 eq. of
Fe(TTP)Cl per hour (Figure 2). Experiments with 1, 2, and 4 mol % barely differed,
while the experiment with 10 mol % showed lower performance (Figure 2). This
indicates that catalyst loads of 1-2 mol % were able to process the incoming
diazomethane at very similar rate. Since precursor 6 and diazomethane were in a low
ratio with respect to the substrate, higher catalyst loadings did not accelerate the
reaction. However, consumption of substrate 4 took place at a rate lower than that
associated with the instantaneous conversion of 6 into diazomethane and subsequent
cyclopropanation of alkene 4 to form cyclopropane derivative 5.
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Figure 2. Cyclopropanation of alkene 4 in CDCl3 in the presence of Fe(TPP)Cl with
different catalytic loads. Addition of diazomethane precursor 6 into KOH/H2O
solution was carried out at a rate of 1 eq./h. The dashed line corresponds to the
theoretical maximum reaction rate associated with conversion of 4 into cyclopropane
derivative 5, assuming instantaneous transformation of 4 into diazomethane and
subsequent (2+1) cycloaddition on 4.
The slow addition of diazomethane precursor 6 may raise questions about the
promptness of decomposition of 6 or eventual accumulation of generated
diazomethane in the reaction mixture. For this reason, we carried out an experiment to
explore what the consequence of sudden cease of addition of 6 would be. Thus, we
started the addition rate in the presence of substrate 4 and catalyst 3a (2 mol %), with
an addition rate of 1 eq. of 6 per hour. After 60 min. of reaction time, we stopped this
addition (Figure 3). We observed that this interruption induces complete abortion of
the reaction progress. This indicates that neither diazomethane nor its precursor 6 was
accumulated in the reaction system, despite the less-than-optimal progress of the
reaction (vide supra).
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Figure 3. Cyclopropanation of alkene 4 in CDCl3 in the presence of catalyst 3a (2 %
mol), with addition of diazomethane precursor 6 in KOH/H2O at a rate of 1eq./h. The
arrow indicates interruption of addition of 6. The meaning of the dashed line is that
indicated in Figure 2 caption.
Considering the results of the latter experiment (Figure 3), which show that
only ca 0.5 equivalents of generated diazomethane were being consumed in the
formation of cyclopropane derivative, it can be assumed that at least some part of the
remaining 0.5 equivalents was constantly leaking away together with generated
nitrogen. This escaping diazomethane was possibly passing directly to the gas phase
instead of participating in the cyclopropanation in chloroform.
Experiments testing the performance of metalloporphyrin dendrimers 3b-f
(G’0-G’4) on the cyclopropanation reaction of alkene 4 using 2 mol % of catalyst
were carried out under same conditions as described previously. Surprisingly, our
results showed that the reaction progress was almost unvaried when Fe(TPP)Cl was
replaced by simple metalloporphyrins 3a and 3b (G’0) and also by analogous
dendrimers up to the second generation (3c, 3d). However, the reaction rate decreased
considerably with the transition to third- (3e) and fourth- (3f) generation dendrimeric
catalysts (Figure 4). The kinetic plots of catalysts 3e and 3f showed sigmoidal
character, with a relative latency at the beginning of the reaction, during which the
progress of the reaction was very slow. This period corresponded to 40 minutes for
third-generation dendrimer 3e and to 2 hours for fourth-generation dendrimer 3f.
Surprisingly, after these induction times the reaction progresses accelerated to rates
similar to those found for lower-generation catalysts (Figure 4). In order to ensure that
the catalytic activity of these dendrimers rely on the presence of the iron atom,
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additional blank test with non metallated dendrimers 2b-f were carried out. As
expected, no product formation was observed after 180 min under the described
reaction conditions.
Figure 4. Kinetic profiles corresponding to the conversion of alkene 4 into
cyclopropane derivative 5 in the presence of catalysts Fe(TPP)Cl, 3a, and 3b-f (G’0-
G’4). The reaction conditions are those reported in Figure 2 caption.
These results are compatible with a zero-order kinetic behaviour for substrate
4 under the slow injection conditions when small size catalysts are used. Thus, for
first and second generation dendrimers 3c and 3d the kinetic profiles fit to zero-order
kinetics for conversions up to 90 % (the r2 value was 0.998 in both cases, see Figure
5) according to the following equation:
100- [4] = kobst
(1)
The values obtained for kobs are 0.93 min-1 for 3c (G’1) and 0.98 min-1 for 3d (G’2),
thus confirming the very similar catalytic ability of small dendrimers.
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In the case of third and fourth generation dendrimers 3e and 3f the respective
kinetic profiles were satisfactorily fitted23 to a standard sigmoidal function of type
- x
in the following form:
S( x )=1/ (1+e )
100
100- [4] =
(2)
é
ù
1+exp - a t - t
(
)
ë
û
The values obtained for the adjustable exponential parameter  decay on going from
third to fourth generation catalysts. Thus, for third generation dendrimer 3e it was
found that 0.051 min-1 and for its fourth generation congener 3f the corresponding
value is 0.038 min-1. The optimized induction time parameters  were found to be
quite different since for 3e 87 min and in the case of 3f 172 min. As a
consequence, when catalyst 3e is considered an almost linear zero order behaviour is
reached for conversions between 20 % (t=60 min) and 80 % (t=120 min), with an
apparent slope of 1.00 min-1, a value very close to those found for 3c and 3d. In the
case of fourth generation catalyst 3f, the much larger induction time and the lower
exponential factor result in a significantly lower catalytic ability.
Figure 5. Conversion profiles for catalytic dendrimers 3c-f. Points correspond to
experimental data and lines were obtained by means of eqs. (1) (3c,d) and (2) (3e,f).
In general, sigmoidal behaviour of kinetic plots can be due to two possible
phenomena: autocatalysis 24 and cooperative effects. 25 In the former case, the
sigmoidal kinetic profile stems from the acceleration26 or inhibition27 generated by the
reaction product or by one reactant.28 In our case, lower catalysts do not show this
12

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sigmoidal profile and the reaction product, namely cyclopropane derivative 5 is inert
as far as the rate of the (2+1) process is concerned. Therefore, we reasoned that
cooperative effects involving dendrimers 3d,f are most likely due to aggregation
processes. It is noteworthy that aggregation29 and self-assembling30 phenomena have
been observed in dendrimers containing related cores such as phthalocyanines31 ,
BINOL-Zn complexes,32 and polyether dendrons.12,33 In addition, it has been reported
that the tendency to aggregation increases with the generation number of the
dendrimer.34
We investigated the structural properties of metal-free dendrimers 2c-f using
molecular mechanics simulations35 (see the Experimental Section) in order to get a
better understanding of the experimentally observed catalytic effects. We optimized
the starting geometries and sampled the different conformations by Molecular
Dynamics (MD) simulations. Figure 6 shows the shape of the most stable
conformations at 298 K (within 4 kJ/mol) of dendrimers 2c (G1) and 2d (G2) in
chloroform solution. The geometries thus obtained show that small reactants such as
diazomethane and alkene 5 can reach the active site at the core of these dendrimers.
This is due to one important feature of these dendrimers, namely the relatively long
distance of ca. 16 Å between two collinear branching points at the periphery of the
5,10,15,20-tetraphenylporphyrin core.
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Figure 6. Axial (A and C) and side (B and D) views of the most stable conformations
(within 4 kJ/mol) of dendrimers 2c (G1, A and B) and 2d (G2, C and D) in chloroform
solution. In all cases, porphyrin cores are highlighted in blue.
In order to quantify the shape of dendrimers 2c-f (G1-G4), we took the sphere
and the cylinder as two extreme models. To do this, we first computed the radius of
gyration36 of each dendrimer of mass M and n-atoms of mass mi as
1/2
n
é
ù
1
R =
m r - g r - g
)(
ê
(
)
ú
M å
g
i
i
i
ë
û
i=1
(3)
where the position vector of the center of masses is given by
n
1
g =
m r
i i
M å
i=1
(4)
The square of Rg can be expressed as the trace of the gyration tensor S in the form
æ
ç
ç
ç
ç
è
ö
÷
÷
÷
÷
ø
2
1
L
0
0
0
2
g
2
R = tr S = tr
0
L2
( )
2
0
0
L3
(5)
2
1
2
2
where the three components of the diagonalized tensor S are assigned as
.
L > L2 > L3
With these data, the asphericity37 as of the dendrimer being considered is defined as
1
2
1
2
2
2
3
as = L - L + L
(
)
2
(6)
2 holds and hence a =0. Therefore, a quantifies the
2
1
2
For a perfect sphere,
L = L2 = L3
s
s
departure of the dendrimer from a perfect sphere. Similarly, acyclindricity34 ac can be
defined as
2
2
ac = L2 - L3
(7)
2
Again, for a perfect cylinder ac=0 since
2. Low values of a permit to identify a
L2 = L3
c
shape close to that expected for a cylindric molecular structure. The average values of
Rg, as and ac obtained along the MD simulations for 2c-f are reported in Table 1.
Asphericity and the evolution of the two latter magnitudes is gathered in Figure 7.
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Table 1. Average valuesa of radii of gyration (
, in Å), components of the
Rg
, in Å2) and acylindricities
as
L
diagonalised tensor S (
, in Å), asphericities (
i
, in Å2) of dendrimers 2c-f (G1-G4).
ac
(
2c-f
Rg
L
L2
L3
as
ac
1
9.9 ± 1.1
70.1 ± 1.7
22.7 ± 8.4 7.1 ±1.7
55.1 ± 4.1
15.8 ± 2.4
21.9 ± 5.8
16.4 ± 6.2
G1
G2
G3
G4
10.9 ± 0.6 77.0 ± 8.1
12.7 ± 0.4 77.9 ± 6.5
32.8 ± 6.8 10.9 ±1.8 54.2 ± 5.5
50.2 ± 5.4 33.7 ± 2.0 35.9 ± 4.9
17.0 ± 3.6 197.1 ± 3.7 55.9 ± 2.2 36.3 ±1.5 150.9 ± 4.0 19.5 ±3.3
aAverage values obtained from MD simulations after 1ns of production time (See
Figure 7).
Figure 7. Asphericities and acylindricities of dendrimers 2c-f along the MD
simulations.
Our results indicate that, in effect, the acylindricities for the different
generations of dendrimers are quite similar, in agreement with the C4 symmetry axis
imposed by the porphyrin moiety. In addition, the asphericities of dendrimers 2c-e
(G1-G3) are quite similar and low. These results are compatible with the similar
behaviour observed for 3c-e with respect to 3b (G’0), 3a and Fe(TPP)Cl. However,
the similarities in acylindricity do not provide any clear explanation for the sigmoidal
kinetic behaviour of 3e,f (G’3, G’4). Since we hypothesized that cooperative effects
leading to the formation of aggregates should cause this behaviour, we analysed the
aggregation ability of dendrimers 2c (G1) and 2f (G4) by MD simulations in
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chloroform. At least three interaction models between cylinder-like dendrimers can be
envisaged, as it is shown in Figure 8. In the side and axial approaches, both
dendrimers interact along parallel or collinear orientations of the two porphyrin
systems, as shown in Figure 8, whereas in the case of the perpendicular approach both
porphyrin moieties interact along a T-shaped pattern. We tested the three interaction
models for G1 and G4. The results are gathered in Figure 9.
Figure 8. Possible side (A), axial (B) and perpendicular (C) approaches for two units
of cylinder-like dendrimers 2e,f (G3-G4). Rsd, Rax and Rpp denote the minimal
distances between the two porphyrin rings.
Our MD simulations show that, after 50 ps of production time, the interacting
units of 2c (G1) show a very low number of contacts between the two dendrimers
even in the case of the axial pattern (Figure 9). Actually, none of the three interaction
patterns of G1 resulted to be dynamically stable, a result compatible with the presence
of monomeric catalytic dendrimers 3c and hence a normal kinetic behaviour in the
cyclopropanation reaction. In contrast, fourth generation dendrimer 2f showed a much
slower motion after 50 ps of MD simulation, with dimeric structures of similar
energies. Among them, axial and perpendicular interactions were persistent, the
former offering more contact surface and shorter distances between the porphyrin
moieties (Figure 9). These results are compatible with persistent dimeric or, in
general, oligomeric, structures of 2f (G4) and therefore for their Fe-containing
catalysts 3f (G’4).
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Figure 9. Side (A), axial (B), and perpendicular (C) interaction models for
dendrimers 2c (G1) and 2f (G4), after 50 ps of MD simulations in chloroform.
Minimal porphyrin-porphyrin distances (See Figure 7) are given in Å. Solvent
accessible surfaces (SAS) are shown for the different dendritic units, with a probe
radius of 1.4 Å.
We confirmed the distinct aggregation patterns of 2c and 2f by performing
further MD simulations under periodic boundary conditions (PBC) and with explicit
treatment of the solvent. Thus, in the case of 2c 3,139 molecules of chloroform were
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included, whereas MD-PBC simulations with 2f were carried out with a box of
similar size including 1,699 molecules of chloroform. The resulting ensembles were
stabilized at 298 K and the respective calculations were run at constant temperature
and volume for 2 ns.
Figure 10. MD-PBC simulations with axial dimeric structures of first and fourth
generation dendrimers 2c (A,B) and 2f (C,D) in chloroform at 298 K. The solvent
accessible surfaces (probe radius: 1.4 Å) for dimers of 2c (A) and 2f (C) are indicated.
Snapshots gathered in (A) and (C) correspond to the production times indicated in (B)
and (D), respectively. The energies and the Rax values along production times for
axial dimers corresponding to 2c (B) and 2f (D) are also shown.
Our results indicate that the axial dimer of 2c is not stable: after 612 ps both
monomeric structures move independently as in can be observed in Figure 10A,B to
reach an average Rax distance of ca. 32 Å. This result confirms that the catalytic
behaviour of 3c (and those associated with low size analogues) can be understood in
18

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terms of monomeric intermediates along the catalytic cycle. In contrast, axial dimer of
2f was stable along the production time, with an average Rax value of ca. 27 Å that
permits multiple van der Waals contacts between both dendrimeric units. Therefore,
explicit treatment of the solvent compresses the dimeric structures and shows that
these aggregates are not fleeting species. By extension, we concluded that fourth
generation dendrimers could exist as dimers and higher order aggregates combining
the three kinds of approaches shown in Figures 8 and 9. On the basis of its similar
sigmoidal behaviour, third generation dendrimers will exhibit a similar tendency to
form aggregates.
To verify experimentally the different behaviour of metal free non-
paramagnetic dendrimers 2c and 2f, we carried out different Diffusion-Ordered NMR
Spectroscopy38 (DOSY) experiments with these compounds at several concentrations
1
in CDCl3. We performed H-DOSY experiments because of the high sensitivity of
this technique, which permitted measurements at relatively low concentrations,
especially in the case of fourth generation dendrimer 2f. Figure 11 shows the 2D
spectra for both compounds, in which we have represented in the x-axis the part of the
1H spectra corresponding to the benzylic signals associated with the Ar-CH2-O
moieties of both dendrimers. We observed that the relative diffusion rates for these
signals were similar and easier to monitor at low concentrations (see the y-axes of
Figure 11). The respective diffusion coefficients are gathered in Table 2.
Table 2. Diffusion parameters of dendrimers 2c,f (G1,G4).
Conc. (mg/mL)
D (m2/s)a
rH (Å)b
Dendrimer
2c (G1)
2c (G1)
2f (G4)
11
54
7
5.44 x 10-10
5.44 x 10-10
4.76 x 10-10
3.34 x 10-10
11.1
11.1
12.7
36
40
18.1
2f (G4)
2.51 x 10-10
24.1
2f (G4)
1
b
aDiffusion parameters D obtained by 2D H-DOSY experiments. Diffusion radii
estimated by means of the Stokes-Einstein equation with C=4.
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1
Figure 11. 2D H-NMR data for dendrimers 2b (A) and 2f (B) in CDCl3 at different
concentrations. The inset in (A) corresponds to signals for 2b at 11 mg/mL.
In the case of 2c (G1), we measured similar diffusion coefficients at relatively
high concentrations of 11 mg/mL and 54 mg/mL. These values correspond to
identical diffusion radii rH estimated by means of the Stokes-Einstein39 theory:
kBT
(8)
D =
CphrH
According to eq. (8) the diffusion coefficient D varies inversely with the size of a
hypotethical sphere of radius rH. kB is the Boltzmann’s constant,  is the viscosity of
the surrounding fluid (in our case chloroform, for which =5.42 x 10-4 Pa/s at 298 K)
and C is a constant that depends on the boundary conditions at the particle-solvent
interface, and varies from C=6 to C=4 for spherical particles. From our NMR data we
obtained for 2c (G1) the rH value reported in Table 2 for C=4, which corresponds to
approximate spheres associated with monomeric species moving under slip boundary
20

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conditions.40 This result is in line with the radius of gyration of ca. 10 Å computed for
1
monomeric 2c (see Table 1). Therefore, on the basis of the H-DOSY data, we
concluded that, in agreement with our kinetic and MD data, first generation dendrimer
2b (G1) does not aggregate significantly, at least up to the highest concentration
studied.
The situation changed when the behaviour of dendrimer 2f (G4) was analysed
at different concentrations (Table 2). In this case, we obtained different D values at
different concentrations. Interestingly, the diffusion coefficients D obtained from the
1H-DOSY experiments decreased, as the samples were more concentrated. At our
lowest concentration of 7 mg/mL the rH value was also the lowest one, slightly
smaller than -but comparable to- the average radius of gyration of ca. 17 Å. At our
highest concentration of 40 mg/mL (we could not obtain accurate NMR spectra at
higher concentrations because of solubility issues), the rH value is of the same
magnitude that (but slightly higher than) our computed radius for the dimer of 2f (G4),
which was calculated to be of ca. 21 Å. On the basis of these results, we concluded
that at the concentrations studied, higher generation dendrimer 2f (G4) forms dimers
and, most likely, higher aggregates.
From our MD computational data and our DOSY NMR results, we interpret
our kinetic experimental results in terms of the tendency of third and fourth
generation dendrimers to form aggregates that result in a cooperative effect. First,
higher generation dendrimeric aggregates capture the incoming diazomethane. The
resulting intermediate carbene complexes can be buried inside the oligomeric
structures and only after saturation of the aggregates the (2+1) cycloaddition reaction
starts to proceed efficiently. In addition, generation of more accessible Fe-carbene
complexes on the surface of the aggregates and/or perturbation of the A-B equilibria
(Scheme 3) and the corresponding preferred spin states cannot be ruled out. The final
outcome is that these Fe-porphyrin aggregates show cooperative effects and sigmoidal
kinetic plots similar to those observed in protein analogues such as cytochromes41 and
haemoglobin.42
Conclusions
In this work we report the preparation and assessment of the catalytic properties of
different generations of dendrimers based on Fe(porphyrin) catalytic cores. These
formally D4h-symmetric dendrimers incorporate polyether Fréchet dendritic arms
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around the 5,10,15,20-tetrakis(4-hydroxyphenyl)porphyrin moiety. The reaction
studied is the (2+1) cyclopropanation of a model alkene in the presence of
diazomethane, safely and efficiently generated using the method reported by Morandi
and Carreira. In contrast with the kinetic behaviour observed for other dendrimers
with only one catalytic centre at the core, the reaction proceeds with rates comparable
to those observed for the Fe(TPP)Cl catalyst. Thus, dendrimers from zeroth to second
generation exhibit a normal linear pseudo zero order behaviour, with similar reaction
rates. Structural parameters computed for these dendrimers are compatible with this
result. In contrast, third and fourth generation dendrimers show sigmoidal kinetic
plots, with increasing induction times on going from the third to the fourth generation.
Beyond that point, the cyclopropanation reactions proceed and in the case of third
generation catalyst the observed rate was comparable to those observed for lower
generation catalysts. This distinct behaviour has been attributed to cooperative effects,
generated via aggregation of dendritic units, a process that is only kinetically relevant
for higher generations of dendrimers possessing large surfaces available for axial, side
or perpendicular dendrimer-dendrimer contacts. This interpretation is compatible with
molecular dynamics simulations. Finally, our results suggest that these
macromolecules are efficient catalysts for the cyclopropanation of other alkenes under
safe conditions, thus exploiting the advantages of dendrimers as catalysts.
Experimental section
General experimental methods: Reagents and solvents were purchased from
commercial suppliers and used without further purification. Reagents used were of
ACS reagent grade. Flash chromatography separations were carried out using silica
gel 60 (0.040 – 0.063 mm) if not stated otherwise. NMR spectra were recorded at
Varian Gemini 300 HC spectrometer or at Bruker Avance 500 spectrometer. HRMS
(ESI+) spectra were recorded using LTQ Orbitrap Velos (Thermo Scientific)
instrument. UV-Vis spectra were recorded at Tecan Infinite 200 Pro
spectrophotometer in range of 250-700 nm. Analytical TLC was performed on Merck
TLC Silica gel 60 F254 plates using visualization by UV light at 254 nm and 365 nm.
MS MALDI-TOF spectra were recorded on UltrafleXtreme MALDI-TOF/TOF mass
spectrometer (Bruker Daltonics, Germany), using a 0.3 M solution of indoleacrylic
acid in THF as matrix.
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Water-soluble diazomethane precursor 6 was prepared following the
procedure reported by Morandi and Carreira13. 3-(N-Methyl-N-nitrososulfam-
oyl)benzoic acid (90 mg, 0.33 mmol, 90% purity) was suspended in water (2.7 ml)
and NaHCO3 (35 mg, 0.42 mmol) was added portionwise under stirring. The mixture
was stirred for 1 hour, filtered and the resulting solution of 6 was used immediately in
kinetic experiment. Precursor 3-(N-methyl-N-nitrososulfamoyl)benzoic acid was
purified by dissolution in a minimum quantity of dichloromethane, filtration and
precipitation by pentane from the filtrate. The precipitate was dried under high
vacuum. Its 1H NMR analysis in methanol permitted to verify the ratio of nitrosation,
comparing integrals of methyl group signals of this compound and its precursor 3-(N-
methylsulfamoyl)benzoic acid. Using this method, 90% pure 3-(N-methyl-N-
nitrososulfamoyl)benzoic acid was prepared, with remaining 10% of 3-(N-
methylsulfamoyl)benzoic acid as impurity. Purified 3-(N-methyl-N-nitroso-
sulfamoyl)benzoic acid was stored in a freezer under argon and was used in next few
days in order to ensure unvaried purity of 6 in catalytic experiments. Otherwise, it
was observed that 3-(N-methyl-N-nitrososulfamoyl)benzoic acid slowly decomposes
by denitrosation back to 3-(N-methylsulfamoyl)benzoic acid if let at room
temperature.
Procedures for the synthesis of metalloporphyrin catalysts: Polyaromatic Fréchet
dendrons, of generation number one to four, Br-D1-4, were prepared following the
reported procedure. Their spectral properties were in accordance with those reported
in the literature.19 5,10,15,20-Tetraphenylporphyrin iron(III) chloride (Fe(TPP)Cl)
was prepared from commercial tetraphenylporphyrin as described previously.15
5,10,15,20-tetrakis(4-methoxyphenyl)porphyrin (2a): Commercial 5,10,15,20-
tetrakis(4-hydroxyphenyl)porphyrin 1 (100 mg, 0.147 mmol) was dissolved in DMF
(3 ml). To this solution K2CO3 (200 mg, 1.45 mmol), 18-crown-6 (5 mg, 0.019 mmol)
and iodomethane (1.14 g, 8.02 mmol, 0.5 ml) were added. Reaction mixture was
protected from light and stirred for 20 hours at 70 °C under argon. Then, the solvent
was removed under reduced pressure. The resulting mixture was dissolved in CH2Cl2,
filtered and deposed on a column of alumina (neutral, Brockman II). During the
column separation 4 % of THF in CH2Cl2 was used as mobile phase. After the
precipitation by hexane from CH2Cl2, the title product was obtained as purple solid in
45 % yield (64 mg, 0.066 mmol). Spectral properties of this compound were in
23

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accordance with those reported in the literature43, in which another procedure for the
preparation of title compound is reported.
5,10,15,20-tetrakis(4-benzyloxyphenyl)porphyrin (2b): 5,10,15,20-tetrakis(4-
hydroxyphenyl)porphyrin 1 (100 mg, 0.147 mmol) was dissolved in DMF (3 ml). To
the solution K2CO3 (200 mg, 1.45 mmol), 18-crown-6 (5 mg, 0.019 mmol) and benzyl
bromide (0.72 g, 4.21 mmol) were added. Reaction mixture was protected from light
and stirred for 20 hours at 70 °C under argon. Then, the solvent was removed under
reduced pressure. The resulting mixture was dissolved in CH2Cl2, filtered, deposed on
a column of alumina (neutral, Brockman II) and purified by column separation using
4 % (v/v) of Et2O in CH2Cl2 as mobile phase. After evaporation and precipitation with
an appropriate hexane/CH2Cl2 mixture, the title product was obtained as a purple solid
in 40 % yield (58 mg, 0.056 mmol). Spectral properties of this compound were in
accordance with those reported in the literature,44 in which another procedure for the
preparation of title compound is reported.
Porphyrin dendrimers 2c-e: these compounds were prepared from 5,10,15,20-
tetrakis(4-hydroxyphenyl)porphyrin 1 and bromides Br-D1-3 following the method
reported by Matos, Fréchet et al. and their spectral properties were in accordance with
the literature.45
Porphyrin dendrimer 2f: 5,10,15,20-Tetrakis(4-hydroxyphenyl)porphyrin 1 (6.7
mg, 0.010 mmol) was dissolved in mixture of DMF (1 ml) and toluene (1 ml). To this
solution K2CO3 (30 mg, 0.217 mmol), 18-crown-6 (5 mg, 0.019 mmol) and Br-D4
(200 mg, 0.060 mmol) were added. The resulting reaction mixture was protected from
light and stirred for 20 hours at 70 °C under argon. Then, it was diluted by CH2Cl2
and extracted twice with brine. The organic phase was dried by MgSO4, filtered and
evaporated under reduced pressure. The residue was purified by flash chromatography
on silica gel (toluene/CH2Cl2) and by precipitation with an appropriate mixture of
hexanes/CH2Cl2 to afford the title product as purple glass in 36 % yield (50 mg,
0.0036 mmol). 1H NMR (500 MHz, CDCl3): δ = -2.75 (s, 2H, NH), 4.82-4.93 (m, 224
H, CH2O), 4.97 (s, 16 H, CH2O), 5.13 (s, 8 H, CH2O), 6.41-6.71 (m, 172 H, Ar-H),
6.83 (br s, 8 H, Ar-H), 7.17-7.39 (m, 328 H, phenyl H, phenylene H-3,5), 8.04 (d, 8
H, phenylene H-2,6, J = 7,6 Hz), 8.82 (s, 8 H, porphyrin H). 13C NMR (126 MHz,
CDCl3): δ = 69.85, 69.95, 70.03 (CH2O), 101.48, 106.29, 106.32, 106.38, 127.47,
127.49, 127.53, 127.91, 127.97, 128.47, 128.49, 128.55, 136.68, 139.15, 159.98,
24

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160.05 (Ar, porphyrin, phenylene). UV-Vis (THF) λmax: 425 nm, 518 nm, 557nm, 598
nm, 650 nm. MS (MALDI-TOF) m/z calculated 13774.9 [M+H]+, found 13774.3.
General procedure for the synthesis of metalloporphyrins and dendrimers 3: The
corresponding free-base porphyrin 2 and FeCl2 were dissolved in dry THF and the
reaction mixture thus obtained was refluxed under argon and under protection from
light for 20 hours. After cooling of the solution to room temperature, the mixture was
exposed to open air under further stirring for 20 minutes. The solvent was evaporated
and the obtained residue was purified by flash chromatography on silica gel, using
CH2Cl2/MeOH as mobile phase, in order to remove unreacted FeCl2. Observation of
decay of Soret peak in measured UV-Vis spectra permitted to monitor completion of
iron insertion.20a
Metalloporphyrin 3a: The title compound was prepared as an orange-brown solid in
90 % yield (92 mg, 0.815 mmol) from FeCl2 (130 mg, 1.03 mmol), free-base
porphyrin 2a (100 mg, 0.096 mmol) and THF (30 ml). UV-Vis (THF) λmax: 414, 578,
620. HRMS (ESI+): m/z calculated 788.20805 [M+H]+, found 788.20752. Preparation
of this compound was reported previously46 but spectral properties are unavailable in
the literature.
Metalloporphyrin 3b (G0): The title compound was prepared as an orange-brown
solid in 85 % yield (160 mg, 0.0.085 mmol) from FeCl2 (120 mg, 0.947 mmol), free-
base porphyrin 2b (40 mg, 0.054 mmol) and THF (12 ml). UV-Vis (THF) λmax: 412,
578, 620. HRMS (ESI+): m/z calculated 1092.33325 [M+H]+, found 1092.33331.
Preparation of this compound was reported previously42 but spectral properties are
unavailable in the literature.
Metalloporphyrin 3c (G1): The title compound was prepared as an orange-brown
solid in 76 % yield (128 mg, 0.0647 mmol) from FeCl2 (110 mg, 0.868 mmol), free-
base porphyrin dendrimer 2c (160 mg, 0.0.085 mmol) and THF (25 ml). UV-Vis
(THF) λmax: 412, 576, 616. HRMS (ESI+): m/z calculated 1941.67152 [M+H]+, found
1941.67040.
Metalloporphyrin 3d (G2): The title compound was prepared as an orange-brown
solid in 90 % yield (125 mg, 0.0340 mmol) from FeCl2 (100 mg, 0.785 mmol), free-
base porphyrin dendrimer 2d (135 mg, 0.0375. mmol) and THF (21 ml). UV-Vis
(THF) λmax: 423, 582, 616. MS (MALDI-TOF): m/z calculated 3639.9 [M]+, found
3640.2, loss of C7H6 (calc. m/z 3549.9, found 3549.8).
25

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Metalloporphyrin 3e (G3): The title compound was prepared as an orange-brown
solid in 96 % yield (35 mg, 0.0025 mmol) from FeCl2 (100 mg, 0.785 mmol), free-
base porphyrin dendrimer 2e (115 mg, 0.0165 mmol) and THF (25 ml). UV-Vis
(THF) λmax: 422, 506 (very weak), 576 (very weak). MS (MALDI-TOF): m/z
calculated 7035.9 [M]+, found 7035.4; loss of C7H6 (calc. m/z 6945.8, found 6945.9).
Metalloporphyrin 3f (G4): The title compound was prepared as an orange-brown
solid in 75 % yield (112 mg, 0.0158 mmol) from FeCl2 (25 mg, 0.197 mmol), free-
base porphyrin dendrimer 2e (45 mg, 0.0033 mmol) and THF (5 ml). UV-Vis (THF)
λmax: 424, 508 (very weak), 582 (very weak). MS (MALDI-TOF): m/z calculated
13827.7 [M]+ , found 13853.1.
General procedure for the kinetic experiments with catalysts 3a-d: A solution of
1-chloro-4-(prop-1-en-2-yl)benzene 4 (16.7 mg, 0.110 mmol, 0.016 ml), 1,2,3-
trimethoxybenzene (internal standard, 10 mg, 0.059 mmol) and the corresponding
metalloporphyrin catalyst 3a-d (2 mol%, 0.0022 mmol) in CDCl3 (0.4 ml) was added
to an aqueous solution of KOH (6 M, 1 ml) in a 5 ml flask sealed with a septum. The
resulting biphasic mixture was vigorously stirred for 5 minutes. Then, keeping the
magnetic stirring, slow addition of freshly prepared aqueous solution of diazomethane
precursor 6 (0.122 M, 2.7 ml) was started using an automatic syringe pump, keeping
the addition rate at 0.9 ml/hour, which corresponds to 1 equivalent of 6 per hour. At
the start of the addition, an open 1 ml plastic syringe without plunger, previously
filled with a KOH solution (6 M, 0.3 ml), was introduced into the flask via needle to
lead off excess of gas phase during the addition process. Aliquots of 0.020 ml were
withdrawn from the organic phase by means of a microsyringe after a short cease of
stirring. The aliquots were withdrawn every 20 minutes after the start of the addition
of 6 solution and also shortly before starting the experiment. The aliquots were
diluted by CDCl3 to stop the reaction and analysed by 1H NMR. The reaction progress
was monitored by calculation of substrate concentration decrease from the NMR data
1
of the crude reaction mixture. Integrals of the H-NMR signal of the substrate methyl
group (δ, ppm: 2.12) in each sample were compared with the integral of internal
standard methyl groups (δ, ppm: 3.87, 3.86), using the aliquot taken before starting
the addition of 6 as reference.
Blank experiments were performed under identical conditions but in the
absence of catalysts 3. No reaction progress was observed during the time of 3 hours.
26

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Experiment with interruption of the addition of diazomethane precursor 6 was
carried out by following the general procedure using metalloporphyrin 3a as catalyst,
but the addition of 6 solution was stopped after 60 minutes. Since that moment,
aliquots were withdrawn every 5 minutes during the next 20 minutes. No significant
reaction progress was observed after interruption of the addition of 6.
Procedure for the kinetic experiments using 3e or 3f as catalysts: Under the
conditions reported for the previous general procedure, metallodendrimers 3e and 3f
formed emulsions when stirred in the biphasic system, which could result in a slower
progress of the reaction. To avoid the formation of emulsions, the flask size was
changed from 12 x 45 mm to 15 x 55 mm and the size of the magnetic stirrer bar from
5 x 12 mm to 8 x 12 mm. The amount of CDCl3 used was increased to 0.6 ml.
1,2,3-Trimethoxybenzene (internal standard): This compound is commercially
available and was used without further purification. 1H NMR (500 MHz, CDCl3): δ =
3.86 (s, 3H, OCH3), 3.87 (s, 6H, OCH3), 6.59 (d, 2H, ArH), 7.00 (t, 1H, ArH).
1-Chloro-4-(prop-1-en-2-yl)benzene (4): this compound is commercially available
1
and was used without further purification. H NMR (500 MHz, CDCl3): δ = 2.12 (s,
3H, -CH3), 5.09 (s, 1H, =CH2), 5.34 (s, 1H, =CH2), 7.28 (d, 2H, ArH, J = 8.51 Hz),
7.38 (d, 2H, ArH, J = 8.80 Hz).
1-Chloro-4-(1-methylcyclopropyl)benzene (5): this (2+1) cycloadduct was obtained
as colourless oil by column chromatography from the different reaction mixtures
following the general procedure for kinetic experiments. Spectral properties are in
accordance with those reported in the literature.13 1H NMR (500 MHz, CDCl3): δ =
0.70-0.75 (m, 2H, CH2), 0.80-0.84 (m, 2h, CH2), 1.38 (s, 3H, CH3), 7.14-7.24 (m, 4H,
ArH).
1H-DOSY experiments: The different experiments were carried out on a Bruker 500
AVANCE equipped with a z-gradient BBO probe. Each DOSY experiment was
recorded using the lebbpgp2s sequence. The number of scans was 16. The strength of
the gradient was changed from 2 % to 95% using a 50 G cm-1 gradient unit. The value
of big delta  was 200 ms and little delta  was 800 ms. A delay of 5 ms was used to
avoid the formation of eddy currents.
Computational methods: All the computational studies reported in this paper were
based upon molecular mechanics47 (MM) and molecular dynamics (MD).48 In both,
the MM3 method developed by Allinger et al. as implement in the MacroModel49
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package was used. All MD simulations were performed with SHAKE50 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 dendrimers51 of this size. 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 and temperature
of the whole system were equilibrated. 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 library52 were written. In
the case of MD simulations under periodic boundary conditions (MD-PBC) in
chloroform, a specific force field potential optimized for liquid simulations
(OPLS_2005)53 was used as implemented on Desmond package.54 These simulations
were performed using periodic boundary conditions within the canonical NVT
ensemble at 298.15 K and a cubic box of 90 Å of side length. The system was
equilibrated for 2 ns with time steps of 1 ps.
Acknowledgements
The work carried out by the Czech authors was supported by the Ministry of
Education, Youth and Sports of the Czech Republic (Project MSM6046137305) and
by the Czech Science Foundation (Projects 304/10/1951 and P503/11/0616). P. V.
also thanks the DIPC for a visiting fellowship. Financial support to the Spanish
authors was provided by the Ministerio de Economía y Competitividad (MINECO) of
Spain and FEDER (project CTQ2013-45415-P), the UPV/EHU (UFI11/22 QOSYC),
and the Basque Government (GV/EJ, grant IT-324-07). The authors thank the
SGI/IZO-SGIker UPV/EHU and the DIPC for generous allocation of computational
and analytical resources.
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