Zwitterionic amidinates as effective ligands for platinum nanoparticle hydrogenation catalysts

Article abstract of DOI:10.1039/c6sc05551f

Ligand control of metal nanoparticles (MNPs) is rapidly gaining importance as ligands can stabilize the MNPs and regulate their catalytic properties. Herein we report the first example of Pt NPs ligated by imidazolium-amidinate ligands that bind strongly through the amidinate anion to the platinum surface atoms. The binding was established by¹⁵N NMR spectroscopy, a precedent for nitrogen ligands on MNPs, and XPS. Both monodentate and bidentate coordination modes were found. DFT showed a high bonding energy of up to -48 kcal mol^-1 for bidentate bonding to two adjacent metal atoms, which decreased to -28 ± 4 kcal mol^-1 for monodentate bonding in the absence of impediments by other ligands. While the surface is densely covered with ligands, both IR and¹³C MAS NMR spectra proved the adsorption of CO on the surface and thus the availability of sites for catalysis. A particle size dependent Knight shift was observed in the¹³C MAS NMR spectra for the atoms that coordinate to the surface, but for small particles, ～1.2 nm, it almost vanished, as theory for MNPs predicts; this had not been experimentally verified before. The Pt NPs were found to be catalysts for the hydrogenation of ketones and a notable ligand effect was observed in the hydrogenation of electron-poor carbonyl groups. The catalytic activity is influenced by remote electron donor/acceptor groups introduced in the aryl-N-substituents of the amidinates; p-anisyl groups on the ligand gave catalysts several times faster the ligand containing p-chlorophenyl groups.

Full text of DOI:10.1039/c6sc05551f

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Zwitterionic amidinates as effective ligands for platinum
nanoparticle hydrogenation catalysts
Received 00th January 20xx,
Accepted 00th January 20xx
a,
a
b
a
a
a
L. M. Martínez-Prieto, * I. Cano, A. Márquez, E. A. Baquero, S. Tricard, L. Cusynato, I. del
a
a
c
c
a
b,
Rosal, R. Poteau, Y. Coppel, K. Philippot, B. Chaudret, J. Campora * and P. W. N. M. van
DOI: 10.1039/x0xx00000x
a,
Leeuwen *
www.rsc.org/
Ligand control of metal nanoparticles (MNPs) is rapidly gaining importance as ligands can stabilize the MNPs and regulate
their catalytic properties. Herein we report the first example of Pt NPs ligated by imidazolium-amidinate ligands that bind
1
5
strongly through the amidinate anion to the platinum surface atoms. The binding was established by N NMR
spectroscopy, a precedent for nitrogen ligands on MNPs, and XPS. Both monodentate and bidentate coordination modes
–1
were found. DFT showed a high bonding energy of up to - 48 kcal.mol for bidentate bonding to two adjacent metal
–
1
atoms, which decreased to - 28 ± 4 kcal.mol for monodentate bonding in the absence of impediments by other ligands.
13
While the surface is densely covered with ligands, both IR and C MAS NMR spectra proved the adsorption of CO on the
1
3
surface and thus the availability of sites for catalysis. A particle size dependent Knight shift was observed in the C MAS
NMR spectra for the atoms that coordinate to the surface, but for small particles, ~1.2 nm, it almost vanished, as theory
for MNPs predicts; this had not been experimentally verified before. The Pt NPs were found to be catalysts for the
hydrogenation of ketones and a notable ligand effect was observed in the hydrogenation of electron-poor carbonyl
groups. The catalytic activity is influenced by remote electron donor/acceptor groups introduced in the aryl-N-substituents
of the amidinates; p-anisyl groups on the ligand gave catalysts several times faster the ligand containing p-chlorophenyl
groups.
carbenes (NHCs) and carbodiimides (Scheme 1), in particular
.
(p-
Introduction
1,3-dicyclohexylimidazolium-2-di-p-tolylcarbodiimide
tol)
(ICy
NCN), was identified as an effective ligand to produce ultra-
4
small ruthenium nanoparticles (Ru NPs) with a size ca. 1 nm.
The interest in metal nanoparticles (MNPs) is growing fast in
both the academic and industrial community thanks to their
applications in multiple fields such as sensors, medicine,
Due to their zwitterionic structure, the nitrogen atoms present
a large electron-donor capability and coordinate strongly to
transition metals. The coordination chemistry of such
imidazolium-amidinate ligands has been investigated a short
1
optoelectronics and catalysis. In particular, MNPs have a high
catalytic activity in some specific transformations like
hydrogenation, polymerization, oxidation and C–C coupling
2
reactions. Their high potential in catalysis arises from their
5
while ago by some of us. In analogy with amidinates, which
.(p-
2
1
1
frequently coordinate in a μ -κ N, κ N´ bridging mode, ICy
particular electronic configuration and large surface area, and
the potential to combine the advantages of homogeneous and
heterogeneous catalysts. The stability and activity of MNPs are
strongly influenced by the ligands used as stabilizers, which are
tol)
NCN forms multi-bridged binuclear “paddlewheel”
complexes of copper (I). Besides, small changes on the N-
substituents give us the possibility to modify their electronic
properties. For example, introducing electron acceptor/donor
moieties (–Cl or –OMe) in these pending groups enables us to
modulate the surface properties of MNPs.
3
able to modify their surface properties.
The exploration of new families of ligands capable to stabilize
MNPs and modify their reactivity is always a challenge. In a
recent publication, the betaine-type adduct of N-heterocyclic
By the use of spectroscopic techniques, such as NMR or FT-IR,
the coordination and dynamics of surface ligands of MNPs can
be properly investigated. Recently, the coordination of NHC
ligands to ruthenium and platinum nanoparticles was
6
investigated by solid-state NMR spectroscopy. Moreover,
NMR studies on Ru and Pt NPs stabilized by hexadecylamine
(HDA) confirmed that Pt displays a Knight shift (due to the
presence of free electrons on the surface) which is much
7
stronger than that of Ru. This effect was also observed in Pt
NPs of 1.2 and 2.0 nm, for which the different electronic states
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8
resulted in unequal magnitudes of Knight shift. However, bis-phenylmethanediimine
(Ph) 15
NC N) (Scheme 1). Non-
(
ultra-small Pt NPs (< 1nm) behave as molecular species commercial carbodiimides were obtained in high yields by
9
without free electrons and no Knight shift occurs. Another desulphurization of the corresponding thioureas with I
2
in the
, using literature procedures. The symmetric
6 4 2
H ) C=S (R = OMe, Cl) were readily synthesized
1
7
important instrument to characterize the surface of the presence of NEt
nanoparticles is the use of carbon monoxide (CO) as a probe thioureas (p-RC
molecule, since CO coordination can be especially useful to from thiophosgene and the corresponding aniline. N-labeled
3
1
5
8
,10
(Ph)
15
determine the active sites.
diphenylthiourea used to prepare NC N was obtained from
1
7a
Theoretical calculations are of great importance in order to phenylisothiocyanate and aniline.
With this method we
1
5
shed more light on experimental data, as for example to expected to form the singly N-labeled product, but the ESI-
secure the assignment of experimental solid state NMR MS spectrum of the thiourea showed a signal for the
spectra or for the calculation of properties that cannot be corresponding anion of which the isotopic pattern was
1
1
14
2
measured experimentally. In the context of the nanoparticle consistent with a statistical 1:2:1 mixture of the normal ( N ),
1
4
15
15
surface chemistry, the theoretical calculations provide detailed monolabeled ( N N) and doubly-labeled isotopologues ( N ).
2
information not only on the coordination mode of the species As shown in Scheme S1 (see SI, sectionS1), scrambling of the
15
1
bound to the nanoparticle surface, but also on the chemical
2
N
label
indicates
that
aniline
addition
to
1
3
reactions that may take place on these surfaces.
phenylisothiocyanate is reversible.
Ligand-stabilized metal NPs are effective catalysts for Most of Pt NPs reported in this paper were conveniently
hydrogenation of olefin, carbonyl and nitro functionalities, as obtained by reaction of tris(2-norbornene)platinum(0)
1
4
well as aromatics. In this context, Pt NPs have shown [Pt(NBE) ] in THF under 3 bar H in the presence of the
3
2
6
b,15
important chemoselectivities in hydrogenation of olefin
corresponding imidazolium-amidinate ligand (Scheme 2).
1
and nitro groups. Herein we present a series of Pt NPs ligated Herein we report for the first time the use of Pt(NBE) as
6
3
.(Ar)
by imidazolium-amidinates (ICy NCN) which exhibit an metallic precursor in the synthesis of Pt NPs by the
exciting ligand effect in the hydrogenation of carbonyl groups organometallic approach. The advantages of Pt(NBE) versus
3
when electron donor/acceptor groups are introduced in the N- the typical Pt precursors [tris(dibenzylideneacetone)
substituents. These Pt NPs were characterized by the state-of- diplatinum
(0);
Pt (DBA)
2
or
dimethyl(1,5-
7
3
-8,18
the-art techniques (TEM, HRTEM, WAXS, TGA and EA) and cyclooctadiene)platinum(II); Pt(CH ) (COD)] are evident.
3
2
studied their surface chemistry through the coordination of CO First, the purification of the obtained nanoparticles is
FT-IR and solid state MAS NMR). Here a clear correlation simplified as the norbornane formed during the decomposition
(
between the Knight shift of adsorbed CO and the NPs size was can be rapidly eliminated under vacuum and makes it this
observed. In addition, the coordination of the imidazolium- complex a “clean” precursor. And, second, the highly reactive
amidinate ligands was investigated in Pt and Ru NPs by XPS, Pt(NBE) requires less time for the formation of Pt NPs under
3
1
solid state N MAS NMR and DFT calculations.
5
H . Thus, the use of Pt(NBE) as precursor is advantageous
2 3
both for the formation and purification of Pt NPs. Different
.
(p-tol)
amounts of ICy
NCN were employed for the synthesis of Pt
.
(p-
Results and Discussion
NPs, specifically 0.1, 0.2 and 0.5 molar equiv. (Pt/ICy
tol)
.(p-tol)
NCN0.1, Pt/ICy
.(p-tol)
NCN0.2 and Pt/ICy
NCN0.5), with the
Synthesis and characterization of Pt NPs
aim to obtain different sizes and reactivities. Indeed,
Transmission Electronic Microscopy (TEM) micrographs of
Zwitterionic adducts of N,N-dicyclohexylimidazolidene and
.
(Ar)
diarylcarbodiimide (ICy NCN; Ar = Ph, p-Tol, p-anysil, p-
ClC ) were prepared similarly to previously reported
betaine-type adducts, by reaction of N-heterocyclic carbene
ICy) and suitable carbodiimide, namely bis(4-
.(p-tol)
.(p-tol)
.(p-tol)
Pt/ICy
exhibit Pt NPs with a mean diameter of 2.3 (0.3), 2.1 (0.2) and
.9 (0.4) nm respectively (Figure 1), and one observes a
NCN0.1
,
Pt/ICy
NCN0.2 and Pt/ICy
NCN0.5
6 4
H
4
,5
1
(
a
correlation between the quantity of ligand and the average
size of the obtained NPs; more ligand leads to smaller
particles. This behavior was already observed in our previous
(
p-tol)
methylphenyl)methanediimine
methoxyphenyl)methanediimine
(
NCN),
bis(4-
bis(4-
(p-anisyl)
(
)
NCN),
(
p-ClC
H
6 4
15
NCN) and N-labelled
chlorophenyl)methanediimine (
.(p-tol)
4
work with Ru/ICy
NCN, and also with other type of
Scheme 2. Synthesis of platinum nanoparticles using imidazolium-amidinate
ligands as stabilizers.
Scheme 1. Synthesis of zwitterionic imidazolium-amidinate ligands.
2
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.
(p-tol)
Figure 2. HRTEM image of Pt/ICy
NCN0.2 (left, right
bottom) and Fast Fourier Transformation Analysis (right,
top) with the planar reflections.
.
(p-tol)
.(p-tol)
Figure 1. TEM images and size histograms of (a) Pt/ICy
NCN0.1, (b) Pt/ICy
NCN0.2
.(p-tol)
and (c) Pt/ICy
NCN0.5.
6
a,19
20
aminosilanes and sulfonated Surface studies
.(p-tol)
ligands, such as NHCs,
1
2
.(p-tol)
diphosphines.
Pt/ICy
NCN0.1 and Pt/ICy
NCN0.2
.(p-tol)
The surface chemistry of Pt/ICy
NCN NPs was studied by
micrographs revealed NPs that are very well distributed and
.
monodisperse in size, while the image for Pt/ICy
Fourier Transform infrared (FT-IR) and magic angle spinning
(p-tol)
NCN0.5
13
15
solid-state C and N NMR (MAS-NMR) with and without
cross-polarization (CP). CO was used as a probe molecule as it
is well known that coordination of CO allows the identification
showed a worse dispersion. For an unknown reason, the range
of sizes of these NPs increases with the amount of ligand,
while the monodispersity is lost.
10,22
of different available surface sites on metal nanoparticles.
.
(p-tol)
High resolution TEM (HRTEM) micrographs of Pt/ICy
NCN0.2
Commonly, CO is adsorbed onto the metal surface either in a
show crystalline Pt NPs (Figure 2), displaying the face centered
cubic (fcc) structure typical of bulk Pt. Fast Fourier
Transformation (FFT) applied to the image of Figure 2 revealed tol)
the reflections corresponding to the (111), (200) and (111)
bridging (COb) or in a terminal (COt) mode. Figure 3 shows
.(p-
attenuated total reflectance (ATR) FT-IR spectra of Pt/ICy
NCN NPs after bubbling CO during 5 min in a THF solution.
.(p-tol)
The FT-IR spectrum of Pt/ICy
NCN0.1 [Figure 3; (a)] presents
atomic planes.
-1
-1
two distinct bands, at 1845 cm and 2038 cm , which can be
respectively attributed to CO coordinated on the Pt surface in
a bridging (COb) and in a terminal mode (COt). The stretching
band attributed to COb is very intense, evidencing that a large
part of the CO is coordinated in a bridging mode. Analogous
stretching vibrations for adsorbed CO were previously
Wide-Angle X-ray Scattering (WAXS) analyses performed on
.
(p-tol)
.(p-tol)
solid samples of Pt/ICy
.
NCN0.1, Pt/ICy
NCN0.2 and
(p-tol)
Pt/ICy
NCN0.5 confirmed the crystallinity of these Pt NPs,
which retain the fcc structure (see SI, Figures S17-S19). The
coherence lengths indicated by the Radial Distribution
Function (RDF) resultant from WAXS analysis are slightly higher
than the mean diameters determined by TEM. WAXS analysis
23
observed in Pt(111) crystal surfaces and Pt NPs. The IR
.(p-tol)
spectrum of Pt/ICy
NCN0.2 displays similar frequencies at
.
(p-tol)
revealed a coherence length of 2.5 nm for Pt/ICy
.
NCN0.1
NCN0.5
,
,
-1
-1
816 cm and 2032 cm , but here the ratio COt/COb has
1
(p-tol)
.(p-tol)
2.2 nm for Pt/ICy
NCN0.2, and 2.1 nm for Pt/ICy
increased [Figure 3; (b)] in comparison with the previous one.
.(p-tol)
This trend persists for Pt/ICy
while the mean diameters observed by TEM were 2.3, 2.1 and
.9 nm, respectively.
NCN0.5, and the intensities of
1
-1
CO bands (1808 and 2032 cm ) decrease in relation to the
characteristic C=N absorption frequencies of the amidinate
-1
ligand at 1630 and 1598 cm [Figure 3; (c)] Here we observe
The Pt NPs were obtained in acceptable yields (60-70%; based
on Pt), and the metal content determined by
thermogravimetric analysis (TGA). The Pt content was 90.1%
an evident relation between the COt/COb ratio and the
.
(p-tol)
.(p-tol)
for Pt/ICy
NCN0.1, 77.3% for Pt/ICy
NCN0.2, and 60.1%
amount of ligand used. We think that both the size and the
.
(p-tol)
for Pt/ICy
NCN0.5. Moreover, elemental analysis (EA) of the
presence of more ligand on the surface increase the amount of
.(p-tol)
COt at the cost of COb, such that 1.9 nm Pt/ICy
NPs revealed that the amounts of C, H and N are in good
agreement with the ratio of these elements in the ligand (C,
NCN0.5 NPs
contains mostly COt. It is noteworthy that when we decrease
.(p-tol)
79.25 %; H, 8.42 %; N, 12.32 %), suggesting that the
the amount of ICy
NCN from 0.5 to 0.1 equiv., we observe
imidazolium-amidinate ligand remains intact at the platinum
surface (see SI, Table S1). It is important to mention that the
a slight shift of the CO bands to higher frequency (from 1808
-1
to 1845 cm for COb and from 2032 to 2038 cm for COt). This
-1
.
(p-tol)
Pt:L ratio in Pt/ICy
coordinated ligand at the platinum surface, as the number of
NCN0.5 shows a large quantity of
behavior is in agreement with a higher surface coverage of CO
.(p-tol)
in Pt/ICy
from the Pt surface (See SI, Figure S25). The displacement of
NCN0.1, which removes more electron density
.
(p-tol)
ICy
NCN molecules is approximately half of the surface
atoms (Ptsurface ~ 50 % of Pttotal).
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3
.(p-tol)
Figure 4. C CP-MAS NMR spectrum of Pt/ICy
NCN0.5 NPs.
.
(p-tol)
When the Pt/ICy
3
NCN0.5 NPs (1.9 nm) were exposed to 1
13
1
bar of CO during 20 h at r.t., the C MAS NMR spectrum
Figure 5; (c)] showed a very broad peak centered at ca. 360
[
ppm which corresponds to coordinated CO. This broad and
high frequency resonance can be assigned to a Knight-shifted
1
3
13
CO signal. In the C MAS spectra of Pt/ICy
.(p-tol)
NCN0.2 (2.1
13
NCN0.1 (2.3 nm) after reaction with CO we
.
(p-tol)
nm) and Pt/ICy
also observed the broad peak of CO at 390 and 400 ppm
respectively [Figure 5; (b) and (a)]. Thus, when the size of the
NPs decreases, the CO signal is displaced to lower frequency.
Because of the fast relaxation associated with the presence of
surface electrons (paramagnetic effect), the efficiency of the
.
(p-tol)
.(p-tol)
Figure 3. ATR FT-IR spectra of (a) Pt/ICy
and (c) Pt/ICy
NCN0.1, (b) Pt/ICy
NCN0.2
.
(p-tol)
NCN0.5 after CO adsorption.
the CO stretching frequency in relation with the quantity of CO magnetization transfer in the CP experiments is dramatically
8
,23b,24
has been previously described for surfaces and MNPs.
reduced and no signal for the coordinated CO could be
3
1
Thanks to FT-IR we obtained the first indication about the observed in the C CP-MAS spectra (see SI, bottom of Figures
coordination mode of the imidazolium-amidinate ligand. S28, S30, S32). As we observed an evident relationship
.
(p-tol)
Comparing the IR spectra of the ligand ICy
.
NCN (see SI, between the size and the magnitude of the Knight shift on the
.(p-tol)
NCN0.5 (see SI, Figure CO band, we decided to synthesize very small Pt/ICy
S26), we observed a clear 100 cm displacement of the strong NPs with the intention to suppress the Knight shift completely.
(p-tol)
Figure S20) and the particle Pt/ICy
-
NCN
1
-1
stretching C=N bands, from 1530 and 1495 cm to 1630 and Pt NPs of ca. 1.2 (0.3) nm (see SI, Figure S8) were prepared
.(p-
-1
7,23a
1598 cm , which suggests that the coordination of ICy
tol)
using a well-known two-step procedure.
NCN takes place through the NCN moiety. These observed decomposed under 1 bar of CO in THF, forming the colloid
2
Pt (DBA)3 was
5
,25
frequencies are in agreement with reported values.
x y z
Pt (CO) (THF) , and after washing this colloid with pentane, 0.2
.
(p-tol)
.(p-
Coordination of CO on the Pt NPs was also studied by solid- equiv. of ICy
tol)
NCN were added to obtain Pt/CO-ICy
13
1
3
state NMR. The C CP-MAS NMR spectrum obtained for
NCN0.2 NPs (Scheme 3). The
C MAS spectrum of
13
.
(p-tol)
13
NCN0.5 before exposition to CO displays most of Pt/CO/ICy
.(p-tol)
Pt/ICy
NCN0.2 [Figure 5; (d)] after reaction with CO
NCN ligand (Figure 4). showed a broad peak at 230 ppm due to bridging CO (COb)
.
(p-tol)
the characteristic signals of the ICy
The group of peaks at 125 ppm (a) corresponds to the and two sharp peaks at 210 ppm and 194 ppm which
aromatic ring of the p-tolyl moiety and the signal at 116 ppm correspond to terminal (COt) and multi-terminal CO (nCOt),
(
b) belongs to the aromatic imidazolium backbone. The respectively. These ones are the values expected for bridging
8
,9,18b
distinctive peak at 58 ppm (c) is attributed to the methine and terminal CO in Pt NPs.
group next to the nitrogen atom. The cyclohexyl methylene remaining broad Knight-shifted CO resonance at 350 ppm due
1
resonances are observed between 32 ppm and 25 ppm (d) to the CO coordinated on the larger NPs. C Knight-shifted
However, we still observe a
3
7
-9,26
overlapping with the p-tolyl methyl group resonance at 25 resonances have already been observed in Pt NPs,
.
ppm (e). As was previously observed for Ru/ICy
but this
NCN, the is the first case which reports a direct dependence of the size
(p-tol)
signals for the Cipso of the p-tolyl group and the imidazolium of Pt NPs with the degree of the Knight shift observed,
and carbodiimide quaternary NCN atoms are not clearly perceiving a displacement of the CO band as the nanoparticle
1
3
observable in the C spectrum (usually in the 130–150 ppm size decreases (2.3 nm - 2.1 nm - 1.9 nm), and at 1.2 nm the
range; see SI, Figure S33) due to a line broadening caused by Knight shift is almost suppressed (Figure 5).
.
(p-tol)
4
the coordination of ICy
NCN at the metal surface.
4
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1
5
.(Ph)
15
Figure 6. N CP/Hahn-echo MAS of (a) Pt/CO/ICy NC N0.2 and (b)
1
3
.(p-tol)
Figure 5. C MAS NMR spectrum of (a) Pt/ICy
NCN0.1 (2.3 nm), (b)
.
.(Ph)
15 + .
-
.
(p-tol)
.(p-tol)
[H ICy NC N] [BPh4] .
Pt/ICy
Pt/CO/ICy
r.t.).
NCN0.2 (2.1 nm), (c) Pt/ICy
NCN0.5 (1.9 nm) and (d)
.
(p-tol)
13
NCN0.2 (1.2 nm) after exposure to CO (1 bar, 20 h, at
.
(Ph)
15
reacting ICy NC N with HOAc in the presence of NaBPh .
4
1
5
To understand the state and coordination mode of these
amidinate ligands, we used the labelled adduct 1,3-
dicyclohexylimidazolium-2-di-
Indeed the solid-state N CP/Hahn-echo MAS spectrum of this
compound exhibits two signals at 116 and 266 ppm, attributed
to the protonated and non-protonated N atoms, respectively.
The former is ca. four-fold as intense as the latter, because the
CP effect is much more intense in the protonated nitrogen due
to the presence of the strong N-H dipolar coupling [Figure 6;
.
(Ph)
15
phenylcarbodiimide(ICy NC N) and studied its coordination
1
on the NP metal surface by N MAS NMR spectroscopy.
5
.
(Ph)
15
ICy NC N was fully characterized by NMR (liquid and solid
state) and DFT calculations (see SI, section S1). Employing the
(b)]. Solution NMR spectra in CD Cl (see SI, section S1)
2 2
.
aforementioned synthetic method, Pt/ICy NC N NPs with
(Ph)
15
0
.5
indicate that the cation exists as a 2:1 mixture of two isomers
obtained by protonation of either one of the two N-atoms. DFT
calculations confirm the experimental shifts and corroborate
an average size of 1.9 (0.2) nm (see SI, Figure S9) were
1
5
prepared (Scheme 1). These NPs were studied by N MAS
1
5
.
(Ph)
15
+
-
NMR but we could not observe any detectable signal in
Hahn-echo NMR [see SI, Figure S36; (a)] not even in
N
N
that the two E/Z isomers of [ICy NC NH] [BPh ] can coexist
4
1
5
as evidenced by their relative energy difference of 1.1
-1
CP/Hahn-echo MAS NMR [see SI, Figure S36; (b)], which are
usually employed to detect broad NMR signals. The lack of
signals is possibly due to the Knight shift as discussed above.
To suppress the Knight shift we synthesized Pt NPs of ca. 1.2
kcal.mol . In the same way, as for non-protonated ligands, the
E/Z isomers are more stable than the Z/Z isomer by -3.4
-1
-1
kcal.mol and -2.3 kcal.mol (see SI, Figure S59). Thus, the
1
5
peaks at 120 and 260 ppm in the N CP/Hahn-echo MAS NMR
spectrum of
.
(Ph)
15
.(Ph)
15
nm with labelled ICy NC N, Pt/CO/ICy NC N (see SI,
0
.2
1
5
.
(Ph)
15
Pt/CO/ICy NC N correspond to a minor part of the ligand
Figure S10). The N CP/Hahn-echo MAS NMR spectrum
displays two sharp signals at 120 and 260 ppm [Figure 6; (a)].
The sharpness of the signals points to a non-coordinated
nitrogen compound, as the signals of coordinated ligands are
usually broad. The intense peak at 120 ppm is reminiscent of a
protonated nitrogen ligand, therefore we prepared the singly-
protonated phenyl betaine adduct as its tetraphenylborate salt
0
.2
that has been protonated during the synthesis and the signal
1
of which is strongly enhanced thanks to the N CP-MAS
5
1
5
experiment. However, we were not able to detect
N
.
(Ph)
15
15
resonances of coordinated ICy NC N in N Hahn-echo MAS
NMR, most likely because of the deleterious effect of the NP
surface electrons (see SI, Figure S38).
.
(Ph)
15
+
-
[
ICy NC NH] [BPh ] . In contrast with the strongly basic
4
X-ray photoelectron spectroscopy (XPS) is an ideal technique
to measure the elemental composition and chemical state of
surface catalysts. Recently, this technique has been described
as a useful tool to investigate the binding mode of NHC ligands
.
ligand Me IiPr NCN reported by Kuhn, aryl imidazolium-
(iPr)
27
2
.
(Ar)
amidinate ICy NCN (e. g. Ar = Tol) does not react with water
to a significant extent, but they are immediately protonated by
.
acetic acid (HOAc). [ICy NC NH] [BPh ] was obtained
(Ph)
15
+
-
2
8
4
on a metal surface. Thus, we applied XPS to study the
coordination of the imidazolium-amidinate ligands in our Pt
.
(p-tol)
NPs. The N 1s signals of ICy
NCN present binding energies
(BE) of 401.3 and 397.4 eV [Figure 7, (a), blue]. The highest BE
peak at 401.3 eV can be assigned to the tightly bound
electrons of the nitrogen atoms of the imidazolium fragment.
The second peak at 397.4 eV derives from the N atoms of the
2
9
.
(p-tol)
amidinate group, which bear partial negative charges. The
.
Scheme 3. Synthesis of Pt/CO/ICy
NCN0.2 NPs.
(p-tol)
coordination of ICy
NCN through the latter N-atoms to the
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tol)
NCN0.2 NPs is 71.1 eV. The main contribution is located at
3
1.0 eV, which is characteristic of Pt(0), and an additional
0
7
contribution at 72.7 eV is attributed to the surface platinum
.
(p-tol)
atoms linked to the nitrogen atoms of ICy
3
NCN (Pt(δ+))
1
[Figure 7, (b)].
Coordination of imidazolium-amidinates to metal surfaces
3
Amidinates have a rich coordination chemistry as they can
2
1
coordinate to a single metal center either in terminal (κ ),
2
3
chelating (κ ) modes, and, less often they can even bind in η
mode, like an allyl group. The amidinate can also bridge two
1
metal centers, i.e., in μ -κ N, κ N´mode. On a metal surface
1
2
one N-atom can bridge more than two metal atoms and thus a
variety of coordination modes results. As the measurements
on Pt NPs gave not satisfactory evidence for the bonding mode
1
5
15
in N NMR spectroscopy we turned to different metals for
N
NMR spectral data. As ruthenium presents insignificant or no
.
Knight shift, we synthesized Ru/ICy NCN NPs as reported
(Ph)
4
before stabilized with 0.1, 0.2, 0.5 and 1 equiv. of the
15
N
Figure 7. X-ray photoelectron spectroscopy (XPS) of (a) the N 1s signals
.(p-tol)
.(p-tol)
labelled ligand and studied the coordination of the ligand by
of ICy
NCN (blue) and Pt/ICy
NCN0.2 (red), (b) the Pt 4f5/2 and
1
5
.(Ph)
15
.(p-tol)
.(p-
solid state N MAS NMR. The resulting Ru/ICy NC N NPs
have sizes between 1.0 and 1.3 nm, they are very well
dispersed and show a narrow size distribution (see SI, Figures
S11-S14). As for Pt NPs, we perceived a correlation between
the size and the amount of ligand used during the synthesis;
the size increases when less ligand is used.
4
f
7/2 signals of Pt/ICy
NCN0.2 and (c) the N 1s signals of Pt/ICy
ClC6H4)
.(p-tol)
.(p-anisyl)
NCN0.2 (top), Pt/ICy
NCN0.2 (center) and Pt/ICy
NCN0.2
platinum surface involves a loss of electron density, which
increases the binding energy (400.1 eV) compared to the N-
.
(p-tol)
atoms of free ICy
of the peaks of the two fragments, as can be seen in Figure 7
a) (red). This signal is the result of convolutions of peaks
NCN (397.4 eV). This leads to the overlap
15
.(Ph)
15
In the N CP/Hahn-echo MAS NMR spectra of Ru/ICy NC N
NPs (see SI, Figure S43) we can see clearly the peak around
(
corresponding to imidazolium and amidinate N atoms,
coordinated or not. In order to improve our understanding of
these binding energies, we theoretically compared the natural
1
20 ppm corresponding to the protonated amidinate ligand, as
.(Ph)
was already observed for Pt/CO/ICy NC N . Furthermore,
15
0
.2
15
a new broad featureless signal is observed underneath the
N
.
(Ph)
charges of the N atoms of the ICy NCN ligand, free and
resonance of the protonated imidazolium-amidinate ligand.
Note that for Ru NPs stabilized with 1 equiv. [see SI, Figure
S43, (a)], we also observed a sharp peak at 212 ppm assigned
2
1
1
coordinated in μ -κ N, κ N´ mode to a model Ru carbonyl
cluster (see SI, Figure S60). Interestingly, no change is
observed in the natural charges of the N atoms of the
imidazolium fragment by coordination of the ligand on the
cluster surface. However, the anionic character of the N atoms
of the amidinate moiety is partially reduced, as a result of the
balance between σ-donation and π-backdonation. Thus, the
coordination of the ligand induces the decrease of the charge
difference between the N atoms of both moieties leading to
overlap of the peaks of the two fragments as observed in
Figure 7 (a) (red). This result suggests that the coordination of
the ligand to the nanoparticle is through the N atoms of the
amidinate moiety. We deconvoluted the N 1s signals of
.
(p-tol)
Pt/ICy
NCN0.2 at 399.9 eV in three contributions with
different binding energies, at 401.1, 399.7 and 398.2,
-
corresponding to δ , neutral and δ N atoms, respectively
+
[
Figure 7, (c), center]. When the electron-withdrawing ligand
.
6 4
(p-ClC H )
ICy
NCN is used as stabilizer, the contribution of the
δ+
peak at 401.1 (N ) intensifies, generating an increase of the
average BE of the N 1s signal to 400.8 eV [Figure 7, (c), top].
.
(p-anisyl)
On the other hand, the N(1s) signals of Pt/ICy
NCN0.2
containing the electron donor OMe substituent, display the
δ-
opposite behavior, intensifying the peak at 398.2 (N ) and
decreasing the global BE to 398.7 eV [Figure 7, (c), bottom].
.
The binding energy of Pt 4f7/2 in the XPS spectra of Pt/ICy
15
.(Ph)
15
Figure 8. N CPMG MAS NMR of Ru/ICy NC N stabilized with (a) 1
(p-
equiv., (b) 0.5 equiv., (c) 0.2 equiv. and (d) 0.1 equiv.
6
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1
to the excess of free ligand. N Hahn-echo MAS NMR spectra 219 ppm in C MAS NMR, cannot be observed due to overlap
5
13
(
see SI, Figures S45, S48, S54, S57) allowed the amplification of with the broad peak of COb centered at 230 ppm (see SI,
1
this new broad N resonance relative to the signal of the Figure S51). The calculated N shifts of monocoordinated
5
15
.
(Ph)
15
protonated free ligand. Unfortunately, the broadness and the ICy NC N after insertion of CO are 151 ppm for the
poor signal to noise ratio of these experiments still preclude a migrated N-atom and 308 ppm for the non-coordinated N-
1
5
clear characterization of the N signals. In order to increase atom (Figure 9). After a careful analysis of NPA charges on this
1
the sensitivity of the N MAS experiments, we used the Carr- cluster model, we conclude that this significant unshielding of
5
3
3
Purcell-Meiboom-Gill pulse sequence (CPMG). It works well the latter is due to a delocalization of the negative charge on
for NMR resonances that have long spin-state lifetimes but the CO-Ru fragment and the localization of the π bond
1
5
significant inhomogeneous broadening. Figure 8 displays the between C and this N-atom (see SI, Figures S62 and S63). A
1
5
.(Ph)
N CPMG MAS NMR spectra of Ru/ICy NC N NPs stabilized charge analysis on its Ru55NP counterpart leads to the same
15
.
(Ph)
with the different amounts of ICy NC N. With this series of conclusion (see SI, Figure S64). This 308 ppm value is in the
1
experiments and DFT calculations on the chemical shifts we range of N chemical shifts observed for imines.
15
5
36
.
(Ph)
could establish the different states and coordination modes of Subsequently, the energetics of ICy NCN coordination onto
the amidinate at the Ru surface. The broad peak centered at the Ru surface was investigated by DFT calculations. The
.
(Ph)
15
ca. 250 (+/-100) ppm corresponds to coordinated ICy NC N chosen model is a Ru nanoparticle of 55 atoms with a hydride
which can coordinate in different ways. Following coverage of 1.6 hydrides per ruthenium surface atom, which
computational strategy successfully used for computing H and has a size of ca. 1nm (Ru H ). This model, apart from having a
a
1
5
5 70
1
3
.(Ph)
C chemical shifts, a [Ru ] carbonyl cluster was first used as a size similar (~ 1nm) to our Ru/ICy NCN NPs, has been
6
1
model for Ru NPs as larger systems cannot be conveniently already satisfactory employed by some of us to determine
1
3
handled. The chemical shifts were calculated by DFT studies the preferred surface composition of Ru NPs as a function of
4
and compared with the observed ones (see SI, Figure S61). environmental conditions from an application of the ab initio
37
that provides a connection
.
(Ph)
15
When ICy NC N bridges two adjacent Ru atoms, the thermodynamics method,
estimated deltas are 221 and 205 ppm [see SI, Figure S61, (a)] between the microscopic and macroscopic regimes. In the
2
κ coordination to one metal is not a stable configuration, vide present case, the DFT calculations showed that the most stable
(
1
infra). For κ coordination the calculated chemical shifts are coordination mode is through the two nitrogen atoms of the
44 ppm for the non-coordinated nitrogen and 118 ppm for amidinate as the Z/Z conformer to two adjacent Ru-atoms (μ -
2
2
1
1
-1
the bound one [see SI, Figure S61, (b)]. These values change to κ N, κ N´), with a binding energy of -47.9 kcal.mol . The
62 and 134 ppm if there is π-stacking between the phenyl binding of the same conformer through only one N atom has a
2
-1
groups and the ruthenium surface [see SI, Figure S61, (c)]. In stability of -33.3 kcal.mol , while that of monocoordination of
-1
view of the broadness of the resonances centered at ca. 250 the E/Z conformer is -25 kcal.mol (Figure 10). When the
1
ppm (Δν1/2 = 100-300 ppm), the N NMR spectrum suggests ligand was initially bound to a single Ru atom as bidentate
5
2
(κ N, N´), geometry optimization led to a more favorable
that all three coordination modes are present.
1
Lastly, the broad peak observed between 315 and 380 ppm in terminal κ N coordination mode, as observed for some
1
5
.(Ph)
15
5
the N CPMG MAS NMR spectra of Ru/ICy NC N NPs recently reported Cu complexes. Were the bonding
Figure 8) is attributed to a species resulting from an insertion prevailingly polar, such bidentate coordination mode could be
reaction of amidinate and carbon monoxide on the surface. favored, as observed for amidinate or carboxylate derivatives
(
3
8
This conclusion was corroborated by pressurization of of the alkali and rare earth metals. In summary, the
.
Ru/ICy NC N NPs with CO (1 bar, r.t., 20h), which led to adsorption energy per Ru-N bond of a single amidinate which
(Ph)
15
13
0
.2
3
5
a significant increase of these resonances (Figure 9).
ins
is not sterically discomforted by its mutual interaction with
.(Ph)
-1
Unfortunately, the peak corresponding to CO , expected at other ICy NCN ligands lies between -24 and -33 kcal.mol .
It is interesting to note that the interaction between the
.
(Ph)
ICy NCN ligand and the Ru55 nanoparticle does not involve a
displacement of the surface hydrides, considering that the loss
1
5
.(Ph)
15
.(Ph)
1
Figure 9. N CPMG MAS NMR of Ru/ICy NC N0.2 (a) before and (b) after
55 70
Figure 10. Coordination modes of ICy NCN at the Ru H surface (a) κ N
13
15
-1
1
exposure to CO (1 bar, 20 h, at r.t.). (c) Calculated N NMR
monocoordinated Z/E conformer (Eads
-1
monocoordinated Z/Z conformer (Eads: -33.3 kcal.mol ); (c) μ2-κ N,
:
-25.0 kcal.mol ); (b) κ N
.(Ph)
1
displacements of ICy NCN after CO insertion on a [Ru
6
] cluster model.
1
-1
κ N´bicoordinated Z/Z conformer (Eads: -47.9 kcal.mol ).
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-
1
of four H
2
molecules is disfavored by +20.6 kcal.mol (see SI,
1
(p-tol)
1
Table 1. Hydrogenation of styrene catalyzed by Pt/ICy·
NCN0.2
2
Figure S65). The maximum number of μ -κ N, κ N´ coordinated
c
c
.
(Ph)
Entry
Substrate
Products
Conv. (%)
-1
ICy NCN ligands that we can fit on the Ru55 surface is six (see
SI, Figure S66), which corresponds with Ru NPs stabilized with
TOF (h )
a
1
>99
10
12800
0
.1 equiv. of the ligand. The adsorption strength per betaine is
b
-1
2
75300
lowered from -47.9 kcal.mol in the case of a single ligand to -
-1
2
9.1 kcal.mol for the maximum number of them (i. e., 6). For
1
κ coordinated amidinates one could fit perhaps a few more
a. Reaction conditions: Substrate (32 mmol), Pt NPs (0.0025mmol of Pt
assuming 77.3 % of Pt from TGA analysis), THF (3 mL), 1h, T = 333K, P= 5 bar.
ligands on the surface, which is still energetically favorable. b. Reaction conditions: Substrate (320 mmol), Pt NPs (0.0025mmol of Pt
.
(Ph)
15
Thus, the Ru/ICy NC N NPs stabilized with 0.2, 0.5 and 1 assuming 77.3 % of Pt from TGA analysis), THF (10 mL), 10min, T = 333K, P= 5
.
(Ph)
15
bar.
equiv. have a second sphere of non-coordinated ICy NC N
which is strongly bonded to the first sphere by ionic and π-π
stacking interactions. At least some part of the second sphere
1
c. Conversions and products identities were determined by H NMR (average of
two runs).
1
5
is present in the protonated form as indicated by N NMR.
We shall now evaluate the coordination energy of the species
resulting from an insertion reaction of CO into the Ru-N bonds,
·
(p-anisyl)
6 4
·(p-ClC H )
(
Pt/ICy
NCN0.2 and Pt/ICy
NCN0.2; see SI Figures
S15 and S16). The catalytic results gave interesting differences
in terms of activity depending on the type of stabilizing ligand
used. In general, all nanocatalysts hydrogenated olefinic and
C=O bonds, but, as was expected for Pt NPs, they were not
capable of hydrogenating aromatic rings; e.g. the
ins
which we shall call CO , responsible for the broad peak
1
5
observed between 315 and 380 ppm in the N NMR spectrum
of carbonylated nanoparticles using the [Ru55] cluster model.
We initially considered a Ru55(CO)66 cluster, with a coverage
corresponding to 1.5 CO per surface Ru atom, as established in
·
(p-tol)
hydrogenation of styrene catalyzed by Pt/ICy
NCN0.2, gave
1
2
selectively ethylbenzene with a maximum turn over frequency
previous ab initio thermodynamics calculations.
1
The
-1
1
.(Ph)
(TOF) of 75.300 h (Table 1). This high TOF value demonstrates
the high catalytic power of this system in hydrogenation of
olefinic double bonds. This is peculiar in view of the high
coverage with strongly bound imidazolium-amidinate ligands
and indicates that these ligands play a favorable role as
ins electron donors.
2
adsorption energies of μ -κ N, κ N´ bicoordinated ICy NCN,
1
ins
κ N monocoordinated Z/Z conformer and the CO compound
-1
are slightly endothermic by 3-5 kcal.mol whatever the ligand,
probably owing to the crowding of carbon monoxides on the
surface. This is why we considered the adsorption properties
on a Ru55(CO)59 cluster. The adsorption energy of the CO
.
(Ph)
15
-1
0.2
Interestingly, 1.2 nm Pt/CO/ICy NC N NPs prepared from
compound becomes exothermic by -27.3 kcal.mol – a value
similar to the Ru-N bond energy –, and its grafting mode is
Pt
2 3
(DBA) and CO (Scheme 3) were totally inactive in the
hydrogenation of styrene, due to their surface poisoned by CO.
7
similar to what has been obtained on the small [Ru
see SI, Figure S67). Although its adsorption is strongly
exothermic, it is significantly less strongly bound than
6
] cluster
,23a
Indeed, as expected from previous works
the IR spectrum
(
of such NPs, recorded immediately after the synthesis,
.
(Ph)
1
1
2
presented two characteristic bands for COt and COb at 2041
2
bicoordinated ICy NCN ligands (μ -κ N, κ N´ and κ N,N´)
-1
-
1
-1
between -47 kcal.mol and -76 kcal.mol depending on the
and 1859 cm , respectively which remained essentially
unchanged when these are exposed to CO (see SI, Figure S24).
(
-1
grafting site, i.e. between -24 and -38 kcal.mol per Ru-N
bond, close to the values calculated for the Ru55 70 model).
.
(Ph)
15
This confirmed that the Pt surface of Pt/CO/ICy NC N0.2 NPs
was totally covered with CO due to their synthesis conditions,
thus explaining why these NPs are completely inactive as
hydrogenation catalyst.
H
These results suggest that, according to thermodynamics, CO
insertion will more likely occur on the monocoordinated
amidinate ligands.
·
(p-anisyl)
·(p-
1
5
The catalytic behavior of Pt NPs Pt/ICy
ClC
NCN0.2, Pt/ICy
In conclusion, the DFT calculations fully support the NMR
1
6 4
H )
·(p-tol)
NCN0.2 and Pt/ICy
NCN0.2 was studied in the
2
measurements in that the Ru NPs are covered with μ -κ N,
1
1
hydrogenation of 4-phenyl-3-buten-2-one, 3-methyl-2-
cyclohexenone and 4-nitrobenzaldehyde (Table 2, entries 1-9).
All reactions were carried out with Pt NP synthesized with 0.2
equiv. of the corresponding amidinate ligand as the results
changed little for Pt NPs prepared with 0.1 or 0.5 equiv. (Table
S2). In all cases, the olefins were smoothly hydrogenated (in
less than 1 h), but the carbonyl groups reacted more slowly.
After 20 h of reaction, ketone and aldehyde groups were
κ N´ amidinates, κ coordinated amidinates, and free ligand in
part in protonated form. The counter anion of the latter is not
known as the synthesis of the MNPs does not involve salts. In
1
5
the absence of conclusive NMR measurements for Pt NPs we
propose that the coordination mode is the same as that found
for Ru.
Catalytic studies
To probe the catalytic activity and chemoselectivity of the new partially hydrogenated in different grades depending on the N-
·
(p-tol)
NPs we chose Pt/ICy
NCN0.2 as model system and tested it aryl group of the ligand. We observed a slight increase in
in the hydrogenation of several substrates containing various activity with the electron-donor strength of these substituents.
functional groups such as olefinic bonds, carbonyl groups, and Thus, the NPs stabilized with the strongest donor ligand,
·
(p-anisyl)
aromatic rings. In addition, we investigated the influence of N- Pt/ICy
NCN0.2, were the most active systems in the
aryl groups with different electronic properties using Pt NPs hydrogenation of the carbonyl group. This trend was more
ligated to functionalized imidazolium-amidinate ligands pronounced for ethyl pyruvate (Table 2, entries 10-12).
8
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·
(p-anisyl)
(p-tol)
·(p-ClC6H4)
Table 2. Hydrogenation reactions catalyzed by Pt/ICy
NCN0.2 , Pt/ICy·
NCN0.2 and Pt/ICy
NCN0.2.
c
Conv. (%)
Select.
b
Entry/ Pt NPs
Substrate
Products
c
·
(p-anisyl)
a
>
99
/3 = 79:21
99
/3 = 81:19
1
2
3
/ Pt/ICy
NCN0.2
2
2
2
(
p-tol)
a
>
/ Pt/ICy·
NCN0.2
·
(p-ClC6H4)
(p-anisyl)
a
>99
/ Pt/ICy
NCN0.2
/3 = 86:14
·
a
>99
/6 = 67:33
4
5
6
/ Pt/ICy
NCN0.2
5
5
5
(
p-tol)
a
>99
/6 = 68:32
/ Pt/ICy·
NCN0.2
·
(p-ClC6H4)
(p-anisyl)
a
>99
/6 = 78:22
/ Pt/ICy
NCN0.2
·
a
98
/9/10 = 52:2:44
7
8
9
/ Pt/ICy
NCN0.2
8
8
8
(
p-tol)
a
98
/9/10 = 53:1:44
/ Pt/ICy·
NCN0.2
9
/9/10 = 56:4:38
8
·
(p-ClC6H4)
a
/ Pt/ICy
NCN0.2
·
(p-anisyl)
b
1
1
0/ Pt/ICy
NCN0.2
99
86
(
p-tol) b
1/ Pt/ICy·
NCN0.2
·
(p-ClC6H4)
b
1
2/ Pt/ICy
NCN0.2
24
·
(p-anisyl)
b
1
1
1
3/ Pt/ICy
NCN0.2
96
47
33
(
p-tol)
b
4/ Pt/ICy·
NCN0.2
·
(p-ClC6H4)
b
5/ Pt/ICy
NCN0.2
a. Reaction conditions: Substrate (0.5 mmol), Pt NPs (0.0025mmol of Pt assuming 77.3 % of Pt from TGA analysis), THF (0.75 mL), 20 h, r.t., 5 bar.
b. Reaction conditions: Substrate (0.5 mmol), Pt NPs (0.0025mmol of Pt assuming 77.3 % of Pt from TGA analysis), THF (0.75mL), 3 h, r.t., 5 bar.
1
c. Conversions, selectivities and products identities were determined by H NMR (average of two runs).
Significant differences of reactivity between the three We have successfully ligated zwitterionic amidinates to Pt NPs
nanosystems were observed in the hydrogenation of this which leads to the peculiar property that the charges of the
substrate. This ligand effect was confirmed in the anions need no compensation by cationic metal ions as in
hydrogenation of 2,2,2-trifluoroacetophenone (Table 2, entries clusters that contain thiolates on the surface for instance.
1
3-15), for which also the Pt NPs ligated by the stronger donor Usually N-based ligands are weakly binding ligands to MNPs,
·
(p-anisyl)
ligand ICy
NCN provided the most active nanocatalyst for but unexpectedly amidinates bind strongly to the Pt surface
1
5
this reaction. We conclude that more electron-rich Pt NPs yield atoms. We have shown that N NMR spectroscopy can be
faster catalysts, but as yet we cannot speculate on the used for the study of the adsorption mode of the nitrogen
15
mechanism.
ligand to the surface with the use of N enriched ligands. The
disturbing Knight shifts on the chemical shifts of the surface
bound nuclei could be largely suppressed when small Pt NPs
were used. Amidinates may well find broader application in
MNP and metal nanocluster (MNC) synthesis and catalysis.
Conclusions
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Journal Name
Even more so because subtle electronic modification of the N-
aryl groups of the amidinates has an effect on the catalytic
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1
Acknowledgements
This work was supported by CNRS, UPS-Toulouse, INSA, and
IDEX/Chaires d'Attractivité de l’Université Fédérale Toulouse
Midi-Pyrénées, and the Government of Spain (MINECO) /
FEDER funds of the EU (project CTQ2015-68978-P). The
authors thank V. Collière and L. Datas for TEM facilities
1
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5
0
(TEMSCAN, UPS), P. Lecante (CEMES, CNRS) for WAXS
5
,
measurements, C. Bijani for NMR measurements, and P.
Jankowski and A. Chapman for useful inspiration on the
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2
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3
synthesis of Pt NPs by reduction of Pt(NBE) . The authors also
acknowledge the HPCs CALcul en MIdi-Pyrénées (CALMIP-
HYPERION and CALMIP-EOS, grants P0611 and P1415) for
generous allocations of computer time.
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