A combined experimental-computational study of benzoxaborole crystal structures

Article abstract of DOI:10.1039/c4ce00313f

Benzoxaboroles are organoboron molecules which are gaining growing interest in different fields, notably for the development of new drugs. However, extensive characterization of these molecules in the solid state is still lacking. Here, questions related to the structure and spectroscopic signatures of crystalline benzoxaborole phases are thus addressed, using a combined experimental-computational approach. Two simple benzoxaboroles were studied: 1,3-dihydro-1-hydroxy-2,1-benzoxaborole (denoted as BBzx) and 5-fluoro-1,3-dihydro-1-hydroxy-2,1-benzoxaborole (also referred to as AN2690, a newly developed antifungal drug). First, the crystal structures of AN2690 and BBzx at room temperature are discussed, emphasizing the intermolecular interactions which play an important role in their formation. Then, results of IR and multinuclear (¹H, ¹¹B, ¹³C and ¹⁹F) solid state NMR characterization are presented, together with density functional theory (DFT) calculations which were carried out to assist in the interpretation of the spectra. Finally, the influence of polymorphism and anisotropic thermal expansion properties of the crystal structures on the NMR parameters of BBzx and AN2690 is discussed.

Full text of DOI:10.1039/c4ce00313f

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A combined experimental-computational study of
benzoxaborole crystal structures†
Cite this: CrystEngComm, 2014, 16,
999
4
a
a
a
a
Saad Sene, Dorothée Berthomieu, Bruno Donnadieu, Sébastien Richeter,
a
a
a
a
b
Joris Vezzani, Dominique Granier, Sylvie Bégu, Hubert Mutin, Christel Gervais
a
and Danielle Laurencin*
Benzoxaboroles are organoboron molecules which are gaining growing interest in different fields,
notably for the development of new drugs. However, extensive characterization of these molecules in
the solid state is still lacking. Here, questions related to the structure and spectroscopic signatures of
crystalline benzoxaborole phases are thus addressed, using a combined experimental-computational
approach. Two simple benzoxaboroles were studied: 1,3-dihydro-1-hydroxy-2,1-benzoxaborole
(denoted as BBzx) and 5-fluoro-1,3-dihydro-1-hydroxy-2,1-benzoxaborole (also referred to as AN2690, a
newly developed antifungal drug). First, the crystal structures of AN2690 and BBzx at room temperature
are discussed, emphasizing the intermolecular interactions which play an important role in their formation.
Received 11th February 2014,
Accepted 18th March 2014
1
11
13
19
Then, results of IR and multinuclear ( H, B, C and F) solid state NMR characterization are presented,
together with density functional theory (DFT) calculations which were carried out to assist in the interpretation
of the spectra. Finally, the influence of polymorphism and anisotropic thermal expansion properties of the
crystal structures on the NMR parameters of BBzx and AN2690 is discussed.
DOI: 10.1039/c4ce00313f
www.rsc.org/crystengcomm
benzoxaborole (denoted as BBzx, Fig. 1a), with pK
a
~8.9 and
This particular reactivity has been
the key to the discovery of a series of benzoxaborole-
1
. Introduction
1
,6,13
pK ~7.3, respectively.
a
Boronic acids (R–B(OH) ) are a family of molecules which
have a wide range of applications. They are commonly used
2
1
6–9
based drugs.
One of the most studied to date is
in organic synthesis as reagents in Miyaura–Suzuki coupling
5-fluoro-1,3-dihydro-1-hydroxy-2,1-benzoxaborole (AN2690 or
2
3
reactions, in materials science for the synthesis of sensors
“Kerydin” – Fig. 1b), which is a broad-spectrum antifungal
4
5
6,7,9
or Covalent Organic Frameworks (COFs), and in medicine.
More recently, benzoxaboroles, which are hemi-esters of
drug developed for the treatment of onychomycosis.
Other systematic investigations of benzoxaboroles have been
carried out, showing that they have a broad spectrum of
6
–12
arylboronic acids, have attracted much attention (Fig. 1).
8
,9
Like boronic acids, benzoxaboroles are Lewis acids, which
can undergo conversion from trigonal to tetrahedral geome-
try in the presence of a nucleophile. However, this conversion
takes place much more easily than in the corresponding
boronic acids, as illustrated for example by the difference
in pKa between phenylboronic acid and the related
potential therapeutic applications.
(Fig. 1c) has interesting properties as
inflammatory agent for the treatment of psoriasis and atopic
For example, AN2728
a
topical anti-
8
a,9
dermatitis,
while SCYX-7158 (Fig. 1d, also referred to as
AN5568) is being studied for the treatment of human African
8
b,9
trypanosomiasis (sleeping sickness).
a
Institut Charles Gerhardt de Montpellier, UMR 5253, CNRS-UM2-UM1-ENSCM,
Place E. Bataillon, CC1701, 34095 Montpellier cedex 5, France.
E-mail: dlaurenc@univ-montp2.fr; Fax: +33 4 67 14 38 58; Tel: +33 4 67 14 38 02
b
Sorbonne Universités, UPMC Univ Paris 06, CNRS, Collège de France,
UMR 7574, Chimie de la Matière Condensée de Paris, F-75005, Paris, France
†
Electronic supplementary information (ESI) available: Le Bail refinements of
the XRD powder patterns, solution NMR spectra, TGA, comparison of the XRD
data and structures of AN2690 and BBzx with those of previously reported
structures of these 2 compounds, calculated vibrational modes of AN2690
(PED included) and BBzx, GIPAW calculated NMR parameters for the different
reported structures of AN2690 and BBzx, and geometrical features of the
different calculated models. CCDC 986106. For ESI and crystallographic data
in CIF or other electronic format see DOI: 10.1039/c4ce00313f
Fig. 1 Examples of benzoxaboroles.
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So far, investigations on benzoxaboroles have mainly
was dissolved in 80 mL of methanol under magnetic stirring.
The solution was cooled to 0 °C using an ice bath. NaBH4
(2.79 g, 73.8 mmol) was then added progressively in order to
avoid any excessive effervescence due to the formation of H2.
Once the addition was over, the ice bath was removed and
the solution was stirred for 2 hours while gradually warming
to room temperature. The progress of the reaction was moni-
tored by thin layer chromatography (silica gel, toluene eluent).
The reaction mixture was then slowly acidified with 250 mL
of HCl (3 M aqueous solution) and stirred for 15 minutes.
The solution was subsequently extracted with diethyl ether
(4 × 80 mL). The combined organic fractions were then dried
focused on developing their synthesis, evaluating their reac-
tivity in solution (notably as sugar receptors) or studying
6
,11a
their potential therapeutic applications.
However, only a
handful of benzoxaborole-based structures have been fully
1
1a,14–18
characterized in solution and in the solid state.
To
the best of our knowledge, the molecule for which the most
spectroscopic data are available is 1,3-dihydro-1-hydroxy-2,1-
benzoxaborole (i.e. the simplest benzoxaborole, denoted as
1
13
BBzx in Fig. 1a), whose H and C NMR spectra in solution
1
1
14,16–18
and B solid state NMR spectrum have been reported.
Density-functional theory (DFT) calculations were also
performed on this molecule, notably to calculate Raman and
with anhydrous MgSO and concentrated. The resulting white
4
1
1
14,18
IR vibration modes and B NMR parameters.
In contrast,
powder was dissolved in 100 mL of chloroform. The solution
was stirred for 30 minutes, filtered under vacuum in order to
remove the insoluble impurities, and finally concentrated. A
final purification was performed using silica-gel column
for other molecules like AN2690, extensive characterizations
in the solid state using techniques like solid state NMR are
still missing, despite the fact that these could be useful
for the analysis of its local environment within complex
materials or pharmaceutical formulations, especially in cases
where X-ray diffraction analyses are impaired.
2 2
chromatography (CH Cl eluent), leading to a pure fraction
of compound 1 (yield: 88%).
1
6
H NMR (200 MHz, DMSO-d ): δ 4.49 (d, 2H, J = 5.6 Hz,
–CH ), 5.61 (t, 1H, J = 5.6 Hz, –OH), 7,09 (td, 1H, J = 8.9 and
Due to the increasing interest in benzoxaboroles, we
found it timely to look in more depth not only at their crystal
structures but also their spectroscopic signatures in the solid
state. In particular, when it comes to pharmaceutical applica-
tions, polymorphism is an important point to consider, and a
means to distinguish different polymorphs needs to be
2
3.3 Hz, H ), 7,31 (dd, 1H, J = 9.9 and 3.2 Hz, H ), 7,61
ar
ar
(dd, 1H, J = 8.7 and 5.3 Hz, Har) ppm.
Synthesis of 5-fluorobenzoxaborole (2) – AN2690. Com-
pound 1 (4.60 g, 22.4 mmol) was dissolved under stirring in
60 mL of anhydrous diethyl ether (the Schlenk flask having
been placed initially under a flow of Argon). The solution was
cooled to a temperature lower than −30 °C using an
1
9
established. Here, we thus present a comparative study of
two benzoxaboroles in the solid state using a combined
experimental-computational approach: the antifungal drug
AN2690 (Fig. 1b) and its non-fluorinated analogue BBzx
2
acetone–liquid N bath. n-BuLi (19 mL, 47.1 mmol) was then
−
1
added dropwise at a flowrate of 2.7 mL min using a syringe
(
Fig. 1a). The AN2690 phase was synthesized, purified and
pump. After the addition, the solution was stirred for 1 hour.
i
crystallized as part of this work (as detailed below), while for
BBzx, a commercial crystalline phase was studied (after
verifying its purity). First, we compare the crystal structures
of AN2690 and BBzx in terms of intermolecular interactions.
Then, their IR and multinuclear solid state NMR spectra are
presented and discussed on the basis of DFT calculations of
IR vibrational modes and NMR parameters. Finally, the
importance of taking into account temperature effects for the
crystalline phases of these benzoxaboroles is discussed, by
showing how and why the temperature may affect their
spectral properties, notably the solid state NMR ones.
B(O Pr)
3
(6 mL, 24.6 mmol) was then added in the same way.
Once the addition was complete, the cooling bath was
removed and the solution was stirred overnight under argon
while gradually warming to room temperature. The reaction
mixture was slowly acidified with 170 mL of H SO (2 M
2 4
aqueous solution) and stirred for 15 min. It was then
extracted with diethyl ether (3 × 80 mL). The combined
organic fractions were dried with anhydrous MgSO and con-
4
centrated, leading to the formation of a yellow oil. After one
night of slow evaporation at room temperature under air,
white crystals formed in the oil. They were isolated by
adding 3 mL of toluene (in which AN2690 is less soluble
than the impurities), filtering the mixture under vacuum,
and then washing the white powder with n-pentane. The
filtrate was concentrated, leading once more to a yellow oil,
in which white crystals formed again after one night under
air at room temperature. The same cycle (crystallization–
washing–filtration) was thus performed as long as crystals
continued to form in the oil. The white solid fractions recovered
were combined and a final recrystallization in water at
100 °C was then performed in order to purify compound 2
(yield 45%). At this stage, if traces of boric acid are still
2
. Experimental section
2
.1 Syntheses
Sodium borohydride (NaBH4, 98+%, Acros Organics),
-bromo-5-fluorobenzaldehyde (98%, Alfa Aesar), n-butyllithium
2
(n-BuLi, 2.5 M in hexane, Sigma-Aldrich), triisopropyl borate
i
(B(O Pr) , 98+%, AcroSeal, Acros Organics), and 1,3-dihydro-1-
3
7 7 2
hydroxy-2,1-benzoxaborole (C H BO , abbreviated here as
BBzx, Sigma Aldrich) were used as received. Reagent grade
solvents and acids were used in all reactions without further
purification, unless specified.
1
1
present (as seen by B NMR), they can be removed by silica
gel column chromatography (CH Cl eluent). The two steps
Synthesis of 2-bromo-5-fluorobenzyl alcohol (1). The
2
2
2
-bromo-5-fluorobenzaldehyde precursor (4.77 g, 23.5 mmol)
leading to the formation of AN2690 (compound 2) are shown
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2
0
Experimental intensities were integrated from several series
of exposures; the total data set was a sphere. An empirical
absorption correction was then applied using spherical har-
21
monics implemented in a SCALE3 ABSPACK scaling algorithm.
Structure resolution of the single crystal XRD data of
AN2690. The structure was solved by using direct methods
2
2
Scheme 1 A two-step synthetic protocol for the preparation of AN2690.
and subsequent differences Fourier maps, then refined by
2
least squares procedures on weighted F values using
2
3
in Scheme 1, and the purification protocol for the second step
in Scheme 2.
SHELXL-97, as included in the WinGx system programs for
24
Windows (WinGX version 2013.3 – July 2013). All non-
hydrogen atoms were assigned anisotropic displacement
parameters and refined without positional constraints.
Hydrogen atoms were constrained to ideal geometries and
refined with fixed isotropic displacement parameters. Least
squares refinement proceeded smoothly to give the residuals
1
6
H NMR (300 MHz, DMSO-d ): δ 4.97 (s, 2H, H7), 7.16
td, 1H, JH–H,H–F = 8.5 Hz, JH–H = 3.2 Hz, H5), 7.25 (dd, 1H,
JH–F = 9.7 Hz, JH–H = 3.2 Hz, H3), 7.75 (dd, 1H, J = 8.7 Hz,
(
H–H
1
3
1
JH–F = 5.3 Hz, H6), 9.25 (s, 1H, H2) ppm. C( H) NMR
6
(
150.9 MHz, DMSO-d ): δ 69.5 (d, JC–F = 3.1 Hz, C7), 108.5
(
d, JC–F = 22.1 Hz, C3), 114.4 (d, JC–F = 22.0 Hz, C5), 132.6
shown in Table 1.
1
(d, JC–F = 9.3 Hz, C6), 156.6 (d, J
= 8.9 Hz), 164.2 (d, J
46.4 Hz) ppm. B NMR (125.4 MHz, DMSO-d ): 31.8 ppm (s).
=
C–F
Solution NMR experiments.
H NMR spectra were
C–F
11
6
2
recorded using Bruker 300 or 200 MHz NMR spectrometers
at frequencies of 300.13 and 200.13 MHz, respectively.
1
9
6
F NMR (282.4 MHz, DMSO-d ): −110.3 ppm (td, J
= 9.6
H–F
1
9
and 5.9 Hz).
F NMR spectra were recorded using a Bruker 300 MHz
NMR spectrometer operating at a frequency of 282.40 MHz.
1
3
1
13
The
C NMR and 2D H– C HMQC (Heteronuclear
2
.2 Characterization
General characterization. IR spectra were recorded in
Multiple-Quantum Correlation) NMR spectra were recorded
using a Bruker 600 MHz NMR spectrometer operating at a
1
3
11
transmission mode on KBr pellets using an Avatar 320 FTIR
spectrometer. Thermogravimetric analysis (TGA) measurements
were performed on a Perkin Elmer apparatus under air flow
with a hold time of 1 min at 25 °C and a temperature increase
C frequency of 150.94 MHz. B NMR spectra were recorded
using a Bruker 400 MHz NMR spectrometer at a frequency of
128.38 MHz.
Solid state NMR experiments. All solid state NMR
experiments were performed using a Varian VNMRS 600 MHz
(14.1 T) NMR spectrometer. A 3.2 mm Varian T3 HXY magic
−1
from 25 to 800 °C at a rate of 5 °C min .
X-ray diffraction measurements. X-ray diffraction powder
patterns of AN2690 and BBzx were recorded in capillary
mode using a PANalytical X'pert MPD-Pro diffractometer
equipped with a primary hybrid monochromator block, at
the Cu Kα wavelength (λ = 1.5406 Å) (40 kV and 40 mA). Mea-
surements were performed at room temperature between 4°
and 70° in 2θ, using a step size of 0.017° and a counting time
per step of 600 s. Details on the refinement of the powder
diffractograms of AN2690 and BBzx can be found in the ESI.†
A single crystal of AN2690 (0.22 × 0.10 × 0.04 mm) was
selected and measured at room temperature (T = 293 K).
Measurements were made using an Oxford Diffraction,
XCalibur-I four circles kappa-geometry diffractometer,
equipped with a large Be window CCD area-detector, using
1
13
11
angle spinning (MAS) probe was used for H, C and
B
experiments, while a 2.5 mm Varian T3 HFXY probe was
1
9
1
used for F experiments. The operating frequencies for H,
1
3
11
19
C, B and F were 599.82, 150.83, 192.44 and 564.33 MHz,
respectively. All NMR experiments were performed under
temperature regulation in order to ensure that the
temperature inside the rotor is 20 °C (except for the variable-
1
9
temperature F NMR studies mentioned in the discussion).
2
5 1
Windowed-DUMBO
H-MAS experiments were carried
out at a spinning speed of 10 kHz. The RF field strength was
100 kHz, the duration of one DUMBO element was 34.4 μs,
and the observation window was 0.8 μs. Four transients were
acquired with a recycle delay of 1024 s for AN2690 and BBzx
(in both cases, the recycle delay chosen corresponds to full
2
0
Mo-Kα monochromatized radiation (λ
Intensity measurements were carried out by performing ω
scans of Bragg peaks in the range 2.91° < θ <29.01°.
= 0.71073 Å).
1
H relaxation). A scaling factor was applied to the frequency
1
axis to ensure its accurate calibration. H chemical shifts
were referenced to external adamantane at 1.8 ppm (used as
a secondary reference).
1
13
H– C CPMAS NMR spectra were recorded spinning at
2
1
0 kHz, using a contact time of 2.5 ms (ramped pulse), and
00 kHz spinal-64 H decoupling during acquisition. A
1
recycle delay of 128 s was used for AN2690 and BBzx. A total
of 320 and 106 transients were recorded for AN2690 and
1
3
BBzx, respectively.
C chemical shifts were referenced
externally to adamantane (used as a secondary reference); the
high frequency peak was set to 38.5 ppm.
Scheme 2 Procedure for the purification of AN2690.
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Table 1 Crystallographic data and structure refinement for AN2690
CCDC
986106
Structure
Single crystal
Empirical formula
7 6 2
C H BFO
151.93
293(2)
−1
M
r
/g mol
Temperature/K
λ/Å
0.71073
Triclinic
P¯1
Crystal system
Space group
a/Å
b/Å
c/Å
α/°
β/°
γ/°
4.0277(2)
6.3237(6)
14.0649(14)
97.110(8)
91.015(6)
100.632(7)
349.07(5)
2
3
V/Å
Z
−3
ρcalc/g cm
1.445
2.984
−1
μ/mm
F(000)
1764
ωmin–ωmax/°
2.91 to 29.01°
Index ranges
Reflns collected
−5 ≤ h ≤5; −7 ≤ k ≤ 7; −17 ≤ l ≤ 17
8573
Independent reflns
1413 (Rint = 0.0197)
99.9%
Empirical correction
0.9743 and 0.9953
Full-matrix least-squares on F
1413/0/100
Completeness to θ = 29.2°
Absorption correction
Max. and min. transmission
Refinement method
Data/restraints/parameters
2
2
Goodness-of-fit on F
S = 1.044
R indices [for 2890 reflections with I > 2σ(I)]
R indices (for all 3693 data)
R
R
1
= 0.0370, wR
2
2
= 0.0906
= 0.0976
1
= 0.0480, wR
2
2
2
2
2
Weighting scheme [where P = (F
o
+ 2F
c
)/3]
Calc w = 1/[s (F
0.150 and −0.166 e Å
o
) + (0.0461P) + 0.060P]
3
Largest diff. peak and hole
1
1
B MAS NMR spectra were recorded spinning at 20 kHz
MAS. The single pulse experiments were performed with a
DFT calculations on molecular models. Molecular models
of BBzx and AN2690 were studied, both as single molecules
and dimers. It should be noted that DFT calculations were
also carried out on a fluorobenzene molecule (C H F), as
1
~
45° solid pulse of 1.25 μs and 100 kHz spinal-64
decoupling during acquisition. A recycle delay of 100 s was
used for AN2690 and 32 s for BBzx (corresponding in both
cases to full relaxation of B). A total of 50 and 340 tran-
sients were recorded for AN2690 and BBzx, respectively.
B chemical shifts were referenced to external NaBH
42.05 ppm (used as a secondary reference).
H
6
5
mentioned later in the manuscript.
Geometry optimizations and IR frequency calculations
1
1
2
6
were carried out within the ab initio Gaussian code, using
1
1
27
4
at
the hybrid B3LYP functional, and an all-electron Gaussian
−
8
−
basis set 6-311++g(d,p). SCF convergence was set to 10 for
the energy during geometry optimisation and frequency
calculations.
1
9
The F MAS NMR spectrum of AN2690 was recorded spin-
ning at 20 kHz. The single pulse experiment was performed
with a 90° pulse of 2.5 μs and 80 kHz CW (continuous wave)
Normal mode analyses were made using the potential
1
H decoupling during acquisition. A recycle delay of 60 s was
energy distribution (PED), calculated according to previous
1
9
28,29
used and a total of 4 transients were recorded. F chemical
shifts were referenced to external commercial PTFE at
studies,
using the hessian matrix calculated by the
B3LYP/6-311++g(d,p) method. Only contributions larger than
10% were considered for simplicity. A set of (3N − 6) Wilson–
Decius coordinates (N = number of atoms) was used and
combined to take into account symmetries, such as cycle
symmetries. IR absorption intensities were calculated from
−122.4 ppm (used as a secondary reference).
2
.3 Computational details
2
6,30
Models. Density functional theory calculations were
the atomic polar tensors.
carried out on two types of models: molecular models and
periodic unit cell models. Molecular models were used to
assist in the interpretation of the IR spectrum of AN2690,
while periodic unit cell models were used to determine how
IR and solid state NMR spectroscopy can be used to distinguish
the different crystalline forms of AN2690 and BBzx.
DFT calculations on periodic unit cell models. DFT
calculations were carried out on the crystalline structures of
the different crystalline forms of BBzx and AN2690, described
as infinite periodic systems using periodic boundary
conditions. The unit cell parameters and symmetry were set
according to the experimental single-crystal XRD data, and
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kept fixed during the geometry optimizations. Experimental
atomic positions were used as a starting point for the
geometry, and then relaxed by DFT.
The quadrupolar interaction can then be characterized by the
quadrupolar coupling constant C and the asymmetry param-
Q
eter η
Q
, which are defined as C
Q
= eQVzz/h and η
Q
= (Vyy
−
3
1
Geometry optimization was performed using the VASP,
V )/V . The Q values reported by Pyykkö were used in these
xx
zz
3
2
33
44
19
Crystal09 and/or QUANTUM-ESPRESSO (QE) codes. The
different combinations of calculation codes, functionals and
basis sets tested on the two forms of AN2690 are summarized
in Table 2. For the Crystal09 calculations, SCF convergence
calculations. For the F chemical shift calculations, the
reference system was fluoroapatite and a scaling factor k = 0.8
1
9
45
was applied, in line with recent GIPAW calculations on F.
−
7
−10
was set to 10 and 10 for the energy during geometry opti-
misation and frequency calculations, respectively. For the
VASP and QE calculations, the positions of all atoms were
relaxed until the total energy difference between the loops
3
. Results and discussion
3.1 Synthesis and purification of AN2690
Different strategies have been described in the literature for
−
4
−10
7a,15,46,47
was less than 10 eV and 10
Ry, respectively. It should be
the synthesis of AN2690.
The most common route
7a
noted that the number of k-points used for the VASP calcula-
tions on AN2690 was set to 36 (4 × 4 × 4 grid), as no signifi-
cant difference in energy was observed for a higher number
uses 2-bromo-5-fluorobenzaldehyde as a precursor. Baker et al.,
who were the first to describe the synthesis of AN2690 starting
from this precursor, obtained the pure product after 4 steps
(reduction–protection of the alcohol–cyclisation–deprotection)
with ~60% overall yield. Similar synthetic routes were then
3
4
of k points (5 × 5 × 5 grid). The Grimme correction was
included in some of the calculations to take into account the
weak dispersion forces, because in the systems studied here,
Van der Waals interactions are particularly relevant in
describing intermolecular forces. Calculations including the
4
7
46
used by Ding et al. and Gunasekera et al. who optimized
the reaction and reduced it to 2 steps with ~40% and ~65%
overall yield, respectively.
3
5
Grimme correction are referred to as B3LYP-D* (Crystal 09).
The methodology we decided to use here to synthesize
4
6
First principles calculations of NMR parameters were car-
ried out using the GIPAW method (Gauge Including Projector
AN2690 was the one described by Gunasekera et al. which
presents the advantage of being a practical procedure for
large scale syntheses of benzoxaboroles. It involves 2 steps:
4
0
Augmented Wave) on the structures obtained after geome-
try optimization using the QE code. The GIPAW method is
indeed increasingly being used in materials science to calcu-
late the NMR parameters of organic, inorganic and hybrid
(i) reduction of 2-bromo-5-fluorobenzaldehyde and (ii) one-
i
pot reaction with NaH, n-BuLi and B(O Pr)
3
, followed by acid
treatment of the reaction medium and column chromatogra-
phy to purify the product. Our attempts to reproduce this
synthesis led to overall yields ~25%, much lower than those
reported in the literature (~65%). Thus we adapted the
procedure in order to try to increase the yield.
4
1,42
materials.
The wave functions are expanded on a plane
wave basis set with a kinetic energy cut-off of 80 Ry. The inte-
gral over the first Brillouin zone was performed using a
Monkhorst-Pack 4 × 4 × 4 k point grid. The isotropic chemical
shift δiso is defined as δiso = −[σ − σref ]/[1 − σref ] where σ is
the isotropic shielding and σref is the isotropic shielding of
the same nucleus in a reference system (as previously
Concerning the first step, which is the reduction of the
fluorinated benzaldehyde using NaBH , we noticed the pres-
4
ence of an impurity that was insoluble in chloroform, which
4
3
11
described). The principal components Vxx, Vyy, and Vzz of
3
was identified as B(OH) by B MAS NMR. We found that it
the electric field gradient (EFG) tensor, defined as |V | ≥
can be successfully eliminated by washing the product with
chloroform, as boric acid is poorly soluble in this solvent,
and then performing a silica gel column chromatography. In
doing so, the alcohol (compound 1) used in the next step
is pure.
zz
|V
xx| ≥ |Vyy|, are obtained by diagonalisation of the tensor.
Table 2 Periodic DFT calculation methods for geometry optimizations
of AN2690 forms
In order to further improve the yield in the second step,
Code
Functional
Basis Set
which is the most critical, Et O was first replaced by THF.
2
a,b
However, the excessive formation of insoluble unidentified
products was observed in the reaction mixture, indicating
that THF is a less appropriate solvent. The procedure was
Crystal09 (ref. 32)
B3LYP
B3LYP-D*
B3LYP
B3LYP
PBE
BS-A
BS-A
BS-A
a,b
"
"
"
"
a,c
c,d
BS-B
BS-B
then tested using Et O as a solvent, but avoiding the use of
c,d
2
3
1
e
f
NaH, which was replaced by n-BuLi for the deprotonation
and debromination of the alcohol (Scheme 1). After acidic
VASP
GGA-PBE
BS-C
BS-D
3
3
e
g
QE
GGA-PBE
treatment and extraction with Et O, a yellow oil was obtained.
a
2
BS-A: all electron Gaussian basis-set for B: 621/21/1; for C: 621/21/1;
b
At this stage, column chromatography was first performed in
order to purify the product, but it led to a very small amount
of the pure product, because in several of the fractions col-
lected from the column, AN2690 was found to remain mixed
with other impurities. For better purification, we developed a
new strategy after having observed that crystals of AN2690
for O: 631/31/1; for F: 6211/411/1; and for H: 31/1. Five tolerances
setting the accuracy of the mono and bi-electron integrals: 8 7 7 8 25.
c
Five tolerances setting the accuracy of the mono and bi-electron
d
36 e
integrals: 6 6 6 6 12. BS-B: pob-TZVP.
approximation.
potentials.
PBE-generalised gradient
BS-C: valence electrons described by PAW pseudo-
BS-D: valence electrons described by norm conserving
3
7 f
3
8 g
3
9a
39b
pseudopotentials in the Kleinman Bylander form.
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1
5,17,46
form in the crude oil (see Scheme 2 and Experimental
section). The desired compound AN2690 was thus obtained
in 40% overall yield after a final recrystallization step in
water. Although this is still lower than the one reported by
with those already published in the literature,
with the
1
3
assignments of the C resonances of AN2690 being proposed
here for the first time. It should be noted that in agreement
with previous observations, the C signal of the carbon
linked to boron is significantly broadened, and thus barely
1
3
4
6
Gunasekera et al., it is nevertheless the best we could
1
3
achieve starting from 2-bromo-5-fluorobenzaldehyde. Most
observable on the C solution NMR spectra.
1
13
11
importantly, no impurities were observed by H, C, B and
1
9
3.2 Characterization in the solid state
F solution NMR, and Le Bail refinements of the XRD data
recorded on the microcrystalline powder of AN2690 also
confirmed its purity (see Fig. S1 in the ESI†).
AN2690 and BBzx were characterized in the solid-state using
X-ray diffraction, IR and solid state NMR spectroscopy, as
well as TGA. Below, XRD, IR and NMR results are successively
discussed, while TGA data can be found in the ESI† (Fig. S4).
X-ray diffraction. The XRD powder patterns of AN2690 and
the commercial BBzx phase, both recorded in capillary mode,
are shown in Fig. 2. In both cases, the diffractograms were
compared to those simulated from the crystal structures
The solution NMR spectra of AN2690 can be found in the
supporting information, together with those of the non-
fluorinated analogue, BBzx (Fig. S2 and S3 in the ESI†). All
resonances were assigned unambiguously (Tables S1 and S2
in the ESI†), and the J coupling values were determined
4
8
based on previous NMR studies of fluorinated aromatics.
The spectra reported here for AN2690 and BBzx are consistent
49
previously reported for these two compounds (ESI,† Fig. S5).
Fig. 2 Top left: XRD powder patterns of AN2690 (red) and BBzx (blue) recorded at room temperature. Bottom left: crystal structures of AN2690
16
and BBzx (polymorph P(1)), corresponding to the crystalline phases studied here. Right: Hirshfeld surface fingerprint plots of AN2690 and BBzx
(
polymorph P(1)). On the Hirshfeld surface fingerprint plots, d
e
is the distance from a point on the Hirshfeld surface to the nearest nucleus outside
50
the surface, while d
i
is the distance from a point on the surface to the nearest nucleus inside the surface.
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In the case of AN2690, the XRD pattern of the microcrys-
talline powder we had synthesized was different from the one
expected based on the crystal structure previously reported by
Madura et al. Le Bail refinements were thus performed on
the experimental diffractogram of AN2690 (Fig. S1 in the
ESI†), and a single crystal of sufficient quality was also iso-
lated, which was analyzed by single-crystal XRD analysis. The
new structure is essentially the same as the previously
reported one: same space group, similar lattice parameters,
and similar positioning of the molecules in the unit cell
of the Hirshfeld surface fingerprint plots of AN2690 and BBzx
(Fig. 2, right) finely makes evident the different inter-
molecular interactions mentioned above, with notably the
signature of OH⋯O hydrogen bonds, and evidence of the
C–H⋯F close contacts. Concerning AN2690, the differences
in intermolecular interactions along and perpendicularly to
the (bc) plane may perhaps be related to the anisotropy in its
thermal expansion. Indeed, it appears that the thermal
expansion is the strongest when it is perpendicular to the
(bc) plane, i.e. where the weakest intermolecular interactions
(i.e. interplanar stacking) occur.
1
5
(ESI,† Table S3 and Fig. S6). Thus, the discrepancy in the
powder patterns is not due to the formation of a new poly-
morph of AN2690, all the more since the Hirshfeld surface
fingerprint plots of both forms of AN2690 are nearly identical
IR spectroscopy. The IR spectra of AN2690 and BBzx are
shown in Fig. 3. These are in agreement with the crystal
structures, with the presence of a broad O–H stretching band
5
0
−1
(ESI,† Fig. S7). The differences in their powder patterns may
centered at ~3300 cm , due to the H-bonding in the solid-
rather result from the fact that XRD measurements were not
state. Indeed, as mentioned above, the crystal structures of
BBzx and AN2690 are both formed of benzoxaborole mole-
cules facing each other and interacting through H-bonds.
To assist in the interpretation of the other IR vibration
bands, DFT calculations were carried out on molecular
models of both structures, composed of either a single mole-
cule of AN2690 and BBzx, or of dimers of these molecules
(involving H-bonds). A similar approach had previously been
proposed in the literature for the study of the vibrational
performed at the same temperature (293 K for us vs. 100 K
1
5
for Madura et al.), and that AN2690 undergoes an aniso-
tropic thermal expansion. Indeed, the a lattice parameter
increased by nearly 4% between both measurements, while b
and c varied by less than 0.5%. It should be noted that exam-
ples of anisotropic thermal expansion have been reported
5
1
previously for molecular crystals, and the importance of
taking them into account in the pharmaceutical context has
5
1a
17
been emphasized.
modes of benzoxaboroles. The geometry of the dimers, after
In the case of BBzx, two different polymorphs have been
reported in the literature. The crystal structure of BBzx was
first described by Zhdankin et al. who found that this mole-
cule can crystallize in the triclinic P ¯1 space group, with two
optimization, is very similar to the one adopted by the mole-
cules in the solid state (see the ESI,† Table S4, for AN2690).
The analysis of the calculated vibration frequencies for BBzx
and AN2690 was then performed (see the ESI,† Tables S5 and
S6). After the comparison of the experimental and calculated
vibration frequencies, and of the Potential Energy Distribution
(PED) analysis of the calculated vibrational modes (see ESI), it
appears clearly, for example, that the C–F stretching
1
6
independent molecules in the unit cell (polymorph referred
to as P(1)). Another polymorph (referred to as P(2)) was then
1
7
obtained for this molecule by Adamczyck-Wozniak et al.,
with a monoclinic P2 space group and also two independent
1
−
1
molecules in the unit cell. The packing of the molecules in
both polymorphic forms is very similar (see the ESI,† Fig. S8).
Here, Le Bail refinements on the experimental powder pat-
tern recorded at room temperature show that it corresponds
to the P(1) polymorph (see the ESI,† Fig. S1), with only
slightly different lattice parameters compared to the previ-
ously published structure, due to the difference in tempera-
ture in the measurements (293 K for us vs. 173 K for
Zhdankin et al.). However, it is worth noting that the cell
parameters vary much less with temperature compared to
those of AN2690. In the course of our study, no single crystal
of BBzx of sufficient quality could be isolated to record and
solve a room-temperature structure.
frequency for AN2690 is observed at 1250 cm on the experi-
−1
mental IR spectrum, the calculated frequency being ~1264 cm
for the dimer model. It is worth noting that (i) the νC–F
frequency calculated for AN2690 is of the same order of
magnitude as those of other molecules like fluorobenzene
−
1
(νC–F(calc) = 1235 cm ), making the assignment of this
vibration band unambiguous; (ii) the vibrational mode at
−
1
1264 cm in the dimer is actually composite, with the C–F
Many similarities appear between the structures of
AN2690 and BBzx. As shown in Fig. 2, both are composed of
benzoxaborole dimers, which interact with each other
through H bonds, and then pile through weaker π-stacking
interactions, perpendicularly to the aromatic cycles. In the
case of AN2690, the presence of a fluorine atom leads to
additional C–H⋯F interactions with neighbouring aromatic
cycles (shortest intermolecular C–H⋯F distance is ~2.6 Å). It
has been shown that such interactions, although of weak
Fig. 3 IR spectra of AN2690 (red) and BBzx (blue). The “*” symbol
indicates the C–F stretching frequency of AN2690.
52
energy, can contribute to the crystal packing. The comparison
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stretching representing only 20% of the mode (see the PED
analysis in the ESI†); and (iii) when the periodic model of this
structure is considered (not just the dimer), a similar value was
correspond to aromatic protons only, while those between
~6.5 to ~8.2 ppm correspond to both aromatic and hydroxyl
protons of BBzx. Finally, it should be noted that for both
AN2690 and BBzx, the high chemical shifts of the hydroxyl
protons are consistent with the presence of strong H-bonds in
−1
found for the calculated C–F frequency (νC–F(calc) = 1275 cm ).
Solid state NMR. Multinuclear solid state NMR
characterizations were then performed on AN2690 and BBzx
5
4
the solid state.
1
13
11
19
13
13
(
Fig. 4) in order to extract experimental H, C, B (and F)
In the C CPMAS NMR spectra, finely resolved C reso-
nances were observed (Fig. 4b). The signals which can be eas-
NMR parameters. To assist in the interpretation of the
spectra, GIPAW calculations were carried out on periodic
2
ily assigned are those of the CH group, which is centered at
5
3
models of the structures shown in Fig. 2, The calculated
NMR parameters can be found in Tables 3 and 4.
~70 ppm for both molecules, and the carbon linked to the
fluorine, which is centered at ~166 ppm for AN2690 and split
1
13
19
The H NMR spectra are shown in Fig. 4a. Using homonu-
in two due to the C– F J coupling. The other signals were
1
3
clear decoupling during the acquisition (the DUMBO
scheme), it was possible for both molecules to resolve reso-
nances coming from the methylene groups between 4.0 and
assigned by comparison with the solution C NMR spectra
and confirmed by the GIPAW calculations (Tables 3 and 4,
and Fig. S10 in the ESI†). In contrast with solution NMR, the
5
5
5
.0 ppm. In the case of AN2690, a lower resolution is
carbon linked to the boron is observable in the solid state;
it is clearly resolved in the case of AN2690 (centered at
1
19
achieved due to the additional H⋯ F dipolar coupling,
which results in a strong overlap of the signals of aromatic
and hydroxyl protons between ~5.2 and ~8.2 ppm.
Concerning BBzx, a better resolution is obtained in this area
of the spectrum and two groups of signals can be distin-
guished. Based on the GIPAW calculations (Tables 3 and 4,
and Fig. S9 in the ESI†), the signals between ~5.2 to ~6.5 ppm
1
3
~123 ppm), while it overlaps with other C resonances in the
case of BBzx (centered at ~130 ppm). Concerning BBzx, it
should be noted that most of the signals of the two crystallo-
graphically independent molecules cannot be resolved by 1D
1
3
C solid state NMR, a result which is not fully surprising
13
given the GIPAW calculated C chemical shifts (which are
1
13
11
19
Fig. 4 H, C, B and F solid state NMR spectra of AN2690 (red) and BBzx (blue).
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Table 3 Experimental and calculated NMR parameters for AN2690. Calculated values reported here are those obtained for the structure solved at
293 K (after VASP DFT relaxation of the atomic positions)
1
13
11
19
H NMR
C NMR
B NMR
F NMR
δ
iso (ppm)
δiso (ppm)
δ
iso (ppm)
C
Q
(MHz)
η
Q
δ
iso (ppm)
a
a
a
b
a
H
Exp
Calc
C
Exp
Calc
B
B
Exp
Calc
32.3
Exp
2.8
Calc
Exp
0.51
Calc
0.59
F
Exp
Calc
—
—
5 to 8
—
C
C
C
C
C
C
C
1
123.6
154.6
108.3
165.7
116.6
133.2
71.8
126.1
159.7
110.6
174.8
118.9
136.4
74.9
1
31.1
3.26
F
1
−108.6
−109.7
H
H
2
8.0
6.5
—
6.2
6.9
4.4
4.9
2
3
4
5
6
7
3
—
—
5 to 8
H
H
H
H
5
6
7A
7B
4 to 5
a
b
13
19
11
11
11
Estimated experimental errors are ~0.2 ppm for δiso
(
C) and δiso
(
F), ~0.1 ppm for δiso
(
B), ~0.02 MHz on C
Q Q
( B) and ~0.03 for η ( B).
56
11
Using the scaling factor suggested by Charpentier et al., the calculated C
Q
(
B) value becomes: C (calc) = 2.65 MHz.
Q
Table 4 Experimental and calculated NMR parameters for BBzx. Calculated values reported here are those obtained for the P(1) polymorph (after
4
9c
VASP DFT relaxation of the atomic positions)
1
13
11
H NMR
C NMR
B NMR
δ
iso (ppm)
δiso (ppm)
δ
iso (ppm)
C
Q
(MHz)
η
Q
a
a,b
a,b
c
a,b
H
Exp
Calc (P(1))
C
Exp
Calc (P(1))
B
Exp
Calc (P(1))
Exp
2.9
Calc (P(1))
Exp
0.48
Calc (P(1))
H
H
H
H
H
H
H
H
H
H
H
H
H
H
1
6.3 to 8
7.7
7.8
7.0
7.0
6.3
5.8
5.6
5.7
7.1
7.1
4.5
4.6
4.5
4.6
C
C
C
C
C
C
C
C
C
C
C
C
C
C
1
~130.3
~130.3
~129.2
~129.2
126.6
127.8
~130.3
~129.2
121.1
121.1
153.7
153.7
72.0
132.9
133.1
131.7
131.7
128.8
130.3
133.3
130.9
121.0
121.0
158.8
159.2
73.6
B
B
1
31.1
31.6
31.5
3.27
3.28
0.56
0.56
8
8
2
2
2
9
9
3
5 to 6.3
3
10
4
10
4
11
5
11
5
6.3 to 8
4 to 5
12
7A
14A
7B
14B
12
6
13
7
14
72.0
73.7
a
b
13
19
11
11
11
Estimated experimental errors are ~0.2 ppm for δiso
(
C) and δiso
(
F), ~0.1 ppm for δiso
Q
(
B), ~0.02 MHz for C
Q
(
B) and ~0.03 for η
Q
(
B).
18
c
Experimental values reported by Bryce et al.:
C
Q
= 2.8 ± 0.1 MHz, η
B) values become: C (calc) = 2.66 and 2.67 MHz.
= 0.45 ± 0.10 and δiso = 31.0 ± 2.0 ppm. Using the scaling factor
5
6
11
suggested by Charpentier et al., calculated C
Q
(
Q
1
8
very close). One point which is worth mentioning at this
stage is that for both AN2690 and BBzx, the C chemical
shifts obtained with the GIPAW calculations are shifted
observations,
the two crystallographically independent
1
3
11
benzoxaboroles of BBzx cannot be resolved by B MAS NMR.
For both phases, the experimental δiso values are found to be
in good agreement with the ones calculated by GIPAW, while
systematic errors were observed for the B quadrupolar
parameters, with a systematic overestimation of C . Similar
systematic errors have been reported by Bryce and co-workers
for boronic acids, when comparing the C ( B) values deter-
mined experimentally to those calculated using GIPAW.
should be noted that Charpentier and co-workers have
proposed to apply a scaling factor to the B quadrupolar
parameters calculated using GIPAW in order to improve the
(generally overestimated) compared to the experimental
1
1
positions (Tables 3 and 4, Fig. S10†). This shift is less pro-
nounced for the methylene carbon but reaches up to ~5 ppm
for one of the C atoms of the pentacycle, and up to 9 ppm for
the C linked to F. At this stage, we have no interpretation of
this shift, and it is a point we are still looking into.
Q
1
1
Q
5
5a
It
1
1
The B MAS NMR spectra show very similar lineshapes
for both molecules (Fig. 4c). The spectra were simulated
1
1
11
considering the presence of a single boron site. The B NMR
parameters extracted from the fitted lineshapes are very
close, with δiso at ~31.1 ppm, CQ ~2.8–2.9 MHz and ηQ
5
6
agreement between experimental and calculated values.
Here, when applying a similar correction factor, the calcu-
lated C values fall closer to the experimental ones.
~
0.48–0.51. It should be noted that in line with previous
Q
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1
9
Finally, the F NMR spectrum of AN2690 shows a unique
signal centered at ~−108.6 ppm (Fig. 4d), and the experimen-
tal chemical shift is in very good agreement with the one cal-
This difference is not biased by the calculation methodology
used to perform geometry relaxations, as many different
methods were tested (see Table 2), which all led to similar
1
7
19
culated by GIPAW. At this stage, only the O solid state NMR
spectra of BBzx and AN2690 have not been recorded yet, due
to the very low natural abundance of oxygen-17. However,
based on the results of the GIPAW calculations of O NMR
parameters (see the ESI,† Tables S7 and S8) and on previous
results. Thus, F NMR may serve as a probe of the aniso-
tropic thermal expansion of the crystal lattice of AN2690.
1
9
To see whether the predicted variations in F isotropic
shifts with temperature could be observed experimentally,
1
7
1
9
variable-temperature F NMR experiments were performed
between +20 and −20 °C. While the expected increase in
isotropic chemical shifts over that range of frequencies
should have been ~0.15 ppm, a decrease of 0.09 ppm was
observed experimentally. This shows that the changes in
lattice parameters are not the only factors which contribute
5
7
studies in solution, it should be easy to distinguish the two
different O atoms of the benzoxaboroles.
Influence of anisotropic thermal expansion and
polymorphism on NMR signatures of benzoxaboroles. As
mentioned previously, recognizing the crystalline form of a
drug is highly important for pharmaceutical applications, as
issues like anisotropic thermal expansion properties or
polymorphism need to be taken into account and distinguished.
Indeed, the physical properties of polymorphs are generally
different, with, in some cases, measureable variations in their
dissolution properties and bioavailability. In addition to
X-ray diffraction, spectroscopic techniques have thus also
been developed to characterize cases of polymorphism in
molecular materials, such as IR, terahertz spectroscopy,
and solid state NMR.
1
9
to the variations in F NMR parameters of AN2690 with
temperature, and that other parameters such as changes in
thermal motion (local dynamics around the atoms) should be
4
1
considered. As a matter of fact, DFT calculations of vibra-
tional modes of the two AN2690 structures (modeled as
1
9
−1
infinite periodic systems), show that a difference of 6 cm in
C–F vibration frequencies can be expected between 293 K and
100 K, indicating that the vibrational properties will indeed
be different in both cases, and, as a consequence, the local
5
8
59
6
0
19
environment of F as well.
For the small benzoxaborole molecules studied herein,
two situations can be distinguished: for BBzx, two polymorphic
forms have been described (P(1) and P(2)), while for AN2690,
only a single polymorph has been isolated so far, but which
presents measureable anisotropic thermal expansion proper-
ties (see above). We therefore wondered whether solid state
NMR would be sufficiently sensitive to bring evidence of the
differences in local environments of BBzx and AN2690 mole-
cules in the different crystalline forms described so far. In
order to answer this point, GIPAW calculations of the NMR
parameters were carried out on the two polymorphic forms
of BBzx and on the two crystal structures of AN2690 (recorded
at different temperatures). Results are gathered in Tables S7
and S8 (ESI†).
All in all, the above study shows how combined
experimental-computational studies can help determine
whether spectroscopic techniques like solid state NMR can
be used (or not) to elucidate cases of polymorphism for
benzoxaborole structures in particular. More importantly, for
the first time, we also attempted to distinguish the respective
influence of temperature-related changes in lattice parame-
1
9
ters and of thermal motion on one NMR parameter, the
F
isotropic chemical shift of AN2690. Such considerations
should be taken into account more systematically when
6
1
NMR–crystallography approaches are used to solve crystal
structures, and when discrepancies between experimental
and calculated NMR parameters are attributed to tempera-
5
5c,62
ture effects.
1
13
11
17
Concerning BBzx, the calculated H, C, B and O NMR
parameters of the two polymorphs are nearly identical, which
is not fully surprising as the crystal packing is essentially the
same in both cases (Table S8 in the ESI†). The minor changes
4. Conclusion
In this manuscript, we have shown how the combination of
several characterization techniques (including multinuclear
solid state NMR) and DFT computational modeling (involving
calculations of IR and NMR spectral signatures) is necessary
to understand in detail the crystal structure of simple
benzoxaborole molecules, such as those currently being
studied for pharmaceutical applications. Particular emphasis
was made on the importance of taking into account tempera-
ture effects, as we have shown how polymorphism and aniso-
tropic thermal expansion can influence not only XRD powder
patterns but also solid state NMR spectra. Thus, this work
should help in the development of more precise “NMR crys-
tallography” approaches, by shedding light on the different
parameters which can affect the NMR spectra of molecular
crystals and which can lead to discrepancies between experi-
mental and calculated parameters. Beyond the study of the
1
3
in C NMR parameters are all within the error of the uncer-
tainties of the GIPAW calculations, and simulations of the
1
3
calculated C NMR spectra of both polymorphs suggest that
it would be impossible to distinguish them unambiguously
1
3
by C solid state NMR.
In the case of AN2690, the anisotropic variations in lattice
1
13
parameters have a limited impact on the calculated H, C,
1
7
11
O and B NMR parameters (Table S7 in the ESI†). The only
parameter which may be sufficiently sensitive to lead to
measurable differences on the solid state NMR spectra (in a
1
9
reasonable timescale) is the F isotropic chemical shift.
Indeed, whatever the calculation method used to relax the
1
9
geometries of both crystalline forms, the F chemical shift
calculated for the room-temperature structure is lower by at
least 0.7 ppm compared to the structure recorded at 100 K.
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BBzx and AN2690 molecules, this work will be useful for the
investigation of complex materials containing benzoxa-
boroles, especially in cases where techniques complementary
to X-ray diffraction (such as solid state NMR) are needed to
fully elucidate their structure. We are currently looking into
this direction, through the development of hybrid materials
involving benzoxaboroles, and using solid state NMR tech-
niques to elucidate structural issues.
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Acknowledgements
The authors acknowledge the CNRS and the Agence
Nationale de la Recherche (ANR “BOROMAT” project) for
funding. This work was granted access to the HPC resources
of CINES (Jade) under the allocations C2013076866 and
C2014076866 made by GENCI (Grand Equipement National
de Calcul Intensif) for geometry optimizations and IR calcula-
tions. NMR spectroscopic calculations were performed on the
IDRIS supercomputer centre of the CNRS (project: 091461).
Further details on the computation method can be provided
on demand. Dr J.-P. Flament is acknowledged for his assis-
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