The influence of the molecular system on the performance of heteronuclear decoupling in solid-state NMR

Article abstract of DOI:10.1016/j.jmr.2011.02.013

The intensity of the carbon signal in a CPMAS experiment has been measured for two CH and three CH₂ moieties in four test molecules under different phase-modulated proton decoupling conditions and as a function of the spinning rate. The proton

Full text of DOI:10.1016/j.jmr.2011.02.013

Journal of Magnetic Resonance 210 (2011) 75–81
Contents lists available at ScienceDirect
Journal of Magnetic Resonance
journal homepage: www.elsevier.com/locate/jmr
The influence of the molecular system on the performance of heteronuclear
decoupling in solid-state NMR
b
c
Guillaume Gerbaud a,1, Stefano Caldarelli a, , Fabio Ziarelli , Stéphane Gastaldi
⇑
a Aix Marseille Université, ISm2 UMR 6263, Campus de Saint Jérôme, Service 511 F-13013 Marseille, France
b Spectropole, Fédération de Sciences Chimique de Marseille Université d’Aix Marseille III, Site de Saint Jérôme Service 511, France
c Equipe de Chimie Moléculaire Organique, LCP UMR 6264, Boite 562, Université Paul Cézanne, Aix-Marseille III, Faculté des Sciences St Jérôme, Avenue Escadrille
Normandie-Niemen, 13397 Marseille Cedex 20, France
a r t i c l e i n f o
a b s t r a c t
Article history:
The intensity of the carbon signal in a CPMAS experiment has been measured for two CH and three CH2
moieties in four test molecules under different phase-modulated proton decoupling conditions and as a
function of the spinning rate. The proton decoupling schemes investigated were the golden standard
TPPM and three of the GTn family.
Received 3 December 2010
Revised 9 February 2011
Available online 17 February 2011
Aim of this analysis was to better describe experimentally the impact and limitations of phase-
modulated decoupling.
Sizeable differences in the response to decoupling were observed in otherwise chemically identical
molecular fragments, such as the CHCH2 found in tyrosine, phenyl-succinic acid or 9-Anthrylmethyl-
malonate, probably due to differences in spin-diffusion rates.
Keywords:
Solid-state NMR
Heteronuclear decoupling
CPMAS
TPPM
GTn
In keeping with known facts, the efficiency of the decoupling was observed to decrease with the MAS
rate, but with somewhat different trends for the tested systems.
Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction
This situation is usually described as a ‘‘homogeneous’’ interac-
tion, a term that often translates into a reluctance to be manipu-
The impressive technological advances experienced by NMR of
solids may induce the vision of a natural convergence of this do-
main of applications with its relative field, solution-state NMR. In
fact, methods from this latter are becoming available for solids
while concepts arisen in the solid-state area, such as the use of
the anisotropy of the magnetic interactions, are becoming wide-
spread tools in solution studies. However, one should not under-
estimate the specificities of organic solids, some of which are not
yet dominated by the current status of technology. The main fac-
tor in cause here is the intimate structure of the proton dipolar
coupled network, generically dubbed the proton ‘‘bath’’ in loose
analogy with a thermostat. The size and the characteristics of this
latter depend on the molecular shape, as well as on the crystal
packing. In fact, the proton–proton dipolar interaction dies out
relatively slowly, covering a few bond distances [1]. Therefore,
an extended number of actor spins are to be taken into account
for the description of an organic material. The frequency spec-
trum of the resulting Hamiltonian is a particularly intertwined
combination of contributions from the original coupled spins.
lated by RF pulses, due to the facility of exchange of spin
polarization terms among the protons (fast spin-diffusion regime)
and to the increased rotary resonance conditions available in the
overall Hamiltonian. A first consequence arising from this situa-
tion is the difficulty to achieve high-resolution proton spectra.
Consequently, diluted nuclei are still a major target for NMR in
solids.
Thus, proton heteronuclear decoupling remains a crucial and
delicate step in NMR spectroscopy of organic solids towards opti-
mum spectral sensitivity and resolution.
To this respect, the influence of the proton bath at the level of
heteronuclear decoupling is particularly intriguing. On one hand
the proton–proton interaction lends a helpful self-decoupling ef-
fect [2], while on the other hand it still hampers a ‘‘clean’’ manip-
ulation of the proton spins by RF pulses. Also, the presence of
interferences with the averaging from the proton CSA has been
proposed from the very early times [3] to be a further major source
of trouble for decoupling. As a consequence, the discovery of effec-
tive ways of performing proton decoupling in solids has lagged
behind the achievements of solution-state NMR, where the ques-
tion is basically solved.
⇑
Corresponding author.
E-mail address: s.caldarelli@univ-cezanne.fr (S. Caldarelli).
A substantial leap forward to this respect has been the introduc-
tion of phase/amplitude modulated irradiation techniques [4]. The
proposed methods are based on angle or amplitude modulation of
1
Present address: BIP CNRS
Marseille Cedex 20, France.
– UPR 9036, 31, Chemin Joseph Aiguier 13402,
1090-7807/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved.
doi:10.1016/j.jmr.2011.02.013

76
G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
the applied decoupling field [5–18] on symmetry rules [19], or just
on experimental searches directly on the spectrometer [20,21].
Although generally convenient and up to the task, these meth-
ods have been shown to suffer from the need of parametric optimi-
zation for best performances. Hence, a constant effort is observed
to produce new experimental decoupling procedures increasingly
robust [15,17,22]. This outstanding experimental progress has
been accompanied by the search of a theoretical description suit-
able to reproduce the key aspects of the phase-modulated decou-
pling, namely their sensitivity (or lack of) to the periodicity and
amplitude of the modulation, or to the influence of the irradiation
offset.
Theoretical analysis of the behavior of multiparametric decou-
pling sequences have been performed by several authors [23–27].
The improvement of modulated RF pulses over continuous-
wave (CW) irradiation is apparent in numerical simulation, and
the positive role of a sizeable proton spin-diffusion was high-
lighted from the early studies [24]. Multimodal Floquet analysis
was applied to try to decode the interplay of the three averaging
fields (MAS, the decoupling RF and its modulation). This kind of
analysis reveals and quantifies well the destructive interferences
of the three fields, showing that the most negative effects on
decoupling come from resonances between the RF irradiation
and its modulation [23].
a parametric comparison of the decoupling performance of some
phase-modulated pulse. The methods tested were the widespread
forerunner TPPM and Gaussian-envelope cosine modulations
(GTn), which have shown to be more robust than TPPM with re-
spect to the parametric response [15]. The parameter explored
were the MAS frequency, the irradiation offset and the ones
describing the phase modulation.
2. Materials and methods
All experiments were performed on a Bruker DRX-400 spec-
trometer at a B0 field of 9.4 T in a commercial Bruker probehead
using 2.5 mm rotors. Cross-polarization experiments were per-
formed with a variable amplitude contact time[28]. The decoupling
field was set at 96.0 kHz. All the decoupling pulses were written in
a unique shaped pulse, of a duration corresponding to eight mod-
ulation periods, in order to minimize the effect of possible defor-
mation of the shape pulse repetition in the pulse timing. Line
intensities were measured directly with the spectrometer soft-
ware. The influence of the CP on the line intensities was taken into
account by using a calibration single-pulse carbon experiment for
each molecule at any given MAS frequency. The value obtained this
way was normalized to the number of carbon-13 moles, deduced
by weighing the sample. We arbitrarily set to 1 the value for gly-
cine recorded under MAS at 10 kHz (on-resonance irradiation).
Of particular interest, the dominance of the proton CSA Hamil-
tonian as the limiting factor in determining a largely non-uniform
parametric response has been highlighted [23].
The challenge for the experimentalist is to determine whether a
single set of parameters can be chosen for a specific experiment to
provide acceptable improvement over non-modulated (CW)
decoupling.
2.1. Samples
The test molecules, as well as the three-letter code used for ref-
erence in the text, are depicted in Fig. 1.
Glycine and L-tyrosine hydrochloride salt were obtained from
In fact, most calculations and demonstrations of decoupling
methods concern model systems, the current consensus being that
the decoupling behavior is mostly influenced by small molecular
motifs, typically the immediate surrounding of the target nucleus,
while the influence of the extended proton homonuclear couplings
(spin-diffusion, spin-bath) has not been assessed exactly.
In fact, the structure of the internal Hamiltonians, as well as
their degree of interference, it is likely to be at variations for any
combination of spin system, MAS and decoupling conditions,
which may have an impact on the optimal parametrization of the
decoupling. It is noteworthy that this kind of reasoning led to the
development of experimentally optimized continuously modu-
lated decoupling pulses [15,21].
commercial sources, and used as such.
9-Anthrylmethyl-2-13C-malonate was synthesized according to
Ref. [29], using 99.9% 13C-enriched diethylmalonate.
Phenyl-succinic acid, selectively 13C labeled at the CH2 position,
was synthesized according to the procedure described in Appendix
A. Both labeled compounds were confirmed to be more than 99%
enriched by solution-state NMR.
2.2. Decoupling pulse sequences
The sequences used in this work belong to the family of period-
ically phase-modulated pulses, which can be described in terms of
In this context, the reaction of a given molecular site to decou-
pling is believed to be determined by its multiplicity (thus different
for CH2, CH or CH3). The role of the surrounding proton spins is
usually summarized to
a single parameter, for instance the
‘‘strength’’ of the spin bath or the spin-diffusion rate constant. This
approximation does provide some agreement with the experimen-
tal results, but it does not yield a satisfactory explanation of the
spin dynamics, especially because it is not easy to evaluate a priori
the proton bath parameters for a solid [24].
One important issue for the experimentalist is to know how
much effort should be put in the parametric optimization, a task
that is particularly demanding for sample with an intrinsic low sig-
nal to noise. To this respect, the crucial point is to determine if it is
possible to transfer safely a parameter set optimized for a test sam-
ple to the case of interest. As a corollary, it is important to assess
the intensity gain introduced by of the use of phase-modulated
decoupling.
In this work we characterized the heteronuclear decoupling
behavior in a few molecular fragment, some of which serve as typ-
ical NMR standards for setting up the decoupling conditions and
the rest of which bear similar chemical functions, all carrying
CH2 or CH groups. We submitted this ensemble of compounds to
Fig. 1. The samples used in this work, together with the acronyms used throughout
the text. (a) Glycine. (b) L
-tyrosine hydrochloride. (c) Anthrylmethyl 2-13C malon-
ate. (d) 2-Phenyl-succinic 3-13C acid. The analyzed carbons are the CH and CH2
elements, indicate by the asterisks for the ambiguous cases.

G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
77
a fundamental harmonic,
m
mod, and of the maximum phase jump,
sional experiments [20]. We reported in Table 1 this information in
D
/. Two-pulse phase modulation (TPPM), which is a series of
the form of the time, T1/e, for which the decay assumes the 1/e frac-
pulses of length
corresponds to a square-wave with
s
mod and alternating phase (ꢀ/0, /0), in this optics
tional value of the first point in the echo (taken for s = 0). For reg-
m
mod = 1/(2 ꢁ mod) and / = 2/
s
D
ular, monoexponential time envelopes, T1/e corresponds to T0 .
2
. The other decoupling pulses used in this work are constructed as a
combination of a Gaussian-envelope, cut at 10% of the maximum
intensity, multiplied by the fundamental cosine mode. The conse-
quent broadening induced in the harmonic response has been
shown to provide better parametric stability [15]. The broadening
can be modulated by varying the number of periods, n, of the fun-
damental mode spanned by the Gaussian. In this paper we limit
our comparison to TPPM and three elements of the GTn family
(n = 2, 4 and 8).
All systems, with the exception of AMM, have similar lifetimes.
However, glycine and tyrosine spin-echo decays have very little
degree of biexponential behavior, compared to PSA and AMM. An
analysis of the measured relaxation times (Table 1) points out that
these two latter systems are also characterized by much slower
relaxation rates, suggesting a possibly different impact of spin-dif-
fusion with respect to glycine and tyrosine chlorohydrate. Indeed,
these two molecules have been selected as NMR standards also be-
cause of their favorable relaxation properties.
Analysis of Table 1 demonstrates that, consistently with the
above discussion, a multi-exponential behavior of the signal decay
was observed in many cases. Interestingly, even if the AMM sample
is strongly biexponential, a long decay can be still achieved for the
signal of this molecule, since the fast decay of its broad component
is compensated for by the longest decay time measured for the
narrow component.
2.3. Choice of the parameter space
We explored for all molecular systems a decoupling parameter
space involving:
– the reduced phase-modulation period, sR equals to smod/srf
(thirteen values between 0.3 and 1.5);
– the phase modulation maximum excursion, /MAX (ten values
between 0° and 90°);
3.2. Indicators of the decoupling quality
– the MAS spinning rate (five values from 10 to 30 kHz);
– two values of the irradiation offset, of 2 kHz difference (5 ppm)
with respect to each other.
Although the spin-echo method described above constitutes an
optimal test for decoupling, it is not a viable one in the case of a
systematic study, especially considering the long relaxation times
of some of our samples.
3. Results and discussion
The ultimate goals of perfect proton decoupling are better
intensity and resolution of the diluted spin spectrum. Linewidth
and intensity are thus the natural indicators to monitor decoupling
performances. As detailed in the previous section, these two
parameters would be totally correlated in an ergodic (i.e. monoex-
ponentially relaxing) system, corresponding to a single Gaussian/
Lorentzian line form. In the general case, at any rate, the removal
of any broadening interaction has to translate in a direct increase
in the signal intensity. The converse, however, could be not true.
For instance, this is particularly the case for the contributions aris-
ing from the splitting of the signal induced by the presence of mod-
ulated perturbations, such as decoupling irradiation and MAS,
which appear in the form of multiple sidebands shifted by integer
combinations of the RF and spinning frequency [33].
Thus, while linewidths are good descriptors of phenomena
affecting markedly the quality of decoupling, the line intensities
are better choices to accompany the global process, including the
finer effects due to higher order terms of the involved interactions.
We shall thus use this latter indicator for describing the decoupling
behavior of modulated schemes around their best performance
conditions.
3.1. Pre-characterization of the samples
To evaluate the performance of decoupling on different samples
before starting a systematic analysis, we first measured some of
the parameters influencing the linewidth of a typical MAS spec-
trum, recorded with standard but non-optimized decoupling
(TPPM with a phase jump of 15°, 10 kHz spinning rate). A thorough
analysis of linewidth sources in carbon spectra has been performed
by Van der Hart and Campbell [30]. We focus here on two aspects:
structural disorder (and in general refocussable broadening) and
incomplete proton decoupling. In principle, both components can
be assessed via the analysis of a spin-echo indirect detection. In-
deed, the effect of this experiment is to produce decay times con-
stants, T02, unaffected by the resonance dispersion associated to
disorder, which influences and often dominates the direct experi-
ment time constant, Tꢁ2. In the case of non-ideal proton decoupling
of organic solids, a more pronounced broadening of the foot rather
than of the line as a whole is observed.[24] This can be seen as a
signature of a partitioning of the spin system, that is to say the
break up of the observed coherences into different reservoirs with
characteristic lifetimes. This partition may arise from polymor-
phism or to be intrinsic to the interaction at play [31,32]. In a
spin-echo curve, an effect of this type appears through a multi-
modal decay, with at least two appreciably distinct time constants.
Alternatively, this same effect could be detected in the frequency
domain from deviations from ‘‘regular’’ line shapes (i.e. Gaussian
or Lorentzian ones) in the signal, if a very good definition of the
foot of the line can be achieved [24]. In this preliminary part of
the study, the degree of biexponentiality of the spin-echo curve,
that is the ratio of the slow and fast component of the decay, has
been monitored as one characteristics of the system undergoing
decoupling. It should be noted here that, although a biexponential
function fits all of our experimental curves, higher partitioning of
the lineshape cannot be excluded.
3.3. Facility of decoupling of the observed systems
A point that must be addressed in trying to detect any depen-
dence of decoupling on the molecular system is to determine a
scale of facility of decoupling. A first indication to this respect
comes already from Table 1, by comparison of T1/e and T0 values,
2l
as well as of the biexponentiality degree. It appears that TYR is
the easiest system to decouple, followed by GLY. On the other
hand, AMM and PSA are the most difficult carbon to decouple.
As a complement of information, continuous-wave decoupling
provides the less biased measure of the facility with which a given
sample can be decoupled. Moreover, we analyzed the evolution of
the linewidth with the MAS rate as a way of characterizing the atti-
tude towards decoupling of the observed systems (Table 2). The
values in Table 2 corresponding to MAS at 10 kHz reflect closely
the results observed for TPPM (Table 1), with the exception of a
inversion of order for PSA and AMM.
The measurement of the lifetime of the signal of a rare nucleus
in an indirect spin-echo experiment holds an interest on its own, as
long-lived signals correspond to higher sensitivity of multidimen-

78
G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
Table 1
Spin-echo characterization of the samples under analysis, using TPPM (
D
/ = 15°) at 10 kHz MAS rate.
ꢁ
a
b
Ilb
T1H (s)
T1C (s)
T02s (ms)
b
T02l (ms)
b
FWHH (Hz)
T2 (ms)
T1/e (ms)
Is
GLY CH2
TYRa CH2
60
27
50
90
75
5.3
11.8
6.4
3.5
4.2
33
32
36
34
14
16
5
10
39
60
84
95
90
61
40
2.8
1.8
5.7
5.6
6.9
40.3
34.5
39.9
66.9
42.5
0.4
0.8
0.7
7.1
21.8
4.3
62
10
302
271
TYRb
a-CH
PSA CH2
AMM CH
a
Time for which the spin-echo top has decayed to 1/e of the initial value (i.e. for
s
= 0).
b
Result of a biexponential fit to the target function: Is
e
-t/T2s + Il e-t/T2l, where the indexes ‘‘l’’ and ‘‘s’’ stay for ‘‘long’’ and ‘‘short’’, respectively.
Table 2
Evolution of the CW linewidths with the MAS rate for the samples in Fig. 1.
point to note is that PSA, AMM and TYR possess the same CH2CH
fragment. While a precise explanation of the behavior depicted in
Table 2 would require an accurate description of the proton Ham-
iltonian, it appears logical to suggest that the surrounding protons
rather than the number of attached ones dominates the decoupling
spin dynamics.
System
MAS (kHz)
10
15
75
139
62
161
101
20
85
194
80
188
102
25
94
295
143
215
116
30
GLY CH2
TYRa CH2
73
42
60
133
101
98
–
217
262
134
TYRb
a-CH
3.4. Quantification of the gain in decoupling associated to phase-
modulated pulse irradiation and robustness of the decoupling
PSA CH2
AMM CH
A practical point that has not attracted the same amount of
investigation is the determination of the gain in decoupling effi-
ciency induced by PM methods over CW, which may also be a func-
tion of the system under study. This information illustrates firstly
whether is worthwhile spending time optimizing the decoupling
parameters and secondly provides an experimental insight on the
role of the molecular system in the decoupling result. Fig. 2 is a
representation of the line intensity produced by TPPM in two sys-
tems, GLY and AMM, while varying phase and amplitude of the RF
modulation, as well as the MAS rate. The volume encompassed by
the drawn surface is the one for which the line intensity is 20%
higher than the one produced by CW decoupling. Thus, for GLY
at 10 kHz MAS rate TPPM overdoes CW decoupling for a large
selection of parameters, up to a maximum of about 150% for the
best conditions. On the other end, at 30 kHz spinning rate, while
the gain over CW induced by TPPM is much higher at the optimum,
only a narrow selection of parameters outperforms the most basic
of the decoupling schemes. This volume is a measure of the toler-
ance of decoupling performance to the settings of the phase mod-
ulation. A visual comparison shows that TPPM is worth applying on
GLY even for miscalibrated setups, contrary to AMM. Indeed, the
case of the AMM system is radically different. While at low
spinning rates TPPM does not produces dramatic intensity gains
The general trend of the carbon linewidth with increasing MAS
respects the anticipated degradation, due to reduction of the self-
decoupling contribution of the homonuclear proton couplings,
although remarkable differences are observed among the five tar-
get signals.
The less affected by increasing spinning rates are the CH2 of GLY
and the CH of AMM, which both show moderate increase in the
linewidth in going from 10 to 30 kHz MAS rates. In light of the re-
sults summarized in Table 1, it is however likely that this simili-
tude is rather driven by opposite trends: a strong, for GLY not
really affected by increasing MAS rates, and a weak, for AMM al-
ready quenched at moderate MAS rates, self-decoupling effect.
The CH2 signal in TYR broadens with the MAS rate, till beyond
detection at 30 kHz spinning rate, while the neighboring CH signal
width also broadens significantly. The PSA CH2 shows an interme-
diate behavior, doubling its linewidth in going from 10 to 30 kHz.
Again, these trends could be qualitatively be used as a rough scale
of strength of the proton homonuclear coupling assistance to het-
eronuclear decoupling.
These results would be surprising if a prevision had to be made
on the basis of the main unit, either a CH or a CH2. An interesting
Fig. 2. Graphical representation of the gain in decoupling performance of TPPM over CW. On two carbon sites (GLY on the left and AMM on the right-hand side), as a function
of /MAX R and of the MAS rate. The volumes encompass the parameter space in which the TPPM produces line intensities of 20% or more higher than CW. The line intensities
are normalized to the corresponding CW experiment, set to 100.
,
s

G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
79
over CW, a large selection of modulation parameters ameliorate
the outcome of CW at high spinning speeds, up to a factor of almost
two in amelioration of TPPM vs. CW decoupling.
pling. This system is also the one for which CW lineshapes degrade
the fastest with increasing MAS rates (Table 2). On the other end of
the scale we may place AMM, for which CW at high MAS frequen-
cies is still providing good performances, and for which concur-
rently phase-modulated methods do not improve much on it. For
GLY and PSA, although both being a CH2 unit, the CW behavior
seems different, PSA degrading faster. However, the response to
phase-modulated pulses (relative to CW) is very similar. The out-
standing exception to the general trend is AMM at 10 kHz MAS,
where little improvement in the decoupling outcome is achieved
through phase-modulated pulses. This is probably due to the facile
first-stage (i.e. for the narrow component) decoupling obtained for
this molecule, as Table 1 shows that AMM indeed possesses the
longest observed T02 (twice as long as the other ones) even in not
optimized conditions. Finally, it can be observed GTn methods pro-
duce a great improvement in terms of a broader range of stability
with respect to TPPM.
Table 3 translates and generalizes the previous comparison, by
reporting the fraction of the overall parametric volume for which a
given method produces at least 20% more intensities than CW, for
all molecules. Since the CW response of our samples degrades dif-
ferently with MAS (Table 2), we reported separately the specific
behavior at the spinning frequency of 10 kHz (Table 3A), as well
as the global performance over the ensemble of five spinning rates
(Table 3B). The variations of the performance of the phase-modu-
lated methods as a function of the molecular system are rather dra-
matic. Best results are obtained for the case of tyrosine, where up
to 58% of the parametric volume explored was effective (for the
GT2 method) in improving considerably over CW. Incidentally
tyrosine is one of the most common test samples for proton decou-
Table 3
3.5. Best decoupling parametrization
Decoupling efficiency of phase-modulated pulses vs. CW irradiation. Fraction of the
explored parameter space (see Fig. 2) for which a given phase-modulated method
outperforms CW irradiation of at least 20%. A. MAS rate of 10 kHz B. Sum over MAS
rates from 10 to 30 kHz.
The final aspect to explore is the variation of the optimal phase
modulation parametrization over the studied systems and decou-
pling pulses. Fig. 3 summarizes the outcome of the best decoupling
coordinates found in our parametric search for the tested mole-
cules and methods. Intensity values were normalized as explained
in the methods section. The top panels represents the best decou-
pling achieved, in terms of normalized intensity of the carbon sig-
nal, as a function of the spinning rate. In the bottom panels we
show the value of the phase jump for which this maximum value
of the intensities were attained, for any given MAS frequency. In al-
most all cases the best reduced period of modulation was found to
be at 0.92. The exception is the GT2 pulse, which shows a few local
maxima of similar associated intensity, the best one being at a va-
lue of 1.04 for the reduced period. In this case 0.92 is one of the sec-
ondary maxima. This is in agreement with previous studies and
partial theoretical explanations, which find usually the best
System
Pulse
TPPM (%)
GT2 (%)
GT4 (%)
GT8 (%)
Panel A
TYRb
TYRa
GLY
PSA
AMM
18
11
10
5
54
32
41
38
0
50
34
38
33
0
30
20
23
20
0
0
Panel B
TYRb
TYRa
GLY
PSA
AMM
34
28
16
9
58
50
34
25
9
53
47
28
25
12
41
37
20
16
7
8
Fig. 3. Evolution of optimal decoupling performance with increasing the MAS rate, for on-resonance decoupling measured on the five systems of Fig. 1. Top panels: line
intensity vs. MAS rate. For each system, the intensity values are referenced to the 10 kHz MAS rate experiment. Slightly different normalization values were used for each
system for the sake of readability. Bottom panels: optimal phase jump /MAX vs. MAS rate. Results for the four decoupling pulses (TPPM, GT2, GT4, GT8) are from the right to
the left. In almost all cases the best reduced period, sTPPM/sRF, was found to be 0.92 (see text).

80
G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
phase-modulation period close to the RF one [3,19,25]. However,
our sampling in this dimension is not fine enough to exclude the
presence of more localized maxima.
To account for the many sources of refocussable linewidths (see
above), we concentrate our analysis on variations in line intensi-
ties, rather than on their absolute values. For clarity of reading of
the plots, GLY and TYR line intensities were normalized to 1 for
MAS of 10 kHz, while those of AMM and PSA were assigned a value
of 0.6.
Inspection of Fig. 3 demonstrates a few clear trends. As ex-
pected [15], decoupling is well performing at moderate spinning
rates, for all molecules. With respect to increasing MAS rate, the
samples divide into two families. While the quality of decoupling
for PSA and AMM degrades monotonically with increasing spin-
ning rates, GLY and TYR show an intensity drop up to 25 kHz
MAS rate, followed by a recover for 30 kHz. In most cases, aug-
menting the MAS rate required increasingly wider phase jumps
to achieve the best performance (Fig. 3). Since the effectiveness
of phase-modulated decoupling depends on the interplay of the
proton homonuclear dipolar and CSA interactions, a finer theoret-
ical analysis of the MAS rate dependence of the line intensity
would be required to accurately describe the different behavior.
For the case of TPPM and GLY, the best phase jump at 10 kHz is
10–15°, while larger angles of up to 40° are most effective at
30 kHz MAS rate. Similar trends are observed for all the samples
of this study. GTn decoupling achieves comparable or better inten-
sities with respect to TPPM, while the associated best phase jump
is usually slightly larger. The GT8 pulse presents the most stable
rate. Among the tested decoupling methods, GT8 provides the
most stable conditions in terms of phase-modulation parameter-
ization, and GT4 was found the overall most tolerant to misset.
The compounds studied divided in two families, one of which
with weak response to phase-modulated methods, with respect
to plain continuous-wave irradiation. More complicated molecu-
lar systems could carry portions belonging to both families. The
differences among the systems studied here are likely to be
linked to the evolution of the proton bath structure with the
spinning rate, and to its non-ergodic partitioning. This study
has no ambition of completeness, but it provides evidence that
a proper model for spin dynamics in organic solids resist over-
simplification. Particularly, it appears not prudent to generically
predict the decoupling behavior on the basis of a given carbon
proton multiplicity.
Acknowledgment
We are grateful to the Spectropôle, Fédération de Sciences
Chimiques (CNRS FR 1739) de Marseille, for privileged spectrome-
ter time access.
Appendix A
A.1. Synthesis of the phenyl-succinic acid
A new synthetic route was designed to obtain selectively la-
beled phenyl-succinic acid, according to the following scheme:
1- LDA
EtO2C
Ph
2- EtO2C 13CH2Br
(59%)
HCl 11N
(57%)
HO2C
Ph
EtO2C
Ph
13CH2
13CH2
EtO2C
HO2C
behavior with respect to the phase jump, since it remains in the
30–40° range for all MAS frequencies. The other methods (GT2
and GT4) have an intermediate behavior.
A.2. Diethyl 2-phenylsuccinate-313
C
The effect of changing the proton irradiation frequency of plus
or minus 2 kHz results in a small variation of the line intensities,
but the general trend of Fig. 3 is conserved (not shown).
4. Conclusions
We tested a few phase-modulated proton heteronuclear decou-
pling methods on five carbon sites (three CH2 and two CH) on four
different molecular systems. These latter were classified with re-
spect to their intrinsic proton decoupling attitude by testing the
degradation of the CW irradiation efficiency upon increasing the
MAS rate.
Phase-modulated methods are most effective for decoupling-
resistant molecular systems, according to this scale. Interestingly,
this is the case even for moderate spinning rates for which CW
decoupling provides exploitable linewidths and intensities. No
single set of parameters was found to be optimum for all tested
molecules, so that care should be applied in transposing the pro-
ton heteronuclear decoupling parametrization optimized on one
molecule to an unknown one. It is the amplitude of the phase
modulation, rather than its reduced period, that has been found
to be most sensitive to the molecular system and to the spinning
A solution of ethyl phenylacetate (100 mg, 0.61 mmol) in 2 ml
of dry THF was cooled at ꢀ78 °C. A 2 M LDA solution (350 l,
l
0.7 mmol) was slowly added and stirred 1 h at the same tempera-
ture. Ethyl 2-bromoacetate-213C (102 mg, 0.61 mmol) was then
added dropwise. The reaction mixture was allowed to warm to
room temperature overnight. After dilution with water, the reac-
tion was extracted three times with Et2O and dried. The solvent
was removed in vacuum and the crude material was subjected to
column chromatography on silica gel (EtOAc/pentane 0:100 to 5/
95) to afford the product (90 mg, 0.36 mmol, 59%). 1H NMR
(300 MHz, CDCl3): 7.30 (m, 5H); 4.25-4.04 (m, 5H); 3.18 (ddd,
J1CꢀH = 131.5, JH2 ꢀH = 16.8, JH3 ꢀH = 10.0, 1H); 2.66 (ddd, J1CꢀH = 130.5,
JH2 ꢀH = 16.8, J3HꢀH = 5.3, 1H); 1.21 (q, J = 7.4, 6H.%). 13C NMR
(75 MHz, CDCl3): 38.3 (13CH2).

G. Gerbaud et al. / Journal of Magnetic Resonance 210 (2011) 75–81
81
A.3. 2-phenyl-succinic acid-313
C
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A
solution of diethyl 2-phenylsuccinate-313
C
(90 mg,
0.36 mmol) in 3 ml of 11 N HCl was refluxed overnight. The solu-
tion was then slowly cooled to 0 °C allowing the crystallization
of the product. The filtration and drying by vacuo afforded the pure
product (40 mg, 0.21 mmol, 57%). 1H NMR (300 MHz, CD3OD): 7.29
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