Signal enhancement in NMR spectra of half-integer quadrupolar nuclei via DFS-QCPMG and RAPT-QCPMG pulse sequences

Article abstract of DOI:10.1016/S0009-2614(03)01345-9

Two signal enhancement schemes capable of providing large signal-to-noise gains in static and magic-angle spinning NMR spectra of the central transition of half-integer quadrupolar nuclei are presented. Amplitude-modulated double-frequency sweeps (AM-DFS)

Full text of DOI:10.1016/S0009-2614(03)01345-9

Chemical Physics Letters 379 (2003) 1–10
www.elsevier.com/locate/cplett
Signal enhancement in NMR spectra of half-integer
quadrupolar nuclei via DFS–QCPMG and
RAPT–QCPMG pulse sequences
*
Robert W. Schurko , Ivan Hung, Cory M. Widdifield
Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ont., Canada N9B 3P4
Received 11 March 2003; in final form 6 June 2003
Published online: 2 September 2003
Abstract
Two signal enhancement schemes capable of providing large signal-to-noise gains in static and magic-angle spinning
NMR spectra of the central transition of half-integer quadrupolar nuclei are presented. Amplitude-modulated double-
frequency sweeps (AM-DFS) and rotor-assisted population transfer (RAPT) pulse sequences are used as preparatory
sequences in combination with the quadrupolar Carr–Purcell Meiboom–Gill (QCPMG) pulse sequence to obtain large
signal enhancements ranging from one to two orders of magnitude. Specific applications to two spin-3/2 nuclei (87Rb
and 39K) and one spin-5/2 nucleus (85Rb) are presented.
Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction
on half-integer quadrupolar nuclei. Examples in-
clude the quadrupolar Carr–Purcell Meiboom–Gill
(QCPMG) sequence [4], the rotor-assisted popu-
lation transfer (RAPT) scheme [5] and the appli-
cation of adiabatic frequency sweeps (notably, fast
amplitude-modulated (FAM) pulses [6] and dou-
ble-frequency sweeps (DFS) [7,8]). The impetus for
much of this research is that many of the half-
integer quadrupolar nuclei, which constitute 73%
of NMR-active nuclides in the periodic table, are
relatively unreceptive nuclei, making the NMR
experiment inherently insensitive due to low natu-
ral abundance, low gyromagnetic ratios, large nu-
clear quadrupole moments, dilution of the nuclide
of interest or any combination of the preceding
[9,10].
Experimental and technological advances in the
past 15 years have brought solid-state NMR of
half-integer quadrupolar nuclei to the forefront of
solid-state characterization methods [1]. Perhaps
most notable was the introduction of the multiple-
quantum magic-angle spinning (MQMAS) experi-
ment in 1995 [2], which enabled high-resolution
NMR of half-integer quadrupolar nuclei in the
solid state [3]. Another focus has been the devel-
opment of pulse sequences aimed at improving
signal-to-noise in solid-state NMR experiments
* Corresponding author. Fax: +519-973-7098.
E-mail address: rschurko@uwindsor.ca (R.W. Schurko).
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0009-2614(03)01345-9

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R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
Fig. 1. The (a) QCPMG, (b) DFS–QCPMG, and (c) RAPT–QCPMG pulse sequences.
The QCPMG pulse sequence, which consists of
half-integer quadrupolar nuclei were explored in
detail by Haase and co-workers [16]. They found
that by using weak rf fields and/or fast sweep
rates (i.e., adiabatic frequency sweeps), it is pos-
sible to create adiabatic Dm ¼ 1 level crossings
(adiabatic passage), which result in pairwise
population interchanges, while Dm ¼ 2 crossings
remain unaltered (sudden passage). The net result
is a transfer of the spin population of outer
Zeeman levels to the +1/2 and )1/2 levels, yield-
ing a theoretical signal enhancement of a factor
of 2I, where I is the spin of the quadrupolar
nucleus. Kentgens and co-workers [7,17] demon-
strated that the application of time-dependent
AM-DFS is efficient for central-transition en-
hancement in NMR experiments on single-crys-
tals and polycrystalline solids, as well as for
enhancement of multiple-quantum (MQ) to sin-
gle-quantum (SQ) conversion in MQMAS NMR
experiments [8].
an initial p=2 pulse followed by a train of p pulses,
is pictured in Fig. 1a. With judicious choice of
phase cycling, inter-pulse delays and pulse widths,
the QCPMG sequence can be used to acquire a
long train of spin echoes, which when Fourier
transformed, yields a spectrum composed of echo
spikelets. Depending on the desired resolution,
these spectra can exhibit increases in signal inten-
sity of greater than an order of magnitude. The
QCPMG sequence has been implemented in ex-
periments on stationary samples and in magic-
angle spinning (MAS) experiments [11], and has
also been employed for the detection of the direct
dimension in MQMAS–QCPMG NMR experi-
ments [12]. A number of often neglected half-
integer quadrupolar nuclei have been studied with
this technique, including 67Zn in model com-
pounds for metalloproteins [13], 25Mg, 39K, 67Zn
and 87Sr in a series of inorganic polycrystalline
solids [14] and 35Cl in a high-field NMR study of
organic hydrochloride salts [15].
The rotor-assisted population transfer (RAPT)
pulse sequence was introduced as an alternative to
adiabatic frequency-swept passages for MAS ex-
periments on spin-3/2 nuclei. It is similar to the
Frequency-swept RF fields and their effects on
signal enhancement of the central transition of

R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
3
fast-amplitude modulated pulses of Vega and co-
workers [6], who applied such pulses to enhancing
MQ–SQ transfer in MQMAS. The RAPT se-
quence consists of a phase-alternating X–X pulse
train followed by a short delay prior to applying a
central-transition selective p=2 pulse. In these ex-
periments, the frequency is not swept as in the
DFS-type experiments; rather, the frequency is
held constant and the coherence transfers result
from the adiabatic motion of the rotor. The effect
of these rotor-synchronized amplitude-modulated
pulses is to saturate the satellite transitions,
thereby providing a theoretical maximum central
transition enhancement of 2. This methodology
was recently extended to MAS NMR of spin-5/2
nuclei [18] (satellite saturation pulse sequences
have theoretical signal enhancements of a factor of
I þ 1=2, and experimental signal enhancements of
2.5 are reported).
In this Letter we present an experimental study
of combinations of the aforementioned pulse se-
quences aimed at achieving overall signal gains
ranging from one to two orders of magnitude.
Specifically, we present the DFS–QCPMG and
RAPT–QCPMG schemes (Figs. 1b, c), and their
application to the study of two spin-3/2 nuclei
(87Rb and 39K) and one spin-5/2 nucleus (85Rb). In
each case, a RAPT or DFS sequence is used as a
preparatory sequence serving to invert and/or
saturate the satellite transition populations as de-
scribed above. The QCPMG sequence is then used
to enhance the signal of the resulting population-
enhanced central transition. A comparison of
Hahn-echo, RAPT–Hahn-echo, DFS–Hahn-echo,
QCPMG, RAPT–QCPMG and DFS–QCPMG
NMR experiments is presented, along with full
details of the optimized experimental parameters.
In all cases, the DFS–QCPMG and RAPT–
QCPMG experiments provide signal enhance-
ments close to those predicted by theory.
obtained from Aldrich and Alfa Aesar, respec-
tively. Samples were finely ground before packing
into 4 mm outer diameter ZrO NMR rotors.
Solid-state 87Rb, 39K and 85Rb NMR spectra
were acquired on a Varian Infinity Plus spec-
1
trometer with a wide-bore 9.4 T (m0ð HÞ ¼ 400
MHz) Oxford magnet operating at m0 ¼ 130:80,
18.65 and 38.59 MHz for 87Rb, 39K and 85Rb, re-
spectively. A Varian/Chemagnetics 4 mm double-
resonance HX MAS NMR probe was used for
87Rb NMR experiments, while a Varian/Chemag-
netics 4 mm triple-resonance HXY MAS NMR
probe was used to acquire 39K and 85Rb NMR
spectra. Achievement of high forward-to-reflected
power while tuning to the low 39K Larmor fre-
quency was accomplished by attaching a Varian/
Chemagnetics Low Gamma Tuning Box to the
T3-HXY 4 mm probe.
Static and MAS Hahn-echo experiments utilized
a pulse sequence of the form p=2 ꢀ s1ꢀ p ꢀ s2 –
acquire, with central-transition selective p=2 and p
pulses (i.e., non-selective pulses were scaled by
(I þ 1=2Þꢀ1) and interpulse delays s1 and s2. For all
MAS echo experiments, the first interpulse delay
(s1) and the spinning speed (mrot) are synchronized,
by setting s1 to NðmrotÞꢀ1, where N is an integer. For
87Rb, 39K and 85Rb, the p=2 pulse widths were 3.5,
5.25 and 1.75 ls, respectively, with corresponding
87
39
rf fields of m1ð RbÞ ¼ 35:7, m1ð KÞ ¼ 23:8 and
m1ð RbÞ ¼ 48:1 kHz. All 87Rb NMR experiments
85
featured a recycle delay of 1.0 s and spectral width
of 100 kHz. 39K static and MAS NMR experiments
were acquired with 80 and 30 kHz spectral win-
dows, respectively, and a recycle delay of 3.0 s.
Spectral widths of 200 and 100 kHz were employed
for 85Rb static and MAS NMR experiments, re-
spectively, with a recycle delay of 0.5 s. The static
87Rb Hahn-echo was acquired with interpulse de-
lays s1 ¼ 60 ls and s2 ¼ 40 ls. All 87Rb MAS ex-
periments were performed at a spinning frequency
of mrot ¼ 10 kHz; the rotor-synchronized Hahn-
echo was recorded with s1 ¼ 100 ls and
s2 ¼ 30 ls. For the static 39K Hahn-echo experi-
ment s1 was set to 200 ls in order to minimize the
effects of acoustic ringing and a pre-acquisition
delay (s2) of 100 ls was employed. All 39K MAS
NMR experiments were performed at mrot ¼ 10
kHz; the MAS Hahn-echo employed s1 ¼ 400 ls
2. Experimental
KHCO3 samples were obtained from Aldrich
and used without further purification. Samples of
RbClO4 were precipitated from a concentrated
aqueous solution of RbCl and NaClO4, which were

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R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
and s2 ¼ 200 ls. 85Rb static and MAS (mrot ¼ 15
kHz) Hahn-echo experiments used s1 ¼ 50 ls and
s2 ¼ 40 ls and s1 ¼ 66:7 ls and s2 ¼ 36:7 ls, re-
spectively.
Hahn-echo experiments were all processed by
shifting to the top of the echo before Fourier
transformation and using exponential multiplica-
tion with Lorentzian broadening (LB). All varia-
tions of QCPMG experiments were processed with
LB between 2 and 5 Hz, except for static 39K and
85Rb QCPMG and DFS–QCPMG spectra, where
LB of 20 Hz was employed. Relative signal in-
tensities were compared by numerical integration
of the spectra using NUTS software (Acorn
NMR).
3. 87Rb NMR experiments
The 87Rb NMR nucleus was chosen for initial
tests of these sequences due to its high receptivity
and moderate nuclear quadrupole moment (eQ ¼
0:13 b); as a result, all static and MAS NMR
experiments required collection of only 128 tran-
sients. RbClO4 is an ideal sample for such studies
due to the fact that there is a single Rb site with
Fig. 2. (a) Static 87Rb Hahn-echo and DFS-echo NMR spectra of RbClO4 along with corresponding QCPMG experiments. The
vertical scale of both echo spectra is augmented by a factor of 4. (b) 87Rb MAS Hahn-echo, RAPT-echo, DFS-echo, QCPMG, RAPT–
QCPMG and DFS–QCPMG NMR spectra of RbClO4. All spectra were acquired with 128 scans. Integrated intensities with respect to
the static and MAS 87Rb Hahn-echo experiments are located to the right of each spectrum.

R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
5
87
CQð RbÞ ¼ 3:3 MHz and gQ ¼ 0:2 [19]. Compar-
sweep rate, k, of 4.0 GHz sꢀ1, and an adiabaticity
parameter of A ¼ 0:32, where the adiabaticity
parameter, A, is defined as A ¼ m21=k [20]. For a
very fast sweep rate, the value of A will be low
(e.g., 0.001) and the passage of the satellite tran-
sitions with the frequency sweep is sudden. In this
condition of fast passage, the spin populations are
not observed to change in the laboratory frame
and no central transition signal enhancement is
observed. A higher value of A (e.g., A > 0:1) may
correspond to an adiabatic passage, where the
sweep rate through the satellite transitions is
slow enough that the level populations become
saturated or inverted in the laboratory frame.
The adiabaticity parameter must also be cho-
sen such that adiabatic passage occurs for the
single-quantum transitions (i.e., ꢁ1=2 to ꢁ3=2
for spin-3/2) but is sudden with respect to dou-
ble-quantum or higher-order transitions. Fur-
ther information regarding the optimization of
DFS pulse sequences is thoroughly explained
elsewhere [8,20].
ison of the static Hahn-echo and DFS–Hahn-echo
spectra (Fig. 2a) reveals a signal enhancement of
2.1, in agreement with predicted enhancements
for DFS static spectra of spin-3/2 nuclei [8] (the
integrated intensity of the static Hahn-echo ex-
periment is normalized to 1.0 and all signal en-
hancements are reported as factors with respect to
this normalized value). The DFS–Hahn-echo
scheme consists of a DFS pulse followed by a
Hahn-echo for detection of the signal. The DFS is
implemented using a converging amplitude-mod-
ulated pulse described in [7], with starting fre-
quency, ms, and final frequency, mf , where ms > mf
(Fig. 3a). The starting frequency, ms ¼ 1:7 MHz,
lies just outside the extremities of the ꢁ1=2 to
ꢁ3=2 satellite transition powder patterns and is
approximately equal to, or a bit greater than the
quadrupolar frequency (mQ ¼ 3CQ=ð2Ið2I ꢀ 1ÞÞ).
The 87Rb DFS pulse swept a frequency range of
ca. 1.6 MHz over a period of 400 ls, which was
divided into 3460 steps. This corresponds to a
Fig. 3. (a) Time-domain representation of a converging DFS pulse and corresponding schematic representation of the DFS in the
frequency domain. (b) Fourier transformed frequency-domain representation of the DFS pulse used in 87Rb NMR experiments (top
trace) along with simulation of the RbClO4 powder pattern including the ꢁ1=2 to ꢁ3=2 satellite transitions (bottom trace).

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R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
Careful choice of the final frequency, mf , is inte-
enhancement of the central transition (i.e., ap-
proximately a factor of 2.1).
gral in maximizing signal enhancement and ensur-
ing that there is minimal distortion of the central
transition powder pattern. For example, the 87Rb
central transition powder pattern of RbClO4 has a
breadth of approximately 15 kHz, which theoreti-
cally requires the DFS to halt at ca. mf ¼ 10 kHz;
however, a series of experiments testing signal en-
hancement as a function of mf reveal that the end of
the sweep must occur far from the edge of the
central transition pattern (spectra not shown). For
example, optimum signal enhancement with mini-
mal distortion of the powder pattern (i.e., powder
pattern most resembling the pure Hahn-echo pat-
tern) was obtained when the DFS was ended at
mf ¼ 146 kHz. The reason for this is that the DFS
pulse does not perfectly sweep the predefined fre-
quency range, as evidenced by performing a Fou-
rier Transform of the complete DFS time-domain
waveform (Fig. 3b). The frequency representation
of the DFS does not have well-defined, clear-cut
boundaries; rather, both the inner and outer edges
are gradual in their descent.
The static 87Rb QCPMG and DFS–QCPMG
spectra (Fig. 2a) were acquired with 24 Meiboom-
Gill (MG) loops, an acquisition period per echo
(sa) of 1.64 ms and interpulse and interacquisition
delays s1; s2; s3; s4 of 30, 40, 20 and 30 ls, re-
spectively (see Figs. 1a, b). For the DFS–QCPMG
experiment, the applied DFS pulse has the same
parameters as described for the static DFS–Hahn-
echo experiment. It is noted that in all cases re-
ported herein, the use of DFS as a preparation
pulse does not appear to influence the application
of the subsequent pulse sequences, nor the shape
of the powder patterns. Integration of the 87Rb
QCPMG static spectrum reveals a signal en-
hancement of a factor of 16 in comparison to the
standard Hahn-echo experiment. Variable degrees
of signal-to-noise enhancement are possible with
the QCPMG experiment, depending upon the de-
sired resolution of the spikelet manifold. The
QCPMG parameters were chosen to provide close
resemblance of the spikelet manifold to the static
NMR powder patterns. The DFS–QCPMG ex-
periment yields a signal enhancement factor of 33;
thus, the DFS pulse sequence preceding the Hahn-
echo or QCPMG sequence provides similar signal
We now discuss and compare the Hahn-echo,
RAPT-echo and DFS-echo experiments and their
QCPMG counterparts under conditions of magic-
angle spinning. The QCPMG MAS sequence em-
ployed s1 ¼ s2 ¼ 100 ls, s3 ¼ s4 ¼ 96:5 ls, 72 MG
loops and sa ¼ 6:0 ms. s3 and s4 were set according
to the equation 2Nsr ¼ sa þ s3 þ s4 þ sp, where N is
an integer, sr is the rotor period, s3 ¼ s4, and sp is
the duration of the ÔselectiveÕ p pulse [11]. DFS
MAS experiments were performed in the same
manner as the non-spinning experiments. The
RAPT pulse sequence (Fig. 1c) consists of a series
of repeating X–X units composed of two oppositely
phased (0°, 180°) pulses of equal duration, each of
which is preceded by a 100 ns delay. As suggested
by a previous study [5], the time for one X–X unit
was initially set to a value of approximately 4=CQ,
and subsequently optimized to 1.6 ls (i.e., the du-
ration of each pulse was 0.7 ls) and for simplicity,
the duration of the complete RAPT sequence was
set equal to the rotor period. The X–X unit was
repeated 62 times and a delay of 0.8 ls (which we
denote sRAPT) was employed before the initial p=2
pulse of the succeeding pulse sequences. Little
variation was found in the signal enhancement
upon lengthening or shortening the overall RAPT
train duration, in accordance with a previous report
[5]. The RAPT and DFS pulse sequences provide
signal enhancements of 1.6 and 1.7, respectively, in
comparison to the Hahn-echo MAS NMR spec-
trum which has a normalized integrated intensity of
1.0 (Fig. 2b). The QCPMG MAS NMR experiment
has an enhancement factor of 16, and preparatory
RAPT and DFS sequences nearly double that sig-
nal enhancement.
The 87Rb NMR experiments on RbClO4 pro-
vide a fast and efficient means of optimizing
QCPMG, RAPT and DFS parameters. In all
cases, the RAPT and DFS preparatory sequences
are equally successful in providing approximately
double the signal enhancement of standard
QCPMG NMR experiments. It is obvious that a
significant augmentation of the powder pattern
S=N can be achieved with QCPMG and in the case
of 87Rb, this enhancement is clearly superfluous
due to the inherently high sensitivity of the nu-

R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
7
cleus; however, this is an invaluable aid to the
NMR characterization of less favourable nuclei
such as 39K and 85Rb (vide infra).
small gyromagnetic ratio makes it a challenging
nucleus for solid-state NMR experiments (i.e., at
9.4 T, m0 ¼ 18:65 MHz). In addition, NMR ex-
periments at low frequencies such as this are often
plagued by acoustic probe ringing. Even in 39K
spin-echo experiments, which have the potential of
reducing the deleterious effects of probe ringing,
echo delays must often be prohibitively long,
thereby decreasing the effective signal.
A comparison of static 39K Hahn-echo, DFS-
echo, QCPMG and DFS–QCPMG NMR spectra
of KHCO3 (CQ ¼ 1:49 MHz, gQ ¼ 0:24) [21] are
shown in Fig. 4a. In this set of experiments, the
4. 39K NMR experiments
Rapid acquisition of solid-state 39K NMR ex-
periments is highly desirable, due to the common
occurrence of potassium in many biological and
inorganic materials of interest. 39K has a high
natural abundance (93.1%) and relatively small
quadrupole moment (eQ ¼ 0:055 b). However, its
Fig. 4. (a) Static 39K Hahn-echo and DFS-echo NMR spectra of KHCO3 and corresponding QCPMG experiments. (b) 39K MAS
Hahn-echo, RAPT-echo, DFS-echo and corresponding QCPMG NMR spectra of KHCO3. Integrated intensities with respect to the
static and MAS 87Rb Hahn-echo experiments and are located to the right of each spectrum. QCPMG experiments were acquired with
ca. 10 times less scans than corresponding echo experiments.

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R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
collection of 18 144 transients (over 908 min) was
required for the Hahn- and DFS-echo experiments
in order to obtain a reasonable signal-to-noise
ratio. All 39K DFS experiments were acquired with
ms ¼ 850 kHz and mf ¼ 85 kHz over a period of 508
ls with 2200 steps, meaning k ¼ 1:51 GHz sꢀ1 and
A ¼ 0:38. For the QCPMG and DFS–QCPMG
experiments, spectra with comparable or superior
signal-to-noise ratios were obtained with only 1824
transients (92 min). Static QCPMG experiments
employed 19 MG loops, a sa of 1.25 ms and in-
terpulse and interacquisition delays of s1 ¼
s2 ¼ 200 ls and s3 ¼ s4 ¼ 100 ls. The integrated
intensities of the static Hahn-echo and QCPMG
spectra are coincidentally equal to 1.0; however,
the QCPMG experiment provides a signal en-
hancement of greater than an order of magnitude,
as evidenced by acquisition times which are re-
duced by a factor of ca. 10. Both the DFS–Hahn-
echo and DFS–QCPMG sequences provided
signal enhancements of ca. 1.9 with respect to the
corresponding Ônon-DFSÕ experiments, indicating
that the preparatory DFS pulse is an attractive
and important addition to the standard QCPMG
sequence in this case.
implying overall signal enhancements of ca. 20–30
times.
5. 85Rb NMR experiments
Despite the high natural abundance of 85Rb
(72.15%), it has a larger quadrupole moment
(eQ ¼ 0:27 b) and a significantly lower gyromag-
netic ratio (m0 ¼ 38:59 MHz at 9.4 T) than 87Rb,
and is accordingly less often examined in solid-
state NMR experiments. We chose to conduct
experiments on 85Rb due to the fact that it is less
receptive, but more importantly because it is a
spin-5/2 nucleus, which will have different central
transition signal enhancement factors from the
RAPT and DFS pulse sequences. For instance,
two separate amplitude-modulated RAPT se-
quences with different modulation frequencies af-
fect the outer and inner satellite transitions
consecutively, resulting in partial saturation of all
satellites of a spin-5/2 nucleus, which yields signal
enhancements of a factor of ca. 2.5 [18]. A con-
verging DFS pulse, which first inverts populations
of the outer satellites followed by inner satellite
population inversion has the potential of provid-
ing a maximum signal enhancement of five times
for single crystals or ca. three times for polycrys-
talline powder samples [8].
Static 85Rb Hahn-echo and DFS-echo NMR
spectra involved the acquisition of 8480 transients,
whereas corresponding QCPMG experiments were
completed with the collection of 848 scans
(Fig. 5a). The DFS experiments were optimized
for maximum signal enhancement using ms ¼ 1:95
MHz and mf ¼ 200 kHz over a period of 1200 ls
and 6120 steps, with k ¼ 1:458 GHz sꢀ1 and
A ¼ 1:59. Static QCPMG experiments employed
95 MG loops, sa ¼ 0:85 ms, and s1; s2; s3 and s4
all set to 40 ls. Comparison of Hahn-echo and
DFS-echo experiments reveal a signal enhance-
ment of 2.9 in the latter. Surprisingly, in the cor-
responding QCPMG spectra (which have an
overall signal enhancement of 15 times), a signal
enhancement of ca. 3.8 times is obtained with
DFS–QCPMG. The reason for this additional
signal enhancement is unknown at this time. It is
noteworthy that the 85Rb nucleus in RbClO4 has
A comparison of 39K MAS Hahn-, RAPT-,
DFS-echo and corresponding QCPMG NMR
spectra is shown in Fig. 4b. All of the QCPMG
experiments were completed in 41 min (752
scans), whereas corresponding echo experiments
took 372 min to complete (7392 scans). In the 39K
RAPT MAS experiments, the time for each X–X
unit was optimized to 3.9 ls (pulse duration 1.85
ls) and was repeated 25 times, with sRAPT
¼
2:5 ls. QCPMG MAS NMR experiments utilized
81 MG loops, sa ¼ 3:33 ms, s1 ¼ s2 ¼ 200 ls and
s3 ¼ s4 ¼ 128:25 ls. Despite our best attempts at
optimizing the pulse sequence parameters, a signal
enhancement of only 1.5 was achieved with the
RAPT-echo experiment. However, a signal en-
hancement close to two times (with respect to the
QCPMG experiment) was obtained in the corre-
sponding RAPT–QCPMG experiment. DFS-echo
and DFS–QCPMG experiments resulted in signal
enhancements of 1.7 and 3.0, respectively. It is
important to stress here that the QCPMG spectra
presented in Fig. 4 were all acquired with ca. 10
times less scans than their echo counterparts,

R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
9
Fig. 5. (a) Static 85Rb Hahn-echo and DFS-echo NMR spectra of RbClO4 and corresponding QCPMG experiments. The vertical scale
of both echo spectra is augmented by a factor of 2. (b) 85Rb MAS Hahn-echo, RAPT-echo, DFS-echo and corresponding QCPMG
NMR spectra of RbClO4. Integrated intensities with respect to the static and MAS 85Rb Hahn-echo experiments are located to the
right of each spectrum. QCPMG experiments were acquired with 10 times less scans than corresponding echo experiments.
transverse relaxation properties well suited for
QCPMG experiments, as very long trains of spin
echoes are easily obtained which result in immense
signal enhancements.
All 85Rb Hahn-echo and QCPMG MAS spectra
(Fig. 5b) were acquired with collection of 3360 and
336 transients, respectively. In RAPT experiments
the length of the X–X unit was set to 2.08 ls and
repeated 31 times; sRAPT was set to 2.18 ls. The re-
cently published technique featuring two distinct
consecutive amplitude-modulated RAPT sequences
[18] was not applied in the set of experiments re-
ported herein, though this method is expected
to provide further signal enhancements. The
QCPMG MAS NMR experiments utilized 53 MG
loops, sa ¼ 3 ms, s1 ¼ s2 ¼ 66:7 ls and s3 ¼ s4 ¼
98:25 ls. RAPT- and DFS-echo experiments
resulted in signal enhancement of 1.8 and 2.2, re-
spectively. The QCPMG MAS NMR experiments
were conducted to produce very high resolu-
tion spectra, so a signal enhancement of only seven
times is obtained (modification of the QCPMG

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R.W. Schurko et al. / Chemical Physics Letters 379 (2003) 1–10
parameters could easily result in further signal en-
hancementsof two orthree times). RAPT–QCPMG
and DFS–QCPMG experiments provide additional
enhancement factors of 2.0 and 2.6, respectively.
RC) of Canada. R.W.S. is also grateful to the
Canadian Foundation for Innovation (CFI), the
Ontario Innovation Trust (OIT) and the Univer-
sity of Windsor for funding the Solid-State NMR
Facility at the University of Windsor. I.H. thanks
the Centre for Catalysis and Materials Research
(CCMR) at the University of Windsor for research
funding.
6. Conclusions
The DFS pulse sequence has been successfully
combined with the QCPMG pulse sequence for
both static and MAS NMR experiments. The DFS–
QCPMG scheme provides signal enhancements of
approximately a factor of 2 for spin-3/2 nuclei and
2.6–3.8 times for spin-5/2 nuclei compared to the
standard QCPMG experiments. Similarly, the
combination of RAPT with the QCPMG sequence
for MAS experiments yields signal enhancements of
approximately a factor of 1.5–2.0 for spin-3/2 and
spin-5/2 nuclei. The RAPT sequence generally
provides slightly less signal enhancement in com-
parison to the DFS experiment; however, the for-
mer is trivial to implement whereas the latter
requires a fair degree of optimization. At the very
least, the DFS experiments require a rough estimate
of CQ in order to properly set the DFS parameters
(notably, the success of the DFS pulse depends on
prudent selection of the final frequency, mf ). The
QCPMG experiments provide greater than an order
of magnitude of signal enhancement, with the cou-
pled RAPT or DFS preparatory sequences offering
the potential of reducing experimental times further
by close to an order of magnitude (since signal-to-
noise scales as the square root of the total number of
transients acquired), thereby making these pulse
schemes extremely attractive for the study of unre-
ceptive half-integer quadrupolar nuclei. Of equal
importance is the potential application of the DFS-
and RAPT–QCPMG sequences in further work on
optimization of RAPT and DFS pulse sequences,
due to the greatly reduced experimental times of
these experiments.
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This research was funded by the Natural Sci-
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