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An adaptable NMR broadband decoupling scheme
8 Match 1996
CHEMICAL PHYSICS LETTERS ELSEVIER
ChemicalPhysicsLeners250 (1996) 523-527
An adaptable NMR broadband decoupling scheme Eriks Kup e a Ray Freeman b a VarianNMR Instruments. 28 Manor Road. Walton.on-Thames. Swrey. I0"!2 2QF, UK b Department of Chemistry, Lensfield Road. Cambridge CB2 IEW. UK
Received27 December1995;in final form I 1 January1996
Abstract
A broadband hetemnuclear decoupling scheme for high resolution liquid phase NMR spectroscopy is described, based on adiabatic fast passage with a linear frequency sweep. It is shown that the flexible choice of shaping function for the radiofrequencyamplitude profile allows the method to be adapted to fit a wide range of sample parameters and experimental conditions. The practical limitations on phase cycling are emphasized. Expressions are derived t~ guide the choice of operating parameters so as to achieve a large effective bandwidth, low radiofrequency power dissipation, or weak cycling sidebands in the decoupled spectrum. 1. I n t r o d u c t i o n
Heavier and heavier demands are being made on heteronuclear decoupling schemes as NMR spectrometers are designed for high field operation, and as more applications involve decoupling nuclei with a wide chemical shift range, such as t3C or ~SN. Decoupling of a two-spin system (IS) in an isotropic liquid requires repeated inversion of the heteronuclear spins at a rate that is fast in comparison with the relevant spin-spin coupling constant J~s, and the spin inversion must remain effective for a wide range of chemical shifts. Significant improvements in the effective decoupling bandwidth have recently been achieved by the intr~uction of adiabatic fast passage [1-8] to invert the spins, instead of the more usual composite radiofrequency pulses. Residual imperfections in the spin inversion are compensated by the appropriate phase cycling [9,10]. We describe here a family of decoupling sequences that has the advantage of considerable flexibility; the parameters can be adapted to meet the practical demands of a wide range of experiments -
large or small coupling constants, the permissible radiofrequency power dissipation, the allowable peak radiofrequ~-ncy voltage, the desired resolution in the observed decoupled spectrum, and the acceptable level of cycling sidebands. We quantify one aspect of the performance in terms of a figure of merit 2~rAF"
_==
,B2(rms)
(1)
where A F* is the frequency range (in Hz) over which the decoupled line retains 80% of its full height, and B2(rms) is the constant radiofrequency level that would have the san~e power dissipation as the actual amplitude-modulated B2 field. In addition one needs to specify the magnitude of the heteronuclear coupling constant [Jts[, the observed linewidth A u in the absence of residual splittings, and the maximum height of the cycling sidebands, expressed as a percentage of the height of the decoupled line. Consider the case where we wish to detect the spectrum of the S spins while decoupling a heteronuclear species I. The first requirement is that the I spins, initially aligned along + z are carried to -z by
0009-2614/96/$12.00 © 1996ElsevierScienceB.V. All rights reserved Pll S0009-2614(96)00042-5
524
E. Kupe, R. Freeman~ Chemical Physics Letters 250 (1996) 523-527
the adiabatic passage. This can be achieved if the sweep rate satisfies the adiabatic condition,
klO/dt] < 'YBeff
(2) where Bar is the effective radiofrequency field, the resultant of B 2 and the offset AB. The rate dO/dt is a function of both the sweep rate and the instantaneous radiofrequency intensity B 2. It is usual to define an adiabaticity parameter Q( t) = ~lB~/klO/dtl. (3) A value Q > 5 has been recommended [2]. Expressed in tet'ms of the radiofrequency level B2 and the offset AB, the adiabaticity parameter becomes +
Q(t)= [ dAB
dB2["
(4)
I The critical region of any adiabatic sweep is the section near exact resonance for a given chemical species, where the adiabatic condition is usually most difficult to satisfy
Qo" (dAB/dr)"
(5)
We consider &mplitude profiles where the radiofrequency has its peak intensity B2(max) at resonance. Then, in the case of a linear frequency sweep Eq. (5) simplifies to {~/B2(max)}'T 2 rAF '
Q0-
(6)
where A F is the total sweep range (in Hz). If we introduce a quality factor ~ - - A F * / A F representing the ratio of the effective decoupling bandwidth to the total sweep range, and a power factor f--B2(rms)/B2(max) < I, we may rewrite the figure of merit as _ = =
f
a2(rms)r f2Q0
.
(7)
Consequently, in contrast to composite-pulse decoupiing schemes where _~ is a constant, adiabatic decoupling enjoys a figure of merit that depends on several experimental variables, and in principle it can be very high indeed. Although neither ~ nor f change very drastically, the performance can be significantly improved by increasing B2(rms) to a level set by the pe~'missible radiofrequency heating of the
sample, by increasing the pulse duration up to the limit set by J,s, and by employing a low adiabaticity factor. For the most efficient decoupling we suggest Qo = 1 [11]. High figures of merit are achieved by "sailing close to the wind" for all these parameters. Note that two different adiabatic decoupling schemes can only properly be compared if B2(rms), 7", and Q0 are all specified. 2. "WURST* deooupling We start from the premise that the radiofrequency should be swept as a linear function of time and that the radiofrequency amplitude should remain constant, at least over the main central part of the sweep range. This has the important advantage that the I spins experience virtually the same sweep conditions irrespective of chemical shift. (Note that this runs counter to the philosophy behind some other adiabatic passage schemes, such as the tangential sweep and the hyperbolic secant pulse.) However, a sweep of finite range and strictly constant amplitude leaves the I spins at a slight inclination with respect to the +z axis, and is therefore not optimal, and if the radiofrequency is abruptly switched off at the ends of the sweep, the adiabatic condition is violated. We may easily take care of these end effects by rounding-off the sharp edges of a rectangular pulse [7,12]. We choose to do this with an amplitude profile that follows the general "sausage-shaped" function B2(t) -- B2(max ) [1 - [sin(/3t)In], (8) where the index n is an even integer and can be quite large [7], and where /3t runs from - ' n ' / 2 to + ~ / 2 . This is the origin of the name WURST (wideband, uniform rate, smooth truncation) and the index n is added to denote the severity of the round-off function, hence, for example, WURST-20. The index n is important because it determines the ratio ~ of effective decoupling bandwidth A F* to total sweep range AF. Once we have determined the permissible sweep rate, n must be set according to the sweep range A F and the pulse duration T, so that the rounding of the edges of the amplitude profile is not too abrupt. This effect has been analyzed in detail [! !] by solving the Bloch equations, with the conclusion that n ~ TAF/2 gives a broad spin inversion profile with just a hint of raised
E. gupe, R. Freeman/Chemical Physics Letters 250 (1996) 523-527
Z
2
/"
/ *
I
~t.: '
",- ~
)~.i '~ 3I
,,, ....... ~__ ,,
'
~ 'i - .
'
,,
:
,-"'i"
.~o..-
t
;~, .....
'
""
t
.-a
.L.-:'4-4- - ' " '
. . . .
,,
I
.
~d
a)
/
e
b)
Fig. i. Magnetization trajectories calculated for adiabatic fast passage (Q = 10) using amplitude profiles shaped according to (a) a rectangle, (b) A = A 0 ( l - Isin(/3t)l ,o). Note the marked pie. cessinnal motion about the eff~tive field in (a), which accounts for the poorer dacoupiing performance of CHIRP-95 compared with WURST- 10.
"shoulders" at the edges; n - T&F/4 generates a slightly narrower profile without any shoulders. We find that good spin inversion profiles go hand-in-hand with efficient decoupling performance. In the limit of no smoothing at all (n=oo) WURST becomes identical with CHIRP-95 decoupiing [8]. Unfortunately, the sudden change in 0 at the edges of the sweep violates the adiabatic condition, causing the magnetization to nutate about the effective field Befr instead of lemaining locked along
525
it (Fig. 1). This creates oscillations it) the spin inversion profile across the entire bandwidth (Fig. 2a), a most undesirable feature for decoupling applications. Although these imperfections are to some extent compensated by phase cycling, this is only at the cost of an increased level of cycling sidebands. Furthermore, some radiofrequency power is "wasted" in these end-regions by extending the sweep range AF in an attempt to approach the adiabatic condition. The rounded-off amplitude profile of WURST uses the radiofrequency power saved at the beginning and end of the sweep to boost performance in the central region (Fig. 2b). Another adverse consequence of using a rectangular profile is an increased sensitivity to radiofrequency field inhomogeneity; this becomes particularly important at low B2 levels. Mz
1B2/2x ( I d t , )
4.0
0
.IJD
U
Mz t,O
0.5.
cI
0.0"
-0-,
'
-LO LO
•lO I
U
i
0 5
0.0
d "°t ~
-0.5 -i.0
-
~.o
,o~o
e~o AH:
.no,o
.2o:o
Fig. 2. Spin inversion profiles as a function of resonance offset for (a) CHIRP-95 with a sweep rate of 20 MHz s - i (b) WURST-10 with a sweep rate of 29.5 MHz s- t. Both used Q = 4, T = 1 ms, and had the same power dissipation (yB2(rms)/21r = 3.57 kHz). The abrupt edges of the amplitude profile of CHIRP-95 introduces spurious oscillations (a) whereas the smoothed amplitude profile of WURST-10 ensures a much more uniform inversion behavior
(b).
o~
os
t~ m
tJ
20
.
.
.
/Wz
Fig. 3. Simulation of the amplitude profiles (left) and the corresponding spin inversion behaviour (fight) for (a) WURST-2 with •YB2(max)/21r = 5.31 kHz, (b) WURST-10 with ?B2(max)/21r = 3.93 kl-lz, (c) WURST-40 with "),b2(max)/21r = 3.55 kHz, and (d) CHIRP-95 with ~,B2(max)/21r = 3.25 kHz; all have (2 = 4 and -/B2(rms)/2qr = 3.25 kHz. When an optimized (non.linear sweep [13] is used with WURST-2, the shape of the inversion profile (a) is improved (dashed curve).
526
E. Kupe, R. Freeman/ Chemical Physics Letters 250 f1996) 523-527
At the other extreme, n =-2 corresponds to a cosine-squared amplitude profile, which may be combined with a non-linear frequency sweep [13] to generate a spin inversion profile quite similar to that of the hyperbolic secant pulse [2]. A high figure of merit is achieved at the cost of a much higher peak radiofrequency level B2(max), which could cause problems of breakdown of probe capacitors. This leaves a wide latitude (2 ~; n < co) for tailoring the properties of the WURST pulse to match different ex~imental demands. Fig. 3 shows the amplitude profiles and the corresponding spin inversion performance of a series o:f WURST pulses for different n values. The key to the WURST scheme is its flexibility; the parameters can be chosen to emphasize a broad effective decoupling bandwidth A F ' , a low radiofrequency power dissipation {B2(rms)] 2, a low peak radiofrequency level B2(max), small residual splittings in the decoupled spectrum, or weak cycling sidebands. 3. Pulse duration T As with all pulsed decoupling schemes, the pulse repetition rate should be fast compared with [,/zsl. The main result of failure to satisfy this condition is to increase the intensity of the outer cycling sidebands [1 i]. We quantify this requirement in terms of a dimensionless parameter m=,(T,/is) "1. Because I / T determines the sweep rate for a given total sweep range A F, the parameter m should not be too large, otherwise the adiabatic condition Eq. (2) is compromised, The lower the value of m, the broader the effective decoupling bandwidth A F * , an advantage gained at the cost of more intense cycling sidebands. Specification of the value of m allows a comparison to be made between various decoupling schemes even if the coupling constants ,/zs differ in the test samples; comparisons at different m values could be quite misleading. We suggest a minimum value m = 4. If we set m = 5 the maximum cycling sideband intensity is approximately 2% [11]. This is tree irrespectiveof the method used. Then we determine the sweep rate A F / T from Eq. (6) =
2,n.q0
(9)
Here the permissible peak radiofrequency intensity 7B2(max)/2'rt may well oe the limiting factor.
4. Phase cycles Residual imperfections in spin inversion can be compensated by the use of suitable phase cycles. These are often combinations of the five step cycle (0°, 60 °, 150°, 60 °, 0 °) of Tycko et al. [9] with the four step cycle (0 °, 0 °, 180°, 180°) of Levitt [10]. By suitably nesting one such cycle within another, supercycles of 20, 25, 80, or 100 steps can be constructed, but we must remember two limitations - the supercycles merely convert the residual imperfections into undesirable cycling sidebands [14]. and there is no point in employing a supercycle so long that it becomes comparable with the spin-spin relaxation time of the observed nucleus [15]. For applications in biochemical NMR, where the relaxation times are relatively short (of the order of 50 to 100 ms) and the acquisition time is seldom more than about 200 ms, very extensive phase cycles are unre. alistic. Therefore the choice of phase cycle depends on the application in mind. Whereas several existing schemes cope adequately with proton decoupling, where the maximum bandwidth AF* = 10 kHz, the real challenge is to detect proton resonances decoupied from nuclei with a wide chemical ~hift dispersion, for example 13C or 15N. If I ffi ~3C and S = ~H, decoupling the aliphatic region (assuming JcH ffi 140 Hz, and using m = 5) would require a pulse duration T ffi 1.43 ms, implying an overall duration of 28.6 ms for a 20-step supercycle. Even longer pulse durations may be used for ISN decoupling (`/NH = 90 Hz, T = 2.22 ms) or for long-range homonuclear decoupiing (,/He = 10 Hz, T ffi 20 ms). Consequently the length of very complicated supercycles, for example the 80-step sequence [8], may far exceed the recorded duration of the free induction decay• Under such conditions it is doubtful that the spins could distinguish between a 5 × 4 and a 5 × 16 phase cycle. A different situation may be encountered in applications to small molecules with long spin-spin relaxation times, for example where I =- tH and S = 13C. Here the more extensive supercycles help to smooth out the shorter-term imperfections of spin inversion at the expense of reduced decoupled line intensities and stronger cycling sidebands. Even in such situations, a 25-step supercycle constructed from the 5step cycle of Tycko et al. [9] nested within an identical 5-step cycle would seem to be perfectly
E. Kupe, R. Freeman / Chemical Physics Letters 250 (1996) 523-527
:-
527
50 kHz
I
II "
I
i
Fig. 4. Experimental performance of WURST-40 for observation of protons in methyl iodide at 750 MHz while decoupling 13C at 188.6 MHz. The de,coupler offset was stepped through a 60 kHz band in 1 kHz steps. The effective decoupling bandwidth A F ' = 5 0 kHz, corresponding to a figure of merit ~ - - 18.2. The radiofrequency level was ,yB2(rms)/2~ = 2.75 kHz, T = 1.3 ms, Q-- 1.2, J--- 151 Hz, and m ==5. No line broadening or pL ~se correction was applied to the experimental datL
adequate for WURST-20, which in fact performs rather better than CHIRP-95 with the 80-step super-
cycle [8]. 5. Conclusions WURST decoupling comprises an entire family of adiabatic fast passage schemes. The version best adapted to a particular application depends on the nature of the sample (the nuclei involved, the coupling constant, and the sensitivity to heating effects), the electrical characteristics of the radiofrequency probe, and the level of cycling sidebands that may be tolerated in the observed spectrum. We conclude that appropriate shaping of the amplitude profile is a key factor in optimizing decoupling periormance, but that very extensive phase cycling is seldom necessary, in contrast with the conclusions drawn by Fu and Bodenhausen [8,16]. One rather demanding application is to decouple J3C while observing protons in a high-field spectrometer (750 MHz). Fig. 4 demonstrates that WURST-40 achieves an effective decoupling bandwidth of 50 kHz, corresponding to a figure of merit ~, = 18.2. The cycling sidebands are below 3% of the intensity of the decoupled peak, about the same as those recorded with GARP decoupiing [14,17] but about four times the intensity of those observed for WALTZ-16 decoupling [14,18]. Acknowledgements We are indebted to Geoffrey Bodenhausen for providing a copy of an article [16] prior to publication.
References [I] S. L. McCall and E. L. Hahn, Phys. Rev. 183 (1969) 457. [2] J. Baum, R. Tycko, and A. Pines, Phys. Rev. A. 32 (1985) 3435. [3] C. J. Hardy, W. A. Edelstein, and D. Vails, J. Magn. Resort. 66 (1986) 470. [4] T. F-jiwara, T. Anai, N. Kurihara, and K. Nagayama, J. Magn. Reson.A. 104 (1993) 103. [5] Z. $tamk, Jr., K. Bartuek, and Z. Stamk, J. Magn. Resort. A. 107 0994) 24. [6] M. R. Bendall, J. Magn. Reson. A. 112 (1995) 126. [7] E. Kupe and R. Freeman, J. Magn. Reson. A. ! 15 (1995) 273. [8] R. Fu and G. Bedenhausen. Chem. Phys. Left. 245 (1995) 415. [9] R. Tycko, A. Pines, and R. Gluckenheimer, J. Chem. Phys. 83 (1985) 2775. [10] M. H. L~vitt and R. Freeman, J. Magn. Reson. 43 (1981) 502. [11] E. Kupe and R. Freeman, J. Magn. Reson. A. 117 (1995) 246. [12] J. M. Bi~hlen and G. Bodenhausen, J. Magn. Resort. A. 102 0993) 293. 113] E. Kupe and R. Freeman, J. Magn. Resort. A. (in press). [14] A. J. Shaka, P. B. Barker, C. J. Bauer, and R. Freeman, J. Magn. Reson. 67 (1986) 396. [15] M. H. Levitt, R. Freeman, and T. Frenkiel, Adv. Magn. Reson. I I (1983) 47. [16] R. Fu and G. Bodenhausen. J. Magn. Resort.(in press). [17] A. J. Shaka, P. Barker, and R. Freeman, J. Magn. Reson. 6 ~. (1985) 547. [18] A. J. Shaka, J. Keeler, and R. Freeman, J. Magn. Resort. 53 (1983) 313.
CHEMICAL PHYSICS LETTERS ELSEVIER
ChemicalPhysicsLeners250 (1996) 523-527
An adaptable NMR broadband decoupling scheme Eriks Kup e a Ray Freeman b a VarianNMR Instruments. 28 Manor Road. Walton.on-Thames. Swrey. I0"!2 2QF, UK b Department of Chemistry, Lensfield Road. Cambridge CB2 IEW. UK
Received27 December1995;in final form I 1 January1996
Abstract
A broadband hetemnuclear decoupling scheme for high resolution liquid phase NMR spectroscopy is described, based on adiabatic fast passage with a linear frequency sweep. It is shown that the flexible choice of shaping function for the radiofrequencyamplitude profile allows the method to be adapted to fit a wide range of sample parameters and experimental conditions. The practical limitations on phase cycling are emphasized. Expressions are derived t~ guide the choice of operating parameters so as to achieve a large effective bandwidth, low radiofrequency power dissipation, or weak cycling sidebands in the decoupled spectrum. 1. I n t r o d u c t i o n
Heavier and heavier demands are being made on heteronuclear decoupling schemes as NMR spectrometers are designed for high field operation, and as more applications involve decoupling nuclei with a wide chemical shift range, such as t3C or ~SN. Decoupling of a two-spin system (IS) in an isotropic liquid requires repeated inversion of the heteronuclear spins at a rate that is fast in comparison with the relevant spin-spin coupling constant J~s, and the spin inversion must remain effective for a wide range of chemical shifts. Significant improvements in the effective decoupling bandwidth have recently been achieved by the intr~uction of adiabatic fast passage [1-8] to invert the spins, instead of the more usual composite radiofrequency pulses. Residual imperfections in the spin inversion are compensated by the appropriate phase cycling [9,10]. We describe here a family of decoupling sequences that has the advantage of considerable flexibility; the parameters can be adapted to meet the practical demands of a wide range of experiments -
large or small coupling constants, the permissible radiofrequency power dissipation, the allowable peak radiofrequ~-ncy voltage, the desired resolution in the observed decoupled spectrum, and the acceptable level of cycling sidebands. We quantify one aspect of the performance in terms of a figure of merit 2~rAF"
_==
,B2(rms)
(1)
where A F* is the frequency range (in Hz) over which the decoupled line retains 80% of its full height, and B2(rms) is the constant radiofrequency level that would have the san~e power dissipation as the actual amplitude-modulated B2 field. In addition one needs to specify the magnitude of the heteronuclear coupling constant [Jts[, the observed linewidth A u in the absence of residual splittings, and the maximum height of the cycling sidebands, expressed as a percentage of the height of the decoupled line. Consider the case where we wish to detect the spectrum of the S spins while decoupling a heteronuclear species I. The first requirement is that the I spins, initially aligned along + z are carried to -z by
0009-2614/96/$12.00 © 1996ElsevierScienceB.V. All rights reserved Pll S0009-2614(96)00042-5
524
E. Kupe, R. Freeman~ Chemical Physics Letters 250 (1996) 523-527
the adiabatic passage. This can be achieved if the sweep rate satisfies the adiabatic condition,
klO/dt] < 'YBeff
(2) where Bar is the effective radiofrequency field, the resultant of B 2 and the offset AB. The rate dO/dt is a function of both the sweep rate and the instantaneous radiofrequency intensity B 2. It is usual to define an adiabaticity parameter Q( t) = ~lB~/klO/dtl. (3) A value Q > 5 has been recommended [2]. Expressed in tet'ms of the radiofrequency level B2 and the offset AB, the adiabaticity parameter becomes +
Q(t)= [ dAB
dB2["
(4)
I The critical region of any adiabatic sweep is the section near exact resonance for a given chemical species, where the adiabatic condition is usually most difficult to satisfy
Qo" (dAB/dr)"
(5)
We consider &mplitude profiles where the radiofrequency has its peak intensity B2(max) at resonance. Then, in the case of a linear frequency sweep Eq. (5) simplifies to {~/B2(max)}'T 2 rAF '
Q0-
(6)
where A F is the total sweep range (in Hz). If we introduce a quality factor ~ - - A F * / A F representing the ratio of the effective decoupling bandwidth to the total sweep range, and a power factor f--B2(rms)/B2(max) < I, we may rewrite the figure of merit as _ = =
f
a2(rms)r f2Q0
.
(7)
Consequently, in contrast to composite-pulse decoupiing schemes where _~ is a constant, adiabatic decoupling enjoys a figure of merit that depends on several experimental variables, and in principle it can be very high indeed. Although neither ~ nor f change very drastically, the performance can be significantly improved by increasing B2(rms) to a level set by the pe~'missible radiofrequency heating of the
sample, by increasing the pulse duration up to the limit set by J,s, and by employing a low adiabaticity factor. For the most efficient decoupling we suggest Qo = 1 [11]. High figures of merit are achieved by "sailing close to the wind" for all these parameters. Note that two different adiabatic decoupling schemes can only properly be compared if B2(rms), 7", and Q0 are all specified. 2. "WURST* deooupling We start from the premise that the radiofrequency should be swept as a linear function of time and that the radiofrequency amplitude should remain constant, at least over the main central part of the sweep range. This has the important advantage that the I spins experience virtually the same sweep conditions irrespective of chemical shift. (Note that this runs counter to the philosophy behind some other adiabatic passage schemes, such as the tangential sweep and the hyperbolic secant pulse.) However, a sweep of finite range and strictly constant amplitude leaves the I spins at a slight inclination with respect to the +z axis, and is therefore not optimal, and if the radiofrequency is abruptly switched off at the ends of the sweep, the adiabatic condition is violated. We may easily take care of these end effects by rounding-off the sharp edges of a rectangular pulse [7,12]. We choose to do this with an amplitude profile that follows the general "sausage-shaped" function B2(t) -- B2(max ) [1 - [sin(/3t)In], (8) where the index n is an even integer and can be quite large [7], and where /3t runs from - ' n ' / 2 to + ~ / 2 . This is the origin of the name WURST (wideband, uniform rate, smooth truncation) and the index n is added to denote the severity of the round-off function, hence, for example, WURST-20. The index n is important because it determines the ratio ~ of effective decoupling bandwidth A F* to total sweep range AF. Once we have determined the permissible sweep rate, n must be set according to the sweep range A F and the pulse duration T, so that the rounding of the edges of the amplitude profile is not too abrupt. This effect has been analyzed in detail [! !] by solving the Bloch equations, with the conclusion that n ~ TAF/2 gives a broad spin inversion profile with just a hint of raised
E. gupe, R. Freeman/Chemical Physics Letters 250 (1996) 523-527
Z
2
/"
/ *
I
~t.: '
",- ~
)~.i '~ 3I
,,, ....... ~__ ,,
'
~ 'i - .
'
,,
:
,-"'i"
.~o..-
t
;~, .....
'
""
t
.-a
.L.-:'4-4- - ' " '
. . . .
,,
I
.
~d
a)
/
e
b)
Fig. i. Magnetization trajectories calculated for adiabatic fast passage (Q = 10) using amplitude profiles shaped according to (a) a rectangle, (b) A = A 0 ( l - Isin(/3t)l ,o). Note the marked pie. cessinnal motion about the eff~tive field in (a), which accounts for the poorer dacoupiing performance of CHIRP-95 compared with WURST- 10.
"shoulders" at the edges; n - T&F/4 generates a slightly narrower profile without any shoulders. We find that good spin inversion profiles go hand-in-hand with efficient decoupling performance. In the limit of no smoothing at all (n=oo) WURST becomes identical with CHIRP-95 decoupiing [8]. Unfortunately, the sudden change in 0 at the edges of the sweep violates the adiabatic condition, causing the magnetization to nutate about the effective field Befr instead of lemaining locked along
525
it (Fig. 1). This creates oscillations it) the spin inversion profile across the entire bandwidth (Fig. 2a), a most undesirable feature for decoupling applications. Although these imperfections are to some extent compensated by phase cycling, this is only at the cost of an increased level of cycling sidebands. Furthermore, some radiofrequency power is "wasted" in these end-regions by extending the sweep range AF in an attempt to approach the adiabatic condition. The rounded-off amplitude profile of WURST uses the radiofrequency power saved at the beginning and end of the sweep to boost performance in the central region (Fig. 2b). Another adverse consequence of using a rectangular profile is an increased sensitivity to radiofrequency field inhomogeneity; this becomes particularly important at low B2 levels. Mz
1B2/2x ( I d t , )
4.0
0
.IJD
U
Mz t,O
0.5.
cI
0.0"
-0-,
'
-LO LO
•lO I
U
i
0 5
0.0
d "°t ~
-0.5 -i.0
-
~.o
,o~o
e~o AH:
.no,o
.2o:o
Fig. 2. Spin inversion profiles as a function of resonance offset for (a) CHIRP-95 with a sweep rate of 20 MHz s - i (b) WURST-10 with a sweep rate of 29.5 MHz s- t. Both used Q = 4, T = 1 ms, and had the same power dissipation (yB2(rms)/21r = 3.57 kHz). The abrupt edges of the amplitude profile of CHIRP-95 introduces spurious oscillations (a) whereas the smoothed amplitude profile of WURST-10 ensures a much more uniform inversion behavior
(b).
o~
os
t~ m
tJ
20
.
.
.
/Wz
Fig. 3. Simulation of the amplitude profiles (left) and the corresponding spin inversion behaviour (fight) for (a) WURST-2 with •YB2(max)/21r = 5.31 kHz, (b) WURST-10 with ?B2(max)/21r = 3.93 kl-lz, (c) WURST-40 with "),b2(max)/21r = 3.55 kHz, and (d) CHIRP-95 with ~,B2(max)/21r = 3.25 kHz; all have (2 = 4 and -/B2(rms)/2qr = 3.25 kHz. When an optimized (non.linear sweep [13] is used with WURST-2, the shape of the inversion profile (a) is improved (dashed curve).
526
E. Kupe, R. Freeman/ Chemical Physics Letters 250 f1996) 523-527
At the other extreme, n =-2 corresponds to a cosine-squared amplitude profile, which may be combined with a non-linear frequency sweep [13] to generate a spin inversion profile quite similar to that of the hyperbolic secant pulse [2]. A high figure of merit is achieved at the cost of a much higher peak radiofrequency level B2(max), which could cause problems of breakdown of probe capacitors. This leaves a wide latitude (2 ~; n < co) for tailoring the properties of the WURST pulse to match different ex~imental demands. Fig. 3 shows the amplitude profiles and the corresponding spin inversion performance of a series o:f WURST pulses for different n values. The key to the WURST scheme is its flexibility; the parameters can be chosen to emphasize a broad effective decoupling bandwidth A F ' , a low radiofrequency power dissipation {B2(rms)] 2, a low peak radiofrequency level B2(max), small residual splittings in the decoupled spectrum, or weak cycling sidebands. 3. Pulse duration T As with all pulsed decoupling schemes, the pulse repetition rate should be fast compared with [,/zsl. The main result of failure to satisfy this condition is to increase the intensity of the outer cycling sidebands [1 i]. We quantify this requirement in terms of a dimensionless parameter m=,(T,/is) "1. Because I / T determines the sweep rate for a given total sweep range A F, the parameter m should not be too large, otherwise the adiabatic condition Eq. (2) is compromised, The lower the value of m, the broader the effective decoupling bandwidth A F * , an advantage gained at the cost of more intense cycling sidebands. Specification of the value of m allows a comparison to be made between various decoupling schemes even if the coupling constants ,/zs differ in the test samples; comparisons at different m values could be quite misleading. We suggest a minimum value m = 4. If we set m = 5 the maximum cycling sideband intensity is approximately 2% [11]. This is tree irrespectiveof the method used. Then we determine the sweep rate A F / T from Eq. (6) =
2,n.q0
(9)
Here the permissible peak radiofrequency intensity 7B2(max)/2'rt may well oe the limiting factor.
4. Phase cycles Residual imperfections in spin inversion can be compensated by the use of suitable phase cycles. These are often combinations of the five step cycle (0°, 60 °, 150°, 60 °, 0 °) of Tycko et al. [9] with the four step cycle (0 °, 0 °, 180°, 180°) of Levitt [10]. By suitably nesting one such cycle within another, supercycles of 20, 25, 80, or 100 steps can be constructed, but we must remember two limitations - the supercycles merely convert the residual imperfections into undesirable cycling sidebands [14]. and there is no point in employing a supercycle so long that it becomes comparable with the spin-spin relaxation time of the observed nucleus [15]. For applications in biochemical NMR, where the relaxation times are relatively short (of the order of 50 to 100 ms) and the acquisition time is seldom more than about 200 ms, very extensive phase cycles are unre. alistic. Therefore the choice of phase cycle depends on the application in mind. Whereas several existing schemes cope adequately with proton decoupling, where the maximum bandwidth AF* = 10 kHz, the real challenge is to detect proton resonances decoupied from nuclei with a wide chemical ~hift dispersion, for example 13C or 15N. If I ffi ~3C and S = ~H, decoupling the aliphatic region (assuming JcH ffi 140 Hz, and using m = 5) would require a pulse duration T ffi 1.43 ms, implying an overall duration of 28.6 ms for a 20-step supercycle. Even longer pulse durations may be used for ISN decoupling (`/NH = 90 Hz, T = 2.22 ms) or for long-range homonuclear decoupiing (,/He = 10 Hz, T ffi 20 ms). Consequently the length of very complicated supercycles, for example the 80-step sequence [8], may far exceed the recorded duration of the free induction decay• Under such conditions it is doubtful that the spins could distinguish between a 5 × 4 and a 5 × 16 phase cycle. A different situation may be encountered in applications to small molecules with long spin-spin relaxation times, for example where I =- tH and S = 13C. Here the more extensive supercycles help to smooth out the shorter-term imperfections of spin inversion at the expense of reduced decoupled line intensities and stronger cycling sidebands. Even in such situations, a 25-step supercycle constructed from the 5step cycle of Tycko et al. [9] nested within an identical 5-step cycle would seem to be perfectly
E. Kupe, R. Freeman / Chemical Physics Letters 250 (1996) 523-527
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527
50 kHz
I
II "
I
i
Fig. 4. Experimental performance of WURST-40 for observation of protons in methyl iodide at 750 MHz while decoupling 13C at 188.6 MHz. The de,coupler offset was stepped through a 60 kHz band in 1 kHz steps. The effective decoupling bandwidth A F ' = 5 0 kHz, corresponding to a figure of merit ~ - - 18.2. The radiofrequency level was ,yB2(rms)/2~ = 2.75 kHz, T = 1.3 ms, Q-- 1.2, J--- 151 Hz, and m ==5. No line broadening or pL ~se correction was applied to the experimental datL
adequate for WURST-20, which in fact performs rather better than CHIRP-95 with the 80-step super-
cycle [8]. 5. Conclusions WURST decoupling comprises an entire family of adiabatic fast passage schemes. The version best adapted to a particular application depends on the nature of the sample (the nuclei involved, the coupling constant, and the sensitivity to heating effects), the electrical characteristics of the radiofrequency probe, and the level of cycling sidebands that may be tolerated in the observed spectrum. We conclude that appropriate shaping of the amplitude profile is a key factor in optimizing decoupling periormance, but that very extensive phase cycling is seldom necessary, in contrast with the conclusions drawn by Fu and Bodenhausen [8,16]. One rather demanding application is to decouple J3C while observing protons in a high-field spectrometer (750 MHz). Fig. 4 demonstrates that WURST-40 achieves an effective decoupling bandwidth of 50 kHz, corresponding to a figure of merit ~, = 18.2. The cycling sidebands are below 3% of the intensity of the decoupled peak, about the same as those recorded with GARP decoupiing [14,17] but about four times the intensity of those observed for WALTZ-16 decoupling [14,18]. Acknowledgements We are indebted to Geoffrey Bodenhausen for providing a copy of an article [16] prior to publication.
References [I] S. L. McCall and E. L. Hahn, Phys. Rev. 183 (1969) 457. [2] J. Baum, R. Tycko, and A. Pines, Phys. Rev. A. 32 (1985) 3435. [3] C. J. Hardy, W. A. Edelstein, and D. Vails, J. Magn. Resort. 66 (1986) 470. [4] T. F-jiwara, T. Anai, N. Kurihara, and K. Nagayama, J. Magn. Reson.A. 104 (1993) 103. [5] Z. $tamk, Jr., K. Bartuek, and Z. Stamk, J. Magn. Resort. A. 107 0994) 24. [6] M. R. Bendall, J. Magn. Reson. A. 112 (1995) 126. [7] E. Kupe and R. Freeman, J. Magn. Reson. A. ! 15 (1995) 273. [8] R. Fu and G. Bedenhausen. Chem. Phys. Left. 245 (1995) 415. [9] R. Tycko, A. Pines, and R. Gluckenheimer, J. Chem. Phys. 83 (1985) 2775. [10] M. H. L~vitt and R. Freeman, J. Magn. Reson. 43 (1981) 502. [11] E. Kupe and R. Freeman, J. Magn. Reson. A. 117 (1995) 246. [12] J. M. Bi~hlen and G. Bodenhausen, J. Magn. Resort. A. 102 0993) 293. 113] E. Kupe and R. Freeman, J. Magn. Resort. A. (in press). [14] A. J. Shaka, P. B. Barker, C. J. Bauer, and R. Freeman, J. Magn. Reson. 67 (1986) 396. [15] M. H. Levitt, R. Freeman, and T. Frenkiel, Adv. Magn. Reson. I I (1983) 47. [16] R. Fu and G. Bodenhausen. J. Magn. Resort.(in press). [17] A. J. Shaka, P. Barker, and R. Freeman, J. Magn. Reson. 6 ~. (1985) 547. [18] A. J. Shaka, J. Keeler, and R. Freeman, J. Magn. Resort. 53 (1983) 313.