- Email: [email protected]
Sideband suppression in magic-angle-spinning NMR by a sequence of 5 π pulses
Solid State Nuclear Magnetic Elsevier Science Publishers
Resonance, 2 (1993) B.V., Amsterdam
143
143-146
Short Communication
Sideband suppression in magic-angle-spinning NMR by a sequence of 5 T pulses Zhiyan Song, Oleg N. Antzutkin, Division (Received
of Physical 15 March
Chemistry, 1993;
Xiaolong Feng and Malcolm H. Levitt *
Arrhenius accepted
Laboratory,
23 March
University
of Stockholm,
S-106
91 Stockholm,
Sweden
1993)
Abstract We report a symmetrical sequence is almost evenly Keywords:
solid-state
NMR;
sequence of 5 7~ pulses for total sideband suppression spaced and shorter than previous 4 and 6 r pulse methods. CP/MAS;
0926-2040/93/$06.00
author. 0 1993 - Elsevier
NMR.
The
TOSS
Solid-state magic-angle-spinning (MAS) NMR of a powder sample yields a sharp centerband and a set of spinning sidebands for each inequivalent nuclear site, if the spinning frequency w,/27r is less than or comparable to the chemical shift anisotropy [l]. Although the spinning sidebands are potentially a source of information as to the shielding anisotropies, more often than not they only cause undesirable spectral overlap. Since spinning speeds are mechanically limited, it is often not possible to suppress the sidebands by rapid sample rotation, and radio-frequency pulse methods such as TOSS (total sideband suppression) must be used instead [2-111. The original method [2,3] used 4 carefully-timed v pulses in order to prepare transverse magnetization with phases differing from crystallite to crystallite in such a way that the rotational echoes [l] are removed. The signal is Fourier transformed to give a spectrum containing only centerbands at the isotropic shift positions. A number of problems of TOSS have been
* Corresponding
in magic-angle-spinning
Science
Publishers
B.V.
identified: (i) It is sensitive to imperfections in the r pulses [6,11]. (ii> The pulse sequence is quite long, leading to a loss of intensity in the case of signals with short coherence decay times T2. (iii) TOSS can lead to a further loss of signal if used in the regime w, < q,Ar, where o0 is the Larmor frequency and Aa the shift anisotropy. In extreme cases, the centerband intensity can vanish or be inverted [S]. (iu> Problems are encounted in cases such as 13C spectroscopy, where abundant spins such as lH must be decoupled; Hartmann-Hahn transfer between the spin species can be induced by the rr pulses on the 13C leading to loss of signal [2]. (u) It is sometimks impossible to implement the sequence at high spinning speed if the rf field strength is limited. The sample moves significantly during each rf pulse, and in extreme cases, the rr pulses may need to be placed so close to each other in time that they overlap. These problems have motivated some further developments; TOSS has been combined with multiple-pulse sequences during signal acquisition [5]. Sequences of 6 pulses have been proposed which are shorter and have more evenlyAll rights
reserved
144
2. Song et al. /Solid State Nucl. Magn. Reson. 2 (1993) 143-146
spaced pulses [7,8]. Two-dimensional methods have been advanced which avoid the loss of centerband intensity and of the anisotropy information [9,10]. In addition, a different type of pulse sequence (SELTICS) has been proposed exploiting bursts of continuous rf irradiation rather than discrete n- pulses [12]. This latest method is apparently much shorter in duration than TOSS: One version leads to strong frequency-dependent phase shifts of the signals but spans only 0.5 of a rotational period 2rr/w,. A longer version does not induce these phase shifts and spans one rotational period. The shortest TOSS sequence reported so far lasts 1.169 times a rotational period
where 0r = w,T, then the powder-averaged centerbands all have the same phase in the spectrum, within an integer multiple of 7~.Eqn. (2) is known as the “Hahn echo” condition [2]. Curiously, eqns. (1) and (2) have only been examined for even values of II, in which case, solution is difficult. Before our complete analytical solution for y1= 4, reported elsewhere [13], only numerical solutions have existed [2,6-g]. However, an analytical solution is easily obtained for n = 5 if symmetry is assumed, i.e., e3 = rr, 19,=2~- e2, and 0, =27r- 0,. The imaginary parts of eqns. (1) vanish, and we get:
[71.
In this communication, we demonstrate TOSS sequences involving 5 n- pulses which do not lead to frequency-dependent phase shifts and which last between 0.7227 and 1.0000 times a rotational period 2~/w,. The 5 Z- sequence lasting an entire rotational period has the added attraction of having rather evenly-spaced pulses with timings given by simple analytical formulae. In addition, we describe a sequence which does not give ideal phase behaviour but spans only 0.4670 of a rotational period. The theory of TOSS has received much attention and two treatments have been given: Dixon [2] originally concentrated on the time-translation symmetry of the powder-average signal, while later workers explained the sideband suppression in terms of the “alignment of centerbands” [4,6,8]. As will be discussed elsewhere [13], the latter explanation is partially erroneous, but in any case, the results agree: The sidebands in the powderaveraged spectrum are suppressed after a sequence of IZ rr pulses with timings or,. . . , T,, satisfying the TOSS equations: (-l)“e’“‘q+l=O
2k
(1)
q=l
where eq = o,rq, and m = 1 and 2. There is an optional subsidiary condition for the time T at the initiation of signal acquisition. If T satisfies -2
5 (-l)n+qe4+eT=0 q=l
(2)
-4 cos(8,)
+ 4 cos(19,)+3
-4 c0s(2el)
+ 4 c0s(2e,)
=0
(form
= 1)
- 1 = 0 (for m = 2) (3)
These lead immediately to the solution: 8, = Arccos( 7/24) e2 = Arccos( - 11/24) 8, =r
(4)
e, = 2,n- - 8, e5 = 2~ - 8,
describing a set of symmetrically-disposed and almost evenly-spaced GTpulses contained within a single rotational period. By symmetry, the Hahnecho condition (2) is satisfied for 8, = 2a. Signal acquisition should therefore start one whole rotational period after the preparation of transverse magnetization. In fractions of a rotor period, the timings are: 0,/2r=O.2029 0,/2n-=0.3258 e3/271.=o.5000 8,/2n-= 0.6742
(5)
e,/2T= 0.7971 eT/271. = 1 .oooo
Starting from this analytical solution, it is easy to generate complete lines of feasible 5 r solutions numerically. Fig. 1 shows such a set of solutions, where the X-axis represents the time measured in fractions of the rotation period after
2. Song et al./Solid
State Nucl.
Magn.
Reson.
2 (1993)
145
143-146
0.2002, 0,/2~ = 0.4239, 8s/2~ = 0.4670. The analytical form for this sequence, derived elsewhere [131, is: 0, = Arccos{( - 13 + 5&%)/152}; 0s = Arccos{( - 51 + 7m)/152}; &, = Arccos{( - 13 - 54595 >/ 152}; 13~ = Arccos{(51 7\/195)/152). Th’ is sequence generates strong frequency-dependent phase shifts (since eqn. (2) cannot be satisfied) and has two pulses inconveniently close, but is even shorter than the newly reported SELTICS sequence [12]. It is related trivially to a known TOSS sequence [3] by removing one rotor period. Fig. 1. A continuous set of 5 v pulse TOSS sequences (solid lines give the rr pulse timings) with the “Hahn-echo” condition (broken line). The horizontal axis is time in fractions of a rotational period 2r/or. Horizontal sections give (a) the symmetrical sequence of 5 rr pulses; (b) the shortest known TOSS sequence without a frequency-dependent phase shift: the “Hahn echo” coincides with the last pulse; (c) the shortest possible TOSS sequence of 4 rr pulses: the first pulse is at zero time and may be omitted; the “Hahn echo” is inaccessible.
creation of in-phase transverse magnetization, and the Y-axis is arbitrary. Any horizontal section through this plot represents a solution to eqns. (1) with 19r/27~, . . . , 0,/27r at the positions given by the 5 thick curves. The dashed curve represents the value of OT/2r satisfying eqn. (2). If 6,~ 8,, initiation of acquisition at time T generates a spectrum without phase shifts. The solution of eqn. (4) corresponds to a horizontal section at point a. Another solution of note is at point b, representing the shortest known sequence satisfying eqn. (1) with a physically-realizable solution for eqn. (2). It has been found numerically to correspond to the values: 0,/2~ t3,/2n0,/2~ 0,/2n0,/2~
= = = = =
0.1366 0.2892 0.4254 0.6341 0,/2r = 0.7227
C .W+
b.4
(6)
The section at point c has f3,/2rr = 0, and corresponds to the shortest known 4 r pulse TOSS sequence with 6,/2~ = 0.1228, 0,/2~ =
kHz Fig. 2. r3C spectra of r.-tyrosine hydrochloride powder with 486 scans. (a) Normal CP/MAS; (b) TOSS with symmetrical sequence of 5 rr pulses; (c) conventional TOSS with 4 v pulses [3].
146
The symmetrical 5 rr pulse sequence of eqn. (4) is demonstrated experimentally in Fig. 2. This shows 13C MAS spectra of L-tyrosine hydrochloride powder (Sigma, USA, no further purification) spinning at w,/2rr = 2.000 kHz in a standard Bruker double bearing 4 mm rotor system (ZrO, rotors, Kel-F end caps). The spectra were obtained on a MSL-200 spectrometer at 4.7 T, using an external EN1 LPI10 high-power amplifier for the i3C pulses (w,/2n- = 109 kHz), and cross-polarization from the protons [14] with mixing time 5 ms. The proton rf field was enhanced by 3 dB during the TOSS sequence to avoid Hartmann-Hahn matching during the i3C pulses. Fig. 2a shows the ordinary CP/MAS spectrum revealing numerous overlapping sidebands. With the TOSS sequence of 5 n- pulses [Fig. 2b, timings as in eqn. (411, the sidebands are effectively suppressed and many of the centerbands are enhanced, as described previously [4,8]. An almost identical spectrum is obtained using the conventional 4 v pulse TOSS sequence (Fig. 2c, timings as in ref. 3) except for a slight loss of intensity from some peaks, presumably due to T, relaxation. Both Fig. 2b and 2c exploited extensive phase cycling of all r pulses, in phase steps of 2rr/3, to select the appropriate ( + 1) + ( F 1) coherence pathway transfers [15], thereby avoiding the effects of pulse imperfections. However, good sideband suppression could also be obtained without this precaution. Additional experimental results, including those from the shorter sequences described above, will be presented later [13]. In summary, we have demonstrated a new sequence of 5 r pulses for sideband suppression. The sequence is short, employs almost evenlyspaced n- pulses and has a simple analytical solution. It appears to offer significant advantages
Z. Song et al. /Solid State Nucl. Magn. Reson. 2 (1993) 143-146
over previous 4 and 6 pulse solutions and may present a good alternative to methods involving continuous radio-frequency bursts [ 121.
Acknowledgments
The authors thank J. Hong and G.S. Harbison for ref. 12 prior to publication, and N.C. Nielsen for discussions. This work has been supported by the Swedish Natural Science Research Council.
References 1 M.M. Maricq and J.S. Waugh, J. Chem. Phys., 70 (1979) 3300. 2 W.T. Dixon, .7. Chem. Phys., 77 (1982) 1800. 3 W.T. Dixon, J. Schaeffer, M.D. Sefcik, E.O. Stejskal and R.A. McKay, J. Magn. Reson., 49 (1982) 341. 4 E.T. Olejniczak, S. Vega and R.G. Griffin, .I. @em. Phys., 81 (1984) 4804. 5 D.P. Raleigh, E.T. Olejniczak, S. Vega and R.G. Griffin, J. Am. Chem. Sot., 106 (1984) 8302. 6 D.P. Raleigh, E.T. Olejniczak, S. Vega and R.G. Griffin, J. Magn. Reson., 72 (1987) 238. 7 N.C. Nielsen, H. Bildsoe and H.J. Jakobsen, J. Magn. Reson., 80 (1988) 149. 8 D.P. Raleigh, E.T. Olejniczak and R.G. Griffin, J. Chem. Phys., 89 (1988) 1333. 9 A.C. Kolbert and R.G. Griffin, Chem. Phys. Lett., 166 (1990) 87. 10 H. Geen and G. Bodenhausen, J. Chem. Whys., 97 (1992) 2928. 11 S. Ding and C. Ye, Solid State Nucl. Magn. Reson., 1 (1992) 235. 12 J. Hong and G.S. Harbison, J. Magn. Reson., in press. 13 O.N. Antzutkin, 2. Song, X. Feng and M.H. Levitt, to be published. 14 A. Pines, M.G. Gibby and J.S. Waugh, J. Chem. Phys., 59 (1973) 569. 15 G. Bodenhausen, H. Kogler and R.R. Ernst, J. Mugs. Reson., 58 (1984) 370.
Resonance, 2 (1993) B.V., Amsterdam
143
143-146
Short Communication
Sideband suppression in magic-angle-spinning NMR by a sequence of 5 T pulses Zhiyan Song, Oleg N. Antzutkin, Division (Received
of Physical 15 March
Chemistry, 1993;
Xiaolong Feng and Malcolm H. Levitt *
Arrhenius accepted
Laboratory,
23 March
University
of Stockholm,
S-106
91 Stockholm,
Sweden
1993)
Abstract We report a symmetrical sequence is almost evenly Keywords:
solid-state
NMR;
sequence of 5 7~ pulses for total sideband suppression spaced and shorter than previous 4 and 6 r pulse methods. CP/MAS;
0926-2040/93/$06.00
author. 0 1993 - Elsevier
NMR.
The
TOSS
Solid-state magic-angle-spinning (MAS) NMR of a powder sample yields a sharp centerband and a set of spinning sidebands for each inequivalent nuclear site, if the spinning frequency w,/27r is less than or comparable to the chemical shift anisotropy [l]. Although the spinning sidebands are potentially a source of information as to the shielding anisotropies, more often than not they only cause undesirable spectral overlap. Since spinning speeds are mechanically limited, it is often not possible to suppress the sidebands by rapid sample rotation, and radio-frequency pulse methods such as TOSS (total sideband suppression) must be used instead [2-111. The original method [2,3] used 4 carefully-timed v pulses in order to prepare transverse magnetization with phases differing from crystallite to crystallite in such a way that the rotational echoes [l] are removed. The signal is Fourier transformed to give a spectrum containing only centerbands at the isotropic shift positions. A number of problems of TOSS have been
* Corresponding
in magic-angle-spinning
Science
Publishers
B.V.
identified: (i) It is sensitive to imperfections in the r pulses [6,11]. (ii> The pulse sequence is quite long, leading to a loss of intensity in the case of signals with short coherence decay times T2. (iii) TOSS can lead to a further loss of signal if used in the regime w, < q,Ar, where o0 is the Larmor frequency and Aa the shift anisotropy. In extreme cases, the centerband intensity can vanish or be inverted [S]. (iu> Problems are encounted in cases such as 13C spectroscopy, where abundant spins such as lH must be decoupled; Hartmann-Hahn transfer between the spin species can be induced by the rr pulses on the 13C leading to loss of signal [2]. (u) It is sometimks impossible to implement the sequence at high spinning speed if the rf field strength is limited. The sample moves significantly during each rf pulse, and in extreme cases, the rr pulses may need to be placed so close to each other in time that they overlap. These problems have motivated some further developments; TOSS has been combined with multiple-pulse sequences during signal acquisition [5]. Sequences of 6 pulses have been proposed which are shorter and have more evenlyAll rights
reserved
144
2. Song et al. /Solid State Nucl. Magn. Reson. 2 (1993) 143-146
spaced pulses [7,8]. Two-dimensional methods have been advanced which avoid the loss of centerband intensity and of the anisotropy information [9,10]. In addition, a different type of pulse sequence (SELTICS) has been proposed exploiting bursts of continuous rf irradiation rather than discrete n- pulses [12]. This latest method is apparently much shorter in duration than TOSS: One version leads to strong frequency-dependent phase shifts of the signals but spans only 0.5 of a rotational period 2rr/w,. A longer version does not induce these phase shifts and spans one rotational period. The shortest TOSS sequence reported so far lasts 1.169 times a rotational period
where 0r = w,T, then the powder-averaged centerbands all have the same phase in the spectrum, within an integer multiple of 7~.Eqn. (2) is known as the “Hahn echo” condition [2]. Curiously, eqns. (1) and (2) have only been examined for even values of II, in which case, solution is difficult. Before our complete analytical solution for y1= 4, reported elsewhere [13], only numerical solutions have existed [2,6-g]. However, an analytical solution is easily obtained for n = 5 if symmetry is assumed, i.e., e3 = rr, 19,=2~- e2, and 0, =27r- 0,. The imaginary parts of eqns. (1) vanish, and we get:
[71.
In this communication, we demonstrate TOSS sequences involving 5 n- pulses which do not lead to frequency-dependent phase shifts and which last between 0.7227 and 1.0000 times a rotational period 2~/w,. The 5 Z- sequence lasting an entire rotational period has the added attraction of having rather evenly-spaced pulses with timings given by simple analytical formulae. In addition, we describe a sequence which does not give ideal phase behaviour but spans only 0.4670 of a rotational period. The theory of TOSS has received much attention and two treatments have been given: Dixon [2] originally concentrated on the time-translation symmetry of the powder-average signal, while later workers explained the sideband suppression in terms of the “alignment of centerbands” [4,6,8]. As will be discussed elsewhere [13], the latter explanation is partially erroneous, but in any case, the results agree: The sidebands in the powderaveraged spectrum are suppressed after a sequence of IZ rr pulses with timings or,. . . , T,, satisfying the TOSS equations: (-l)“e’“‘q+l=O
2k
(1)
q=l
where eq = o,rq, and m = 1 and 2. There is an optional subsidiary condition for the time T at the initiation of signal acquisition. If T satisfies -2
5 (-l)n+qe4+eT=0 q=l
(2)
-4 cos(8,)
+ 4 cos(19,)+3
-4 c0s(2el)
+ 4 c0s(2e,)
=0
(form
= 1)
- 1 = 0 (for m = 2) (3)
These lead immediately to the solution: 8, = Arccos( 7/24) e2 = Arccos( - 11/24) 8, =r
(4)
e, = 2,n- - 8, e5 = 2~ - 8,
describing a set of symmetrically-disposed and almost evenly-spaced GTpulses contained within a single rotational period. By symmetry, the Hahnecho condition (2) is satisfied for 8, = 2a. Signal acquisition should therefore start one whole rotational period after the preparation of transverse magnetization. In fractions of a rotor period, the timings are: 0,/2r=O.2029 0,/2n-=0.3258 e3/271.=o.5000 8,/2n-= 0.6742
(5)
e,/2T= 0.7971 eT/271. = 1 .oooo
Starting from this analytical solution, it is easy to generate complete lines of feasible 5 r solutions numerically. Fig. 1 shows such a set of solutions, where the X-axis represents the time measured in fractions of the rotation period after
2. Song et al./Solid
State Nucl.
Magn.
Reson.
2 (1993)
145
143-146
0.2002, 0,/2~ = 0.4239, 8s/2~ = 0.4670. The analytical form for this sequence, derived elsewhere [131, is: 0, = Arccos{( - 13 + 5&%)/152}; 0s = Arccos{( - 51 + 7m)/152}; &, = Arccos{( - 13 - 54595 >/ 152}; 13~ = Arccos{(51 7\/195)/152). Th’ is sequence generates strong frequency-dependent phase shifts (since eqn. (2) cannot be satisfied) and has two pulses inconveniently close, but is even shorter than the newly reported SELTICS sequence [12]. It is related trivially to a known TOSS sequence [3] by removing one rotor period. Fig. 1. A continuous set of 5 v pulse TOSS sequences (solid lines give the rr pulse timings) with the “Hahn-echo” condition (broken line). The horizontal axis is time in fractions of a rotational period 2r/or. Horizontal sections give (a) the symmetrical sequence of 5 rr pulses; (b) the shortest known TOSS sequence without a frequency-dependent phase shift: the “Hahn echo” coincides with the last pulse; (c) the shortest possible TOSS sequence of 4 rr pulses: the first pulse is at zero time and may be omitted; the “Hahn echo” is inaccessible.
creation of in-phase transverse magnetization, and the Y-axis is arbitrary. Any horizontal section through this plot represents a solution to eqns. (1) with 19r/27~, . . . , 0,/27r at the positions given by the 5 thick curves. The dashed curve represents the value of OT/2r satisfying eqn. (2). If 6,~ 8,, initiation of acquisition at time T generates a spectrum without phase shifts. The solution of eqn. (4) corresponds to a horizontal section at point a. Another solution of note is at point b, representing the shortest known sequence satisfying eqn. (1) with a physically-realizable solution for eqn. (2). It has been found numerically to correspond to the values: 0,/2~ t3,/2n0,/2~ 0,/2n0,/2~
= = = = =
0.1366 0.2892 0.4254 0.6341 0,/2r = 0.7227
C .W+
b.4
(6)
The section at point c has f3,/2rr = 0, and corresponds to the shortest known 4 r pulse TOSS sequence with 6,/2~ = 0.1228, 0,/2~ =
kHz Fig. 2. r3C spectra of r.-tyrosine hydrochloride powder with 486 scans. (a) Normal CP/MAS; (b) TOSS with symmetrical sequence of 5 rr pulses; (c) conventional TOSS with 4 v pulses [3].
146
The symmetrical 5 rr pulse sequence of eqn. (4) is demonstrated experimentally in Fig. 2. This shows 13C MAS spectra of L-tyrosine hydrochloride powder (Sigma, USA, no further purification) spinning at w,/2rr = 2.000 kHz in a standard Bruker double bearing 4 mm rotor system (ZrO, rotors, Kel-F end caps). The spectra were obtained on a MSL-200 spectrometer at 4.7 T, using an external EN1 LPI10 high-power amplifier for the i3C pulses (w,/2n- = 109 kHz), and cross-polarization from the protons [14] with mixing time 5 ms. The proton rf field was enhanced by 3 dB during the TOSS sequence to avoid Hartmann-Hahn matching during the i3C pulses. Fig. 2a shows the ordinary CP/MAS spectrum revealing numerous overlapping sidebands. With the TOSS sequence of 5 n- pulses [Fig. 2b, timings as in eqn. (411, the sidebands are effectively suppressed and many of the centerbands are enhanced, as described previously [4,8]. An almost identical spectrum is obtained using the conventional 4 v pulse TOSS sequence (Fig. 2c, timings as in ref. 3) except for a slight loss of intensity from some peaks, presumably due to T, relaxation. Both Fig. 2b and 2c exploited extensive phase cycling of all r pulses, in phase steps of 2rr/3, to select the appropriate ( + 1) + ( F 1) coherence pathway transfers [15], thereby avoiding the effects of pulse imperfections. However, good sideband suppression could also be obtained without this precaution. Additional experimental results, including those from the shorter sequences described above, will be presented later [13]. In summary, we have demonstrated a new sequence of 5 r pulses for sideband suppression. The sequence is short, employs almost evenlyspaced n- pulses and has a simple analytical solution. It appears to offer significant advantages
Z. Song et al. /Solid State Nucl. Magn. Reson. 2 (1993) 143-146
over previous 4 and 6 pulse solutions and may present a good alternative to methods involving continuous radio-frequency bursts [ 121.
Acknowledgments
The authors thank J. Hong and G.S. Harbison for ref. 12 prior to publication, and N.C. Nielsen for discussions. This work has been supported by the Swedish Natural Science Research Council.
References 1 M.M. Maricq and J.S. Waugh, J. Chem. Phys., 70 (1979) 3300. 2 W.T. Dixon, .7. Chem. Phys., 77 (1982) 1800. 3 W.T. Dixon, J. Schaeffer, M.D. Sefcik, E.O. Stejskal and R.A. McKay, J. Magn. Reson., 49 (1982) 341. 4 E.T. Olejniczak, S. Vega and R.G. Griffin, .I. @em. Phys., 81 (1984) 4804. 5 D.P. Raleigh, E.T. Olejniczak, S. Vega and R.G. Griffin, J. Am. Chem. Sot., 106 (1984) 8302. 6 D.P. Raleigh, E.T. Olejniczak, S. Vega and R.G. Griffin, J. Magn. Reson., 72 (1987) 238. 7 N.C. Nielsen, H. Bildsoe and H.J. Jakobsen, J. Magn. Reson., 80 (1988) 149. 8 D.P. Raleigh, E.T. Olejniczak and R.G. Griffin, J. Chem. Phys., 89 (1988) 1333. 9 A.C. Kolbert and R.G. Griffin, Chem. Phys. Lett., 166 (1990) 87. 10 H. Geen and G. Bodenhausen, J. Chem. Whys., 97 (1992) 2928. 11 S. Ding and C. Ye, Solid State Nucl. Magn. Reson., 1 (1992) 235. 12 J. Hong and G.S. Harbison, J. Magn. Reson., in press. 13 O.N. Antzutkin, 2. Song, X. Feng and M.H. Levitt, to be published. 14 A. Pines, M.G. Gibby and J.S. Waugh, J. Chem. Phys., 59 (1973) 569. 15 G. Bodenhausen, H. Kogler and R.R. Ernst, J. Mugs. Reson., 58 (1984) 370.